# Rescuing Logic From the Abuse of Bayes’ Theorem: Validity, Soundness, and Probability

By R.N. Carmona

In recent years, there has been a surge in the use of Bayes’ Theorem with the intention of bolstering this or that argument. This has resulted in an abject misuse or abuse of Bayes’ Theorem as a tool. It has also resulted in an incapacity to filter out bias in the context of some debates, e.g. theism and naturalism. Participants in these debates, on all sides, betray a tendency to inflate their prior probabilities in accordance with their unmerited epistemic certainty in either a presupposition or key premise of one of their arguments. The prophylactic, to my mind, is found in a retreat to the basics of logic and reasoning.

An Overview on Validity

Validity, for instance, is more involved than some people realize. It is not enough for an argument to appear to have logical form. An analysis of whether it, in fact, has logical form is a task that is seldom undertaken. When people think of validity, something like the following comes to mind: “A deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. Otherwise, a deductive argument is said to be invalid” (NA. Validity and Soundness. Internet Encyclopedia of Philosophy. ND. Web.).

Kelley, however, gives us rules to go by:

1. In a valid syllogism, the middle term must be distributed in at least one of the premises
2. If either of the terms in the conclusion is distributed, it must be distributed in the premise in which it occurs
3. No valid syllogism can have two negative premises
4. If either premise of a valid syllogism is negative, the conclusion must be negative; and if the conclusion is negative, one premise must be negative
5. If the conclusion is particular, one premise must be particular (Kelley, D.. The Art of Reasoning. WW Norton & Co. 2013. Print. 243-249)

With respect to the first rule, any argument that does not adhere to it commits the fallacy of undistributed middle. Logically, if we take Modus Ponens to be a substitute for a hypothetical syllogism, then undistributed middle is akin to affirming the consequent. Consider the following invalid form:

All P are Q.

All R are P.

∴ All R are Q.

When affirming the consequent, one is saying Q ⊃ P. It is not surprising that these two fallacies are so closely related because both are illegitimate transformations of valid argument forms. We want to say that since all P are Q and all R are P, therefore all R are Q in much the same way we want to infer that P ⊃ Q. Consider the well-known Kalam Cosmological Argument. No one on both sides questions the validity of the argument because validity, for many of us, is met when the conclusion follows from the premises. However, one can ask whether the argument adheres to Kelley’s rules. If one were to analyze the argument closely enough, it is very arguable that the argument violates Kelley’s fourth rule. The issue is that it takes transposing from the fifth rule to fourth rule because the argument does not violate the fifth and therefore, appears valid. However, when restated under the fourth rule, the problem becomes obvious. In other words, the universe is a particular in both Craig’s conclusion and in the second premise of his argument. Let’s consider the KCA restated under the fourth rule:

There are no things that are uncaused.

There is no universe that is uncaused.

∴ All universes have a cause.

Restating it this way appears controversial only because the argument seems to presuppose that there is more than one universe. Two negatives must have properties in common. Put another way, since there are many of all things, then the universe cannot be the only thing of its kind, if we even agree that the universe is like ordinary entities at all. Craig, perhaps unintentionally, attempts to get a universal from a particular, as his argument restated under the fourth rule shows. Given this, we come to the startling conclusion that Craig’s KCA is invalid. Analyses of this kind are extremely rare in debates because most participants do not know or have forgotten the rules of validity. No amount of complexity hides a violation of basic principles. The advent of analytic philosophy with Bertrand and Moore led to an increasing complexity in arguments and for the most part, validity is respected. As shown here, this is not always the case, so a cursory analysis should always be done at the start.

Validity is necessary but not sufficient for an argument to prove effective and persuasive. This is why arguments themselves cannot substitute for or amount to evidence. Soundness is determined by taking a full account of the evidence with respect to the argument. The soundness of an argument is established given that the pertinent evidence supports it; otherwise, the argument is unsound. Let us turn to some simple examples to start.

An Overview of Soundness

“A deductive argument is sound if and only if it is both valid, and all of its premises are actually true. Otherwise, a deductive argument is unsound” (Ibid.).

All ducks are birds.

Larry is a duck.

∴ Larry is a bird.

