Commentary on Andy Clark's target article on predictive coding.

“1950’li yıllarda dönemin büyük felsefecileri arasında dinsel inancı savunan bir kişi bile yoktu. 1990’lı yıllarda Yale’den UCLA’ya, Oxford’dan Heidelberg’e kadar birçok yerde insanın manevi yanını savunan ve geliştiren yüzlerce kitap yazılacak, sel olup akacaktı. Aradaki 40 yıllık süre zarfındaysa sadece ve sadece Alvin Plantinga vardı.” Kelly James Clark Tanrı’nın veya tanrıların varlığı sorusu felsefenin ezeli sorularından biri olagelmişse de Nietzsche’nin Tanrı’nın ölümünü ilan ettiği günden bu yana onu doğrularcasına yaşanan acılar, savaşlar, kötülükler bu konudaki tartışmaların sesini uzun süre bastırdı. Ama (...) özellikle yüzyılın ikinci yarısından sonra palazlanan analitik felsefede meydana gelen “metafiziğe dönüş”, dine yakınlık duyan, en azından dinle ilgilenen filozofların tekrar Yahudi-Hıristiyan ve İslam geleneklerinde anlaşıldığı şekliyle Tanrı’nın varlığına duyulan inancın gerekçelerini yeniden değerlendirmelerine, konuya yeni bir bakış ve araçlarla bakmalarına vesile oldu. Alvin Plantinga’nın bu kitabı, yayımlandığı tarihten itibaren “analitik din felsefesi” alanının da en önemli ve sarsıcı eserlerinden biri hâline geldi ve Tanrı’nın ölmediğini ilan etti. Anselmus’tan Hume’a, Kant ve pozitivistlerden John Mackie gibi modern ateologlara kadar felsefe geleneğiyle hesaplaşan Plantinga, bu abidevi çalışmasında ontolojik, kozmolojik ve teleolojik tanrı kanıtlamalarının eski ve yeni biçimlerinin çıkmazlarını, meziyetlerini ve sunduğu imkânları değerlendiriyor. Tanrı’nın varlığına duyulan inanç ile diğer insanların varlığına ve zihinlerine duyulan inanç arasındaki şaşırtıcı ve sarsıcı bağlantıyı ortaya koyuyor. (shrink)

This book argues that there is a joint in nature between seeing and thinking, perception, and cognition. Perception is constitutively iconic, nonconceptual, and nonpropositional, whereas cognition does not have these properties constitutively. The book does not appeal to “intuitions,” as is common in philosophy, but to empirical evidence, including experiments in neuroscience and psychology. The book argues that cognition affects perception, i.e., that perception is cognitively penetrable, but that this does not impugn the joint in nature. A key part of (...) the argument is that we perceive not only low-level properties like colors, shapes, and textures but also high-level properties such as faces and causation. Along the way, the book explains the difference between perception and perceptual memory, the differences between format and content, and whether perception is probabilistic despite our lack of awareness of probabilistic properties. The book argues for perceptual categories that are not concepts, that perception need not be singular, that perceptual attribution and perceptual discrimination are equally fundamental, and that basic features of the mind known as “core cognition” are not a third category in between perception and cognition. The chapter on consciousness leverages these results to argue against some of the most widely accepted theories of consciousness. Although only one chapter is about consciousness, much of the rest of the book repurposes work on consciousness to isolate the scientific basis of perception. (shrink)

Ned Block; IX*—An Argument for Holism1, Proceedings of the Aristotelian Society, Volume 95, Issue 1, 1 June 1995, Pages 151–170.

In a recent paper I argued that agent causation theorists should be compatibilists. In this paper, I argue that compatibilists should be agent causation theorists. I consider six of the main problems facing compatibilism: (i) the powerful intuition that one can't be responsible for actions that were somehow determined before one was born; (ii) Peter van Inwagen's modal argument, involving the inference rule (β); (iii) the objection to compatibilism that is based on claiming that the ability to do otherwise is (...) a necessary condition for freedom; (iv) "manipulation arguments," involving cases in which an agent is manipulated by some powerful being into doing something that he or she would not normally do, but in such a way that the compatibilist's favorite conditions for a free action are satisfied; (v) the problem of constitutive luck; and (vi) the claim that it is not fair to blame someone for an action if that person was determined by forces outside of his or her control to perform that action. And in the case of each of these problems, I argue that the compatibilist has a much more plausible response to that problem if she endorses the theory of agent causation than she does otherwise. (shrink)

