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.     

Ontological realism and sentential form

The standard argument for the existence of distinctively mathematical objects like numbers has two main premises: (i) some mathematical claims are true, and (ii) the truth of those claims requires the existence of distinctively mathematical objects. Most nominalists deny (i). Those who deny (ii) typically reject Quine’s criterion of ontological commitment. I target a different assumption in a standard type of semantic argument for (ii). Benacerraf’s semantic argument, for example, relies on the claim that two sentences, one about numbers and the other about cities, have the same grammatical form. He makes this claim on the grounds that the two sentences are superficially similar. I argue that these grounds are not sufficient. Other sentences with the same superficial form appear to have different grammatical forms. I offer two plausible interpretations of Benacerraf’s number sentence that make use of plural quantification. These interpretations appear not to incur ontological commitments to distinctively mathematical objects, even assuming Quine’s criterion. Such interpretations open a new, plural strategy for the mathematical nominalist.     

When Best Theories Go Bad1

It is common for contemporary metaphysical realists to adopt Quine’s criterion of ontological commitment while at the same time repudiating his ontological pragmatism. 2 Drawing heavily from the work of others—especially Joseph Melia and Stephen Yablo—I will argue that the resulting approach to meta‐ontology is unstable. In particular, if we are metaphysical realists, we need not accept ontological commitment to whatever is quantified over by our best first‐order theories.     

How to have a radically minimal ontology

In this paper I further elucidate and defend a metaontological position that allows you to have a minimal ontology without embracing an error-theory of ordinary talk. On this view ‘there are Fs’ can be strictly and literally true without bringing an ontological commitment to Fs. Instead of a sentence S committing you to the things that must be amongst the values of the variables if it is true, I argue that S commits you to the things that must exist as truthmakers for S if it is true. I rebut some recent objections that have been levelled against this metaontological view.     

Resolving Scheffler and Chomsky’s Problems on Quine’s Criterion of Ontological Commitments

Journal of Indian Council of Philosophical Research - This paper resolves the problems raised by Israel Scheffler and Noam Chomsky against Quine’s criterion of ontological commitment. I call...     

Ostrich Nominalism and Peacock Realism: A Hegelian Critique of Quine

Abstract

My aim in this paper is to offer a Hegelian critique of Quine’s predicate nominalism. I argue that at the core of Hegel’s idealism is not a supernaturalist spirit monism, but a realism about universals, and that while this may contrast to the nominalist naturalism of Quine, Hegel’s position can still be defended over that nominalism in naturalistic terms. I focus on the contrast between Hegel’s and Quine’s respective views on universals, which Quine takes to be definitive of philosophical naturalism. I argue that there is no good reason to think Quine is right to make this nominalism definitive of naturalism in this way – where in fact Hegel (along with Peirce) offers a reasonably compelling case that science itself requires some commitment to realism about universals, kinds, etc. Furthermore, even if Hegel is wrong about that, at least his case for realism is still a naturalistic one, as it is based on his views on concrete universality, which is an innovative form of in rebus realism about universals.     

On the Quinean-analyticity of mathematical propositions

This paper investigates the relation between Carnap and Quine??s views on analyticity on the one hand, and their views on philosophical analysis or explication on the other. I argue that the stance each takes on what constitutes a successful explication largely dictates the view they take on analyticity. I show that although acknowledged by neither party (in fact Quine frequently expressed his agreement with Carnap on this subject) their views on explication are substantially different. I argue that this difference not only explains their differences on the question of analyticity, but points to a Quinean way to answer a challenge that Quine posed to Carnap. The answer to this challenge leads to a Quinean view of analyticity such that arithmetical truths are analytic, according to Quine??s own remarks, and set theory is at least defensibly analytic.     

