# The Negation Strategy

By R.N. Carmona

Every deductive argument can be negated. I consider this an uncontroversial statement. The problem is, there are people who proceed as though deductive arguments speak to an a priori truth. The Freedom Tower is taller than the Empire State Building; the Empire State Building is taller than the Chrysler Building; therefore, the Freedom Tower is taller than the Chrysler Building. This is an example of an a priori truth because given that one understands the concepts of taller and shorter, the conclusion follows uncontroversially from the premises. This is one way in which the soundness of an argument can be assessed.

Of relevance is how one would proceed if one is unsure of the argument. Thankfully, we no longer live in a world in where one would have to go out of their way to measure the heights of the three buildings. A simple Google search will suffice. The Freedom Tower is ~546m. The Empire State Building is ~443. The Chrysler is ~318m. Granted, this is knowledge by way of testimony. I do not intend to connote religious testimony. What I intend to say is that one’s knowledge is grounded on knowledge directly acquired by someone else. In other words, at least one other person actually measured the heights of these buildings and these are the measurements they got.

Most of our knowledge claims rest on testimony. Not everyone has performed an experimental proof to show that the acceleration of gravity is 9.8m/s^2. Either one learned it from a professor or read it in a physics textbook or learned it when watching a science program. Or, they believe the word of someone they trust, be it a friend or a grade school teacher. This does not change that fact that if one cared to, one could exchange knowledge by way of testimony for directly acquired knowledge by performing an experimental proof. This is something I have done, so I do not believe on basis of mere testimony that Newton’s law holds. I can say that it holds because I tested it for myself.

To whet the appetite, let us consider a well-known deductive argument and let us ignore, for the moment, whether it is sound:

P1 All men are mortal.

P2 Socrates is a man.

C Therefore, Socrates is mortal.

If someone were completely disinterested in checking whether this argument, which is merely a finite set of propositions, coheres with the world or reality, I would employ my negation strategy: the negation of an argument someone assumes to be sound without epistemic warrant or justification. The strategy forces them into exploring whether their argument or its negation is sound. Inevitably, the individual will have to abandon their bizarre commitment to a sort of propositional idealism (namely that propositions can only be logically assessed and do not contain any real world entities contextually or are not claims about the world). In other words, they will abandon the notion that “All men are mortal” is a mere proposition lacking context that is not intended to make a claim about states of affairs objectively accessible to everyone, including the person who disagrees with them. With that in mind, I would offer the following:

P1 All men are immortal.

P2 Socrates is a man.

C Therefore, Socrates is immortal.

This is extremely controversial for reasons we are all familiar with. That is because everyone accepts that the original argument is sound. When speaking of ‘men’, setting aside the historical tendency to dissolve the distinction between men and women, what is meant is “all human persons from everywhere and at all times.” Socrates, as we know, was an ancient Greek philosopher who reportedly died in 399 BCE. Like all people before him, and presumably all people after him, he proved to be mortal. No human person has proven to be immortal and therefore, the original argument holds.

Of course, matters are not so straightforward. Christian apologists offer no arguments that are uncontroversially true like the original argument above. Therefore, the negation strategy will prove extremely effective to disabuse them of propositional idealism and to make them empirically assess whether their arguments are sound. What follows are examples of arguments for God that have been discussed ad nauseam. Clearly, theists are not interested in conceding. They are not interested in admitting that even one of their arguments does not work. Sure, what you find are theists committed to Thomism, for instance, and as such, they will reject Craig’s Kalam Cosmological Argument (KCA) because it does not fit into their Aristotelian paradigm and not because it is unsound. They prefer Aquinas’ approach to cosmological arguments. What is more common is the kind of theist that ignores the incongruity between one argument for another; since they are arguments for God, it counts as evidence for his existence and it really does not matter that Craig’s KCA is not Aristotelian. I happen to think that it is, despite Craig’s denial, but I digress.

Negating Popular Arguments For God’s Existence

Let us explore whether Craig’s Moral Argument falls victim to the negation strategy. Craig’s Moral Argument is as follows:

P1 If God does not exist, objective moral values do not exist.

P2 Objective moral values do exist.

C Therefore, God exist (Craig, William L. “Moral Argument (Part 1)”. Reasonable Faith. 15 Oct 2007. Web.)

With all arguments, a decision must be made. First, an assessment of the argument form is in order. Is it a modus ponens (MP) or a modus tollens (MT)? Perhaps it is neither and is instead, a categorical or disjunctive syllogism. In any case, one has to decide which premise(s) is going to be negated or whether by virtue of the argument form, one will have to change the argument form to state the opposite. You can see this with the original example. I could have very well negated P2 and stated “Socrates is not a man.” Socrates is an immortal jellyfish that I tagged in the Mediterranean. Or he is an eternal being that I met while tripping out on DMT. For purposes of the argument, however, since he is not a man, at the very least, the question of whether or not he is mortal is open. We would have to ask what Socrates is. Now, if Socrates is my pet hamster, then yes, Socrates is mortal despite not being a man. It follows that the choice of negation has to be in a place that proves most effective. Some thought has to go into it.

Likewise, the choice has to be made when confronting Craig’s Moral Argument. Craig’s Moral Argument is a modus tollens. For the uninitiated, it simply states: [((p –> q) ^ ~q) –> ~p] (Potter, A. (2020). The rhetorical structure of Modus Tollens: An exploration in logic-mining. Proceedings of the Society for Computation in Linguistics, 3, 170-179.). Another way of putting it is that one is denying the consequent. That is precisely what Craig does. “Objective moral values do not exist” is the consequent q. Craig is saying ~q or “Objective moral values do exist.” Therefore, one route one can take is keeping the argument form and negating P1, which in turn negates P2.

MT Negated Moral Argument

P1 If God exists, objective moral values and duties exist.

P2 Objective moral values do not exist.

C Therefore, God does not exist.

The key is to come up with a negation that is either sound or, at the very least, free of any controversy. Straight away, I do not like P2. Moral realists would also deny this negation because, to their minds, P2 is not true. The controversy with P2 is not so much whether it is true or false, but that it falls on the horns of the objectivism-relativism and moral realism/anti-realism debates in ethics. The argument may accomplish something with respect to countering Craig’s Moral Argument, but we are in no better place because of it. This is when we should explore changing the argument’s form in order to get a better negation.

MP Negated Moral Argument

P1 If God does not exist, objective moral values and duties exist.

P2 God does not exist.

C Therefore, objective moral values and duties exist.

This is a valid modus ponens. I have changed the argument form of Craig’s Moral Argument and I now have what I think to be a better negation of his argument. From P2, atheists can find satisfaction. This is the epistemic proposition atheists are committed to. The conclusion also alleviates any concerns moral realists might have had with the MT Negated Moral Argument. For my own purposes, I think this argument works better. That, however, is beside the point. The point is that this forces theists to either justify the premises of Craig’s Moral Argument, i.e. prove that the argument is sound, or assert, on the basis of mere faith, that Craig’s argument is true. In either case, one will have succeeded in either forcing the theist to abandon their propositional idealism, in getting them to test the argument against the world as ontologically construed or in getting them to confess that they are indulging in circular reasoning and confirmation bias, i.e. getting them to confess that they are irrational and illogical. Both of these count as victories. We can explore whether other arguments for God fall on this sword.

We can turn our attention to Craig’s Kalam Cosmological Argument (KCA):

P1 Everything that begins to exist has a cause.

P2 The universe began to exist.

C Therefore, the universe has a cause. (Reichenbach, Bruce. “Cosmological Argument”. Stanford Encyclopedia of Philosophy. 2021. Web.)

Again, negation can take place in two places: P1 or P2. Negating P1, however, does not make sense. Negating P2, like in the case of his Moral Argument, changes the argument form; this is arguable and more subtle. So we get the following:

MT Negated KCA

P1 Everything that begins to exist has a cause.

P2 The universe did not begin to exist.

C Therefore, the universe does not have a cause.

Technically, Craig’s KCA is a categorical syllogism. Such syllogisms present a universal () or existential quantifier (∃); the latter is introduced by saying all. Consider, “all philosophers are thinkers; all philosophers are logicians; therefore, all thinkers are logicians.” Conversely, one could say “no mallards are insects; some birds are mallards; therefore, some birds are not insects.” What Craig is stating is that all things that begin to exist have a cause, so if the universe is a thing that began to exist, then it has a cause. Alternatively, his argument is an implicit modus ponens: “if the universe began to exist, then it has a cause; the universe began to exist; therefore, the universe has a cause.” In any case, the negation works because if the universe did not begin to exist, then the universe is not part of the group of all things that have a cause.

Whether the universe is finite or eternal has been debated for millennia and in a sense, despite changing context, the debate rages on. If the universe is part of an eternal multiverse, it is just one universe in a vast sea of universes within a multiverse that has no temporal beginning. Despite this, the MT Negated KCA demonstrates how absurd the KCA is. The singularity was already there ‘before’ the Big Bang. The Big Bang started the cosmic clock, but the universe itself did not begin to exist. This is more plausible. Consider that everything that begins to exist does so when the flow of time is already in motion, i.e. when the arrow of time pointed in a given direction due to entropic increase reducible to the decreasing temperature throughout the universe. Nothing that has ever come into existence has done so simultaneously with time itself because any causal relationship speaks to a change and change requires the passage of time, but at T=0, no time has passed, and therefore, no change could have taken place. This leads to an asymmetry. We thus cannot speak of anything beginning to exist at T=0. The MT Negated KCA puts cosmology in the right context. The universe did not come into existence at T=0. T=0 simply represents the first measure of time; matter and energy did not emerge at that point.

For a more complicated treatment, Malpass and Morriston argue that “one cannot traverse an actual infinite in finite steps” (Malpass, Alex & Morriston, Wes (2020). Endless and Infinite. Philosophical Quarterly 70 (281):830-849.). In other words, from a mathematical point of view, T=0 is the x-axis. All of the events after T=0 are an asymptote along the x-axis. The events go further and further back, ever closer to T=0 but never actually touch it. For a visual representation, see below:

Credit: Free Math Help

The implication here is that time began to exist, but the universe did not begin to exist. A recent paper implies that this is most likely the case (Quantum Experiment Shows How Time ‘Emerges’ from Entanglement. The Physics arXiv Blog. 23 Oct 2013. Web.). The very hot, very dense singularity before the emergence of time at T=0 would have been subject to quantum mechanics rather than the macroscopic forces that came later, e.g., General Relativity. As such, the conditions were such that entanglement could have resulted in the emergence of time in our universe, but not the emergence of the universe. All of the matter and energy were already present before the clock started to tick. Conversely, if the universe is akin to a growing runner, then the toddler is at the starting line before the gun goes off. The sound of the gun starts the clock. The runner starts running sometime after she hears the sound. As she runs, she goes through all the stages of childhood, puberty, adolescence, adulthood, and finally dies. Crucially, the act of her running and her growth do not begin until after the gun goes off. Likewise, no changes take place at T=0; all changes take place after T=0. While there is this notion of entanglement, resulting in a change occurring before the clock even started ticking, quantum mechanics demonstrates that quantum changes do not require time and in fact, may result in the emergence of time. Therefore, it is plausible that though time began to exist at the Big Bang, the universe did not begin to existthus, making the MT Negated KCA sound. The KCA is therefore, false.

Finally, so that the Thomists do not feel left out, we can explore whether the negation strategy can be applied to Aquinas’ Five Ways. For our purposes, the Second Way is closely related to the KCA and would be defeated by the same considerations. Of course, we would have to negate the Second Way so that it is vulnerable to the considerations that cast doubt on the KCA. The Second Way can be stated as follows:

We perceive a series of efficient causes of things in the world.

Nothing exists prior to itself.

Therefore nothing [in the world of things we perceive] is the efficient cause of itself.

If a previous efficient cause does not exist, neither does the thing that results (the effect).

Therefore if the first thing in a series does not exist, nothing in the series exists.

If the series of efficient causes extends ad infinitum into the past, then there would be no things existing now.

That is plainly false (i.e., there are things existing now that came about through efficient causes).

Therefore efficient causes do not extend ad infinitum into the past.

Therefore it is necessary to admit a first efficient cause, to which everyone gives the name of God. (Gracyk, Theodore. “Argument Analysis of the Five Ways”. Minnesota State University Moorhead. 2016. Web.)

This argument is considerably longer than the KCA, but there are still areas where the argument can be negated. I think P1 is uncontroversial and so, I do not mind starting from there:

Negated Second Way

We perceive a series of efficient causes of things in the world.

Nothing exists prior to itself.

Therefore nothing [in the world of things we perceive] is the efficient cause of itself.

If a previous efficient cause does not exist, neither does the thing that results (the effect).

Therefore if the earlier thing in a series does not exist, nothing in the series exists.

If the series of efficient causes extends ad infinitum into the past, then there would be things existing now.

That is plainly true (i.e., efficient causes, per Malpass and Morriston, extend infinitely into the past or, the number of past efficient causes is a potential infinity).

Therefore efficient causes do extend ad infinitum into the past.

Therefore it is not necessary to admit a first efficient cause, to which everyone gives the name of God.

Either the theist will continue to assert that the Second Way is sound, epistemic warrant and justification be damned, or they will abandon their dubious propositional idealism and run a soundness test. Checking whether the Second Way or the Negated Second Way is sound would inevitably bring them into contact with empirical evidence supporting one argument or the other. As I have shown with the KCA, it appears that considerations of time, from a philosophical and quantum mechanical perspective, greatly lower the probability of the KCA being sound. This follows neatly into Aquinas’ Second Way and as such, one has far less epistemic justification for believing the KCA or Aquinas’ Second Way are sound. The greater justification is found in the negated versions of these arguments.

