Category: ontology

The Philosophy of Batesian Mimicry

By R.N. Carmona

Before I talk about the philosophical depths and conundrums of this type of mimicry, allow me to define it. Batesian mimicry is when one species adapts the features of another, usually poisonous species, so as to protect itself from predators. The most common example is the viceroy who adapted the wing patterns of the monarch for sake of avoiding its predators; note: this might actually be an example of Müllerian mimicry. Evolutionary biologists and geneticists have a handle on the genomic going ons that contribute to this, but philosophically speaking, this form of mimicry is intriguing. It boggles my imagination.

Let me preface my remarks by saying that I’m far from sympathetic to pseudoscience and as such, I don’t think creationism gets any closer to explaining the why of Batesian mimicry. Intelligent design doesn’t either. I highly doubt that the god of the Bible is siding with the prey and therefore, harming the predator. The height of benevolence would want what’s best for both prey and predator and wouldn’t actively harm one or the other. There’s also the case of imperfect mimicry, so if one wants to imagine that a designer is writing code into the fabric of reality, the designer isn’t the perfect designer of monotheism. With that said, my philosophical hold up has nothing at all to do with creationism and/or intelligent design.

My question is this: how did the viceroy know that a monarch’s pattern would protect it from predators? Does it have enough intelligence to understand its surroundings that well? Did it, in other words, survey its surroundings to the degree that it understood that birds avoid monarchs because of their wing patterns? Assuming we relinquish our tendency to belittle animal intelligence, how did the viceroy have the power to put these genetic changes into motion? That, that (!) is a question science doesn’t seem to care to answer. We can vaguely say that nature made this happen, but that moves the question of agency into a vague, mindless concept. Furthermore, it doesn’t explain the power of an animal to rewrite its genome.

Philosophers from Plato to Kant suggested that there may be more to reality than we realize. Before the advent of quantum mechanics, philosophers understood that reality might not be as simple as it appears on what Kant called the phenomenal level. There may be more to it. The powers of mimicry may be a hint. In Doctor Strange, the Ancient One, portrayed by Tilda Swinton, suggested that cells can be made to repair themselves and organize in all sorts of ways. She also implied that doctors like him are accustomed to one known way and are unaware of others. Humans do not have powers of genetic changes that are directed to a given end in the way some animals do. Batesian, Müllerian, and acoustic mimicry might be a most unexpected vindication for thinkers like Kant.

Westworld inclines me to ideas of competing engineers coding and recoding the fabric of our reality. Perhaps the true nature of reality is an elaborate game, a desperate reach for data, a simulation aiming to remap history before the present the engineers find themselves in. Perhaps not. Not everything makes sense; not everything has to. The Ancient One was right about that as well, but there are aspects of nature that don’t appear to be confined to nature and certainly can’t be readily explained by nature in and of itself. The noumenal, the Hegelian Absolute is the overarching objectivity that humans, in all their subjectivity, are striving for. There are phenomena available to our perceptions that may suggest that our arms are much too short to reach up and grasp that object of our desire. Perhaps we are doomed to decades of subjectivity, an existence that never apprehends truth. For some of us, there’s certainly no comfort in that.

Maybe this is the price we pay for being aware of our consciousness. In being aware of our consciousness, we have been disconnected from the full fabric of reality. Because of this awareness, maybe we are veiled from that which lies behind the curtain. We believe ourselves to be on the stage performing in the most meaningful way and in the only way that’s considered significant when in actuality, we are the audience that sees but the shadows of the performance. We can explain mimicry in our very limited ways, but we’ve apprehended only shadows. We have nothing in the way of why and nothing in the way of explaining to what is nothing short of a super power. We have nothing in the way of explaining the will and agency that drives such mimicry and much less the awareness necessary to accomplish it. Plato may have been right. Here we sit in the cave…

An Excerpt From My New Book

It is useful to note that even if Plantinga or any Christian rejects the contra-argument, the first premise can be challenged. Rather than quibble with what is meant by maximal excellence, an atheist can accept the definition as it stands. The atheist can, however, question whether this is possible world W in where a being of maximal excellence exists and explore the consequences if it turns out that this isn’t that possible world. In other words, if this isn’t that specific possible world, then the argument is speaking of a possible world that is inaccessible to the believer and the believer is therefore in no better position to convince the non-believer. Put another way, if a being of maximal excellence doesn’t exist in this possible world, then it possibly exists in another world that cannot be accessed by any of the inhabitants in this world. There is therefore no utility or pragmatic value in belief. The argument would only speak of a logical possibility that is ontologically impossible in this world.