This is my first publication of the distinction between phenomenal consciousness and access consciousness, though not using quite those terms. It ends with this: "The upshot is this: If Searle is using the access sense of "consciousness," his argument doesn't get to first base. If, as is more likely, he intends the what-it-is-like sense, his argument depends on assumptions about issues that the cognitivist is bound to regard as deeply unsettled empirical questions." Searle replies: "He refers to what he calls (...) an "access sense of consciousness." On my account there is no such sense.". (shrink)

Can we consciously see more items at once than can be held in visual working memory? This question has elud- ed resolution because the ultimate evidence is subjects’ reports in which phenomenal consciousness is filtered through working memory. However, a new technique makes use of the fact that unattended ‘ensemble prop- erties’ can be detected ‘for free’ without decreasing working memory capacity.

consciousness comes about as a result of irritating nervous tissue, is just as unaccountable as the appearance of Djin when Aladdin rubbed his lamp.

This paper is about the open future response to fatalistic arguments. I first present a typical fatalistic argument and then spell out the open future response as a response to that argument. Then I raise the question of how the open future response can be independently justified. I consider some possible ways in which the response might be defended, and I try to show that none of these is a plausible, non-question-begging defense. Next I formulate what I take to be (...) the only plausible, nonquestion-begging defense of the open future response. This defense involves both (i) the claim that the laws of nature are indeterministic and (ii) a certain version of the correspondence theory of truth. Finally, I argue that there is a very surprising consequence of justifying the open future response by making the defense in question, namely, that the past is sometimes open. Fatalism is the view that whatever will happen in the future is inevitable, due to certain considerations about truth and time. Fatalism, in turn, is normally taken to imply that there is no such thing as genuine, human free will. Suppose that I am an anti-fatalist. Suppose I believe that Joe Montana is free to choose what he will have for lunch tomorrow, and suppose I take this case to be a paradigmatic example of one involving both evitability and human free will. Now suppose that I meet a fatalist, who presents the following argument.1.. (shrink)

Is consciousness based in prefrontal circuits involved in cognitive processes like thought, reasoning, and memory or, alternatively, is it based in sensory areas in the back of the neocortex? The no-report paradigm has been crucial to this debate because it aims to separate the neural basis of the cognitive processes underlying post-perceptual decision and report from the neural basis of conscious perception itself. However, the no-report paradigm is problematic because, even in the absence of report, subjects might engage in post-perceptual (...) cognitive processing. Therefore, to isolate the neural basis of consciousness, a no-cognition paradigm is needed. Here, I describe a no-cognition approach to binocular rivalry and outline how this approach can help resolve debates about the neural basis of consciousness. (shrink)

Here is a question about mereological simples that I raised in a recent paper.

Often when there is no attention to an object, there is no conscious perception of it either, leading some to conclude that conscious perception is an attentional phenomenon. There is a well-known perceptual phenomenon—visuo-spatial crowding, in which objects are too closely packed for attention to single out one of them. This article argues that there is a variant of crowding—what I call ‘‘identity-crowding’’—in which one can consciously see a thing despite failure of attention to it. This conclusion, together with new (...) evidence that attention to an object occurs in unconscious perception, suggests there may be a double dissociation between conscious perception of an object and attention to that object, constraining the extent to which consciousness can be constitutively attentional. The argument appeals to a comparison between the minimal resolution (or ‘‘grain’’) of object-attention and object-seeing. (shrink)

Visual illusions of number provide a means of investigating the rules and principles through which approximate number representations are formed. Here, we investigated the developmental trajectory of an important numerical illusion – the connectedness illusion, wherein connecting pairs of items with thin lines reduces their perceived number without altering continuous attributes of the collections. We found that children as young as 5 years of age are affected by the illusion and that the magnitude of the effect increased into adulthood. Moreover, (...) individuals with greater numerical acuity exhibited stronger connectedness illusions after controlling for age. Overall, these results suggest the approximate number system expects to enumerate over bounded wholes and doing so is a signature of its optimal functioning. (shrink)