Ultimately, one either succeeds at making the theist play the game according to the right rules or getting them to admit their beliefs are not properly epistemic at all; instead, they believe by way of blind faith and all of their redundant arguments are exercises in circular reasoning and any pretense of engaging the evidence is an exercise in confirmation bias. Arguments for God are a perfect example of directionally motivated reasoning (see Galef, Julia. The Scout Mindset: Why Some People See Things Clearly and Others Don’t. New York: Portfolio, 2021. 63-66. Print). I much prefer accuracy motivated reasoning. We are all guilty of motivated reasoning, but directionally motivated reasoning is indicative of irrationality and usually speaks to the fact that one holds beliefs that do not square with the facts. Deductive arguments are only useful insofar as premises can be supported by evidence, which therefore makes it easier to show that an argument is sound. This is why we can reason that if Socrates is a man, more specifically, the ancient Greek philosopher that we all know, then Socrates was indeed mortal and that is why he died in 399 BCE. Likewise, this is why we cannot reason that objective morality can only be the case if the Judeo-Christian god exists, that if the universe began to exist, God is the cause, and that if the series of efficient causes cannot regress infinitely and must terminate somewhere, they can only terminate at a necessary first cause, which some call God. These arguments can be negated and the negations will show that they are either absurd or that the reasoning in the arguments is deficient and rests on the laurels of directionally motivated reasoning due to a bias for one’s religious faith rather than on the bedrock of carefully reasoned, meticulously demonstrated, accuracy motivated reasoning which does not ignore or omit pertinent facts.

The arguments for God, no matter how old or new, simple or complex, do not work because not only do they rely on directionally motivated and patently biased reasoning, but because when testing for soundness, being sure not to exclude any pertinent evidence, the arguments turn out to be unsound. In the main, they all contain controversial premises that do not work unless one already believes in God. So there is a sense in which these arguments exist to give believers a false sense of security or more pointedly, a false sense of certainty. Unlike my opponents, I am perfectly content with being wrong, with changing my mind, but the fact remains, theism is simply not the sort of belief that I give much credence to. Along with the Vagueness Strategy, the Negation Strategy is something that should be in every atheist’s toolbox.

# Time In Two Dimensions

R.N. Carmona

Lately, I have been thinking a lot about time, both on a personal level and on a philosophical one. Setting aside all of my thoughts on the kind of freedoms and privileges I would need to truly own my time, the phenomenon of time occupies my thoughts, in many ways from the mundane to the complex. When I was younger and far less patient, I would grow incensed having convinced myself that I picked the wrong bus out of the two that showed up at roughly the same time because the other bus eventually drove past mine. As I got older and my philosophical tendencies started to take root ever deeper, I started to notice how whenever the other bus drove by the bus I was on, it would never get too far ahead. In fact, it would arrive at my stop less than a minute before mine did.

So came my idea of virtual simultaneity. From there, I would imagine a parallel me, a sort of ghost, who in another universe got on the other bus and I would imagine how far ahead of me he would be on his walk toward my building. I would then speed up so that I would catch up to my parallel on my way home as means to feel better about not having been on the bus that arrived earlier. This is how I think about time, in a very intimate sense. Nothing stops me in my tracks like an article about time. My mind could be furtherest from time and from philosophy more generally, reading fan theories about a show I am into or looking up the latest sports scores, and when scrolling, an article about time shows up and I am immediately in that headspace. This was the case two days ago when I read Musser’s article “A Defense of the Reality of Time.”

Time is one of the most difficult phenomena to apprehend in the universe. It is as elusive as it is seductive. It is safe to say that no one has won over this lover’s heart. No one has seduced her enough to understand all of her mysteries and secrets. It is because of this that I am often discouraged to write anything about time, despite growing confidence in my philosophical capacities. But just then, Musser said something that got the gears of my mind running.

“Well, what if time had two dimensions?” As a purely algebraic question, I can say that. But if you ask me what could it mean, physically, for time to have two dimensions, I haven’t the vaguest idea. Is it consistent with the nature of time that it be a two-dimensional thing? Because if you think that what time does is order events, then that order is a linear order, and you’re talking about a fundamentally one-dimensional kind of organization.

Musser, George. “A Defense of the Reality of Time”. Quanta Magazine. 16 May 2017. Web.

What if the critical error we continue to make is thinking of time as one-dimensional? What if time has more than one dimension, just like space does? A cursory look at Superstring Theory (ST) will begin to sound exactly like me in a footrace with parallel me. Parallel or possible worlds emerge from the fifth and sixth dimensions of ST. If it were possible to see the fifth dimension, we would be able to take note of similarities and differences between the world we occupy and a parallel world. Perhaps this is what our imagination does. If a runner gets a cramp in her calf a few meters from the finish line, she may envision herself winning the race in a world in where she did not get injured. Perhaps we do, in fact, see the fifth dimension, but I digress.

In the sixth dimension, one would be able to see the universe as it was at the beginning and an array of possibilities. One would, for instance, see universes in where the rate of entropy is lower or higher than in ours. If Boltzmann was correct, and time emerges from basic probabilities, then we would see universes in where .000000001 nanoseconds do not equal a second, but instead, .0.000000001515 nanoseconds equal a second, implying that time moves slightly slower in that universe than it does here. This is to say nothing about the arrow of time, which could move in the opposite direction (see Cartwright, John. “We may have a spotted a parallel universe going backwards in time”. New Scientist. 8 Apr 2020. Web. and De Chant, Tim. “Big Bang May Have Created a Mirror Universe Where Time Runs Backwards”. Nova. 8 Dec 2014. Web.).

In the seventh dimension, one may find themselves in the mirror universe on the other side of the Big Bang, in where the arrow of time travels backwards. The eighth dimension would give one access to exotic universes, with initial conditions so far from our own. In the ninth, one would possess the power to compare and contrast every possible world from worlds very much like our own to worlds decidedly unlike ours. Finally, the tenth dimension exhausts every possibility.

The fact of the matter is that we simply do not fully comprehend our own universe and so, we can be gravely mistaken about time. If one considers ST, and not necessarily whether the theory is true, but rather what the theory can teach us, one quickly notices that ST’s dimensions have consequences for time that are arguably more important than their ramifications for space. If ST is the case or if something close to it is true, time is ultimately nonlinear and therefore, not one-dimensional. So let us walk through what two-dimensional time might look like. First, imagine that the ancestors of homo sapiens in the far off future have invented time machines. If they can travel to and fro in time, time is still one-dimensional. In two dimensions of space, one can move horizontally and vertically. So then the question arises, what would it mean for time to move vertically?

Prior talks about a quasi change or “what is common to the flow of a literal river on the one hand…and the flow of time on the other” (Oaklander, Nathan. Adrian Bardon ed. “A-, B- and R-Theories of Time: A Debate”. The Future of the Philosophy of Time. New York: Routledge, 2012. 23. Print.). Rivers, in our world, do not rise, but they do fall. Setting aside evaporation, which does speak to water traveling upward, for time to flow vertically downward, we can imagine a powerful waterfall. Though this is completely new territory and may look like a new way of thinking about time, anyone who has ever thought about the past as something long dead and inaccessible implies that the flow of time travels vertically downward, forever making the past impossible to re-experience directly. For instance, Emery, et al. write: “According to presentism, only present objects exist. More precisely, presentism is the view that, necessarily, it is always true that only present objects exist. Even more precisely, no objects exist in time without being present” (Emery, Nina, et al. “Time”. Stanford Encyclopedia of Philosophy. 2020. Web.). Presentists therefore, believe that objects in the past are in a state of oblivion, but if Temporal Parts Theory (TPT) is correct, then objects and events in the past are annihilated and their corresponding intervals of time are also annihilated. A brief review of TPT is in order.

The Temporal Parts Theory of Identity (hereon TPT) is derived from the notion of time being, in some sense or to some degree, like space. One can think of, for instance, a linear timeline depicting the years all 46 U.S. Presidents held office. Or one can think of the x-y axis used in physics. Time is represented by the x-axis whilst space is represented by the y. Or one can think of a space-time diagram containing two axes representing space and another to represent time. These sorts of considerations have led some philosophers and scientists to ask whether time is a dimension. According to some accounts, time is the fourth dimension. Time, however, is not always analogous to space. D.H. Mellor discussed these disanalogies at length. He, for instance, concluded that there is no spatial analogue for our feeling of the passing of time. We cannot, in other words, attribute the passing of time to spatial changes (Mellor, D. H. Real Time II. London: Routledge, 1998. 95-96. Print.).

With respect to parts, however, time and space are analogous. Theodore Sider explains:

Temporal parts theory is the claim that time is like space in one particular respect, namely, with respect to parts. First think about parts in space. A spatially extended object such as a person has spatial parts: her head, arms, etc. Likewise, according to temporal parts theory, a temporally extended object has temporal parts. Following the analogy, since spatial parts are smaller than the whole object in spatial dimensions, temporal parts are smaller than the whole object in the temporal dimension. They are shorter-lived.

Sider, Theodore. “Temporal Parts”. 2008. Web.

Consider, as an example, the b-moments in Friedrich Nietzsche’s life. Friedrich Nietzsche’s birth on October 15, 1844 is one b-moment and his death on August 25, 1900 is another. The dates of both represent distinct b-times. On TPT, he is spread out from October 15, 1844 to August 25, 1900. If we were to depict him in a space-time diagram, his parts on our diagram will depict his temporal parts. If we were capable of watching Nietzsche in his infancy, we will be observing a temporal part, then another that resembles it, and then another. If one were to watch infant Nietzsche long enough, his later temporal parts will be slightly bigger than the previous ones. That is to say that Nietzsche is no longer an infant; he is now, for instance, a toddler. So on our space-time diagram, Nietzsche grows the further we move away from his birth. It is also worth noting that temporal parts have spatial parts and vice versa. Nietzsche’s hand, like Nietzsche himself, persisted within the interval of time his life occupies. The parts he was comprised of will also be represented on our space-time diagram.

Nietzsche, therefore, has spatio and temporal parts, so if presentism were correct, the interval of time represented by the ~54 years Nietzsche lived would enter oblivion. The flow of time, as it pertains to Nietzsche’s life, ends and yet, continues. Perhaps a better analogy (though in actuality, this is time moving in three dimensions), presentists seem to imagine that time is like a river, at least on the surface, but within it are whirlpools in where intervals of time meet their end. With difficulty, therefore, one can imagine time in more than one dimension even if one is not convinced of presentism. Consider instead the growing blocking theory (GBT). On GBT, the present and the past are real and the future becomes real when the present edge meets it. Similarly, on the moving spotlight theory (MST), only objects within the spotlight are considered present though objects on the peripheries still exist (Emery, Ibid.). How might two-dimensional time look like under GBT or MST?

For simplicity’s sake, I will consider GBT. Since presentists deny the spatio-temporal parts of the past and thus, bury the past, we can imagine that for presentists, time moves to the right on the x-axis (that is, along the first quadrant of the axis) and also downward on the y-axis (along the fourth quadrant). Growing block theorists, on the other hand, since they believe in the future emerging at the present edge, see time moving in the same direction as presentists on the x-axis, but moving along the y-axis in the opposite direction, upward in the first quadrant. In other words, if the death of temporal parts is a downward movement, the birth of temporal parts is an upward movement.

To pursue a brief tangent, not all theories of time think of time as a line. Eternalists see time in one dimension, but their view of time is more in keeping with a circle. Emery, et al. state:

One version of non-presentism is eternalism, which says that objects from both the past and the future exist. According to eternalism, non-present objects like Socrates and future Martian outposts exist now, even though they are not currently present. We may not be able to see them at the moment, on this view, and they may not be in the same space-time vicinity that we find ourselves in right now, but they should nevertheless be on the list of all existing things.

Ibid.

Another eternalist conception that has been entertained can be called recurrentism. Nietzsche probably explains it best:

What if some day or night a demon were to steal after you into your loneliest loneliness and say to you: “This life as you now live it and have lived it, you will have to live once more and innumerable times more; and there will be nothing new in it, but every pain and every joy and every thought and sigh and everything unutterably small or great in your life will have to return to you, all in the same succession and sequence—even this spider and this moonlight between the trees, and even this moment and I myself. The eternal hourglass of existence is turned upside down again and again, and you with it, speck of dust!”

Would you not throw yourself down and gnash your teeth and curse the demon who spoke thus? Or have you once experienced a tremendous moment when you would have answered him: “You are a god and never have I heard anything more divine.” If this thought gained possession of you, it would change you as you are or perhaps crush you. The question in each and every thing, “Do you desire this once more and innumerable times more?” would lie upon your actions as the greatest weight. Or how well disposed would you have to become to yourself and to life to crave nothing more fervently than this ultimate eternal confirmation and seal?

Nietzsche, Friedrich W, and Walter Kaufmann. The Gay Science: With a Prelude in Rhymes and an Appendix of Songs. New York: Vintage Books, 1974. 373. Print.

On the cosmological interpretation of eternal return (see here), eternalism simply is the idea that time is like a circle. There is a sense in which recurrentism is already implied and though eternalists are usually not committed to the idea of time literally repeating itself, if Socrates and Martian outposts exist, then time and causation are a loop. This implies that some future event will jumpstart the Big Bang and every event in the universe will play out in identical ways all over again. This is precisely the sort of thinking entailed in the presentist’s response to eternalism. Heather Dyke explains:

According to this argument, any theory that assigns ontological privilege to the present moment while also recognizing the existence of non-present times faces an insurmountable problem: it is unable to account for our knowledge that we are located in the present. If anything is certain, surely our knowledge that we are present is! But if past times exist as well as the present time, what is to say we are not located in one of those past times, mistakenly believing ourselves to be present? We might insist that our experience of presentness is so compelling that it must be veridical. But what about Queen Elizabeth I’s experience of presentness? That’s pretty compelling too, yet she is in the past, so her experience misleads her. Perhaps our experience misleads us too.

Dyke, Heather. Presentism and eternalism. Time, metaphysics of, 2011, doi:10.4324/9780415249126-N123-2. Routledge Encyclopedia of Philosophy, Taylor and Francis.