This argument is stated under Kelley’s fifth rule and is no doubt valid. Now, whether or not the argument is sound will have us looking for external verification. We might say that, a priori, we know that there are no ducks that are not birds. By definition, a duck is a kind of bird. All well and good. There is still the question of whether there is a duck named Larry. This is also setting aside the legitimacy of a priori knowledge because, to my mind, normal cognitive function is necessary to apprehend human languages and to comprehend the litany of predicates that follow from these languages. We know that ducks are birds a posteriori, but on this point I digress. Consider, instead, the following argument.

All ducks are mammals.

Larry is a duck.

∴ Larry is a mammal.

This argument, like the previous one, is valid and in accordance with Kelley’s fifth rule. However, it is unsound. This harkens back to the notion that ducks belonging to the domain of birds is not a piece of a priori knowledge. Despite knowing that all ducks are birds, the differences between birds and mammals are not at all obvious. That is perhaps the underlying issue, a question of how identity is arrived at, in particular the failure of the essentialist program to capture what a thing is. The differentialist program would have us identify a thing by pinning down what it is not. It follows that we know ducks are birds because anatomically and genetically, ducks do not have the signatures of mammals or any other phylum for that matter. A deeper knowledge of taxonomy is required to firmly establish that ducks are, in fact, birds.

An exploration of soundness is much more challenging when analyzing metaphysically laden premises. Consider, for example, the second premise of the KCA: “The universe began to exist.” What exactly does it mean for anything to begin to exist? This question has posed more problems than solutions in the literature; for our purposes, it is not necessary to summarize that here. We can say of a Vizio 50-inch plasma screen television that it began to exist in some warehouse; in other words, there is a given point in time where a functioning television was manufactured and sold to someone. The start of a living organism’s life is also relatively easy to identify. However, mapping these intuitions onto the universe gets us nowhere because as I alluded to earlier, the universe is unlike ordinary entities. This is why the KCA has not been able to escape the charge of fallacy of composition. All ordinary entities we know of, from chairs to cars to elephants to human beings exist within the universe. They are, as it were, the parts that comprise the universe. It does not follow that because it is probable that all ordinary things begin to exist that the universe must have begun to exist.

This is a perfect segue into probability. Again, since Bayes’ Theorem is admittedly complex and not something that is easily handled even by skilled analytic philosophers, a return to the basics is in order. I will assume that the rule of distribution applies to basic arguments; this will turn out to be fairer to all arguments because treating premises as distinct events greatly reduces the chances of a given argument being true. I will demonstrate how this filters out bias in our arguments and imposes on us the need to strictly analyze arguments.

Using Basic Probability to Assess Arguments

Let us state the KCA plainly:

Everything that begins to exist has a cause for its existence.

The universe began to exist.

∴ The universe has a cause for its existence.

As aforementioned, the first premise of the KCA is metaphysically laden. It is, at best, indeterminable because it is an inductive premise; all it takes is just one entity within the universe to throw the entire argument into the fire. To be fair, we can only assign a probability of .5 for this argument being true. We can then use distribution to get the probability of the argument being sound, so since we have a .5 probability of the first premise being sound, and given that we accept that the argument is not in violation of Kelley’s rules, we can therefore distribute this probability across one other premise and arrive at the conclusion that the argument has a 50% chance of being true.

This is preferable to treating each premise as an isolated event; I am being charitable to all arguers by assuming they have properly distributed their middles. Despite this, a slightly different convention might have to be adopted to assess the initial probability of an argument with multiple premises. An argument with six individual premises has a 1.56% chance of being true, i.e. .5^6. This convention would be adopted because we want a probability between 0 and 100. If we use the same convention used for simpler arguments with less premises, then an argument with six premises would have a 300% chance of being true. An arguer can then arbitrarily increase the amount of premises in his argument to boost the probability of his argument being true. Intuitively, an argument with multiple premises has a greater chance of being false; the second convention, at least, shows this while the first clearly does not. The jury is still out on whether the second convention is fair enough to more complex arguments. There is still the option of following standard practice and isolating an individual premise to see if it holds up to scrutiny. Probabilities do not need to be used uniformly; they should be used to make clear our collective epistemic uncertainty about something, i.e., to filter out dogma.

Let us recall my negation strategy and offer the anti-Kalam:

Everything that begins to exist has a cause for its existence.

The universe did not begin to exist.

