Mark Balaguer

In this book, Balaguer demonstrates that there are no good arguments for or against mathematical platonism. He does this by establishing that both platonism and anti-platonism are defensible views. Introducing a form of platonism ("full-blooded platonism") that solves all problems traditionally associated with the view, he proceeds to defend anti-platonism (in particular, mathematical fictionalism) against various attacks, most notably the Quine-Putnam indispensability attack. He concludes by arguing that it is not simply that we do not currently have any good argument for or against platonism, but that we could never have such an argument and, indeed, that there is no fact of the matter as to whether platonism is correct.

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.

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.

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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

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)

Platonism is the view that there exist such things as abstract objects — where an abstract object is an object that does not exist in space or time and which is therefore entirely non-physical and nonmental. Platonism in this sense is a contemporary view. It is obviously related to the views of Plato in important ways, but it is not entirely clear that Plato endorsed this view, as it is defined here. In order to remain neutral on this question, the term ‘platonism’ is spelled with a lower-case ‘p’. (See entry on Plato.) The most important figure in the development of modern platonism is Gottlob Frege (1884, 1892, 1893-1903, 1919). The view has also been endorsed by many others, including Kurt Gödel (1964), Bertrand Russell (1912), and W.V.O. Quine (1948, 1951)

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

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

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

It is argued here that the question of whether compatibilism is true is irrelevant to metaphysical questions about the nature of human decision‐making processes—for example, the question of whether or not humans have free will—except in a very trivial and metaphysically uninteresting way. In addition, it is argued that two other questions—namely, the conceptual‐analysis question of what free will is and the question that asks which kinds of freedom are required for moral responsibility—are also essentially irrelevant to metaphysical questions about the nature of human beings.

  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.

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.