The atheist can take it a step further. What Christian theists purport to know about god stems from the Bible. The Bible, in other words, gives us information about god, his character, and his history as it relates to this world. Assuming this is possible world W, does he represent a being having maximal excellence? Is he, for instance, identical to a being who is wholly good? Any honest consideration of parts of the Bible would lead one to conclude that god is not identical to a being who is wholly good; god, in other words, isn’t wholly good. So obvious is his evil that Marcion of Sinope diverged from proto-Orthodox Christians in concluding that the Jewish God in the Old Testament is an evil deity and is in no way the father of Jesus. Yet if he’s evil, then he isn’t wholly good and if he isn’t wholly good, he fails to have maximal excellence.

Moreover, and much more damning to Plantinga’s argument, is that a being of maximal greatness has maximal excellence in all worlds. Therefore, if this being does not have maximal excellence in one of those worlds or more specifically, in this world, then it does not possess maximal greatness. Far from victorious, Plantinga’s argument would taste irreparable defeat and this, in more ways than one.

R.N. Carmona Philosophical Atheism: Counter Apologetics and Arguments For Atheism

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!

On Challenging the Laws of Logic

R.N. Carmona

In the past, I’ve argued that the laws of logic can be challenged or even violated. A response to my post on procedural realism and the Moral Argument mentioned that the laws of excluded middle and non-contradiction have been challenged by analytic philosophers. I found it curious that there was no mention of a challenge to the law of identity, since I think it’s the most easily challenged.

In order to challenge the law of identity, one need only challenge its underlying assumption, namely essentialist ontology. “The essentialist tradition, in contrast to the tradition of differential ontology, attempts to locate the identity of any given thing in some essential properties or self-contained identities” (see here). According to modern physics, as it now stands, all objects are atoms in flux and empty space. Where then is the atomic glue that holds a table or chair together and how does one differentiate between two chairs that look precisely alike without presupposing the essentialist tradition?

The essentialist tradition begs the question when concerning identity, since there’s no way to prove that any one object has essential properties. Interestingly, the reason for presupposing the essentialist tradition might have everything to do with personal identity. People are animate objects, but objects nonetheless. Without essentialism, we can no longer assume that we have a distinct identity. Physically, we are atoms in flux and empty space as well and thus, what we’re left with are second order grounds for personal identity. In other words, we can avoid talk of atoms and empty space and instead look to DNA, neurons, brain anatomy, and so on. In this way we retain our uniqueness without first order grounds.

That aside, if we instead argue from the basis of differential ontology, the law of identity is no longer as unassailable as it appeared. As stated, we would rely on second order grounds. “Differential ontology…understands the identity of any given thing as constituted on the basis of the ever-changing nexus of relations in which it is found, and thus, identity is a secondary determination, while difference, or the constitutive relations that make up identities, is primary.” We would therefore ignore notions of a stable identity and instead look to differences between objects.

Given this, the law of identity (A = A) will be replaced with the law of distinction, i.e., something like A =/= B or C or D and so on. Since A is not B or C or D, then we identify A because it is contrasted with objects in relation to it. We are no longer assuming that there are essential properties that make A, A. This is, after all, what we say of ourselves. We do not say I am me because I have essential characteristics. Instead we contrast ourselves with others; we factor in physical appearance, ethnicity, gender, personality, and so on. We then add other factors like level of income and education, personal tastes, and so on. Clearly none of these characteristics are essential.

Ultimately, the law of identity is not unassailable and can be challenged by uprooting its essentialist assumption. One way of doing so is by positing differential ontology. One can, however, do so by positing human consciousness. In other words, another traditional philosophical assumption (contra-pragmatism) is that there’s a deeper reality that goes beyond our everyday experience; perhaps quantum mechanics hints at this. On the basis of this, we cannot draw ontological conclusions on the basis of our faculties. In other words, the four chairs and dining room table in my living room look distinct because my faculties see them as such. In reality, however, there’s nothing but atomic flux and empty space. This is in no way an attempt to undermine the usefulness of our faculties, but if there’s a deeper layer to reality that we cannot capture, then there’s no way we can argue for essential properties. Furthermore, we wouldn’t be able to argue from difference either. We would, in other words, have to assume the accuracy of our faculties in order to argue for a law of identity.

On The Leibnizian Cosmological Argument

By R.N. Carmona

A Christian on the Humans of New York Instagram page brought up the Leibnizian Cosmological Argument (LCA) and named a few of its Christian defenders. Like I’m fond of pointing out, in naming just Christian defenders of the argument, it is likely he hasn’t considered actual objections. He’s read a degraded form of objections via the lens of these Christian authors. This is why I call apologetics, pseudo-philosophy.

In actual philosophical discourse, the participants in a given discussion are as charitable to one another as possible and they try very hard to ensure that nothing is lost in translation. They constantly correct themselves if they misinterpret what their opponent has said or they attempt to show that their interpretation better captures what their opponent is trying to say. Apologists don’t do this. Apologists straw man an objection, sometimes in ways that seem sophisticated, in order to make the argument or counter-argument easier to address. This is precisely why I advised him to deal with J.L. Mackie, for example–to read him directly and not through the lens of one of his favored authors. Then he would find that even Christians reject the Leibnizian Cosmological Argument (LCA).