We tend to give the present an ontological status greater than that of the past and the future. It appears that the only escape we have is the idea of spatio-temporal oblivion. Queen Elizabeth I is not somewhere in the past under the mistaken impression that she and not us is present. Time, therefore, probably does not have one dimension. Forward implies backward and up implies down, so any linear or circular view of time runs into problems of recurrence and all sorts of time-related paradoxes like the well-known Grandfather Paradox. Without straying too far in quantum mechanics, all of this is already implied in Bell’s Theorem: “Most models of nature are reversible in time; we can run the basic equations backwards in time as easily as forwards in time. This implies that theories with causality forwards in time must also have causality backwards in time; this was ignored by Bell” (t’Hooft, Gerard. “Time, the Arrow of Time, and Quantum Mechanics”. Frontiers. 29 Aug 2018. Web.).

Especially for people high on the idea of the universe being conscious or that there is a god(s), the universe would therefore offer us clues to help us better understand time. Think of the notion of space and time changing places within a black hole. Going back to the paradigm, namely the four-dimensional concept of space-time, time would then have three dimensions and space would have one. As Pösel explains:

Only outside the cylinder does the intersection with a plane at constant height (“at constant time” as seen from the outside) correspond to a snapshot. Inside the cylinder, time and space have switched places. Inside, the intersection image doesn’t show a snapshot – it shows something much more weird: a caleidoscopic combination of many different times. After all, inside, time is not the axial, but the radial coordinate, and all the different distances from the “center” which you see in the sketch correspond to different moments in time. Instead of the spatial structure of the black hole, the sketch shows a strange mix of space and time!

Pössel, Markus. “Changing places – space and time inside a black hole”. Einstein Online. 2010. Web.

I would highly recommend getting a handle of Pössel’s illustrations if you would like to better understand how time and space trade places within a black hole. For our purposes, the fact that this happens in a black hole might offer a clue. Perhaps the lesson to be learned from the inner workings of blacks holes is that time has more than one dimension. Maybe the relativity of time inhered in General and Special Relativity has to do with the fact that time is superimposed or even supervenes on space in a different way relative to one’s direction in space. In other words, time has a horizontal behavior, so to speak. It has a slightly different vertical behavior. Further still, it has another behavior along curved or edged spaces within the dimension of depth. On Earth, we commonly move as though we lived in two-dimensions, so thinking of moving in a third dimension is difficult to conceptualize. We would have to travel in space to get a better idea of how the effects of gravity, over long distances, look like traveling along a curved surface. Or, we can simply think of the difference between Mario on Super Nintendo versus Mario on the Nintendo Switch. When Mario performs any movements in the depth dimension, or to add to our x- and y-axes, a z-axis, he is now covering diagonal domains analogous to the width of a cube, for instance.

To exhaust a well-known example, time moves faster at higher altitudes, the further one is from the Earth’s center. This might be suggestive of time behaving differently along the vertical axis. This also readily explains the relative experiences of someone falling into a black hole and another person seeing this happen. Recall the following:

1. The light coming from the person gets redshifted; they’ll start to take on a redder hue and then, eventually, will require infrared, microwave, and then radio “vision” to see.

2. The speed at which they appear to fall in will get asymptotically slow; they will appear to fall in towards the event horizon at a slower and slower speed, never quite reaching it.

3. The amount of light coming from them gets less and less. In addition to getting redder, they also will appear dimmer, even if they emit their own source of light!

4. The person falling in notices no difference in how time passes or how light appears to them. They would continue to fall in to the black hole and cross the event horizon as though nothing happened. (“Falling Into a Black Hole Sucks!”ScienceBlogs. 20 Nov 2009. Web.)

If the observer never quite sees the faller fall into the back hole while the faller notices no difference in the passage of time and ultimately, crosses the event horizon, time here can be taking on a different behavior along the z-axis, in the dimension of depth along a curved plain. The 3:1 relation of space-time can be simplified with a 3:3 relation which is virtually the same as 1:1 or colloquially, one-to-one. To my mind, if simplicity is the aim, then this is our next recourse. ST was borne out of an attempt to condense the three dimensions of space into one dimension. That unfortunately did not work, at least not as intended. We should therefore attempt to think of time in three dimensions and see how this might help the project of unifying physics.

Ultimately, our theories of time, along with physics, may be impeded by the idea of one-dimensional time. Maybe it is time for us to begin thinking about the behavior of time in two or three dimensions. ST already shows that there are peculiarities about time across multiple dimensions, implying further that the ten dimensions of ST are not dominated by space. In other words, it is not that nine out of the ten dimensions belong to space and still one to time. There could be a disproportion, like a space-time ratio of 6:4, but if ST entails a few dimensions of time, we should begin conceptualizing how time behaves in a multi-dimensional setting. This might help us to finally unravel all of her mysteries and secrets. Until then, I leave you with a mind-bending interpretation of what happens inside of black hole from Christopher Nolan’s “Interstellar.”

# Why Dispositions Make More Sense Than Powers

By R.N. Carmona

Consider what follows some scattered thoughts after reading an excellent paper by Marius Backmann. I think he succeeds in showing how the Neo-Aristotelian notion of powers is incongruous with pretty much any theory of time of note. My issue with powers is more basic: what in the world are Neo-Aristotelians even saying when they invoke this idea and why does it seem that no one has raised the concern that powers are an elementary paraphrase of dispositions? With respect to this concern, Neo-Aristotelians do not even attempt to make sense of our experience with matter and energy. They seem to go on the assumption that something just has to underlie the physical world whereas I take it as extraneous to include metaphysical postulates where entirely physical ones make do. Dispositions are precisely the sort of physical postulates that adequately explain what we perceive as cause-effect relationships. What I will argue is that a more thorough analysis of dispositions is all that is needed to understand why a given a caused some given effect b.

My idea that powers are an elementary paraphrase is entailed in Alexander Bird’s analysis of what powers are. He states:

According to Bird, powers, or potencies, as he calls them alternatively, are a subclass of dispositions. Bird holds that not all dispositions need to be powers, since there could be dispositions that are not characterised by an essence, apart from self-identity. Powers, on the other hand, Bird (2013) holds to be properties with a dispositional essence. On this view, a power is a property that furnishes its bearer with the same dispositional character in every metaphysically possible world where the property is instantiated. If the disposition to repel negatively charged objects if there are some in the vicinity is a power in that sense, then every object that has that property does the same in every metaphysically possible world, i.e. repel negatively charged objects if there are some in the vicinity.

Marius Backmann (2019) No time for powers, Inquiry, 62:9-10, 979-1007, DOI: 10.1080/0020174X.2018.1470569

Upon closer analysis of Bird’s definition, a power just is a disposition. The issue is that Bird and the Neo-Aristotelians who complain that he has not gone far enough have isolated what they take to be a power from the properties of an electron, which is a good example of a particle that repels negatively charged objects given that some are in its vicinity. Talk of possible worlds makes no sense unless one can prove mathematically that an electron-like particle with a different mass would also repulse other negatively charged particles. However, though it can easily be shown that a slightly more massive electron-like particle will repulse other particles of negative charge, its electrical charge will be slightly higher than an electrons because according to Robert Milikan’s calculation, there seems to be a relationship between the mass of a particle and its charge. The most elementary charge is e = ~1.602 x 10^19 coulombs. The charge of a quark is measured in multiples of e/3, implying a smaller charge, which is expected given that they are sub-particles. So what is of interest is why the configuration of even an elementary particle yields predictable “behaviors.”

To see this, let us dig into an example Backmann uses: “My power to bake a cake would not bring a cake that did not exist simpliciter before into existence, but only make a cake that eternally exists simpliciter present. Every activity reduces to a change in what is present” (Ibid.). The Neo-Aristotelian is off track to say we have power to bake a cake and that the oven has power to yield this desired outcome that do not trace back to its parts or as Cartwright states of general nomological machines: “We explicate how the machine arrangement dictates what can happen – it has emergent powers which are not to be found in its components” (Cartwright, Nancy & Pemberton, John (2013). Aristotelian powers: without them, what would modern science do? In John Greco & Ruth Groff (eds.), Powers and Capacities in Philosophy: the New Aristotelianism. London, U.K.: Routledge. pp. 93-112.). Of the nomological machines in nature, Cartwright appears to bypass the role of evolution. Of such machines invented by humans, she ignores the fact that we often wrongly predict what a given invention will do. Evolution proceeds via probabilities and so, from our ad hoc point of view, it looks very much like trial and error. Humans have the advantage of being much more deliberate about what they are selecting for and therefore, our testing and re-testing of inventions and deciding when they are safe and suitable to hit the market is markedly similar to evolutionary selection.

That being said, the components of a machine do account for its function. It is only due to our understanding of other machines that we understand what should go into building a new one in order for it to accomplish a new task(s). Powers are not necessary because then we should be asking, why did we not start off with machines that have superior powers? In other words, why start with percolators if we could have just skipped straight to Keurig or Nespresso machines or whatever more advanced models that might be invented? Talk of powers seems to insinuate that objects, whether complex or simple, are predetermined to behave the way they do, even in the absence of trial runs, modifications, or outright upgrades. This analysis sets aside the cake. It does not matter what an oven or air fryer is supposed to do. If the ingredients are wrong, either because I neglected to use baking powder or did not use enough flour, the cake may not raise. The ingredients that go into baked goods play a “causal” role as well.

Dispositions, on the other hand, readily explain why one invention counts as an upgrade over a previous iteration. Take, for instance, Apple’s A14 Bionic chip. At bottom, this chip accounts for, “a 5 nanometer manufacturing process” and CPU and GPU improvements over the iPhone 11 (Truly, Alan. “A14 Bionic: Apple’s iPhone 12 Chip Benefits & Improvements Explained”. Screenrant. 14 Oct 2020. Web). Or more accurately, key differences in the way this chip was made accounts for the improvement over its predecessors. Perhaps more crucially is that critics of dispositions have mostly tended to isolate dispositions, as though a glass cup’s fragility exists in a vacuum. Did the cup free fall at 9.8m/s^2? Did it fall on a mattress or on a floor? What kind of floor? Or was the cup thrown at some velocity because Sharon was angry with her boyfriend Albert? What did she throw the cup at: a wall, the floor, Albert’s head, or did it land in a half-full hamper with Sharon and Albert’s dirty clothes?

Answering these questions solves the masking and mimicker problems. The masking problem can be framed as follows:

Another kind of counterexample to SCA, due to Johnston (1992) and Bird (1998), involves a fragile glass that is carefully protected by packing material. It is claimed that the glass is disposed to break when struck but, if struck, it wouldn’t break thanks to the work of the packing material. There is an important difference between this example and Martin’s: the packing material would prevent the breaking of the glass not by removing its disposition to break when struck but by blocking the process that would otherwise lead from striking to breaking.

Choi, Sungho and Michael Fara, “Dispositions”The Stanford Encyclopedia of Philosophy (Fall 2018 Edition), Edward N. Zalta (ed.).

I would not qualify that the packing material prevents the glass from breaking by blocking the process that would result if it were exposed. The packing material has its own properties and dispositions that we have discovered through trial and error making this material good at protecting glass. Packing paper was more common, but now we have bubble wrap and heavy duty degradable stretch wrap, also capable of protecting glass, china, porcelain, and other fragile items. The dispositions of these protective materials readily explain why their encompassing of fragile objects protects them from incidental striking or drops. If I were, however, to throw a wrapped coffee mug as hard as I can toward a brick wall, the mug is likely to break. This entails that variables are important in this thing we call cause and effect.

A perfect example is simple collisions of the sort you learn about in an elementary physics course. If a truck and haul speeding down a highway in one direction at ~145 km/h, and a sedan traveling in the opposite direction at cruising speed of ~89 km/h collide, we can readily predict the outcome and that this particular collision is inelastic. The speeding truck would likely barrel through the sedan and the sedan will be pushed in the direction the truck was traveling in. The vehicles’ respective speeds and masses are extremely important in understanding what goes on here. There is no sense in which we can say that trucks just have a power to mow things down because a collision between the truck in our original example and a truck and haul driving at roughly the same speed in the opposite direction results in an entirely difficult outcome, a perfectly elastic collision in where both trucks collide and come to an immediate halt after the effects of the impact are fully realized.

Neo-Aristotelian analyses of powers give us nothing that is keeping with physics. What these explanations demand is something they imagine happening behind the veil of what science has already explained. There are just dispositions and what is needed is a more critical analysis of what is entailed across each instance of cause and effect. Power ontologies beg the question, in any case, because they require dispositions to make sense of powers. That is because powers are just a cursory analysis of cause-effect relationships, a way of paraphrasing that is overly simplistic and ultimately, not analytical enough. Power ontologies, along with talk of dynamism, which properly belongs to Nietzsche not Aristotle, severely undermine the Neo-Aristotelian project. Nietzsche’s diagnosis of causation makes this clear:

Cause and effect: such a duality probably never exists; in truth we are confronted by a continuum out of which we isolate a couple of pieces, just as we perceive motion only as isolated points and then infer it without ever actually seeing it. The suddenness with which many effects stand out misleads us; actually, it is sudden only for us. In this moment of suddenness there is an infinite number of processes that elude us. n intellect that could see cause and effect as a continuum and a flux and not, as we do, in terms of an arbitrary division and dismemberment, would repudiate the concept of cause and effect and deny all conditionality.

Nietzsche, Friedrich W, and Walter Kaufmann. The Gay Science: With a Prelude in Rhymes and an Appendix of Songs. New York: Vintage Books, 1974. 173. Print.

Nietzsche describes a continuum and a flux, in other words, a dynamism thoroughly unlike what can be attributed to Aristotle’s theory of causation. So the fact that Neo-Aristotelians even speak of a dynamism feels like a sort of plagiarism, since they are associating the idea of a dynamism with a thinker that said nothing to that effect. Nietzsche is critical of Aristotle’s causal-teleological marriage and can be seen as explicitly accusing Aristotle and also Hume of arbitrarily splicing a dynamic continuum in an ad hoc manner that does not find justification in metaphysical ideas. If Nietzsche had been properly exposed to modern science, he would probably agree that this splicing does not find justification in physical ideas either. The hard sciences confirm a continuum, preferring complex processes from which predictable results follow. There is just no sense in which we can apply any theory of causation to a chemical reaction. What features in these reactions are the properties and dispositions of the elements involved and how they are constituted explains why we get one reaction or another. Any talk of dynamisms is properly Nietzschean in spirit and as should be clear in his words, there is no invocation of powers.