∴ The universe does not have a cause.

Despite my naturalistic/atheistic leanings, the probability of my argument is also .5 because Craig and I share premise 1. The distribution of that probability into the next premise does not change because my second premise is a negation of his second premise. In one simple demonstration, it should become obvious why using basic probabilities is preferable over the use of Bayes’ Theorem. No matter one’s motivations or biases, one cannot grossly overstate priors or assign a probability much higher than .5 for metaphysically laden premises that are not easily established. We cannot even begin to apply the notion of a priori knowledge to the first premise of the KCA. We can take Larry being a bird as obvious, but we cannot take as obvious that the universe, like all things within it, began to exist and therefore, has a cause.

Now, a final question remains: how exactly does the probability of an argument being sound increase? Probability increases in accordance with the evidence. For the KCA to prove sound, a full exploration of evidence from cosmology is needed. A proponent of the KCA cannot dismiss four-dimensional black holes, white holes, a cyclic universe, eternal inflation, and any theory not in keeping with his predilections. That being the case, his argument becomes one based on presupposition and is therefore, circular. A full account of the evidence available in cosmology actually cuts sharply against the arteries of the KCA and therefore, greatly reduces the probability of it being sound. Conversely, it increases the probability of an argument like the Anti-Kalam being true. The use of basic probability is so parsimonious that the percentage decrease of the Kalam being sound mirrors the percentage increase of the Anti-Kalam being sound. In other words, the percentage decrease of any argument proving sound mirrors the percentage increase of its alternative(s) proving true. So if a full account of cosmological evidence lowers the probability of the Kalam being sound by 60%, the Anti-Kalam’s probability of being true increases by 60%. In other words, the Kalam would now have a 20% probability of being true while its opposite would now have an 80% of being true.

Then, if a Bayesian theorist is not yet satisfied, he can keep all priors neutral and plug in probabilities that were fairly assessed to compare a target argument to its alternatives. Even more to the point regarding fairness, rather than making a favored argument the target of analysis, the Bayesian theorist can make an opponent’s argument the target of analysis. It would follow that their opponent’s favored argument has a low probability of being true, given a more basic analysis that filters out bias and a systematic heuristic like the one I have offered. It is free of human emotion or more accurately, devotion to any given dogma. It also further qualifies the significance of taking evidence seriously. This also lends much credence to the conclusion that arguments themselves are not evidence. If that were the case, logically valid and unsound arguments would be admissible as evidence. How would we be able to determine whether one argument or another is true if the arguments themselves serve as evidence? We would essentially regard arguments as self-evident or tautologous. They would be presuppositionalist in nature and viciously circular. All beliefs would be equal. This, thankfully, is not the case.

Ultimately, my interest here has been a brief exploration into a fairer way to assess competing arguments. All of this stems from a deep disappointment in the abuse of Bayes’ Theorem; everyone is inflating their priors and no progress will be made if that continues to be permitted. A more detailed overview of Bayes’ Theorem is not necessary for such purposes and would likely scare away even some readers versed in analytic philosophy and more advanced logic. My interest, as always, is in communicating philosophy to the uninitiated in a way that is approachable and intelligible. At any rate, a return to the basics should be in order. Arguments should continue to be assessed; validity and soundness must be met. Where soundness proves difficult to come by, a fair initial probability must be applied to all arguments. Then, all pertinent evidence must be accounted for and the consequences the evidence presents for a given argument must be absorbed and accepted. Where amending of the argument is possible, the argument should be restructured, to the best of the arguer’s ability, in a way that demonstrates recognition of what the evidence entails. This may sound like a lot to ask, but the pursuit of truth is an arduous journey, not an easy endeavor by any stretch. Anyone who takes the pursuit seriously would go to great lengths to increase the epistemic certainty of his views. All else is folly.