I believe that time passes. In the last one hundred years or so, many philosophers have rejected this view. Those who have done so have generally been motivated by at least one of three different arguments: (i) McTaggart's argument, (ii) an argument from the theory of relativity, and (iii) an argument concerning the alleged incoherence of talk about the rate of the passage of time. There has been a great deal of literature on McTaggart's argument (although no concensus has been (...) reached).1 There has been a relatively small amount of literature on the argument from the theory of relativity, but this is perhaps not surprising, since most of us philosophers don't understand that theory.2 Meanwhile, there has not been a great deal of literature on the rate of passage argument, and this is surprising, I think, considering that the argument is easy to.. (shrink)

The success of the Bayesian approach to perception suggests probabilistic perceptual representations. But if perceptual representation is probabilistic, why doesn't normal conscious perception reflect the full probability distributions that the probabilistic point of view endorses? For example, neurons in MT/V5 that respond to the direction of motion are broadly tuned: a patch of cortex that is tuned to vertical motion also responds to horizontal motion, but when we see vertical motion, foveally, in good conditions, it does not look at all (...) horizontal. This article argues that the best Bayesian approach to this problem does not require probabilistic representation. (shrink)

This paper argues for including stuff in one's ontology. The distinction between things and stuff is first clarified, and then three different ontologies of the physical universe are spelled out: a pure thing ontology, a pure stuff ontology, and a mixed ontology of both things and stuff. Eleven different reasons for including stuff in one's ontology are given. Then five objections to positing stuff are considered and rejected.

In this note, I will discuss one issue concerning the main argument of Mind in a Physical World (Kim, 1998), the Causal Exclusion Argument. The issue is whether it is a consequence of the Causal Exclusion Argument that all macro level causation (that is, causation above the level of fundamental physics) is an illusion, with all of the apparent causal powers of mental and other macro properties draining into the bottom level of physics. I will argue that such a consequence (...) would give us reason to reject the Causal Exclusion Argument. But there is also a stronger challenge, the charge that, if there is no bottom level of physics, the Causal Exclusion Argument has the consequence that “causal powers would drain away into a bottomless pit and there wouldn’t be any causation anywhere.” (81--page numbers that are not attributed to other works are to Kim, 1998). (shrink)

This paper argues that the “Canberra Plan” picture of physicalistic reduction of mind--a picture shared by both its proponents and opponents, philosophers as diverse as David Armstrong, David Chalmers Frank Jackson, Jaegwon Kim, Joe Levine and David Lewis--neglects ground (Fine, 2001, 2012). To the extent that the point of view endorsed by the Canberra Plan has an account of the physical/functional ground of mind at all, it is in one version trivial and in another version implausible. In its most general (...) form, the point of view of the Canberra Plan is committed to unacceptably treating indexical or name-related facts as part of the ultimate physical/functional ground of the mental. (shrink)

Some people think that pastness, presentness and futurity (and their metric variants, such as being two days past) are genuine propeties of times and events. These putative properties are sometimes called “A properties” and the philosopers who believe in them are often called “A Theorists.” Other philosophers don’t believe in the reality of A properties, but instead say that talk that appears to be about such properties is really about “B relations” – two-place temporal relations like earlier than, simultaneous with, (...) and later than (together with their metric variants, like two days earlier than). The latter philosophers are often called “B Theorists,” and the debate between A Theorists and B Theorists has dominated the philosophy of time since 1908.1 The two views can be put this way. The A Theory: There are genuine, irreducible A properties; talk that appears to be about A properties is not analyzable in terms of B relations. (shrink)

One of the most important issues concerning the foundations ofconscious perception centerson thequestion of whether perceptual consciousness is rich or sparse. The overflow argument uses a form of ‘iconic memory’ toarguethatperceptual consciousnessisricher (i.e.,has a higher capacity) than cognitive access: when observing a complex scene we are conscious of more than we can report or think about. Recently, the overflow argumenthas been challenged both empirically and conceptually. This paper reviews the controversy, arguing that proponents of sparse perception are committed to the (...) postulation of (i) a peculiar kind of generic conscious representation that has no independent rationale and (ii) an unmotivated form of unconscious representation that in some cases conflicts with what we know about unconscious representation. (shrink)

∗ Apologies to Mark Hinchliff for stealing the title of his dissertation. (See Hinchliff, A Defense of Presentism. As it turns out, however, the version of Presentism defended here is different from the version defended by Hinchliff. See Section 3.1 below.).