Suffice to say that a deeper analysis of dispositions also explains away the mimicker problem. Styrofoam plates simply do not break in the way glass plates do and their underlying composition explains why that is. Ultimately, Neo-Aristotelians are not in a good position to get to the bottom of what we call cause and effect. Aside from the difficulties Backmann sheds light on, the notion of powers is incoherent and lacking in explanatory power, especially at levels requiring deeper analysis. Predictably, I can see Neo-Aristotelians invoking an infinite regress of sorts. In other words, is it simply the composition of the glass interacting with the composition of a hardwood floor that results in the glass shattering or is there more to the story? To that I would respond that events like these happen within a causally closed space-time system. It is then when we will be asked who or what decided that a glass cup should break on impact when landing on a hardwood floor? Well, who or what decided that a compound fracture of the tibia is expected given that it receives a strong enough blow from an equally dense or denser object? The Neo-Aristotelian will keep pushing the buck back, demanding deeper levels of analysis, effectively moving the goalposts. What will remain is that there is no intelligence that decided on these things, i.e., there is no teleological explanation involved in these cases, because then they would have to account for undesired ends like broken bones.

In the end, I think that the deepest level of analysis will involve a stochastic process in where degrees of probability encompass possible outcomes. Not every blow leads to a broken tibia. Dropping a glass cup on just any surface is not enough to crack or shatter it. There are cases in where angular momentum as a result of a human foot can change a falling glass cup’s trajectory just enough to ensure that it does not break upon hitting the ground. I have met people quite adept at breaking these kinds of falls with a simple extension of their foot. As such, probabilities will change given the circumstances on a case by case basis. This element of chance at the deepest level of analysis coheres perfectly with the universe we find ourselves in because even the fact that we are beings made of matter, as opposed to beings made of anti-matter, is due to chance. Apparently, God has always rolled dice. On this, I will let Lawrence Krauss have the last word:

Because antiparticles otherwise have the same properties as particles, a world made of antimatter would behave the same way as a world of matter, with antilovers sitting in anticars making love under an anti-Moon.  It is merely an accident of our circumstances, due, we think, to rather more profound factors…that we live in a universe that is made up of matter and not antimatter or one with equal amounts of both.

Krauss, Lawrence. A Universe From Nothing: Why There Is Something Rather Than Nothing. 1st ed. New York, NY: Free Press, 2012. 61. Print.

# Problems With “Neo-Aristotelian Perspectives On Contemporary Science: Dodging the Fundamentalist Threat”

By R.N. Carmona

Before starting my discussion of the first chapter of Neo-Aristotelian Perspectives On Contemporary Science, some prefatory remarks are in order. In the past, I might have committed to reading an entire book for purposes of writing a chapter by chapter review. With other projects in my periphery, I cannot commit to writing an exhaustive review of this book. That remains undecided for now. What I will say is that a sample size might be enough to confirm my suspicions that the Neo-Aristotelian system is rife with problems or even worse, is a failed system of metaphysics. I am skeptical of the system because it appears to have been recruited to bolster patently religious arguments, in particular those of modern Thomists looking to usher in yet another age of apologetics disguised as philosophy. I maintain that apologetics still needs to be thoroughly demarcated from philosophy of religion; moreover, philosophy of religion should be more than one iteration after another of predominantly Christian literature. With respect to apologetics, I am in agreement with Kai Nielsen who stated:

It is a waste of time to rehearse arguments about the proofs or evidences for God or immortality. There are no grounds — or at least no such grounds — for belief in God or belief that God exists and/or that we are immortal. Hume and Kant (perhaps with a little rational reconstruction from philosophers like J.L. Mackie and Wallace Matson) pretty much settled that. Such matters have been thoroughly thrashed out and there is no point of raking over the dead coals. Philosophers who return to them are being thoroughly retrograde.

Nielsen, Kai. Naturalism and Religion. Amherst, N.Y.: Prometheus, 2001. 399-400. Print.

The issue is that sometimes one’s hand is forced because the number of people qualified to rake dead coals is far fewer than the people rehashing these arguments. Furthermore, the history of Christianity, aside from exposing a violent tendency to impose the Gospel by force, also exposes a tendency to prey on individuals who are not qualified to address philosophical and theological arguments. Recently, this was made egregiously obvious by Catholic writer Pat Flynn:

So what we as religious advocates must be ready for is to offer the rational, logical basis—the metaphysical realism, and the reality of God—that so many of these frustrated, young people are searching for who are patently fed up with the absurd direction the secular world seems to be going. They’re looking for solid ground. And we’ve got it.

Flynn, Pat. “A Hole in The Intellectual Dark Web”. World On Fire Blog. 26 Jun 2019. Web.

Unfortunately, against all sound advice and blood pressure readings, people like myself must rake dead coals or risk allowing Christians to masquerade as the apex predators in this intellectual jungle. I therefore have to say to the Pat Flynns of the world, no you don’t got it. More importantly, let young people lead their lives free of the draconian prohibitions so often imposed on people by religions like yours. If you care to offer the rational, logical basis for your beliefs, then perhaps you should not be approaching young people who likely have not had an adequate exposure to the scholarship necessary to understand apologetics. This is not to speak highly of the apologist, who typically distorts facts and evidence to fit his predilections, making it necessary to acquire sufficient knowledge of various fields of inquiry so that one is more capable of identifying distortions or omission of evidence and thus, refuting his arguments. If rational, logical discourse were his aim, then he would approach people capable of handling his arguments and contentions. That is when it becomes abundantly clear that the aim is to target people who are more susceptible to his schemes by virtue of lacking exposure to the pertinent scholarship and who may already be gullible due to existing sympathy for religious belief, like Flynn himself, a self-proclaimed re-converted Catholic.

Lanao and Teh’s Anti-Fundamentalist Argument and Problems Within The Neo-Aristotelian System

With these prefatory remarks out of the way, I can now turn to Xavi Lanao and Nicholas J. Teh’s “Dodging The Fundamentalist Threat.” Though I can admire how divorced Lanao and Teh’s argument is from whatever theological views they might subscribe to, it should be obvious to anyone, especially the Christian Thomist, that their argument is at variance with Theism. Lanao and Teh write: “The success of science (especially fundamental physics) at providing a unifying explanation for phenomena in disparate domains is good evidence for fundamentalism” (16). They then add: “The goal of this essay is to recommend a particular set of resources to Neo- Aristotelians for resisting Fundamentalist Unification and thus for resisting fundamentalism” (Ibid.). In defining Christian Theism, Timothy Chappell, citing Paul Veyne, offers the following:

“The originality of Christianity lies… in the gigantic nature of its god, the creator of both heaven and earth: it is a gigantism that is alien to the pagan gods and is inherited from the god of the Bible. This biblical god was so huge that, despite his anthropomorphism (humankind was created in his image), it was possible for him to become a metaphysical god: even while retaining his human, passionate and protective character, the gigantic scale of the Judaic god allowed him eventually to take on the role of the founder and creator of the cosmic order.”

Chappell, Timothy. “Theism, History and Experience”. Philosophy Now. 2013. Web.

Thomists appear more interested in proving that Neo-Aristotelianism is a sound approach to metaphysics and the philosophy of science than they do in ensuring that the system is not at odds with Theism. The notion that God is the founder and creator of the cosmic order is uncontroversial among Christians and Theists more generally. Inherent in this notion is that God maintains the cosmic order and created a universe that bears his fingerprints, and as such, physical laws are capable of unification because the universe exhibits God’s perfection; the universe is therefore, at least at its start, perfectly symmetric, already containing within it intelligible forces, including finely tuned parameters that result in human beings, creatures made in God’s image. Therefore, in the main, Christians who accept Lanao and Teh’s anti-fundamentalism have, inadvertently or deliberately, done away with a standard Theistic view.

So already one finds that Neo-Aristotelianism, at least from the perspective of the Theist, is not systematic in that the would-be system is internally inconsistent. Specifically, when a system imposes cognitive dissonance of this sort, it is usually good indication that some assumption within the system needs to be radically amended or entirely abandoned. In any case, there are of course specifics that need to be addressed because I am not entirely sure Lanao and Teh fully understand Nancy Cartwright’s argument. I think Cartwright is saying quite a bit more and that her reasoning is mostly correct, even if her conclusion is off the mark.

While I strongly disagree with the Theistic belief that God essentially created a perfect universe, I do maintain that Big Bang cosmology imposes on us the early symmetry of the universe via the unification of the four fundamental forces. Cartwright is therefore correct in her observation that science gives us a dappled portrait, a patchwork stemming from domains operating very much independently of one another; like Lanao and Teh observe: “point particle mechanics and fluid dynamics are physical theories that apply to relatively disjoint sets of classical phenomena” (18). The problem is that I do not think Lanao and Teh understand why this is the case, or at least, they do not make clear that they know why we are left with this dappled picture. I will therefore attempt to argue in favor of Fundamentalism without begging the question although, like Cartwright, I am committed to a position that more accurately describes hers: Non-Fundamentalism. It may be that the gradual freezing of the universe, over the course of about 14 billion years, leaves us entirely incapable of reconstructing the early symmetry of the universe; I will elaborate on this later, but this makes for a different claim altogether, and one that I take Cartwright to be saying, namely that Fundamentalists are not necessarily wrong to think that fundamental unification (FU) is possible but given the state of our present universe, it cannot be obtained. Cartwright provides us with a roadmap of what it would take to arrive at FU, thereby satisfying Fundamentalism, but the blanks need to be filled, so that we get from the shattered glass that is our current universe to the perfectly symmetric mirror it once was.

Lanao and Teh claim that Fundamentalism usually results from the following reasoning:

We also have good reason to believe that everything in the physical world is made up of these same basic kinds of particles. So, from the fact that everything is made up of the same basic particles and that we have reliable knowledge of the behavior of these particles under some experimental conditions, it is plausible to infer that the mathematical laws governing these basic kinds of particles within the restricted experimental settings also govern the particles everywhere else, thereby governing everything everywhere. (Ibid.)

They go on to explain that Sklar holds that biology and chemistry do not characterize things as they really are. This is what they mean when they say Fundamentalists typically beg the question, in that they take Fundamentalism as a given. However, given Lanao and Teh’s construction of Cartwright’s argument, they can also be accused of fallacious reasoning, namely arguing from ignorance. They formulate Cartwright’s Anti-Fundamentalist Argument as follows:

(F1) Theories only apply to a domain insofar as there is a principled way of generating a set of models that are jointly able to describe all the phenomena in that domain.

(AF2) Classical mechanics has a limited set principled models, so it only applies to a limited number of sub-domains.

(AF3) The limited sub-domains of AF2 do not exhaust the entire classical domain.

(AF4) From (F1), (AF2), and (AF3), the domain of classical mechanics is not universal, but dappled. (25-26)

On AF2, how can we expect classical mechanics to acquire more principled models than it presently has? How do we know that, if given enough time, scientists working on classical mechanics will not have come up with a sufficient number of principled models to satisfy even the anti-fundamentalist? That results in quite the conundrum for the anti-fundamentalist. Can the anti-fundamentalist provide the fundamentalist with a satisfactory number of principled models that exhaust an entire domain? This is to ask whether anyone can know how many principled models are necessary to contradict AF3. On any reasonable account, science has not had sufficient time to come up with enough principled models in all of its domains and thus, this argument cannot be used to bolster the case for anti-fundamentalism.

While Lanao and Teh are dismissive of Cartwright’s particularism, it is necessary for the correct degree of tentativeness she exhibits. Lanao and Teh, eager to disprove fundamentalism, are not as tentative, but given the very limited amount of time scientists have had to build principled models, we cannot expect for them to have come up with enough models to exhaust the classical or any other scientific domain. Cartwright’s tentativeness is best exemplified in the following:

And what kinds of interpretative models do we have? In answering this, I urge, we must adopt the scientific attitude: we must look to see what kinds of models our theories have and how they function, particularly how they function when our theories are most successful and we have most reason to believe in them. In this book I look at a number of cases which are exemplary of what I see when I study this question. It is primarily on the basis of studies like these that I conclude that even our best theories are severely limited in their scope.

Cartwright, Nancy. The Dappled World: A Study of The Boundaries of Science. Cambridge: Cambridge University Press, 1999. 9. Print.

The fact that our best theories are limited in their scope reduces to the fact that our fragmented, present universe is too complex to generalize via one law per domain or one law that encompasses all domains. For purposes of adequately capturing what I am attempting to say, it is worth revisiting what Cartwright says about a \$1,000 bill falling in St. Stephen’s Square:

Mechanics provides no model for this situation. We have only a partial model, which describes the 1000 dollar bill as an unsupported object in the vicinity of the earth, and thereby introduces the force exerted on it due to gravity. Is that the total force? The fundamentalist will say no: there is in principle (in God’s completed theory?) a model in mechanics for the action of the wind, albeit probably a very complicated one that we may never succeed in constructing. This belief is essential for the fundamentalist. If there is no model for the 1000 dollar bill in mechanics, then what happens to the note is not determined by its laws. Some falling objects, indeed a very great number, will be outside the domain of mechanics, or only partially affected by it. But what justifies this fundamentalist belief? The successes of mechanics in situations that it can model accurately do not support it, no matter how precise or surprising they are. They show only that the theory is true in its domain, not that its domain is universal. The alternative to fundamentalism that I want to propose supposes just that: mechanics is true, literally true we may grant, for all those motions whose causes can be adequately represented by the familiar models that get assigned force functions in mechanics. For these motions, mechanics is a powerful and precise tool for prediction. But for other motions, it is a tool of limited serviceability.

Cartwright, Nancy. “Fundamentalism vs. the Patchwork of Laws.” Proceedings of the Aristotelian Society, vol. 94, 1994, pp. 279–292. JSTOR, http://www.jstor.org/stable/4545199.

