This Element defends mathematical anti-realism against an underappreciated problem with that view-a problem having to do with modal truthmaking. Part I develops mathematical anti-realism, it defends that view against a number of well-known objections, and it raises a less widely discussed objection to anti-realism-an objection based on the fact that (a) mathematical anti-realists need to commit to the truth of certain kinds of modal claims, and (b) it's not clear that the truth of these modal claims is compatible with mathematical anti-realism. Part II considers various strategies that anti-realists might pursue in trying to solve this modal-truth problem with their view, it argues that there's only one viable view that anti-realists can endorse in order to solve the modal-truth problem, and it argues that the view in question-which is here called modal nothingism-is true.

In this deft and vigorous book, Mark Balaguer demonstrates that there are no good arguments for or against mathematical platonism (ie., the view that abstract, or non-spatio-temporal, mathematical objects exist, and that mathematical theories are descriptions of such objects). Balaguer does this by establishing that both platonism and anti-platonism are defensible positions. In Part I, he shows that the former is defensible by introducing a novel version of platonism, which he calls full-blooded platonism, or FBP. He argues that if platonists endorse FBP, they can then solve all of the problems traditionally associated with their view, most notably the two Benacerrafian problems (that is, the epistemological problem and the non-uniqueness problem).
In Part II, Balaguer defends anti-platonism (in particular, mathematical fictionalism) against various attacks, chief among them the Quine-Putnam indispensability argument. Balaguer's version of fictionalism bears similarities to Hartry Field's, but the arguments Balaguer uses to defend this view are very different. Parts I and II of this book taken together clearly establish that we do not have any good argument for or against platonism.
In Part III, Balaguer extends his conclusions, 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 (ie., whether there exist any abstract objects).
This lucid and accessibly written book breaks new ground in its area of engagement and makes vital reading for both specialists and anyone else interested in thephilosophy of mathematics or metaphysics in general.

Metaphysics, Sophistry, and Illusion does two things. First, it introduces a novel kind of non-factualist view, and argues that we should endorse views of this kind in connection with a wide class of metaphysical questions, most notably, the abstract-object question and the composite-object question. (More specifically, Mark Balaguer argues that there's no fact of the matter whether there are any such things as abstract objects or composite objects-or material objects of any other kind.) Second, Metaphysics, Sophistry, and Illusion explains how these non-factualist views fit into a general anti-metaphysical view called neo-positivism, and explains how we could argue that neo-positivism is true. Neo-positivism is the view that every metaphysical question decomposes into some subquestions-call them Q1, Q2, Q3, etc.-such that, for each of these subquestions, one of the following three anti-metaphysical views is true of it: non-factualism, or scientism, or metaphysically innocent modal-truth-ism. These three views can be defined (very roughly) as follows: non-factualism about a question Q is the view that there's no fact of the matter about the answer to Q. Scientism about Q is the view that Q is an ordinary empirical-scientific question about some contingent aspect of physical reality, and Q can't be settled with an a priori philosophical argument. And metaphysically innocent modal-truth-ism about Q is the view that Q asks about the truth value of a modal sentence that's metaphysically innocent in the sense that it doesn't say anything about reality and, if it's true, isn't made true by reality

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 philosopher considers whether the scientific and philosophical arguments against free will are reason enough to give up our belief in it. In our daily life, it really seems as though we have free will, that what we do from moment to moment is determined by conscious decisions that we freely make. You get up from the couch, you go for a walk, you eat chocolate ice cream. It seems that we're in control of actions like these; if we are, then we have free will. But in recent years, some have argued that free will is an illusion. The neuroscientist (and best-selling author) Sam Harris and the late Harvard psychologist Daniel Wegner, for example, claim that certain scientific findings disprove free will. In this engaging and accessible volume in the Essential Knowledge series, the philosopher Mark Balaguer examines the various arguments and experiments that have been cited to support the claim that human beings don't have free will. He finds them to be overstated and misguided. Balaguer discusses determinism, the view that every physical event is predetermined, or completely caused by prior events. He describes several philosophical and scientific arguments against free will, including one based on Benjamin Libet's famous neuroscientific experiments, which allegedly show that our conscious decisions are caused by neural events that occur before we choose. He considers various religious and philosophical views, including the philosophical pro-free-will view known as compatibilism. Balaguer concludes that the anti-free-will arguments put forward by philosophers, psychologists, and neuroscientists simply don't work. They don't provide any good reason to doubt the existence of free will. But, he cautions, this doesn't necessarily mean that we have free will. The question of whether we have free will remains an open one; we simply don't know enough about the brain to answer it definitively.