# A Refutation of Weaver’s “An Objection to Naturalism and Atheism from Logic”

By R.N. Carmona

Weaver’s argument, although robust, commits what I think is a cardinal sin in philosophy: “An objection from logical considerations against atheism is one which attempts to show that some deliverance of logic is at odds with atheism or something strictly implied by atheism” (Weaver, C.G. (2019). Logical Objections to Atheism. In A Companion to Atheism and Philosophy, G. Oppy (Ed.). https://doi.org/10.1002/9781119119302.ch30). One should not get in the habit of drawing ontological conclusions on the basis of logical considerations and though Weaver makes a good attempt to justify his conclusion, there are too many areas in his composite argument that are vulnerable to attack. There are parts of his composite argument that are clearly stated in his own words, but other parts have to be sifted out from his discussions, specifically on logical monism and classical logical consequence (CLC). Also, the conclusion that atheism is false has to be gathered from his discussion following his claim that ontological naturalism is false.

A general note, prior to proceeding, is in order. Weaver’s paper is quite technical and not at all easy for the untrained eye to read, let alone understand, so I will endeavor to avoid technicality wherever necessary; I will only permit pursuing one technical element because I disagree with Weaver’s treatment of supervenience, how he conveniently begs the question regarding reductionist materialism (if only to ensure that his argument is not met with immediate difficulty), and the conclusion he believes follows. More importantly, I think that the domestication of philosophy within the ivory towers of academia was a critical misstep that needs to be rectified. While analytic philosophy has its use, its abuse makes philosophy the slave of academic elites and therefore, keeps it well out of the reach of ordinary people. Philosophy, therefore, if it is to be understood by laypeople, needs to be communicated in ordinary, relatable language. Since my interest is to, first and foremost, communicate philosophy in an approachable way, I tend to avoid technicalities as much as possible. With that said, it is not at all necessary to quibble with Weaver’s logical proofs of validity (especially because validity matters much less than soundness) or Williamson’s notion that contingentist statements can be mapped onto necessitist ones and vice versa, but that “The asymmetry favours necessitism. Every distinction contingentists can draw has a working equivalent in neutral terms, but the extra commitments of necessitism allow one to draw genuine distinctions which have no working equivalents in neutral terms. If one wants to draw those distinctions, one may have to be a necessitist” (Williamson, T.. “Necessitism, Contingentism, and Plural Quantification.” Mind 119 (2010): 657-748. 86. Web.).

Williamson and Weaver, following his cue, are both guilty of ignoring logical atomism, so ultimately, it does not matter if the validity of logical statements suggests that necessitism about mere propositions is probably true because ultimately, we are not talking about mere propositions but rather Sachverhalte, “conglomerations of objects combined with a definite structure” (Klement, Kevin, “Russell’s Logical Atomism”The Stanford Encyclopedia of Philosophy (Spring 2020 Edition), Edward N. Zalta (ed.)). This is perhaps Weaver’s motivation for dismissing Carnap who was anti-metaphysical. It can be argued, therefore, that reinstating metaphysics or overstating its importance is necessary for any argument against naturalism and/or atheism or conversely, for Theism, to get any traction. The fact remains, however, that propositions comprising a sound logical argument are dependent on real world experiences via the senses. The proposition “there is a cat” may speak to the fact that either i) one believes they have seen a cat in whatever space they find themselves in ii) one knows and can confirm that there is a cat in their vicinity iii) there is presently a cat within ones field of vision. While I grant that propositions can speak to entirely imaginary or, at least, hypothetical entities, all propositions rely on entities we have identified in our common tongue. Therefore, statements like “there is a cat” will always rely on content not necessarily entailed within a given proposition. There is still a question as to the context of such propositions and the preciseness of what one is trying to say.

Weaver’s Composite Argument Against Naturalism and Atheism, and Its Problems

With these preliminary concerns in our rearview, I can now turn to Weaver’s composite argument and provide a few avenues for the atheist to refute his argument.

W1 Since situationspf do not exist (“I will therefore be entitled to reject…the existence of situationsPF” (Weaver, 6).), situationsC exist.

W2 Given situationsC , classical logical consequence (CLC) is the case.

W3 From W2, necessitism is true.

W4 “If necessitism is true, then ontological naturalism is false.”

W5 “Necessitism is true.”

W6 “Therefore, ontological naturalism is false” (Weaver, 15).

W7 From W6, “Necessitism is true and modal properties are indispensable to our best physical theories.”

W8 If W7, “then there is a new phenomenon of coordination (NPC).”

W9 “Necessarily, (if there is an NPC, it has an explanation).”

W10 “Necessarily, [if possibly both (atheism is true and there is an NPC), then it is not possible that the NPC has an explanation]”

C “Therefore, atheism is false” (Weaver, 18).