There is a popular theory in the metaphysics of time according to which time is one of four similar dimensions that make up a single manifold that is appropriately called spacetime. One consequence of this thesis is that changing an object’s orientation in the manifold does not change its intrinsic features. In this paper I offer a new argument against this popular theory. I claim that an especially good performance of a particularly beautiful piece of music, when oriented within the (...) manifold in the normal way, adds to the intrinsic value of the world, but that if the same performance is turned sideways within the manifold, so that it involves a number of different notes spread out in space and all occurring at the same time, then it does not add the same intrinsic value to the world. (shrink)

This is a response to Ian Phillips and Jorge Morales, "The Fundamental Problem with No-Cognition Paradigms," Trends in Cognitive Sciences, 2020.

In “Mathematical Truth,” Paul Benacerraf presented an epistemological problem for mathematical realism.

Worlds, Lewis says this: Let us say that something persists iff, somehow or other, it exists at various times; this is the neutral word. Something perdures iff it persists by having different temporal parts, or stages, at different times, though no one part of it is wholly present at more than one time; whereas it endures iff it persists by being wholly present at more than one time. Perdurance corresponds to the way a road persists through space; part of it (...) is here, and part of it is there, and no part is wholly present at two different places. Endurance corresponds to the way a universal, if there are such things, would be wholly present wherever and whenever it is instantiated. Endurance involves overlap: the content of two different times has the enduring thing as a common part. Perdurance does not.1 Lewis's remarks suggest the following formulations of the two views in the 3D/4D controversy.2.. (shrink)

Michael Tye's response to my “Grain” (Block ) and “Windows” (Block ) raises general metaphilosophical issues about the value of intuitions and judgments about one's perceptions and the relations of those intuitions and judgments to empirical research, as well as specific philosophical issues about the relation between seeing, attention and de re thought. I will argue that Tye's appeal to what is (§. 2) “intuitively obvious, once we reflect upon these cases” (“intuition”) is problematic. I will also argue that first (...) person judgments can be problematic when used on their own as Tye does but can be valuable when integrated with empirical results. (shrink)

According to standard, pre-philosophical intuitions, there are many composite objects in the physical universe. There is, for example, my bicycle, which is composed of various parts - wheels, handlebars, molecules, atoms, etc. Recently, a growing body of philosophical literature has concerned itself with questions about the nature of composition.1 The main question that has been raised about composition is, roughly, this: Under what circumstances do some things compose, or add up to, or form, a single object? It turns out that (...) it is surprisingly difficult to give a satisfactory answer to this question that accords with standard, pre-philosophical intuitions about the universe's composite objects. In fact, the three rival views in response to this question that have received the most support in the literature are (i) that there are no objects composed of two or more parts (which means that there are no stars, chairs, humans, or bicycles);2 (ii) that the only objects composed of two or more parts are living organisms (which still means no stars. (shrink)

Once upon a time, during a large and international conference of the world's leading philosophers, an angel miraculously appeared and said, "I come to you as a messenger from God. You will be permitted to ask any one question you want - but only one! - and I will answer that question truthfully. What would you like to ask?" The philosophers were understandably excited, and immediately began a discussion of what would be the best question to ask. But it quickly (...) became obvious that they needed more time to discuss the matter, so they asked the angel if he could get back to them. The angel was obliging, and said that he would return at the same time the next day. "But be prepared then," he warned them, "for you will only get this one chance." All of the philosophers gathered at the convention worked at a frenzied pace for the next twenty-four hours, proposing and weighing the merits of various questions. Other philosophers from around the world became involved as well, faxing and emailing their suggestions. Some were in favor of asking the kind of practical question that lots of people might like to know the answer to, such as this one: Q1 Is it better to check your oil when the car is hot or when it is cold? But others said they should not squander this rare opportunity, which gave them a chance to learn something about a truly important and intrinsically interesting topic, and after some discussion it was generally agreed that this was right. (shrink)

This is a response to Jerry Fodor’s article, Fodor, J. (1980). "Methodological solipsism as a research strategy in cognitive psychology." Behavioral and Brain Sciences 3: 63-109.

The Anna Karenina Theory says: all conscious states are alike; each unconscious state is unconscious in its own way. This note argues that many components have to function properly to produce consciousness, but failure in any one of many different ones can yield an unconscious state in different ways. In that sense the Anna Karenina theory is true. But in another respect it is false: kinds of unconsciousness depend on kinds of consciousness.

