Confirmation Theory and Indispensability

In this paper I examine Quine's indispensability argument, with particular emphasis on what is meant by 'indispensable'. I show that confirmation theory plays a crucial role in answering this question and that once indispensability is understood in this light, Quine's argument is seen to be a serious stumbling block for any scientific realist wishing to maintain an anti-realist position with regard to mathematical entities.     

Strawson's Anti-Scepticism: A Critical Reconstruction

Strawson suggests an anti‐sceptical strategy which consists in offering good reason for ignoring scepticism rather than trying to refute it, and the reason he offers is that beliefs about the external world are indispensable to us. I give an exposition of Strawson's arguments for the indispensability thesis and explain why they are not strong enough. I then propose an argument based on some of Davidson's ideas in his theory of radical interpretation, which I think can establish the indispensability thesis. Finally, I spell out the force of Strawson's anti‐sceptical strategy by arguing that we have good reason for ignoring scepticism not only because beliefs about the world are indispensable, but also because it is irrational to have both beliefs about the world and sceptical doubts.     

Evidential Holism and Indispensability Arguments

The indispensability argument is a method for showing that abstract mathematical objects exist (call this mathematical Platonism). Various versions of this argument have been proposed (§1). Lately, commentators seem to have agreed that a holistic indispensability argument (§2) will not work, and that an explanatory indispensability argument is the best candidate. In this paper I argue that the dominant reasons for rejecting the holistic indispensability argument are mistaken. This is largely due to an overestimation of the consequences that follow from evidential holism. Nevertheless, the holistic indispensability argument should be rejected, but for a different reason (§3)—in order that an indispensability argument relying on holism can work, it must invoke an unmotivated version of evidential holism. Such an argument will be unsound. Correcting the argument with a proper construal of evidential holism means that it can no longer deliver mathematical Platonism as a conclusion: such an argument for Platonism will be invalid. I then show how the reasons for rejecting the holistic indispensability argument importantly constrain what kind of account of explanation will be permissible in explanatory versions (§4).     

The underdetermination of theory by data and the “strong programme” in the sociology of knowledge

Advocates of the “strong programme” in the sociology of knowledge have argued that, because scientific theories are “underdetermined” by data, sociological factors must be invoked to explain why scientists believe the theories they do. I examine this argument, and the responses to it by J.R. Brown (1989) and L. Laudan (1996). I distinguish between a number of different versions of the underdetermination thesis, some trivial, some substantive. I show that Brown's and Laudan's attempts to refute the sociologists' argument fail. Nonetheless, the sociologists' argument falls to a different criticism, for the version of the underdetermination thesis that the argument requires, has not been shown to be true.     

On the de-naturalization of epistemology

Starting from an overview of approaches to naturalized epistemology, the paper shows, firstly, that Quine's programme yields a sceptical paradox. This means that Quine's attempt to defeat scepticism itself yields a rather strong argument for scepticism and thus against his own programme of naturalized epistemology. Secondly, it is shown that this paradox can be solved by an approach called reflexive-heuristic naturalism. Finally, the paper also raises some fundamental problems which the solution proposed has to leave open. This revised version was published online in August 2006 with corrections to the Cover Date.     

Grounding and the indispensability argument

There has been much discussion of the indispensability argument for the existence of mathematical objects. In this paper I reconsider the debate by using the notion of grounding, or non-causal dependence. First of all, I investigate what proponents of the indispensability argument should say about the grounding of relations between physical objects and mathematical ones. This reveals some resources which nominalists are entitled to use. Making use of these resources, I present a neglected but promising response to the indispensability argument—a liberalized version of Field’s response—and I discuss its significance. I argue that if it succeeds, it provides a new refutation of the indispensability argument; and that, even if it fails, its failure may bolster some of the fictionalist responses to the indispensability argument already under discussion. In addition, I use grounding to reply to a recent challenge to these responses.     

