Mark Balaguer

Let libertarianism be the view that humans are capable of making decisions that are simultaneously undetermined and appropriately non-random. It’s often argued that this view is incoherent because indeterminacy entails randomness (of some appropriate kind). I argue here that the truth is just the opposite: the right kind of indeterminacy in our decisions actually entails appropriate non-randomness, so that libertarianism is coherent, and the question of whether it’s true reduces to the wide-open empirical question of whether certain of our decisions (which I characterize here) are undetermined at the moment of choice. Moreover, the version of libertarianism developed here is entirely naturalistic and event-causal.

I argue in this paper that the debate over composition is factually empty; in other words, I argue that there’s no fact of the matter whether there are any composite objects like tables and rocks and cats. Moreover, at the end of the paper, I explain how my argument is suggestive of a much more general conclusion, namely, that there’s no fact of the matter whether there are any material objects at all. Roughly speaking, the paper proceeds by arguing that if there were a fact of the matter about whether composite objects exist, then it would be either a necessary fact or a contingent fact, and both of these alternatives are implausible.

This book does three main things. First, it defends mathematical platonism against the main objections to that view (most notably, the epistemological objection and the multiple-reductions objection). Second, it defends anti-platonism (in particular, fictionalism) against the main objections to that view (most notably, the Quine-Putnam indispensability objection and the objection from objectivity). Third, it argues that there is no fact of the matter whether abstract mathematical objects exist and, hence, no fact of the matter whether platonism or anti-platonism is true.

This dissertation provides a refutation of the epistemological argument against mathematical platonism; that is, it provides an epistemology of abstract objects, in particular, of mathematical objects. ;After an introductory first chapter, I formulate what I argue is the strongest version of the epistemological argument against platonism. It is stronger than Paul Benacerraf's version because the only plausible way for a platonist to respond to it is to actually provide an epistemology of mathematical objects. ;In chapters three and four, I argue against the platonist epistemologies of Kurt Godel and Penelope Maddy, respectively. The main conclusion of these two chapters is that human beings cannot come into contact with mathematical objects, and that, indeed, it may not even by intelligible to speak in these terms, i.e., to speak of contact between spatio-temporal creatures like ourselves and an aspatial, atemporal mathematical realm. ;In chapter five, I argue that human beings don't need any contact with the mathematical realm in order to attain knowledge of that realm. The argument is based upon the fact that mathematical truths are necessarily true. ;Finally, in chapter six, I develop a second platonist epistemology, i.e., a second refutation of the epistemological argument against platonism. The argument is mostly original, but it relies at one point upon an argument of Michael Resnik's. In a nutshell, my argument is that, since platonists are free to adopt a full-blooded sort of platonism it is easy to explain how human beings could attain knowledge of the mathematical realm. For if all possible mathematical objects exist, then any consistent mathematical theory will accurately describe some collection of mathematical objects. Hence, to attain knowledge of the mathematical realm, one must simply formulate a consistent set of mathematical beliefs.

It is argued here that there is no fact of the matter between direct reference theory and neo-Fregeanism. To get a more precise idea of the central thesis of this paper, consider the following two claims: (i) While direct reference theory and neo-Fregeanism can be developed in numerous ways, they can be developed in essentially parallel ways; that is, for any (plausible) way of developing direct reference theory, there is an essentially parallel way of developing neo-Fregeanism, and vice versa. And (ii) for each such pair of theories, there is no fact of the matter as to which of them is superior; or more precisely, they are tied in terms of factual accuracy. These are sweeping claims that cannot be fully justified in a single paper. But arguments are given here that motivate these theses, i.e., that suggest that they are very likely true.

A number of philosophers have argued in recent years that certain kinds of metaphysical debates—e.g., debates over the existence of past and future objects, mereological sums, and coincident objects—are merely verbal. It is argued in this paper that metaphysical debates are not merely verbal. The paper proceeds by uncovering and describing a pattern that can be found in a very wide range of philosophical problems and then explaining how, in connection with any problem of this general kind, there is always a non-verbal debate to be had. Indeed, the paper provides a recipe for locating the non-verbal debates that surround these philosophical problems. This undermines metametaphysical verbalist views of our metaphysical questions—i.e., views that say that there is no non-verbal debate to be had about some metaphysical question. Finally, the paper also provides a quick argument against actual-literature verbalist views of our metaphysical questions; in other words, the paper argues that in connection with all of our metaphysical questions, it is easy to find examples of non-verbal debates in the actual philosophical literature.

In this largely antimetaphysical treatment of free will and determinism, Mark Balaguer argues that the philosophical problem of free will boils down to an open scientific question about the causal histories of certain kinds of neural events. In the course of his argument, Balaguer provides a naturalistic defense of the libertarian view of free will. The metaphysical component of the problem of free will, Balaguer argues, essentially boils down to the question of whether humans possess libertarian free will. Furthermore, he argues that, contrary to the traditional wisdom, the libertarian question reduces to a question about indeterminacy--in particular, to a straightforward empirical question about whether certain neural events in our heads are causally undetermined in a certain specific way; in other words, Balaguer argues that the right kind of indeterminacy would bring with it all of the other requirements for libertarian free will. Finally, he argues that because there is no good evidence as to whether or not the relevant neural events are undetermined in the way that's required, the question of whether human beings possess libertarian free will is a wide-open empirical question.