According to The Static Theory of Time, time is like space in various ways, and there is no such thing as the passage of time. According to The Dynamic Theory of Time, on the other hand, time is very different from space, and the passage of time is an all-too-real phenomenon. This paper first offers some suggestions about how we should understand these two theories, and then introduces five new arguments for The Dynamic Theory of Time.

Since the publication of Peter van Inwagen's book, Material Beings,1 there has been a growing body of philosophical literature on the topic of composition. The main question addressed in both van Inwagen's book and subsequent discussions of the topic is a question that van Inwagen calls "the Special Composition Question." The Special Composition Question is, roughly, the question Under what circumstances do several things compose, or add up to, or form, a single object? For the purposes of formulating a more (...) precise version of the Special Composition Question, we can adopt the following technical terms. (shrink)

I raised the following question in a recent paper: What are the necessary and jointly sufficient conditions for an object's being a simple? And I proposed and defended this answer (which I called 'MaxCon'): Necessarily, x is a simple iff x is a maximally continuous object. In a more recent paper, Kris McDaniel raises several objections to MaxCon, including, in particular, two objections based on a principle about the supervenience of constitution that he calls 'SoC'. The purpose of the present (...) paper is to address the main objections raised by McDaniel, and to show that none of them poses a serious threat to MaxCon. (shrink)

Elga's presentation of The Sleeping Beauty Problem is often misread, with analyses that impute extra premises and derive false answers to the problem as Elga presented it. Here it is shown that hewing to the text requires that the Sleeping Beauty's degree of belief in a coin flip upon her first awakening is 1/2.

Let’s begin with a simple example. Consider two quarks: one near the tip of your nose, the other near the center of Alpha Centauri. Here is a question about these two subatomic particles: Is there an object that has these two quarks as its parts and that has no other parts? According to one view of the matter (a view that is surprisingly endorsed by a great many contemporary philosophers), the answer to this question is Yes. But I think it (...) is fair to say that according to common sense, the answer to this question is really No, there is no object that has as its only two parts a quark near the tip of your nose and another quark near the center of Alpha Centauri. (shrink)

Elizabeth Karger has suggested an interpretation of Ockham's theory of the modes of common personal supposition ("TM") according to which the purpose of TM is to provide certain distinctions that Ockham will use in formulating a unified theory of immediate inference among certain kinds of sentences. Karger presents a single, powerful rule of inference that incorporates TM distinctions and that is meant to codify Ockham's theory of immediate inference. I raise an objection to Karger's rule, thereby calling into doubt the (...) interpretation of Ockham that is based on attributing that rule to him. (shrink)

In this section, we will start with an influential attempt to define `intelligence', and then we will move to a consideration of how human intelligence is to be investigated on the machine model. The last part of the section will discuss the relation between the mental and the biological.

The problem of freedom and determinism has vexed philosophers for several millennia, and continues to be a topic of lively debate today. One of the proposed solutions to the problem that has received a great deal of attention is the Theory of Agent Causation. While the theory has enjoyed its share of advocates, and perhaps more than its share of critics, the theory’s advocates and critics have always agreed on one thing: the Theory of Agent Causation is an incompatibilist theory. (...) That is, both believers and nonbelievers in the theory have taken it for granted that the most plausible version of the Theory of Agent Causation is one according to which freedom and determinism are incompatible. In fact, so entrenched is this assumption that no one on either side of the debate has ever questioned it. Yet it turns out that this assumption is wrong – the most plausible version of the Theory of Agent Causation is a compatibilist one. (shrink)

This piece is a contribution to a book symposium on Fabrice Correia and Sven Rosenkranz's _Nothing to Come: A Defense of the Growing Block Theory of Time_. I start by considering one of the main objections that has been raised against the Growing Block Theory, namely, the Epistemic Objection, together with Correia and Rosenkranz's response to that objection. This leads to a question about whether Correia and Rosenkranz’s view is a Four-Dimensionalist version of the Growing Block Theory or a Three-Dimensionalist (...) version of the theory. I argue that there are three possible ways Correia and Rosenkranz might respond to this question, and I raise several worries for each of those ways. Then I offer some free advice about how I think Correia and Rosenkranz ought to respond to the question. (shrink)