The Full Unity of the Virtues

The classical doctrine that the moral virtues are unified is widely rejected. Some argue that the virtues are disunified, or even mutually incompatible. And though others have argued that the virtues form some sort of unity, these recent defenses of unity are always qualified, advocating only a partial unity: the unity of the virtues is limited to certain practical domains, or weak in that one virtue implies only moral decency in the fields of other virtues. I argue that something like the classical doctrine—a full unity of the virtues thesis—remains defensible. After reviewing the arguments of partial unity theorists for the claim that the virtues form at least some sort of unity, I examine their main arguments for thinking that this unity is only partial (limited or weak). I then show that these arguments fail, and address some further criticisms (such as the argument that full unity implausibly requires that a person must attain the virtues “all at once”). I do not seek here to prove the truth of the full unity thesis (in fact I suggest a modification of it), but only to refute important extant criticisms of it, and thus to show that it remains a plausible view.     

On the Conceptual Foundations of Anti-Realism

The central premise of Michael Dummett's global argument for anti-realism is the thesis that a speaker's grasp of the meaning of a declarative, indexical-free sentence must be manifested in her uses of that sentence. This enigmatic thesis has been the subject of a great deal of discussion, and something of a consensus has emerged about its content and justification. The received view is that the manifestation thesis expresses a behaviorist and reductive theory of meaning, essentially in agreement with Quine's view of language, and motivated by worries about the epistemology of communication. In the present paper I begin by arguing that this standard interpretation of the manifestation thesis is neither particularly faithful to Dummett's writings nor philosophically compelling. I then continue by reconstructing, from Dummett's texts, an account of the manifestation thesis, and of its justification, that differ sharply from the received view. On my reading, the thesis is motivated not epistemologically, but conceptually. I argue that connections among our conceptions of meaning, assertion, and justification lead to a conclusion about the metaphysics of meaning: we cannot form a clearly coherent conception of how two speakers can attach different meanings to a sentence without at the same time differing in what they count as justifying assertions made with that sentence. I conclude with some suggestions about how Dummett's argument for global anti-realism should be understood, given my account of the manifestation thesis. This revised version was published online in August 2006 with corrections to the Cover Date.     

Dispensability in the Indispensability Argument

One of the most influential arguments for realism about mathematical objects is the indispensability argument. Simply put, this is the argument that insofar as we are committed to the existence of the physical objects existentially quantified over in our best scientific theories, we are also committed to the mathematical objects existentially quantified over in these theories. Following the Quine–Putnam formulation of the indispensability argument, some proponents of the indispensability argument have made the mistake of taking confirmational holism to be an essential premise of the argument. In this paper, I consider the reasons philosophers have taken confirmational holism to be essential to the argument and argue that, contrary to the traditional view, confirmational holism is dispensable.     

On inconsistent entities. A reply to Colyvan

In a recent article M. Colyvan has argued that Quinean forms of scientific realism are faced with an unexpected upshot. Realism concerning a given class of entities, along with this route to realism, can be vindicated by running an indispensability argument to the effect that the entities postulated by our best scientific theories exist. Colyvan observes that among our best scientific theories some are inconsistent, and so concludes that, by resorting to the very same argument, we may incur a commitment to inconsistent entities. Colyvan’s argument could be interpreted, and in part is presented, as a reductio of Quinean scientific realism; yet, Colyvan in the end manifests some willingness to bite the bullet, and provides some reasons why we shouldn’t feel too uncomfortable with those entities. In this paper we wish to indicate a way out to the scientific realist, by arguing that no indispensability argument of the kind suggested by Colyvan is actually available. To begin with, in order to run such an indispensability argument we should be justified in believing that an inconsistent theory is true; yet, in so far as the logic we accept is a consistent one it is arguable that our epistemic predicament could not be possibly one in which we are justified in so believing. Moreover, also if our logic admitted true contradictions, as Dialetheism does, it is arguable that Colyvan’s indispensability argument could not rest on a true premise. As we will try to show, dialetheists do not admit true contradictions for cheap: they do so just as a way out of paradox, namely whenever we are second-level ignorant as to the metaphysical possibility of evidence breaking the parity among two or more inconsistent claims; Colyvan’s examples, however, are not of this nature. So, even under the generous assumption that Dialetheism is true, we will conclude that Colyvan’s argument doesn’t achieve its surprising conclusion.     

