Modern empiricism has been conditioned in large part by two dogmas. One is a belief in some fundamental cleavage between truths which are analytic, or grounded in meanings independently of matters of fact, and truth which are synthetic, or grounded in fact. The other dogma is reductionism: the belief that each meaningful statement is equivalent to some logical construct upon terms which refer to immediate experience. Both dogmas, I shall argue, are ill founded. One effect of abandoning them is, as (...) we shall see, a blurring of the supposed boundary between speculative metaphysics and natural science. Another effect is a shift toward pragmatism. (shrink)

Suppose now that two philosophers, McX and I, differ over ontology. Suppose McX maintains there is something which I maintain there is not. McX can, quite consistently with his own point of view, describe our difference of opinion by saying that I refuse to recognize certain entities. I should protest of course that he is wrong in his formulation of our disagreement, for I maintain that there are no entities, of the kind which he alleges, for me to recognize; but (...) my finding him wrong in his formulation of our disagreement is unimportant, for I am committed to considering him wrong in his ontology anyway. When I try to formulate our difference of opinion, on the other hand, I seem to be in a predicament. I cannot admit that there are some things which McX countenances and I do not, for in admitting that there are such things I should be contradicting my own rejection of them. (shrink)

Kant's question 'How are synthetic judgments a priori possible?' pre- cipitated the Critique of Pure Reason. Question and answer notwith- standing, Mill and others persisted in doubting that such judgments were possible at all. At length some of Kant's own clearest purported.

Realists persuaded by indispensability arguments af- firm the existence of numbers, genes, and quarks. Van Fraassen's empiricism remains agnostic with respect to all three. The point of agreement is that the posits of mathematics and the posits of biology and physics stand orfall together. The mathematical Platonist can take heart from this consensus; even if the existence of num- bers is still problematic, it seems no more problematic than the existence of genes or quarks. If the two positions just described (...) were the only ones possible, there could be no objection to this melding of numbers with genes and quarks. However, the position I call contrastive empiricism (Sober 1990a) stands opposed to both realism and to Van Fraassen's em- piricism. As it turns out, contrastive empiricism entails that coalesc- ing mathematics with empirical science is highly problematic. I believe that there is an important kernel of truth in abductive ar- guments for genes and quarks. But no counterpart argument exists for the case of numbers. Of course, the existence of this third way would be uninteresting, if contrastive empiricism were wholly implausible. However, I will argue that contrastive empiricism captures what makes sense in standard versions of realism and empiricism, while avoiding the excesses of each. This third way is a middle way; it cannot be dismissed out of hand. (shrink)

This paper is a reexamination of Two Dogmas in the light of Quine's ongoing debate with Carnap over analyticity. It shows, first, that analytic is a technical term within Carnap's epistemology. As such it is intelligible, and Carnap's position can meet Quine's objections. Second, it shows that the core of Quine's objection is that he has an alternative epistemology to advance, one which appears to make no room for analyticity. Finally, the paper shows that Quine's alternative epistemology is itself open (...) to very serious objections. Quine is not thereby refuted, but neither can Carnap's analyticity be dismissed as dogma. (shrink)

Discussions of the applicability of mathematics in the natural sciences have been flawed by failure to realize that there are multiple senses in which mathematics can be ‘applied’ and, correspondingly, multiple problems that stem from the applicability of mathematics. I discuss semantic, metaphysical, descriptive, and and epistemological problems of mathematical applicability, dwelling on Frege's contribution to the solution of the first two types. As for the remaining problems, I discuss the contributions of Hartry Field and Eugene Wigner. Finally, I argue (...) that there are epistemological problems concerning the applicability of mathematics that nobody in the philosophical community has yet confronted, though the problems are well known to physicists. (shrink)

The Quine/Putnam indispensability approach to the confirmation of mathematical theories in recent times has been the subject of significant criticism. In this paper I explore an alternative to the Quine/Putnam indispensability approach. I begin with a van Fraassen-like distinction between accepting the adequacy of a mathematical theory and believing in the truth of a mathematical theory. Finally, I consider the problem of moving from the adequacy of a mathematical theory to its truth. I argue that the prospects for justifying this (...) move are qualitatively worse in mathematics than they are in science. (shrink)

Much of the current thought concerning mathematical ontology in volves in some way the Quine/Putnam indispensability argument. The indispensability approach needs to be more thoroughly specified, however, before substantive progress can be made in assessing it. To this end I examine in some detail the ways in which pure mathematics is applied to physical theory; such considerations give rise to three specific issues with which the indispensability approach must come to grips.

Much of the current thought concerning mathematical ontology in volves in some way the Quine/Putnam indispensability argument. The indispensability approach needs to be more thoroughly specified, however, before substantive progress can be made in assessing it. To this end I examine in some detail the ways in which pure mathematics is applied to physical theory; such considerations give rise to three specific issues with which the indispensability approach must come to grips.

The subject with which Mark Colyvan's book deals is timely indeed. While discussions of mathematical ontology have been a mainstay in philosophy of mathematics for the last century (at least), for the last thirty years or so this discussion has begun with (and often not left) the Quine/Putnam indispensability argument. Though the argument is widely cited, to my knowledge this is the first book-length project exclusively dedicated to articulating and defending the Quine/Putnam indispensability argument for mathematical platonism. In the first (...) section below, I shall run through a summary of the book (following its chapter layout) with a few critical remarks. In the second section I shall raise a few critical issues organized topically. (shrink)