A theory of objective mathematical correctness is developed. The theory is consistent with both mathematical realism and mathematical anti-realism, and versions of realism and anti-realism are developed that dovetail with the theory of correctness. It is argued that these are the best versions of realism and anti-realism and that the theory of correctness behind them is true. Along the way, it is shown that, contrary to the traditional wisdom, the question of whether undecidable sentences like the continuum hypothesis have objectively determinate truth values is independent of the question of whether mathematical realism is true.

It is argued here that mathematical objects cannot be simultaneously abstract and perceptible. Thus, naturalized versions of mathematical platonism, such as the one advocated by Penelope Maddy, are unintelligble. Thus, platonists cannot respond to Benacerrafian epistemological arguments against their view vias Maddy-style naturalization. Finally, it is also argued that naturalized platonists cannot respond to this situation by abandoning abstractness (that is, platonism); they must abandon perceptibility (that is, naturalism)

This paper considers the empirical evidence that we currently have for various kinds of determinism that might be relevant to the thesis that human beings possess libertarian free will. Libertarianism requires a very strong version of indeterminism, so it can be refuted not just by universal determinism, but by some much weaker theses as well. However, it is argued that at present, we have no good reason to believe even these weak deterministic views and, hence, no good reason—at least from this quarter—to doubt that we are libertarian free. In particular, the paper responds to various arguments for neural and psychological determinism, arguments based on the work of people like Honderich, Tegmark, Libet, Velmans, Wegner, and Festinger.

I develop here a novel version of the Fregean view of belief ascriptions (i.e., sentences of the form ‘S believes that p’) and I explain how my view accounts for various problem cases that many philosophers have supposed are incompatible with Fregeanism. The so-called problem cases involve (a) what Perry calls essential indexicals and (b) de re ascriptions in which it is acceptable to substitute coreferential but non-synonymous terms in belief contexts. I also respond to two traditional worries about what the sense of a proper name could be, and I explain how my view provides intuitively pleasing solutions to Kripke’s ‘London’–‘Londres’ puzzle and his Paderewski puzzle. Finally, in addition to defending my view, I also argue very briefly against Russellian alternatives to Fregeanism.

This paper develops a novel version of anti-platonism, called semantic fictionalism. The view is a response to the platonist argument that we need to countenance propositions to account for the truth of sentences containing `that'-clause singular terms, e.g., sentences of the form `x believes that p' and `σ means that p'. Briefly, the view is that (a) platonists are right that `that'-clauses purport to refer to propositions, but (b) there are no such things as propositions, and hence, (c) `that'-clause-containing sentences of the above sort are not true-they are useful fictions. Semantic fictionalism is an extension of Hartry Field's mathematical fictionalism, but my defense of the view is not analogous to his. One of the many virtues of my defense is its generality: it explains how we can adopt a fictionalist stance towards all abstract singular terms, e.g., mathematical singular terms and `that'-clauses.

Mathematical fictionalism (or as I'll call it, fictionalism) is best thought of as a reaction to mathematical platonism. Platonism is the view that (a) there exist abstract mathematical objects (i.e., nonspatiotemporal mathematical objects), and (b) our mathematical sentences and theories provide true descriptions of such objects. So, for instance, on the platonist view, the sentence ‘3 is prime’ provides a straightforward description of a certain object—namely, the number 3—in much the same way that the sentence ‘Mars is red’ provides a description of Mars. But whereas Mars is a physical object, the number 3 is (according to platonism) an abstract object. And abstract objects, platonists tell us, are wholly nonphysical, nonmental, nonspatial, nontemporal, and noncausal. Thus, on this view, the number 3 exists independently of us and our thinking, but it does not exist in space or time, it is not a physical or mental object, and it does not enter into causal relations with other objects. This view has been endorsed by Plato, Frege (1884, 1893-1903, 1919), Gödel (1964), and in some of their writings, Russell (1912) and Quine (1948, 1951), not to mention numerous more recent philosophers of mathematics, e.g., Putnam (1971), Parsons (1971), Steiner (1975), Resnik (1997), Shapiro (1997), Hale (1987), Wright (1983), Katz (1998), Zalta (1988), and Colyvan (2001).

This paper argues for a certain kind of anti-metaphysicalism about the temporal ontology debate, i.e., the debate between presentists and eternalists over the existence of past and future objects. Three different kinds of anti-metaphysicalism are defined—namely, non-factualism, physical-empiricism, and trivialism. The paper argues for the disjunction of these three views. It is then argued that trivialism is false, so that either non-factualism or physical-empiricism is true. Finally, the paper ends with a discussion of whether we should endorse non-factualism or physical-empiricism. An initial reason is provided for thinking that non-factualism might be true, but in the end, the paper leaves this question open. The paper also argues against a certain kind of necessitarianism about the temporal ontology debate; but this isn't an extra job—the falsity of this necessitarian view falls out of the other arguments as a sort of corollary.

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