Discussion Note: McCain on Weak Predictivism and External World Scepticism

In a recent paper McCain (2012) argues that weak predictivism creates an important challenge for external world scepticism. McCain regards weak predictivism as uncontroversial and assumes the thesis within his argument. There is a sense in which the predictivist literature supports his conviction that weak predictivism is uncontroversial. This absence of controversy, however, is a product of significant plasticity within the thesis, which renders McCain’s argument worryingly vague. For McCain’s argument to work he either needs a stronger version of weak predictivism than has been defended within the literature, or must commit to a more precise formulation of the thesis and argue that weak predictivism, so understood, creates the challenge to scepticism that he hopes to achieve. The difficulty with the former is that weak predictivism is not uncontroversial in the respect that McCain’s argument would require. I consider the prospects of saving McCain’s argument by committing to a particular version of weak predictivism, but find them unpromising for several reasons.     

A Naturalistic Look into Maddy's Naturalistic Philosophy of Mathematics

This paper discusses Penelope Maddy's (b.1950) naturalistic philosophy of mathematics,which is one of the most influential forms of post-Quinean naturalism in the philosophy of mathematics.Two defining features of Maddy's theory,namely the methodological autonomy of mathematics and the equivalence of Thin Realism and Arealism,are analyzed,and some criticisms of them are posed from within the naturalistic line of thought itself.In the course of this analysis and criticism,the paper will also consider Maddy's objections to the Quinean Indispensability Argument,which are the starting point of her own version of naturalism.     

Probability and certainty: A reexamination of the Lewis-Reichenbach debate

Conclusion I have shown as promised that Reichenbach did not refute either thesis (I) or thesis (II). I have also shown that an argument of Lewis's may be used to establish a weakened version of (I) that has two interesting consequences: if we are to assign probabilities with any justification at all, we must have either certainties or intrinsic probabilities; and if we are frequentists, we must have certainties.     

What's Wrong With Indispensability?

For many philosophers not automatically inclined to Platonism, the indispensability argument for the existence of mathematical objectshas provided the best (and perhaps only) evidence for mathematicalrealism. Recently, however, this argument has been subject to attack, most notably by Penelope Maddy (1992, 1997),on the grounds that its conclusions do not sit well with mathematical practice. I offer a diagnosis of what has gone wrong with the indispensability argument (I claim that mathematics is indispensable in the wrong way), and, taking my cue from Mark Colyvan's (1998) attempt to provide a Quinean account of unapplied mathematics as `recreational', suggest that, if one approaches the problem from a Quinean naturalist starting point, one must conclude that all mathematics is recreational in this way.     

Searle's abstract argument against strong AI

Discussion of Searle's case against strong AI has usually focused upon his Chinese Room thought-experiment. In this paper, however, I expound and then try to refute what I call his abstract argument against strong AI, an argument which turns upon quite general considerations concerning programs, syntax, and semantics, and which seems not to depend on intuitions about the Chinese Room. I claim that this argument fails, since it assumes one particular account of what a program is. I suggest an alternative account which, however, cannot play a role in a Searle-type argument, and argue that Searle gives no good reason for favoring his account, which allows the abstract argument to work, over the alternative, which doesn't. This response to Searle's abstract argument also, incidentally, enables the Robot Reply to the Chinese Room to defend itself against objections Searle makes to it.     