Setting aside that Weaver assumes that suitably precisified situations (situationspf) cannot exist and the problems he would face if just one instance of such a situation does exist, there is a way to show that even on the assumption that just classically precisified situations (situationsC) exist, it doesn’t follow that CLC holds. Weaver seems to think that CLC follows from a schema concerning mere validity: “A deductive argument is valid, just in case, there is no situation in which the premises are true and the conclusion false” (Weaver, 4). I think it is straightforwardly obvious that a typical non sequitur already violates this schema. Consider the following:

P1 If it is cloudy outside, there is a chance of precipitation.

P2 It is cloudy outside.

C Therefore, the Yankee game will be postponed.

The first two premises are true perspectively. In New York City, at this present hour, it is partly cloudy outside and there is thus, a chance of precipitation. However, the conclusion is false because the New York Yankees are not even in Spring training and it is out of the norm for them to have a regular season home game in late January. The above argument can prove true given not only at least one extra premise, but also the fact that it is not winter but spring, and that the MLB regular season is underway. This goes a long way in showing that propositions are usually missing crucial content and are true given specified context. Perhaps, then, Weaver should provide a different schema to ground CLC.

Weaver, unfortunately, does not give an adequate account of what he means by situationspf and what such situations would look like. It is enough to reiterate that the existence of even one such situation takes him back to square one. This is aside from the fact that a rejection of pluralism entails a rejection of arguments operating outside of classical logic, e.g., Plantinga’s Modal Ontological Argument, which rests of the axioms of S5 modal logic. A thorough rejection of free logical systems would limit Theists to the domain of classical logic, which will prove unforgiving since nothing like God seems operative in the real world.

Weaver’s dependence on situationsC and CLC proves problematic and is one place for an atheist to focus on. Another avenue for an atheist to take is W4 and W5. Is the notion that ontological naturalism is false conditional on necessitism being true? I do not think Weaver established that this premise is true. Furthermore, aside from exploring whether these clauses have a conditional relationship, one can simply ask whether necessitism is true. The jury is still out on whether necessitism or contingentism is the case, and there may yet be a synthesis or a handful of alternative positions that challenge both. Given the current state of the debate, I am uncommitted to either position, but I am suspicious of anyone siding with one for sake of attempting to disprove a position they already assume is false, which, in Weaver’s case, are naturalism and atheism.

In plain language, the perspective of necessitists falls flat or appears to be saying something nonsensical. Williamson outlines where disagreement lies:

For instance, a contingentist typically holds that it is contingent that there is the Thames: there could have been no such river, and in those circumstances there would have been no Thames. By contrast, a necessitist typically holds that it is necessary that there is the Thames: there could have been no such river, but in those circumstances there would still have been the Thames, a non-river located nowhere that could have been a river located in England. Thus the contingentist will insist that necessarily if there is the Thames it is a river, while the necessitist allows at most that necessarily if the Thames is located somewhere it is a river.

Williamson, T.. “Necessitism, Contingentism, and Plural Quantification.” Mind 119 (2010): 657-748. 9. Web.

Contingentists deny the necessity of the Thames, whether river or not. These identity discussions extend further when one considers people. Manuel Pérez Otero explores this and tries to synthesize these two opposing point of views (see Otero, Manuel Pérez. “Contingentism about Individuals and Higher-Order Necessitism.” Theoria: An International Journal for Theory, History and Foundations of Science, vol. 28, no. 3(78), 2013, pp. 393–406. JSTOR, http://www.jstor.org/stable/23926328. Accessed 25 Jan. 2021.). Though Otero’s synthesis is tangential for our purposes, it shows that this binary Weaver thinks exists is one of his own making, essentially a false dichotomy. Given the issues necessitism presents for ordinary language, and the likelihood of one of its alternatives being true, it follows that necessitism is probably false. An exhaustive defense of a position I am not committed to is not at all required to show where Weaver has gone wrong.