Quine on intensional entities: Modality and quantification,truth and satisfaction

In this paper, I reconstruct Quine?s arguments against quantified modal logic, from the early 1940?s to the early 1960?s. Quine?s concerns were not technical. Quine was looking for a coherent interpretation of quantified-in English modal sentences. I argue that Quine?s main thesis is that the intended objectual interpretation of the quantifiers is incompatible with any semantic reading of the modal operators, for example as expressing analytic necessity, unless the entities in the domain of quantification are intensions, i.e. definitional entities. The difficulty is that it makes no sense to say of an ordinary object that it bears a property necessarily or contingently when the necessity or contingency in question is analytic. However, starting in 1960, Quine claims that quantified-in modal sentences can be coherently interpreted only as essentialist predications. When we say about an object that it necessarily F?s, we can only coherently mean that it essentially F?s. In the paper, I argue that adequately qualified the thesis is plausible. Two important qualifications are needed. The first is the assumption that satisfaction is an irreducibly predicative notion, making any explication of satisfaction in terms of truth inadequate. The second is the ontological rejection of purely semantic, i.e. merely definitional, entities. With these qualifications in place, Quine?s rejection of the combination of objectual quantifiers and semantic modalities can be upheld. In this way, we vindicate a qualified version of Quine?s conjecture that quantified modal logic is committed to essentialism.     

Hintikka’s Logical Revolution

Hintikka thinks that second-order logic is not pure logic, and because of Gödel’s incompleteness theorems, he suggests that we should liberate ourselves from the mistaken idea that first-order logic is the foundational logic of mathematics. With this background he introduces his independence friendly logic (IFL). In this paper, I argue that approaches taking Hintikka’s IFL as a foundational logic of mathematics face serious challenges. First, the quantifiers in Hintikka’s IFL are not distinguishable from Linström’s general quantifiers, which means that the quantifiers in IFL involve higher order entities. Second, if we take Wright’s interpretation of quantifiers or if we take Hale’s criterion for the identity of concepts, Quine’s thesis that second-order logic is set theory will be rejected. Third, Hintikka’s definition of truth itself cannot be expressed in the extension of language of IFL. Since second-order logic can do what IFL does, the significance of IFL for the foundations of mathematics is weakened.     

Disagreement in Scientific Ontologies

The aim of this article is to discuss the nature of disagreement in scientific ontologies in the light of case studies from biology and cognitive science. I argue that disagreements in scientific ontologies are usually not about purely factual issues but involve both verbal and normative aspects. Furthermore, I try to show that this partly non-factual character of disagreement in scientific ontologies does not lead to a radical deflationism but is compatible with a “normative ontological realism.” Finally, I argue that the case studies from the empirical sciences challenge contemporary metaontological accounts that insist on exactly one true way of “carving nature at its joints.”     

Can Science Cope with More Than One World? A Cross-Reading of Habermas, Popper, and Searle

The purpose of this article is to critically assess the ‘three-world theory’ as it is presented—with some slight but decisive differences—by Jürgen Habermas and Karl Popper. This theory presents the philosophy of science with a conceptual and material problem, insofar as it claims that science has no single access to all aspects of the world. Although I will try to demonstrate advantages of Popper’s idea of ‘the third world’ of ideas, the shortcomings of his ontological stance become visible from the pragmatic point of view in Habermas’s theory of communicative acts. With regard to the critique that the three-world theory has met in both its pragmatic and ontological versions, I will take a closer look at John Searle’s naturalistic counter-position. By teasing out some problematic implications in his theory of causation, I aim to show that Searle’s approach is, in fact, much closer to Popper’s than he might think. Finally, while condoning Habermas’s distinction between the natural world and the lifeworld, I will opt for a pragmatically differentiated view of ‘the real’, rather than speaking of different worlds.     

“The king of France is bald” reconsidered: a case against Yablo

Stephen Yablo has argued for metaontological antirealism: he believes that the sentences claiming or denying the existence of numbers (or other abstract entities or mereological sums) are inapt for truth valuation, because the reference failure of a numerical singular term (or a singular term for an abstract entity or a mereological sum) would not produce a truth value gap in any sentence containing that term. At the same time, Yablo believes that nothing similar applies to singular terms that aim to refer to an entity whose existence or non-existence is a factual matter, e.g. ‘the king of France’: the failure of the presupposition that there is a unique French king makes some sentences with the term ‘the king of France’, in particular “The king of France is bald”, gappy. In this paper I will show that the sentence “The king of France is bald” must be false, and not gappy, according to Yablo’s own criteria and that, furthermore, the presupposition that the term ‘the king of France’ refers presents a fail-safe mechanism in the same way Yablo thinks abstract presuppositions do—this undermines his argument for metaontological antirealism.     