A Truthmaker Indispensability Argument

Recently, nominalists have made a case against the Quine–Putnam indispensability argument for mathematical Platonism by taking issue with Quine’s criterion of ontological commitment. In this paper I propose and defend an indispensability argument founded on an alternative criterion of ontological commitment: that advocated by David Armstrong. By defending such an argument I place the burden back onto the nominalist to defend her favourite criterion of ontological commitment and, furthermore, show that criterion cannot be used to formulate a plausible form of the indispensability argument.     

The Value of Truth and the Care of the Soul

Although the argument against the neo-Darwinian theory of evolution presented by Stephen R. L. Clark in From Athens to Jerusalem is based upon sound principles, it fails to provide an a priori refutation. If it did work, it would refute all objective scientific theories, since all of them make consciousness and subjectivity, as Clark characterises them, incomprehensible. Scientism, the thesis that science is the only source of truth, is Clark's real target, rather than science per se, but he does not diagnose this error as it is made by authors such as Jacques Monod and Richard Dawkins. Scientism is not essential to materialism in general, and a successful version of 'supervenience-materialism'could avoid both reductionism and scientism. However, Clark still has a reply. He may use his discussion of the value of truth to provide a more general critique of materialism, which in my view is far more effective.     

Living in Harmony: Nominalism and the Explanationist Argument for Realism

According to the indispensability argument, scientific realists ought to believe in the existence of mathematical entities, due to their indispensable role in theorising. Arguably the crucial sense of indispensability can be understood in terms of the contribution that mathematics sometimes makes to the super‐empirical virtues of a theory. Moreover, the way in which the scientific realist values such virtues, in general, and draws on explanatory virtues, in particular, ought to make the realist ontologically committed to abstracta. This paper shows that this version of the indispensability argument glosses over crucial detail about how the scientific realist attempts to generate justificatory commitment to unobservables. The kind of role that the Platonist attributes to mathematics in scientific reasoning is compatible with nominalism, as far as scientific realist arguments are concerned.     

Conceptual analysis as armchair psychology: in defense of methodological naturalism

Three proponents of the Canberra Plan, namely Jackson, Pettit, and Smith, have developed a collective functionalist program—Canberra Functionalism—spanning from philosophical psychology to ethics. They argue that conceptual analysis is an indispensible tool for research on cognitive processes since it reveals that there are some folk concepts, like belief and desire, whose functional roles must be preserved rather than eliminated by future scientific explanations. Some naturalists have recently challenged this indispensability argument, though the point of that challenge has been blunted by a mutual conflation of metaphysical and methodological strands of naturalism. I argue that the naturalist’s challenge to the indispensability argument, like naturalism itself, ought to be reformulated as a strictly methodological thesis. So understood, the challenge succeeds by showing (1) that we cannot know a priori on the basis of conceptual analysis of folk platitudes that something must occupy the functional roles specified for beliefs and desires, and (2) that proponents of Canberra Functionalism sometimes tacitly concede this point by treating substantive psychological theories as the deliverances of a priori platitudes analysis.     

Revisiting Quine on Truth by Convention

In “Truth by Convention” W.V. Quine gave an influential argument against logical conventionalism. Even today his argument is often taken to decisively refute logical conventionalism. Here I break Quine’s arguments into two—(i) the super-task argument and (ii) the regress argument—and argue that while these arguments together refute implausible explicit versions of conventionalism, they cannot be successfully mounted against a more plausible implicit version of conventionalism. Unlike some of his modern followers, Quine himself recognized this, but argued that implicit conventionalism was explanatorily idle. Against this I show that pace Quine’s claim that implicit conventionalism has no content beyond the claim that logic is firmly accepted, implicit rules of inference can be used to distinguish the firmly accepted from the conventional. As part of my case, I argue that positing syntactic rules of inference as part of our linguistic competence follows from the same methodology that leads contemporary linguists and cognitive scientists to posit rules of phonology, morphology, and grammar. The upshot of my discussion is a diagnosis of the fallacy in Quine’s master critique of logical conventionalism and a re-opening of possibilities for an attractive conventionalist theory of logic.