This takes us to Weaver’s treatment of supervenience and his New Phenomenon of Coordination (NPC), which states:

Why is it that modal properties and notions enter the verisimilitudinous fundamental dynamical laws of our best and most empirically successful physical theories given that modal properties do not weakly supervene upon the physical or material? (or) How is it that the material world came to be ordered in such a way that it evolves in a manner that is best captured by modally laden physical theorizing or dynamical laws given that modal properties do not even weakly supervene upon the material and non-modal? (Weaver, 17)

If necessitism is probably false, then ontological naturalism still has a chance of being true. This is despite the fact that Weaver failed to show that the falsity of ontological naturalism is conditional on necessitism being true. A stronger route for him to have took is to argue that ontological naturalism is false iff necessitism is true because even if turns out that necessitism is true, ontological naturalism can also be true. Weaver has not established that they are mutually exclusive. Therefore, an atheist can feel no pressure at all when confronted with NPC. This is setting aside that Weaver appears to be undisturbed by the incongruity of our scientific and manifest images. One would think a reconciliation is required before proclaiming that the material world is organized via modally laden physical theories and dynamic laws that supervene, whether strongly or weakly, on the material world.

The primary issue with Weaver’s assessment is the assumption that all atheists must be committed to reductionist materialism or physicalism to be a consistent ontological naturalist. There are alternative naturalisms that easily circumvent Weaver’s NPC because such a naturalist would not be committed to any version of supervenience. As an example, this naturalist can hold, to put it as simply as possible, that scientific theories and models are merely representations. Therefore, the modality of scientific theories need not supervene on the material world at all. Given a representationalist account of scientific theories, perhaps something like a reverse supervenience is the case.

∎∀𝑥∀𝑦(∀𝐹 𝐹𝑥 ≡ 𝐹𝑦 ⟶ ∎∀R R𝑥 ≡ R𝑦 )

Necessarily for any entity and for any entity y, [(if for any material property F, (has F, just in case, has F), then necessarily, for any representational property M, (has M, just in case, has M)].

Scientific theories and models are, in other words, more akin to impressionist paintings than a group of modally laden propositions. This is a more commonsense view in that a scientific model is a portrait of the real world. While there is a feedback between the model and the material world, in that theories have to be tested against reality, theories and models are not conceived in a vacuum. Real world observations impose the postulates of a theory or render a portrait that we call a model. Ptolemy misconstrued planetary orbits and attributed their motions to invisible spheres rather than the ellipses we are familiar with. He was not far off the mark, especially given that there is an intangible involved, namely gravity, but his impression was inexact. This is what a representationalist account of scientific theories would look like and whether something like reverse supervenience is necessary does no real harm to the account.

The last route atheists can take is in Weaver’s conflation of atheism and naturalism. Though I am sympathetic to the conflation, like Nielsen, who stated, “Naturalism, where consistent, is an atheism” (Nielsen, Kai. Naturalism and Religion. Amherst, N.Y.: Prometheus, 2001. 30. Print.), the same need not apply in vice versa. In other words, the following statement need not be the case: “atheism, where consistent, is a naturalism.” While I am also partial to that statement, even going as far as defending it in Philosophical Atheism: Counter Apologetics and Arguments For Atheism, that gods do not exist does not entail that no immaterial beings can exist. It could be the case that no iteration of god exists, but that ghosts do. Weaver’s conflation seems to rest on the assumption that naturalism is the antithesis of supernaturalism. Naturalism is also opposed to paranormal phenomena, so there can be defeaters of naturalism that are not also defeaters of atheism. In other words, a definitive proof of the paranormal does not debase the thesis that gods do not exist. A definitive proof of one’s great grandma roaming the estate does not imply that God or any other god undeniably exists. Nielsen’s statement implies only that a disproof of atheism is also a disproof of naturalism, but this does not work in the other direction.

Ultimately, in light of the composite argument above, one that I think is true to Weaver’s overall argument, fails to disprove ontological naturalism and atheism. There is far too much controversy in a number of places throughout his argument to regard it as convincing. The argument needs to be critically amended or entirely abandoned because in its present form, it does not meet its end. My rebuttal provides fertile ground for further exploration with respect to necessitism, contigentism, and any possible syntheses or alternatives, in addition to what is required to contradict naturalism and atheism. God, whether the idea Theist philosophers defend, or a more common concept tied to a particular religion, is still resolutely resigned to silence, hiddenness, and outright indifference. Therefore, Theists have their own onus that must go beyond even a successful argument against naturalism and/or atheism.

# 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>