The Privilege of the Present: Time and the Trace from Heidegger to Derrida

ABSTRACT

One of the starting points of Derrida’s deconstruction is the idea that metaphysics is dominated by an ontological primacy of the present. It is well known that Derrida took up this thesis of the ‘privilege of the present’ in metaphysics from Heidegger. However, this thesis is mentioned without being developed by Heidegger. What is the meaning of this ontological position? How did it originate? Should we try to go beyond it? And if so, how? In this paper, I would like to start out from Heidegger’s view that the understanding of Being, in the metaphysical tradition, is dominated by the ontological primacy of the present: according to this approach, which goes back to Aristotle’s theory of substance (ousia), Being means constant presence; only that which is constantly present really exists. I will then show that Heidegger himself, in his conception of the past, has renewed the privilege of the present, favoring the ‘having been’ (Gewesenheit) over the past as ‘by-gone-ness’ (Vergangenheit). Finally, I will show how Derrida’s concept of trace may help us to go beyond the privilege of the present.     

Something-We-Know-Not-What,Something-We-Know-Not-Why: Berkeley,Meaning and Minds

It is sometimes suggested that Berkeley adheres to an empirical criterion of meaning, on which a term is meaningful just in case it signifies an idea (i.e., an immediate object of perceptual experience). This criterion is thought to underlie his rejection of the term ‘matter’ as meaningless. As is well known, Berkeley thinks that it is impossible to perceive matter. If one cannot perceive matter, then, per Berkeley, one can have no idea of it; if one can have no idea of it, then one cannot speak meaningfully of it. But if this is Berkeley’s position, then there is a puzzle, because Berkeley also explicitly claims that it is impossible to perceive/have ideas of minds. So if he is relying on a criterion on which terms get their meaning by referring to ideas, then, just as Berkeley rejects talk of material substance, so, too, must he reject talk of mental substance. Famously, however, Berkeley insists that there is no parity between the cases of material and mental substance. It is typically suggested that the disparity between matter and minds rests on the fact that although one cannot strictly speaking perceive minds, nonetheless Berkeley thinks that one can have experiential access to minds via reflection, and that this access allows for meaningful talk of minds. Of course, one can only have reflective experience of one’s own mind. But what of other minds, which one cannot reflectively experience? Here the usual tactic is to suppose that, although one cannot have direct reflective experience of other minds, nonetheless one can indirectly experience such minds via analogy to our own minds, and that this indirect experience grounds the meaningfulness of talk of other minds. In this paper, I argue that the reasoning behind Berkeley’s ‘likeness principle,’ that an idea can only be like another idea, can be generalized to argue against this experience-based account of our access to other minds. I claim instead that Berkeley allows for the meaningfulness of talk of other minds by expanding the criterion of meaning in a different way. I argue that Berkeley holds a criterion of meaning on which a term is meaningful just in case it signifies either an object of experience or an object that one has reason to posit on the basis of experience, i.e., an object that is necessary to explain our experiences. When an object is neither experienced nor explains our experiences, then and only then is Berkeley willing to reject it as meaningless. Thus he writes of “the word matter,” that “it is no matter whether there is such a thing or no, since it no way concerns us: and I do not see the advantage there is in disputing about we know not what, and we know not why” (Principles, §77.) The word is not meaningless merely because we do not know what matter might be; it is meaningless because we also do not know why it should be. Correspondingly, I argue that the term ‘mind’ is meaningful because although we have no experience of minds, nonetheless they play an important role in explaining our experiences.     