A quick example of what I mean: in responding to my Argument From Cosmology, my opponent says that the opposite of my conclusion is as follows: the fact that an x can’t be shown to exist in relation to y doesn’t mean that x doesn’t exist*; in other words, that god can’t be shown to exist in relation to the Earth doesn’t mean god doesn’t exist. Yet on Judaism and Christianity, god created the Earth. Modern science tells us that planets have no creator; they form naturally over an extended period of time. We have real time data of planet formation in other systems. The history of our planet doesn’t resemble anything mentioned in the Bible. By extension, I argue that god doesn’t exist in relation to the universe, since he didn’t create it. Modern cosmology tells us as much.

His assertion is not enough to refute my argument. In fact, all he’s concluding is the opposite of what he misunderstood as my conclusion. My actual conclusion is this: x does not exist in relation to y iff it is necessary that x exist in relation to y. If god did not create the Earth or the universe, he doesn’t exist in relation to either, and by extension, doesn’t exist; however, on Christianity, it is necessary that he does. This is precisely what his favored LCA says. Through the Principle of Sufficient Reason (PSR), for every being or state of affairs that exist, there is a sufficient reason for why they exist. It then adds, that for every being or state of affairs that exist, there is a necessary reason for why they exist. Therefore, god is the necessary and sufficient reason for why these states of affairs exist.

My Argument From Cosmology best captures a decisive criticism of the LCA without directly engaging it. J.L. Mackie stated that PSR need not be assumed by reason. Reason only asks for antecedent causes and conditions that explain each being or state of affairs. These are considered facts until they themselves are explained by something prior to them. On reason, nothing is prerequisite beyond this.

Thus, going back to my conclusion, x does not exist in relation to y iff it is necessary that x exist in relation to y. In order for Christianity to hold true, god would have had to create the Earth and the universe. If we have reason to doubt that he created the Earth, and modern science establishes this conclusively, then we have much reason to doubt that he created the universe. If the Earth can be explained by antecedent causes and conditions, then the universe can as well. My argument offers a number of plausible explanations fielded in modern cosmology all whilst arguing that there cannot be the type of causation Christians would require, i.e., the type of causation that allows for an immaterial agent to create material objects. At best, such causation is unknowable and it is probable that there will be no hard evidence for it; hence the Christian must retreat to agnosticism. At worst, such causation is impossible and there cannot be any evidence for it; thus, the Christian must retreat to atheism.

Ultimately, my argument addresses the LCA by implication, i.e., my argument implies a defeater of the LCA. Therefore, I do not have to address it directly. The same can be said of the KCA. Rebuttals to both arguments are implicit in my argument. That fact alone should give apologists pause.

In any case, my point has been made: apologetics is pseudo-philosophy. Apologists prop it up by being uncharitable and purposely (in most cases) misinterpreting a claim or argument made by atheists. Apologists are also modern sophists: it matters not how things might be or probably are; what matters is what they think is the case, what they say is the case, or what they deem possible–as though possibility implies probability. Apologists are also quite fond of straw men, which they use to make their arguments seem superior to those of their opponents. Unlike them, I have defined PSR correctly and I’ve summarized the LCA charitably. However, I’ve also shown that my Argument From Cosmology considers the LCA, albeit indirectly. My argument implies a decisive blow to the LCA. It is therefore necessary to deal with my argument directly; it isn’t enough to choose a favored argument and deem it superior on the basis of a misinterpretation of my conclusion.

*His assessment is correct assuming that x isn’t necessary with relation to y. The fact that I (x) cannot be explained with relation to an invention (y) doesn’t mean I do not exist. Even the actual inventor of invention (y) doesn’t have this sort of connection to the invention in question. Another agent could have been the inventor. On Christianity, however, there are no other gods and hence no other creators. Thus, if god did not create the Earth, there is reason to doubt he created anything else in the universe and therefore, the universe itself. As stated, for Christianity to be true, it need only be shown that god is necessary in this possible world; the LCA, as originally formulated, wants Anselm’s deity and therefore, on the LCA, god is necessary in all possible worlds. My argument casts much doubt on this, especially since god is the necessary being antecedent to all contingent beings. If this connection fails on a minor front, e.g., god didn’t create all baseballs, that’s fine, for even then he would underlie the reason for the reason of the baseballs, namely human beings. If it fails on a major front, as I’ve shown in the case of the Earth and all planets for that matter, a glaring problem arises for Christians, for even if they posit a being that willed the laws of physics, what they have is a deity far removed from the deity in the Bible. That would make for a separate discussion altogether.

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>