Notice how even Cartwright alludes to the Theistic notion of FU being attributable to a supremely intelligent creator who people call God. In any case, what she is saying here does not speak to the notion that only the opposite of Fundamentalism can be the case. Even philosophers slip into thinking in binaries, but we are not limited to Fundamentalism or Anti-Fundamentalism; Lanao and Teh admit that much. There can be a number of Non-Fundamentalist positions that prove more convincing. In the early universe, the medium of water, and therefore, motions in water, were not available. Because of this, there was no real way to derive physical laws within that medium. Moreover, complex organisms like jellyfish did not exist then either and so, the dynamics of their movements were not known and could not feature in any data concerning organisms moving about in water. This is where I think Cartwright, and Lanao and Teh taking her lead, go astray.

Cartwright, for example, strangely calls for a scientific law of wind. She states: “When we have a good-fitting molecular model for the wind, and we have in our theory (either by composition from old principles or by the admission of new principles) systematic rules that assign force functions to the models, and the force functions assigned predict exactly the right motions, then we will have good scientific reason to maintain that the wind operates via a force” (Ibid). Wind, unlike inertia or gravity, is an inter-body phenomenon in that the heat from the Sun is distributed unevenly across the Earth’s surface. Warmer air from the equator tends toward the atmosphere and moves to the poles while cooler air tends toward the equator. Wind moves between areas of high pressure to areas of low pressure and the boundary between these areas is called a front. This is why we cannot have a law of wind because aside from the complex systems on Earth, this law would have to apply to the alien systems on gas giants like Jupiter and Saturn. This point is best exemplified by the fact that scientists cannot even begin to comprehend why Neptune’s Dark Spot did a complete about-face. A law of wind would have to apply universally, not just on Earth, and would thus, have to explain the behavior of wind on other planets. That is an impossible ask because the composition of other planets and their stars would make for different conditions that are best analyzed in complex models, accounting for as much data as possible, rather than a law attempting to generalize what wind should do assuming simple conditions.

Despite Cartwright’s lofty demand, her actual argument does not preclude Fundamentalism despite what Lanao and Teh might have thought. Cartwright introduces a view that I think is in keeping with the present universe: “Metaphysical nomological pluralism is the doctrine that nature is governed in different domains by different systems of laws not necessarily related to each other in any systematic or uniform way: by a patchwork of laws” (Ibid.). I think it is entirely possible to get from metaphysical nomological pluralism (MNP) to FU if one fills in the blanks by way of symmetry breaking. Prior to seeing how symmetry breaking bridges the gap between MNP and FU, it is necessary to outline an argument from Cartwright’s MNP to FU:

F1 Theories only apply to a domain insofar as there is a principled way of generating a set of models that are jointly able to describe all the phenomena in that domain.

MNP1 Nature is governed in different domains by different systems of laws not necessarily related to each other in any systematic or uniform way: by a patchwork of laws.

MNP2 It is possible that the initial properties in the universe allow these laws to be true together.

MNP3 From F1, MNP1, and MNP2, the emergence of different systems of laws from the initial properties in the universe imply that FU is the probable.

Lanao and Teh agree that F1 is a shared premise between Fundamentalists and Anti-Fundamentalists. As a Non-Fundamentalist, I see it as straightforwardly obvious as well. With respect to our present laws, I think that FU may be out of our reach. As has been famously repeated, humans did not evolve to do quantum mechanics, let alone piece together a shattered mirror. This is why I’m a Non– as opposed to Anti-Fundamentalist; the subtle distinction is that I am neither opposed to FU being the case nor do I think it is false, but rather that it is extremely difficult to come by. Michio Kaku describes the universe as follows: “Think of the way a beautiful mirror shatters into a thousand pieces. The original mirror possessed great symmetry. You can rotate a mirror at any angle and it still reflects light in the same way. But after it is shattered, the original symmetry is broken. Determining precisely how the symmetry is broken determines how the mirror shatters” (Kaku, Michio. Parallel Worlds: A Journey Through Creation, Higher Dimensions, and The Future of The Cosmos. New York: Doubleday, 2005. 97. Print.).

If Kaku’s thinking is correct, then there is no way to postulate that God had St. Peter arrange the initial properties of the universe so that all of God’s desired laws are true simultaneously without realizing that FU is not only probable but true, however unobtainable it may be. The shards would have to pertain to the mirror. Kaku explains that Grand Unified Theory (GUT) Symmetry breaks down to SU(3) x SU(2) x U(1), which yields 19 free parameters required to describe our present universe. There are other ways for the mirror to have broken, to break down GUT Symmetry. This implies that other universes would have residual symmetry different from that of our universe and therefore, would have entirely different systems of laws. These universes, at minimum, would have different values for these free parameters, like a weaker nuclear force that would prevent star formation and make the emergence of life impossible. In other scenarios, the symmetry group can have an entirely different Standard Model in where protons quickly decay into anti-electrons, which would also prevent life as we know it (Ibid., 100).

Modern scientists are then tasked with working backwards. The alternative to that is to undertake the gargantuan task, as Cartwright puts it, of deriving the initial properties, which would no doubt be tantamount to a Theory of Everything from which all of the systems of laws extend, i.e., hypothesize that initial conditions q, r, and s yield the different systems of laws we know. This honors the concretism Lanao and Teh call for in scientific models while also giving abstractionism its due. Like Paul Davies offered, the laws of physics may be frozen accidents. In other words, the effective laws of physics, which is to say the laws of physics we observe, might differ from the fundamental laws of physics, which would be, so to speak, the original state of the laws of physics. In a chaotic early universe, physical constants may not have existed. Hawking also spoke of physical laws that tell us how the universe will evolve if we know its state at some point in time. He added that God could have chosen an “initial configuration” or fundamental laws for reasons we cannot comprehend. He asks, however, “if he had started it off in such an incomprehensible way, why did he choose to let it evolve according to laws that we could understand? (Hawking, Stephen. A Brief History of Time, New York: Bantam Books. 1988. 127. Print.)” He then goes on to discuss possible reasons for this, e.g. chaotic boundary conditions; anthropic principles.

Implicit in Hawking’s reasoning is that we can figure out what physical laws will result in our universe in its present state. The obvious drawback is that the observable universe is ~13.8 billion years old and 93 billion lightyears in diameter. The universe may be much larger, making the task of deriving this initial configuration monumentally difficult. This would require a greater deal of abstraction than Lanao and Teh, and apparently Neo-Aristotelians, desire, but it is the only way to discover how past iterations of physical laws or earlier systems of laws led to our present laws of physics. The issue with modern science is that it does not often concern itself with states in the distant past and so, a lot of equations and models deal in the present, and even the future, but not enough of them confront the past. Cosmological models, for purposes of understanding star formation, the formation of solar systems, and the formation of large galaxies have to use computer models to test their theories against the past, since there is no way to observe the distant past directly. In this way, I think technology will prove useful in arriving at earlier conditions until we arrive at the mirror before it shattered. The following model, detailing how an early collision explains the shape of our galaxy, is a fine example of what computer models can do to help illuminate the distant past:

Further Issues With The Neo-Aristotelian System

A recent rebuttal to Alexander Pruss’ Grim Reaper Paradox can be generalized to refute Aristotelianism overall. The blogger over at Boxing Pythagoras states:

Though Alexander Pruss discusses this Grim Reaper Paradox in a few of his other blog posts, I have not seen him discuss any other assumptions which might underly the problem. He seems to have focused upon these as being the prime constituents. However, it occurs to me that the problem includes another assumption, which is a bit more subtle. The Grim Reaper Paradox, as formulated, seems to presume the Tensed Theory of Time. I have discussed, elsewhere, the reasons that I believe the Tensed Theory of Time does not hold, so I’ll simply focus here on how Tenseless Time resolves the Grim Reaper Paradox.

To see the difference between old and new tenseless theories, it is necessary to first contrast an old tenseless theory against a tensed theory that holds that properties of the pastness, presentness, and futurity of events are ascribed by tensed sentences. The debate regarding which theory is true centered around whether tensed sentences could be translated by tenseless sentences that instead ascribe relations of earlier than, later than, or simultaneous. For example, “the sun will soon rise” seems to entail the sun’s rising in the future, as an event that will become present, whereas the “sun is rising now” seems to entail the event being present and “the sun has risen” as having receded into the past. If these sentences are true, the first sentence ascribes futurity whilst the second ascribes presentness and the last ascribes pastness. Even if true, however, that is not evidence to suggest that events have such properties. Tensed sentences may have tenseless counterparts having the same meaning.

This is where Quine’s notion of de-tensing natural language comes in. Rather than saying “the sun is rising” as uttered on some date, we would instead say that “the sun is rising” on that date. The present in the first sentence does not ascribe presentness to the sun’s rising, but instead refers to the date the sentence is spoken. In like manner, if “the sun has risen” as uttered on some date is translated into “the sun has risen” on a given date, then the former sentence does not ascribe pastness to the sun’s rising but only refers to the sun’s rising as having occurred earlier than the date when the sentence is spoken. If these translations are true, temporal becoming is unreal and reality is comprised of earlier than, later than, and simultaneous. Time then consists of these relations rather the properties of pastness, presentness, and futurity (Oaklander, Nathan. Adrian Bardon ed. “A-, B- and R-Theories of Time: A Debate”. The Future of the Philosophy of Time. New York: Routledge, 2012. 23. Print.).

The writer at Boxing Pythagoras continues:

On Tensed Time, the future is not yet actual, and actions in the present are what give shape and form to the reality of the future. As such, the actions of each individual future Grim Reaper, in our paradox, can be contingent upon the actions of the Reapers which precede them. However, this is not the case on Tenseless Time. If we look at the problem from the notion of Tenseless Time, then it is not possible that a future Reaper’s action is only potential and contingent upon Fred’s state at the moment of activation. Whatever action is performed by any individual Reaper is already actual and cannot be altered by the previous moments of time. At 8:00 am, before any Reapers activate, Fred’s state at any given time between 8:00 am and 9:00 am is set. It is not dependent upon some potential, but not yet actual, future action as no such thing can exist.

I think this rebuttal threatens the entire Aristotelian enterprise. Aristotelians will have to deny time while maintaining that changes happen in order to escape the fact that de-tensed theories of time, which are more than likely the correct way of thinking about time, impose a principle: any change at a later point in time is not dependent on a previous state. That’s ignoring that God, being timeless, could not have created the universe at some time prior to T = 0, the first instance of time on the universal clock. This is to say nothing of backward causation, which is entirely plausible given quantum mechanics. Causation calls for a deeper analysis, which neo-Humeans pursue despite not being entirely correct. The notion of dispositions is crucial. It is overly simplistic to say the hot oil caused the burns on my hand or the knife caused the cut on my hand. The deeper analysis in each case is that the boiling point of cooking oil, almost two times that of water, has something to do with why the burn feels distinct from a knife cutting into my hand. Likewise, the dispositions of the blade have a different effect on the skin than oil does. Causal relationships are simplistic and, as Nietzsche suggested, do not account for the continuum within the universe and the flux that permeates it. Especially in light of quantum mechanics, we are admittedly ignorant about most of the intricacies within so-called causal relationships. Neo-Humeans are right to think that dispositions are important. This will disabuse of us of appealing to teleology in the following manner:

‘The function of X is Z’ [e.g., the function of oxygen in the blood is… the function of the human heart is… etc.] means

(a) X is there because it does Z,
(b) Z is a consequence (or result) of X’s being there.

Larry Wright, ‘Function’, Philosophical Review 82(2) (April 1973):139–68, see 161.

It is more accurate to say that a disposition of X is instantiated in Z rather than that X exists for purposes of Z because in real world examples, a given X can give rise to A, B, C, and so on. This is to say that one so-called cause can have different effects. A knife can slice, puncture, saw, etc. Hot oil can burn human skin, melt ice but not mix with it, combust when near other mediums or when left to increase to temperatures beyond its boiling point, etc. One would have to ask why cooking oil does not combust when a cube of ice is thrown into the pan; what about the canola oil, for a more specific example, causes it to auto-ignite at 435 degrees Fahrenheit and why does this not happen when water is heated beyond its boiling point?

As it turns out then, Neo-Aristotelians are not as committed to concretism as Lanao and Teh would hope. They are striving for generalizations despite refusing to investigate the details of how models are employed in normal science, as was made obvious by Lanao and Teh’s dismissal of Cartwright’s particularism and further, in their argument against Fundamentalism, which does not flow neatly from Cartwright’s argument. For science to arrive at anything concrete, abstraction needs to be allowed, specifically in cases venturing further and further into the past. Furthermore, a more detailed analysis of changes needs to be incorporated into our data. Briefly, when thinking of the \$1,000 bill descending into St. Stephen’s Square, it is a simple fact that we must ask whether there is precipitation or not and if so, how much; we are also required to ask whether bird droppings may have altered its trajectory on the way down?; what effect does smog or dust particles have on the \$1,000 bill’s trajectory; as Cartwright asked, what about wind gusts? What is concrete is consistent with the logical atomist’s view that propositions speak precisely to simple particulars or many of them bearing some relation to one another.

Ultimately, I think that Lanao and Teh fail to establish a Neo-Aristotelian approach to principled scientific models. They also fail to show that FU and therefore, Fundamentalism is false. What is also clear is that they did not adequately engage Cartwright’s argument, which is thoroughly Non-Fundamentalist, even if that conclusion escaped her. This is why I hold that Cartwright’s conclusions are off the mark because she is demanding that generalized laws be derived from extremely complex conditions. It is not incumbent on dappled laws within a given domain of science to be unified in order for FU to ultimately be the case. It could be that due to symmetry breaking, one domain appears distinct from another and because of our failure, at least until now, to realize how the two cohere, unifying principles between the two domains currently elude us. Lanao and Teh’s argument against FU therefore appeals to the ignorance of science not unlike apologetic arguments of much lesser quality. The ignorance of today’s science does not suggest that current problems will continue to confront us while their solutions perpetually elude us. What is needed is time. Like Lanao and Teh, I agree that Cartwright has a lot of great ideas concerning principled scientific models, but that her ideas lend support to FU. A unified metaphysical account of reality would likely end up in a more dappled state than modern science finds itself in and despite Lanao and Teh’s attempts, a hypothetical account of that sort would rely too heavily on science to be considered purely metaphysical. My hope is that my argument, one that employs symmetry breaking to bolster the probability of FU being the case, is more provocative, if even, persuasive.