Importance and Explanatory Relevance: The Case of Mathematical Explanations

A way to argue that something (e.g. mathematics, idealizations, moral properties, etc.) plays an explanatory role in science is by linking explanatory relevance with importance in the context of an explanation. The idea is deceptively simple: a part of an explanation is an explanatorily relevant part of that explanation if removing it affects the explanation either by destroying it or by diminishing its explanatory power, i.e. an important part (one that if removed affects the explanation) is an explanatorily relevant part. This can be very useful in many ontological debates. My aim in this paper is twofold. First of all, I will try to assess how this view on explanatory relevance can affect the recent ontological debate in the philosophy of mathematics—as I will argue, contrary to how it may appear at first glance, it does not help very much the mathematical realists. Second of all, I will show that there are big problems with it.     

On Quine’s Translation Argument

Quine's translation argumnent figures centrally in his views on logic. The goal of this paper is to get clear on that argument. It can be interpreted as an argument to the effect that one should never translate somebody’s speech as going against a law of the translator’s logic. Key to this reading of the translation argument is the premise that one should never translate somebody's speech such that their speech is unintelligible. Ultimately, it is my aim to reject this reading. I argue that only a weaker conclusion—one that says “not most of the time” instead of the stronger “never”—should be attributed to Quine. Accordingly, I propose and defend a weaker version of the first premise that better coheres with the weaker conclusion of the translation argument. Instead of the claim that one should never translate somebody’s speech such that their speech is unintelligible I argue that we should only ascribe to Quine the claim that one should not most of the time translate somebody’s speech in a way that makes it unintelligible. I go on to  sum up the results of my discussion and respond to a criticism of my reading.

     

What is Absolute Undecidability?†

It is often alleged that, unlike typical axioms of mathematics, the Continuum Hypothesis (CH) is indeterminate. This position is normally defended on the ground that the CH is undecidable in a way that typical axioms are not. Call this kind of undecidability “absolute undecidability”. In this paper, I seek to understand what absolute undecidability could be such that one might hope to establish that (a) CH is absolutely undecidable, (b) typical axioms are not absolutely undecidable, and (c) if a mathematical hypothesis is absolutely undecidable, then it is indeterminate. I shall argue that on no understanding of absolute undecidability could one hope to establish all of (a)–(c). However, I will identify one understanding of absolute undecidability on which one might hope to establish both (a) and (c) to the exclusion of (b). This suggests that a new style of mathematical antirealism deserves attention—one that does not depend on familiar epistemological or ontological concerns. The key idea behind this view is that typical mathematical hypotheses are indeterminate because they are relevantly similar to CH.     

Kant's Argument that Existence is not a Determination

In this paper, I examine Kant's famous objection to the ontological argument: existence is not a determination. Previous commentators have not adequately explained what this claim means, how it undermines the ontological argument, or how Kant argues for it. I argue that the claim that existence is not a determination means that it is not possible for there to be non‐existent objects; necessarily, there are only existent objects. I argue further that Kant's target is not merely ontological arguments as such but the larger ‘ontotheist’ metaphysics they presuppose: the view that God necessarily exists in virtue of his essence being contained in, or logically entailed by, his essence. I show that the ontotheist explanation of divine necessity requires the assumption that existence is a determination, and I show that Descartes and Leibniz are implicitly committed to this in their published versions of the ontological argument. I consider the philosophical motivations for the claim that existence is a determination and then I examine Kant's arguments in the Critique of Pure Reason against it.     

Can there be a feature-placing language?

The aim of this article is to argue against the real possibility of languages without subject-predicate structure, so-called feature-placing languages. They were first introduced by Strawson (1959/1990), later given formal expression through Quine's Predicate Functor Logic (Quine, 1960, Quine, 1971/Quine, 1976, Quine, 1992), and further elaboration in (Hawthorne & Cortens, 1995). I argue that, on the presumption that feature-placing languages are not mere notational variants on first-order languages, the idea of such languages is incoherent. The argument for this view rests on two highly plausible views about the conditions for the possibility of sentential meaning in natural languages. If accepted, these two views jointly imply that the sentences of feature-placing languages lack sufficient internal structure to meet the conditions for sentential meaning. Feature-placing languages cannot then count as genuine languages.