When do several objects compose a further object? The last twenty years have seen a great deal of discussion of this question. According to the most popular view on the market, there is a physical object composed of your brain and Jeremy Bentham’s body. According to the second-most popular view on the market, there are no such objects as human brains or human bodies, and there are also no atoms, rocks, tables, or stars. And according to the third-ranked view, there (...) are human bodies, but still no brains, atoms, rocks, tables, or stars. Although it’s pleasant to have so many crazy-sounding views around, I think it would also be nice to have a commonsense option available. The aim of this paper is to offer such an option. The approach I offer begins by considering a mereological question other than the standard one that has been the focus of most discussions in the literature. I try to show that the road to mereological sanity begins with giving the most straightforward and commonsensical answer to this other question, and then extending that answer to further questions about the mereology of physical objects. On the approach I am recommending, it turns out that all of the mereological properties and relations of physical objects are determined by their spatial properties and relations. (shrink)

In a recent Analysis article, Quentin Smith argues that classical theism is inconsistent with certain consequences of Stephen Hawking's quantum cosmology.1 Although I am not a theist, it seems to me that Smith's argument fails to establish its conclusion. The purpose of this paper is to show what is wrong with Smith's argument. According to Smith, Hawking's cosmological theory includes what Smith calls "Hawking's wave function law." Hawking's wave function law (hereafter, "HL") apparently has, among its consequences, the following claim. (...) (1) The unconditional probability that a universe like this one - i.e., a universe with the metric hij and matter field Φ - should begin to exist is 95%.2 Smith then argues that the theist who accepts HL must also accept that the following sentence was once true.3.. (shrink)

According to Conceptual Role Semantics, the meaning of a representation is the role of that representation in the cognitive life of the agent, e.g. in perception, thought and decision-making. It is an extension of the well known "use" theory of meaning, according to which the meaning of a word is its use in communication and more generally, in social interaction. CRS supplements external use by including the role of a symbol inside a computer or a brain. The uses appealed to (...) are not just actual, but also counterfactual: not only what effects a thought does have, but what effects it would have had if stimuli or other states had differed. The view has arisen separately in philosophy and in cognitive science. The source of the view is Wittgenstein and Sellars, but the source in contemporary philosophy is a series of papers by Harman and Field. Other proponents in philosophy have included Block, Horwich, Loar, McGinn and Peacocke. In cognitive science, they include Woods and Miller and Johnson-Laird. (shrink)

The concept of a physical object has figured prominently in the history of philosophy, and is probably more important now than it has ever been before. Yet the question What are physical objects?, i.e., What is the correct analysis of the concept of a physical object?, has received surprisingly little attention. The purpose of this paper is to address this question. I consider several attempts at answering the question, and give my reasons for preferring one of them over its rivals. (...) The account of physical objects that I recommend---the Spatial Location Account---defines physical objects as objects with spatial locations. The intuitive idea behind the Spatial Location Account is this. Objects from all of the different ontological categories---physical objects; non-physical objects like souls, if there are any; propositions; universals; etc.---have this much in common: they all exist in time. But not all of them exist in space. The ones that exist in time and space, i.e., the ones that have spatial locations, are the ones that count as physical objects. (shrink)

This paper is about The Truthmaker Problem for Presentism. I spell out a solution to the problem that involves appealing to indeterministic laws of nature and branching semantics for past- and future-tensed sentences. Then I discuss a potential glitch for this solution, and propose a way to get around that glitch. Finally, I consider some likely objections to the view offered here, as well as replies to those objections.

On a now orthodox view, humans and many other animals possess a “number sense,” or approximate number system, that represents number. Recently, this orthodox view has been subject to numerous critiques that question whether the ANS genuinely represents number. We distinguish three lines of critique – the arguments from congruency, confounds, and imprecision – and show that none succeed. We then provide positive reasons to think that the ANS genuinely represents numbers, and not just non-numerical confounds or exotic substitutes for (...) number, such as “numerosities” or “quanticals,” as critics propose. In so doing, we raise a neglected question: numbers of what kind? Proponents of the orthodox view have been remarkably coy on this issue. But this is unsatisfactory since the predictions of the orthodox view, including the situations in which the ANS is expected to succeed or fail, turn on the kind of number being represented. In response, we propose that the ANS represents not only natural numbers, but also non-natural rational numbers. It does not represent irrational numbers, however, and thereby fails to represent the real numbers more generally. This distances our proposal from existing conjectures, refines our understanding of the ANS, and paves the way for future research. (shrink)