# Print is Now Live on Amazon.com!

Book is now available for purchase here! Here are the Table of Contents to whet the appetite:

Introduction

Chapter 1: Philosophical Approaches to Atheism

Chapter 2: Refuting the Kalam Cosmological Argument

Chapter 3: The Moral Argument Refuted

Chapter 4: Refuting Plantinga’s Victorious Ontological Argument

Chapter 5: On Qualia and A Refutation of the Argument from Consciousness

Chapter 6: Refuting the Fine-Tuning Argument

Chapter 7: The Failures of Aquinas’ Five Ways

Chapter 8: Transcendental Arguments and Presuppositionalism Refuted

Chapter 9: The Argument from Assailability

Chapter 10: The Arguments from History and The Multiplicity of Religions

Chapter 11: The Argument from Cosmology

Chapter 12: On the Leibnizian Cosmological Argument

Conclusion

I hope you guys enjoy!

# The Kalam Cosmological Argument and The Problem of Induction

By R.N. Carmona

Though the Kalam Cosmological Argument (KCA) is a deductive argument, it imports inductive reasoning. Since there’s a distinction between argument and reasoning, it should apply to, at least, some deductive arguments.1 To see where this occurs, it is necessary to restate P1 of the KCA: Whatever begins to exist has a cause.2

Before demonstrating how P1 imports inductive reasoning, a distinction must be made between the common application of the Problem of Induction and what it is it actually entails. The common application of the problem focuses on the notion that given the uniformity of nature, the future will be like the past. For Hume, the uniformity of nature is used to justify induction. It is, however, important to note that Hume never explicitly mentioned induction. The Problem of Induction is derived from Hume’s discussion on causation.3 This notion is at the center of the common application of the Problem of Induction. It does, however, have broader application.

The problem should focus on beliefs concerning matters of fact that extend beyond experience and observation. These beliefs could be about past, unobserved present, and future events, objects, or phenomena.4 This is key to seeing how the first premise of the KCA imports inductive reasoning.

Disregarding discussions on the nature of time, i.e. whether time corresponds with A-theory or B-theory, the past and the future, intuitively speaking, have something in common. In science, predictions are often made about the future and the past; the latter is increasingly being referred to as a retrodiction.5 The reason predictions are necessary about the past and the future is because they are out of the reach of our experience and observational apparatus. Since we cannot directly observe or experience the past and the future, inductive inferences are necessary to draw conclusions about both.

When one argues that, whatever begins to exist has a cause, one is employing inductive reasoning. During one’s lifetime, one has noticed that every effect is preceded by a cause. However, in order to argue that this has always been the case, per Hume, one has to assume the uniformity of nature. It follows that one is making an inductive inference about the past.

From an epistemic standpoint, the Problem of Induction is also the problem of transfer of belief in the evidence. Though it is true that people believe things that lack evidence, conclusions are often supported by evidence. So the problem occurs in the bond between a conclusion and the evidence said to support it–specifically in the transfer from belief in the evidence to belief in a given conclusion. This transfer of belief is what Hume sought to address. He didn’t want to call into question the belief itself, but rather, the grounds of said belief.6

Much of this shouldn’t be news for the Christian or theist. When addressing proponents of scientism or when attempting to downplay the superiority of scientific over religious reasoning, they are both fond of invoking the Problem of Induction.7 Unfortunately, they fail to realize that it’s imported into an argument they’re also quite fond of. If it’s an actual problem, then the implications of the problem apply to the KCA. In other words, if the Problem of Induction cites a lack of justification for beliefs about the past that are out of the range of experience and observation, the Christian and theist aren’t justified in saying that whatever begins to exist has a cause. Since the premise lacks justification, there’s no way to establish its soundness. Therefore, given P2’s connection to P1, we cannot establish the soundness of P2. It follows that we cannot establish the soundness of the argument as a whole.

In the past, I’ve been pointedly critical of the KCA. I focused, for instance, on the concept of causation.8 I also located a common fallacy within the argument.9 One would be hard pressed to establish the soundness of the argument even if P1 didn’t feature inductive reasoning, which the Christian and theist admit has problematic implications. With that said, this isn’t so much a rebuttal of the argument, but rather, another spotlight on the double think of theists, Christians in particular.

It seems as though Christians don’t care to correct the inconsistency within their arguments. They can’t invoke the Problem of Induction whenever it suits them only to discard it whenever it doesn’t. If one is intellectually honest, consistency is required.  If they admit that there’s a Problem of Induction and that it is still without sufficient reply, as apologists have argued, then the implications of the problem are also imported into P1 of the KCA. I find that this conclusion is inescapable.

Works Cited

1 Will, Frederick L.. Is There a Problem of Induction? The Journal of Philosophy, Vol. 39, No. 19, pp. 505-513. 1942. Print.

2 Craig, William L. “In Defense of the Kalam Cosmological Argument”Reasonable Faith.

3 Burns, Samuel R.. The Problem of Deduction: Hume’s Problem Expanded. University of Michigan, Ann Arbor. 2009. Print.

4 Fritz Jr., Charles A.. What is Induction? The Journal of Philosophy, Vol. 57, No. 4, pp. 126-138. 1960. Print.

5 Barrett, Martin, Sober, Elliott. Is Entropy Relevant to the Asymmetry Between Prediction and Retrodiction? (1992); Steinitz, Yuval. Prediction versus Retrodiction in MIll (1994); Begun, David R. Human Evolution: Retrodictions and Predictions (2005); Christopher J. Ellison, John R. Mahoney, James P. Crutchfield. Prediction, Retrodiction, and The Amount of Information Stored in the Present (2009).

6 Oliver, Donald W.. A Re-examination of the Problem of Induction. The Journal of Philosophy, Vol. 49, No. 25, pp. 769-780. 1952. Print.

7 See “Does scientific knowledge presuppose God? A reply to Carroll, Coyne, Dawkins and Loftus” by Vincent Torley

8 See “Dispotions, Causality, and the Kalam Cosmological Argument”

9 See “A Simple Rebuttal: Kalam Cosmological Argument”

# A Brief Introduction to The Philosophy of Time

By R.N. Carmona

For purposes of my forthcoming argument, consider what follows a primer for it. §I will be brief, which isn’t to say it won’t be exhaustive. In it, I will render a summary of competing theories of time and I will also discuss matters germane to my argument. I will summarize A-, B-, and R-theories of time. I will place emphasis on a version of the B-theory that will feature throughout my argument, namely Mellor’s token-reflexive theory. I will do so by reviewing a pivotal discussion in the philosophy of time between Quentin Smith and L. Nathan Oaklander. This discussion will make clear Oaklander’s possible motivations for embracing a B/R-theory of time, a version of which I will defend in §2. I am, however, more concerned with our perception of time and its passing, i.e., the phenomenology of time. Given that, the temporal parts theory of identity will feature in my argument, but with an important difference. I will briefly discuss this theory below. In §2, I will then address possible objections to my argument and briefly sketch its implications if true. I will thus briefly discuss mathematical nominalism and a matter of concern in the philosophy of science.

If anyone feels sufficiently comfortable with the jargon of this discussion, you may feel free to skip §I altogether. Since I want layman and, in particular, people new to this discussion to understand my argument, it is necessary to survey the discussion thus far. Mellor and others have expressed dismay when confronted by the existing literature in the philosophy of time, so any survey has to have a limited scope since it isn’t practical to attempt a survey of all of the existing literature. I will therefore forgo discussing J.J.C. Smart’s date theory of time and Michelle Beer’s co-reporting thesis. I will limit my introduction to the parts forming the whole, namely my argument.

## I

A-Theory of Time

On the A-Theory, there are actual properties of being five days past, becoming present, being present, and being in the near or far future. It follows that my birth becomes more and more past with each passing day. My inevitable death becomes nearer and nearer to the present. What is present will eventually become past and then recede further into the past. This is known as the a-series. Contrary to McTaggart, the A-theorist denies that the a-series is contradictory. Moreover, they believe that the a-series cannot be reduced to b-relations: notions of earlier, later, and simultaneous. B-relations are comprised of b-moments that have different b-times such that b-moment with b-timel occurs earlier than b-moment with b-timell. So if we take, for instance, Friedrich Nietzsche’s death on August 25, 1900, we now have a b-moment. If we then take his birth on October 15, 1844, we have another b-moment. The dates of both represent distinct b-times. The b-relation is twofold, either in his birth being earlier than his death or his death being later than his birth. A-theorists hold that b-times come into existence, i.e., when Nietzsche’s death was future, it had no b-time.

On A-theory, what’s irreducible and essential is the a-time. Events actually do move from future to past once arriving at the present. Or, events have b-times, but the present moves, which gives these b-times real a-times. A-times have what I’ll call an a-relation, which is to say how much earlier or later an a-moment is than the present. If Jane James played volleyball yesterday, is painting right now, and is going to swim tomorrow, then a-momentl is her having played volleyball yesterday, which occurred earlier than her painting right now and a-momentll is her going to swim tomorrow, which will occur later than her painting at present. Mellor described this as an a-scale reserving a-series for the sequence of events located at those times. He adds that there is more to the a-scale than the sequence of a-times. There is a measure reflecting the speed at which one a-time succeeds another.1 Next Monday, for example, succeeds last Monday by seven days and the following Monday will succeed that one by precisely the same number of days. These measures also reflect how long such events are present. Therefore Nietzsche, who lived for ~56 years, occupies 56 years in the past of the a-scale. On the a-scale, entities cannot be located at any single moment since they occupy an interval on the scale.

R-Theory of Time

On the R-theory, temporal relations are unanalyzable, which means that they cannot be reduced to the properties of their terms nor the terms of temporal relations such as pastness, presentness, and futurity. The only category of temporal entities are hence relations. There are no moments or points in time as with both the A- and B-theories. There is no absolute becoming, i.e., the coming into or going out of existence of events. Monadic A-properties are not ascribed to these events. On the R-theory, time is relational and what’s entailed are durations, which similar to the B-theory, consist in dyadic terms. Instead of dyadic terms like earlier than and later than, however, these relations are lasts as long as, lasts longer than, or lasts shorter than.

In explaining Russell’s analysis of the order in relational facts, Oaklander remarks:

These relations hold between relata and facts. Since all series have a direction, Russell differs from McTaggart in both his account of the transitory aspect of time and its direction. For McTaggart what gives time a direction and its transitory character are changing A-characteristics. A Russellian will ground the transitory or dynamic aspect of time in the relation “is earlier than,” and the direction of a whole series is aggregated from the order relations for all the relational facts contained in it.2

There is, in other words, a difference in a and b as related by R and b and a as related by R. If it’s an asymmetrical relation, then one fact holds. If there are such facts as that a R b, i.e., a has an R-relation to b, then such facts can be reduced to a fact about either a or b. This neither makes them innately complex nor entail that they have some properties to distinguish them from c or d. This is what a Russelian means when saying that relations are external. To supplement, an example is necessary. An R-relation is simply in lasts as long as, lasts longer than, or vice versa. So let a be Mary’s wedding and b be Martha’s funeral. If our a and b have some relation R, and the relation is asymmetrical, which is to say that they didn’t have the same duration, then the fact of their relation is reducible to a fact about either event. Therefore, if Mary’s wedding lasts longer than Martha’s funeral, then the fact of their R-relation is simply reducible to the fact that Mary’s wedding lasted longer. The same would hold if the opposite were true. An R-relation is irreducible iff the relation is symmetric.

Unlike the B-theory, the direction of time is not dependent on causation or entropy, which are complex relations that are perhaps derivative of the simpler R-relations. As far as what we perceive, we don’t always perceive causes and their effects directly, and moreover, we don’t perceive entropic relations, i.e., x has less entropy than y. If we are to perceive such relations, we do so only in an extended sense, which is to say that we only do so via the apparatus used in the sciences. It is not an innate perception like the passage of time. On the Russelian theory, the direction of time is contingent on such simpler R-relations.

B-Theory of Time

On the B-theory of time, there are only b-times, which are described in terms of an a-scale. No events are in themselves past, present, or future and though the a-scale seems indispensable, the utility of the a-scale and our perception of the past and the future aren’t reflective of reality. Also, time doesn’t really flow. According to Prior, the passage of time is simply a metaphor.3 If time actually flows, does this flow occur in time or does it take time to occur? If it is the case that time passes, is there not what Prior dubbed a ‘super-time’ in which it does so? If indeed it does flow, then it flows at some rate, but a rate is a movement through time, so how can rate apply to time itself? So if time doesn’t flow at some rate, how can it be said that it flows at all?

The answer to these questions lie in the manner in which we speak about time. What causes the confusion is the way we employ tense-adverbs. This remains a central point of disagreement between A- and B-theorists. A-theorists take tense seriously whilst B-theorists offer tenseless theories of time, which isn’t to say they don’t take tense seriously, but rather, that regardless of our experience, time is not required to be tensed. Since I’ll be defending a B/R-theory of time, I will not belabor this summary. This entire argument will, to some degree, cover the history of the B-theory and also the place it occupies in today’s discussion. Since questions of tense feature heavily in today’s discussion, it is time now to discuss that at length.

Time and Tense

To simplify matters, proponents of tensed theories of time will from here on be called ‘tensers’ and proponents of tenseless theories of time will be called ‘detensers’. One of the earliest approaches to a tensed theory of time is credited to A.N. Prior who makes use of first-order logic in laying out his theory. W.V.O. Quine also made use of first-order logic, but assumed, like others before him, that physicists accept the tenseless theory of time. Tensers sometimes argue that this assumption is at the center of any tenseless theory though in the modern day, physicists following Minkowski have been supplanted by physicists following Einstein, i.e., tenseless theory is assumed to be true because of special relativity. Both Prior’s early tensed theory and Quine’s assumption are problematic. Since, I am offering a B/R-theory of time, I will not spend time on the challenges facing Prior’s tensed theory. I will, however, briefly discuss the difficulties Quine’s assumption faces so that it’s clear why it is necessary to pass from the old to the new tenseless theories of time, which depend on the New Theory of Reference in the philosophy of language. Before doing so, it is necessary to review Prior’s theory and Quine’s assumption because that will only serve to make the new tenseless theory easier to comprehend. To this we now turn.

Prior, following Augustine, stated that the past is the past present and the future is the future present. In applying and reapplying tense-adverbs, individual facts, i.e. facts about a thing, are preserved. We will return to the distinction between individual and general facts in my discussion on change in §II, but the distinction for our current purposes will make clear that the following sentences are about real things. So, to return to one of our previous examples, rather than saying I was born x years ago, we could say: It was the case two months ago that (it was the case only x years ago that (I am being born). In the same vein, we also have the tendency to obscure what our sentences are actually about, as in when we talk about one’s falling off the wagon or one’s homecoming. For instance:

(1) It is now four years since it was the case that I am falling off the wagon.

This could be paraphrased with:

(2) My falling off the wagon has receded four years into the past.

The suggestion here is that this event dubbed, one’s falling off the wagon, has gone through the motion of becoming further and further past. It has gone through this motion since it ended. (2), however, is just a paraphrase of (1) and (2) is not about this event of one’s falling off the wagon, but rather, a complex way of speaking about changes in the individual who fell off the wagon. What looks like changes in events, thence, are actually changes in things.

Prior had to deal with a possible objection, however. Borrowing McTaggart’s example of Queen Anne’s death, it appeared as though his sentence structure couldn’t apply to that example. If sentences like the aforementioned are facts about individual things, then how can such a sentence be about Queen Anne if she’s dead? The statement, rather than expressing an individual fact, is instead expressing a general fact. Even when, for example, we are mistaken in thinking that someone stole one of our possessions, whether someone stole it or not, the general fact can be expressed by stating: I think that (for some specific y (y stole my lunch)). On such a formulation, Queen Anne’s death isn’t a fact about her, but rather, a general fact. Her death becoming more past is not a change in her, but it does express what Prior called a ‘quasi-change’ and “what is common to the flow of a literal river on the one hand…and the flow of time on the other.”4

Quine, on the other hand, in attempting to preserve the tenseless extensional symbolism of sentential and predicate logic, defended his view by appealing to the fact that physicists accept the tenseless theory of time. Concerning natural language, Quine thought that it could be paraphrased by a tenseless language that denotes dates for tenses and substitutes singular phrases. For instance, James was running if uttered at noon on September 15, 2003 becomes James runs before noon on September 15, 2003. As mentioned above, Quine’s attempt to de-tense natural language has been met with a number of challenges and thus runs into difficulties. Not only does his view rest on a misapprehension of physics but also on questionable assumptions concerning the philosophy of language.5 Old tenseless theories of time sometimes relied on Quine’s assumption, but more importantly, they relied on the notion of de-tensing natural language.

To see the difference between old and new tenseless theories, it is necessary to contrast an old tenseless theory against a tensed theory that holds that properties of the pastness, presentness, and futurity of events are ascribed by tensed sentences. The debate regarding which theory is true centered around whether tensed sentences could be translated by tenseless sentences that instead ascribe relations of earlier than, later than, or simultaneous. For example, “the sun will soon rise” seems to entail the sun’s rising in the future, as an event that will become present, whereas the “sun is rising now” seems to entail the event being present and “the sun has risen” as having receded into the past. If these sentences are true, the first sentence ascribes futurity whilst the second ascribes presentness and the last ascribes pastness. Even if true, however, that isn’t evidence to suggest that events have such properties. Tensed sentences may have tenseless counterparts having the same meaning.

This is where Quine’s notion of de-tensing natural language comes in. Rather than saying “the sun is rising” as uttered on some date, we would instead say that “the sun is rising” on that date. The present in the first sentence doesn’t ascribe presentness to the sun’s rising, but instead refers to the date the sentence is spoken. In like manner, if “the sun has risen” as uttered on some date is translated into “the sun has risen” on a given date, then the former sentence does not ascribe pastness to the sun’s rising but only refers to the sun’s rising as having occurred earlier than the date when the sentence is spoken. If these translations are true, temporal becoming is unreal and reality is comprised of earlier than, later than, and simultaneous. Time then consists of these relations rather the properties of pastness, presentness, and futurity.6

Due to advancements in the philosophy of language, however, old tenseless theories have been abandoned. Prior to discussing new tenseless theories, it is necessary to see why old theories fell out of style. The New Theory of Reference, which was first developed by Ruth Barcon Marcus in “Modalities and Intensional Languages” (1961) and which was further developed by Donnellan, Kaplan, Putnam, and others was the reason tensed and tenseless sentences were reconsidered. David Kaplan, in applying the theory to indexicals like ‘now,’ argued that the rule of use of the indexical ‘now’ is that it strictly concerns the time it is spoken and does not ascribe a property of presentness. Thus, the ‘now’ in the “sun is now rising” strictly refers to the date on which the sentence is said. Furthermore, the sentence has no tenseless translation. Kaplan held that translations met two requirements: identical meaning and identical semantic content. Meaning, in this sense, speaks of a sentence’s rule of use, so in the “the sun is now rising,” the rule of use concerns the date it is spoken. If, however, one tacks on “at 7a.m. on October 4, 2001,” then the sentence instead concerns at 7a.m. on October 4, 2001. Therefore, the former cannot translate into the latter and vice versa because the two sentences have different rules of use. It follows that the tokens of either sentence do not translate into the tokens of the other. I will reserve the type-token distinction for my summary of D.H. Mellor’s tenseless theory. The central idea at the core of the new tenseless theory is “that tensed sentences (as uttered on some occasion) are untranslatable by tenseless sentences, but that it is nonetheless the case that tensed sentences ascribe no temporal determinations not ascribed by tenseless sentences.”7

New Tenseless Theories of Time

As far as new tenseless theories are concerned, there are two progenitor theories: Mellor’s token-reflexive theory and Smart’s date theory. Both have been challenged frequently by Quentin Smith and defended just as frequently by L. Nathan Oaklander. Since Mellor’s token-reflexive theory is agreed to be the most developed and serves as the common ancestor of modern tenseless theories, I will trace Smith and Oaklander’s extensive exchanges in order to provide a more thorough understanding of the new tenseless theory. I will then make explicit which theory I am defending and expounding on. I will make clear that Mellor’s intuitions were best served had he placed more emphasis on our experience of time, which is precisely the horns of the issue. These concerns will compose the content in the next section, but for now, let us explore an important exchange between Smith and Oaklander through the lens of Mellor’s token-reflexive theory.

The force of Smith’s challenges and Oaklander’s defenses will neither be understood nor felt unless Mellor’s theory is adequately summarized. A pivotal distinction serving as the core of Mellor’s theory is the type-token distinction. The type-token distinction can present difficulties when applied, but the distinction itself isn’t hard to understand. Take for example the word institution. If asked how many letters are in that word, one may respond with two answers: eleven or six. The first answer is arrived at if one counts all of the letters in the word whilst the second is arrived at if one counts all of the letters once, i.e., if one forgoes counting a letter that is repeated. That is to say that one notes that there are only the letters i, n, s, t, u, and o. In the former reply, one is answering on the basis of tokens whereas in the second reply, one is answering on the basis of types. Tokens refer to particular things and therefore, when we talk of particular facts, we are in turn talking about tokens. Types, on the other hand, refer to abstract objects, e.g., the letter B or the number 2. Mellor employs the distinction in order to find B-truthmakers for A-propositions. To see why this is necessary, I will sketch out the problem Mellor faces.

A-propositions are multifarious, but for simplicity, we will use the example Mellor uses: Jim races tomorrow.8 So if today is June 1, its B-truthmaker, then, is Jim racing on a day occurring after June 1. B-truthmakers, unlike A-truthmakers, are limited to B-facts. The difficulty Mellor faced is that the B-fact “Jim races on June 2” is always a fact, as he thought of all B-facts. Therefore, how can B-facts make propositions true at some times and false at other times? This problem arises because B-theorists acknowledge that A-propositions are sometimes true. B-facts, however, are unlike A-facts in that they don’t come and go, so one B-fact can’t make “Jim races tomorrow” true at some times and false at others. It follows that multiple B-facts are needed; in fact, as many B-facts as there are times in which an A-proposition can have a varying truth value. It therefore takes a new B-fact to make our statement true and false every day of Jim’s life.

The exchange between Smith and Oaklander centers around whether Mellor’s theory is self-contradictory and whether it can be reduced to the old tenseless theory of time. More generally, it centered around whether the new tenseless theory was to be either abandoned or radically revised. The disagreement between them was not resolved, but Smith did find value in what he considered an alternative theory offered by Oaklander. Despite accusing one another of misunderstanding the new tenseless theory, it is clear that they both adequately understood it. What’s more manifest is their opposing frameworks and convictions. Ultimately, the exchange may have played a role, whether large or small, in Oaklander espousing a B/R-theory of time, which isn’t to say he abandoned the tenseless theory entirely, but eventually came to realize that, as it stood, it was incomplete. To summarize their exchange, I will start with Smith’s criticisms of Mellor’s theory.

Smith vs. Oaklander

Smith held that Mellor’s theory wasn’t the final word in this discussion. He also held the theory to be self-contradictory. Smith explains:

Mellor inconsistently holds all five of these positions: (1) tensed sentences have different truth conditions from tenseless sentences and thus are untranslatable by them; (2) tensed sentences have tenseless truth conditions, namely, tenseless facts; (3) these tenseless facts are the only facts needed to make tensed sentences truth; (4) tensed sentences state the facts that are their truth conditions; and (5) tensed sentences state the same facts that are stated by the tenseless sentences that state the former sentences’ truth conditions.9

Smith held that (1) and (5) were incompatible. Since he wanted to develop an internal critique of Mellor’s theory, he assumed “fact” as defined and used by Mellor. Smith thought that Mellor’s definition committed him to three theses that implied the principle of the identity of truth (hereon PITC), which Smith formulates as follows:

If two tokens of the same sentence or two tokens of different sentences state the same fact, F1, they have the same truth conditions; that is, are true iff F1 and every fact implied by F1 exist.10

The theses are as follows: (a) facts only correspond to true sentence tokens or in Mellor’s words, “we are only concerned with sentences expressing judgments, that is, stating what people take to be facts.”11 (b) conditions that are both necessary and sufficient to make sentences true, are facts, i.e., truth conditions; (c ) in keeping with Mellor’s “Jim races tomorrow” example, a token that states some fact is true iff the fact and its implications exist; one fact can imply another iff the one cannot exist unless the other does. For instance, it cannot be the fact that Jim races tomorrow unless there also exists the fact that Jim doesn’t go to the ER because he feels ill. In other words, Jim has to be physically able to race if he is to race tomorrow.

Smith held that Mellor’s theory contradicts PITC and its own assumptions; more specifically, that the combination of (1) and (5) contradicts PITC. To make this contradiction clear, Smith focused on Mellor’s primary example of tensed and tenseless sentences:

Let R be any token of “Cambridge is here” and S be any token of “It is now 1980.” Then R is true if and only if it occurs in Cambridge, and S is true if and if it occurs in 1980. If a sentence giving another’s truth conditions means what it does, R should mean the same as “R occurs in Cambridge” and S should mean the same as “S occurs in 1980.” But these sentences have different truth conditions. In particular, if true at all, they are true everywhere and at all times. If R does occur in Cambridge, that is a fact all over the world, and if S occurs in 1980, that is a fact at all times. You need not be in Cambridge in 1980 to meet true tokens of “R occurs in Cambridge” and “S occurs in 1980.” But you do need to be in Cambridge in 1980 to meet the true tokens, R and S; for only there and then can R and S themselves be true.12

Smith then notes four items about the sentences “It is now 1980” and “S occurs in 1980.” He considers these items to be derivatives of Mellor’s five items mentioned above. The items are as follows: (1) A token of “S occurs in 1980” states only the fact that S occurs in 1980; (2) This fact is the truth condition of any token S of “It is now 1980”; (3) this tenseless fact is the sole fact stated by S, which is a token of a tensed sentence expressing belief in token-reflexive truth conditions; (4) Any token of “S occurs in 1980” has a different truth condition from any token of “It is now 1980” because any token of the latter is true only if it occurs in 1980 and the former is true at all times it is tokened. According to Smith, the combination of (1), (2), and (3) contradict (4) because according to PITC, two tokens of different sentences which state the same fact have the same truth conditions.

There is, however, a way out if one were to reject (4). Given two tokens S and U, if they state the same fact, they are both made true by that same fact. According to Smith, Mellor fails to see the truth-conditional resemblance S and U share. In other words, it is necessary and sufficient for S to be true being that it occurs in 1980, but it is not necessary nor sufficient for U to be true being that it occurs in 1980. There is no difference in their truth conditions, but rather, in what the facts are about. The fact about token S is a fact about it and not U and thus, restricts S to 1980. This does not constitute a further fact about S’s truth conditions. This resolution, according to Smith, reduces Mellor’s new tenseless theory to the old tenseless theory. On this, Oaklander takes Smith to be both mistaken and not fully understanding Mellor’s theory.

This misunderstanding is due to the fact that Mellor is not always clear. This might provide basis for attributing internal inconsistency to his theory. Oaklander argues that a clearer distinction of sentence types and tokens is required to circumvent the contradiction Smith seemingly uncovers. To recap, tokens refer to particular things and therefore, when we talk of particular facts, we are in turn talking about tokens. Types, on the other hand, refer to abstract objects, e.g., the letter B or the number 2. If S, “It is now 1980,” is understood as a type, then it doesn’t have truth conditions. So by extension, tensed sentence types have no truth-value. If, on the other hand, we consider “It is now 1980” and “S occurs in 1980” as tokens, then their truth conditions are identical. According to Oaklander, Smith “interprets Mellor to be saying that “any token of ’S occurs in 1980’ has different truth conditions from any token S of ‘It is now 1980,’ because S is true iff it occurs in 1980 and “S occurs in 1980,” if true at all, is true ‘at all times’ it is tokened.”13 Though it is true that tenseless sentence types are either true or false at all times they are tokened, the tokens themselves are not tokened at different times. Mellor argued that tensed tokens have unqualified truth-values. For example, stating or writing that ‘E is past’ is false given that it occurs before E. Therefore, tensed sentence tokens do not have different truth conditions from the tenseless ones. According to Oaklander, Smith would only arrive at this conclusion given that he confused tokens with types.

Oaklander further argues that the token-reflexive theory can avoid Smith’s objections if it is modified. It is not inconsistent to hold that tensed and tenseless sentence types have tokens with different truth conditions whilst holding that tensed and tenseless sentence tokens have identical truth conditions. Oaklander does not consider this to be a reduction of Mellor’s new tenseless theory to the old one because for Mellor, having identical truth conditions is a necessary but not a sufficient condition for translation of tensed sentences. As a consequence, even if tensed and tenseless sentence tokens have identical truth conditions, it doesn’t entail that tensed sentence tokens can be translated by tenseless sentence tokens. Moreover, contra Smith, this isn’t Mellor’s only reason for rejecting translatability. He, for instance, makes the following claim, which is in keeping with the New Theory of Reference aforementioned: two sentences have the same meaning iff they have the same use. Recall, that according to Kaplan, meaning refers to a sentence’s rule of use. According to Mellor, since tensed sentence tokens have different meanings that differ from those of tenseless sentence tokens, the former cannot be translated by the latter.

Oaklander does acknowledge at least the appearance of difficulty raised by Smith. Specifically, when Smith speaks of one sentence logically entailing another, the inference should be justifiable by truth conditions. One should be able to demonstrate that what makes the first true also makes the other true. If this cannot be done, the truth conditions for one’s sentences are incorrect or one is mistaken about such entailments. Oaklander concedes that Mellor does not consider this objection, but suggests that Mellor has a way to circumvent Smith’s contentions. Mellor makes use of Kaplan’s demonstratives and indexicals and argues that this helps to account for the logical equivalence of “It is now 1980” and “1980 is present.”14 The meaning of “It is now 1980” and “1980 is present” concerns a rule from the time when the tokens are uttered to their tenseless truth conditions. The truth conditions of their tokens will vary since their context of utterance varies. In each case their truth conditions are tenseless notwithstanding. Therefore, any token of “It is now 1980” is true with respect to the time at which the token is spoken iff it is spoken in 1980. The same applies to “1980 is present.” So if the truth conditions of both are identical, there is no longer a difficulty in getting them to be logically equivalent.

Smith responds by alleging that Oaklander misunderstands Mellor’s theory and that the type-token distinction cannot be employed to show that Mellor’s theory is consistent. According to Smith, Oaklander’s misunderstanding of Mellor’s theory lies in the fact that Mellor defines differences in meaning and use of sentence tokens in terms of differences in their truth conditions. If logically contingent sentences, that is to say, sentences that are neither tautologous nor unsatisfiable, have identical truth conditions, then they also have identical meaning and use. Smith maintains that the contradiction is present in Mellor’s theory and that it can only be circumvented by altering the theory. Smith instead chooses to consider whether Oaklander’s revisions have any merit.

Smith accuses Oaklander of merely reproducing the problem Smith pointed out in a different guise. He argues that Oaklander equivocates upon “it” the logical sameness of “It is now 1980” and “1980 is present.” If one were to replace “it” by identifying the relevant tokens, the seeming sameness of their truth conditions disappear. He presents the truth conditions as follows:

Any token S of (1) is true with respect to the context of S’s utterance if and only if the year of S’s context of utterance is 1980.

Any token V of (2) is true with respect to the context of V’s utterance if and only if the year of V’s context of utterance is 1980.15

Recall that Oaklander states that sentence types do not have truth conditions; only tokens do. Smith then considers two 1980 tokens S and V. S and V are true with respect to their utterances iff the year of their context of utterance is 1980. This, according to Smith, brings us back to the problem he raised because their truth conditions lie in the fact that they both occur in 1980. These tenseless facts do not entail each other because it is possible for S to occur in 1980 whilst V does not occur in 1980, if at all. As a consequence, these facts aren’t enough to explain their logical equivalence. Smith asserts that their logical equivalence is explained by the tensed fact, “1980 is present,” because it belongs to both their truth conditions. Given this, we should see that the tensed theory is more in keeping with facts about language and time than Mellor’s token-reflexive theory.

Oaklander responds by arguing that Smith’s objection is valid only if one presupposes a conception of analysis rejected by proponents of the new theory though having been accepted by proponents of the old theory. Oaklander states:

To begin to see what is involved in this last point note that the early defenders of the tenseless view believed that a complete description or analysis of time could be symbolically represented in a non-indexical tenseless language. To give a complete description or analysis involves constructing a single language that performs two functions. First, in its “logical” function, this perspicuous or ideal language (IL) is a symbolic device for representing or transcribing the logic of sentences contained in ordinary language.16

IL has both a logical and an ontological function. The former is the manner in which IL represents the correct logical form all sentences and entailments in a natural language can assume, e.g., well formulated formulae (wffs) in propositional and predicate logic. The latter represents the facts and the kinds of entities that exist. On the old tenseless theory, given logical considerations, one could draw ontological conclusions. For instance, the logic of temporal discourse could be translated into tenseless language, so therefore, time, ontologically speaking, is comprised of immutable temporal relations between terms that do not have A-properties.

Oaklander concedes that due to such assumptions, Smith’s objections to the old token-reflexive theory are strong. This, however, is not an argument against the new token-reflexive theory. In rejecting translatability in determining the nature of time, them who espouse the new theory are rejecting the very basis of Smith’s argument. Detensers accept the A-theorists claim that tense is indispensable when concerning discourse, but deny that in an attempt to capture the nature of time, tense is indispensable. The former is to say that tenseless sentences cannot replace tensed sentences without loss of meaning. In accepting this, thence, any proponent of the new theory is abandoning an IL capable of adequately accounting for both logical and ontological considerations. The ontological function is hence kept distinct from the logical function. Logical connections therefore are not representative of ontological links between facts in reality. There need not be a connection between the facts of “It is now 1980” and “1980 is present” that provides a basis for their truth conditions. Contra smith, tensed facts do not need to be employed in order to account for their logical equivalence. According to the new theory, two sentences with different meanings can correspond to the same fact and to a different one. “It is now 1980” and “1980 is present” can either correspond to the same fact or not. In failing to see this, Smith’s objections are not applicable to the new token-reflexive theory.

Though the discussion didn’t end there, Oaklander’s response adequately defends Mellor’s token-reflexive theory or, at the very least, offers a viable alternative. The distinction he draws given an IL and the isolation of the ontological from the logical allows detensers to reject the notion that logical equivalence provides a basis for the truth conditions of “It is now 1980” and “1980 is present.” Furthermore, they can reject the notion that tensed facts are necessary to explain logical equivalence. This is what allows Mellor to say that the sentences tokens of “Cambridge is here” and “It is now 1980” have different truth conditions. If the ontological is held as distinct from the logical, these sentences can be made true by the same fact or not. Their logical equivalence does not imply that some fact corresponds to it.

Temporal Parts Theory of Identity

Since the Temporal Parts Theory of Identity will feature in my forthcoming argument, I will outline it here. I will then note a difference between the theory as it stands and my version of it, which can constitute a reduction of the theory. This may seem tangential, but even if so, it is a relevant detour because when accounting for our experience of time and its passing, a theory of identity is necessary in any theory of time and specifically, one that is consistent with the theory of time in question. Given the B/R-theory I will offer, I will argue that the temporal parts theory is best suited to meet the criterion of consistency. One will find that in speaking of temporal parts, the detensers’ acceptance of tense being indispensable in regards to temporal discourse will be made apparent. In other words, I will be speaking of earlier temporal parts differing from later ones.

The Temporal Parts Theory of Identity (hereon TPT) is derived from the notion of time being, in some sense or to some degree, like space. One can think of, for instance, a linear timeline depicting the years all 44 U.S. Presidents held office. Or one can think of the x-y axis used in physics. Time is represented by the x-axis whilst space is represented by the y. Or one can think of a space-time diagram containing two axes representing space and another to represent time. These sorts of considerations have led some philosophers and scientists to ask whether time is a dimension. According to some accounts, time is the fourth dimension. Time, however, is not always analogous to space. D.H. Mellor discussed these disanalogies at length.17 He, for instance, concluded that there’s no spatial analogue for our feeling of the passing of time. We can’t, in other words, attribute the passing of time to spatial changes.

With respect to parts, however, time and space are analogous. Theodore Sider explains:

Temporal parts theory is the claim that time is like space in one particular respect, namely, with respect to parts. First think about parts in space. A spatially extended object such as a person has spatial parts: her head, arms, etc. Likewise, according to temporal parts theory, a temporally extended object has temporal parts. Following the analogy, since spatial parts are smaller than the whole object in spatial dimensions, temporal parts are smaller than the whole object in the temporal dimension. They are shorter-lived.18

Recall, as an example, the b-moments in Friedrich Nietzsche’s life. Friedrich Nietzsche’s birth on October 15, 1844 is one b-moment and his death on August 25, 1900 is another. The dates of both represent distinct b-times. On TPT, he is spread out from October 15, 1844 to August 25, 1900. If we were to depict him in a space-time diagram, his parts on our diagram will depict his temporal parts. If we were capable of watching Nietzsche in his infancy, we will be observing a temporal part, then another that resembles it, and then another. If one were to watch infant Nietzsche long enough, his later temporal parts will be slightly bigger than the previous ones. That is to say that Nietzsche is no longer an infant; he is now, for instance, a toddler. So on our space-time diagram, Nietzsche grows the further we move away from his birth. It is also worth noting that temporal parts have spatial parts and vice versa. Nietzsche’s hand, like Nietzsche himself, persisted within the interval of time his life occupies. The parts he was comprised of will also be represented on our space-time diagram.

TPT is consistent with the B-theory and the B/R-theory that I will offer. For example, with regards to distant objects, time and space are alike. M31, though very distant, is just as real as any object in close proximity on Earth. Temporally distant objects, likewise, are real. This is the view known as eternalism, which differs from presentism in denying the thesis that only objects in the present exist. Also, with regards to here and now, time and space are analogous. If, for instance, I’m talking to my friend in China, she may say that it is sunny ‘here’ whilst I may say it is snowing ‘here.’ There’s no disagreement between us. Here is, in other words, relative to the person. The word ‘now’ works in like manner. If I were speaking to Fred, a homo erectus, via a time-traversing telephone, he could express that it is currently 1.8 million years before the advent of our calendars whilst I express that it is 2015. He and I do not disagree. ‘Now,’ like ‘here,’ is relative to the person. This is the gist of the B-theory of time.

Regardless of whether TPT is consistent with my B/R-theory of time, there’s still the question of whether TPT is true. Presenting a philosophical case in defense of the theory and reducing it to a simpler theory will be tasks undertaken in §2. The reduction of the theory is necessary because though detensers do not deny the indispensability of tense when concerning temporal discourse, TPT is, to my mind, mistaken because it bridges the chasm between the logical and ontological aspects previously discussed. In other words, TPT goes from ordinary tensed discourse to a dubious ontological commitment, namely that temporal parts are objects that exist and we can, in some sense, comprehend what they are like.

In the next section, which is my argument, I will attempt to answer the question as to whether anything can have the characteristic of being in time. I will endeavor to show that nothing can have this characteristic. My approach will differ from McTaggart’s because a philosophical theory stands in relation to logical, conceptual, perceptual or actual phenomena in our world. Doing away with the A-series is therefore necessary but not sufficient to show that nothing exists in time, i.e., that time is unreal. If our experience of time is not evidence for real time, one must still account for this experience: ponder its origin, what might this experience hinge on, and whether it is possible for time to exist in isolation of these things. I will endeavor to show that time does not exist in isolation of these and I will argue that some of the literature has hitherto agreed with this assessment. What’s left is to bring together relevant threads of this discussion to draw a conclusion that, at the very least, offers a plausible solution to our conundrum. These threads will consist of valid parts of Mellor’s new token-reflexive theory, the R-theory as defended by Oaklander, and the union of B- and R-theories which will bear some resemblance to but differ in key aspects from Oaklander’s theory. I will also defend TPT, defend my reason for reducing it to a simpler theory of identity, and then relate this reduction to my B/R-theory of time. Then, I will consider objections to my theory, discuss its implications, especially as they relate to the philosophy of science, and introduce mathematical nominalism to circumvent the main problem arising from my theory.

Works Cited

1 Mellor, D. H. Real Time II. London: Routledge, 1998. 8. Print.

2 Oaklander, Nathan. Adrian Bardon ed. “A-, B- and R-Theories of Time: A Debate”. The Future of the Philosophy of Time. New York: Routledge, 2012. 23. Print.

3 Prior, A. N. Papers on Time and Tense. Oxford: Clarendon P., 1968. Print.

4 Ibid. [2]

5 Oaklander, L. Nathan, and Quentin Smith, eds. The New Theory of Time. New Haven: Yale UP, 1994. 10. Print.

6 Ibid. [4]

7 Ibid. [4], p.18-19

8 Ibid. [1], p.27

9 Smith, Quentin (1987). “Problems with The New Tenseless Theory of Time”. Philosophical Studies 52 (3): 371-392.

10 Ibid. [9]

11 Mellor, D. H. Real Time. Cambridge [Cambridgeshire: Cambridge UP, 1981. 28. Print.

12 Ibid. [11], p.24.

13 Oaklander, L. N. (1991). “A Defence of the New Tenseless Theory of Time”. The Philosophical Quarterly 41: 26–38.

14 D. Kaplan (1978). “On the Logic of Demonstratives”. Journal of Philosophical Logic 8: 81-98.

15 Ibid. [5], p.73.

16 Oaklander, L. Nathan (1990). “The New Tenseless Theory of Time: A Reply to Smith”. Philosophical Studies 58 (3): 287 – 292.

17 Ibid. [1], p.95-96

18 Sider, Theodore (2008). “Temporal Parts”. Web. <http://tedsider.org/papers/temporal_parts.pdf>