Richard G. Heck

Nonconceptual Content and the “Space of Reasons”

In The Varieties of Reference, Gareth Evans (1982) argues that the content of perceptual experience is non-conceptual, in a sense I shall explain momentarily.1 More recently, in his book Mind and World, John McDowell (1996) has argued that the reasons Evans gives for this claim are not compelling and, moreover, that Evans’s view is a version of “the Myth of the Given”: More precisely, Evans’s view is alleged to suffer from the same sorts of problems that plague sense-datum theories of perception. In particular, McDowell argues that perceptual experience must be within “the space of reasons”, that perception must be able to give us reasons for, that is, to justify, our beliefs about the world: And, according to him, no state which does not have conceptual content can be a reason for a belief. Now, there are many ways in which Evans’s basic idea, that perceptual content is non-conceptual, might be developed; some of these, I shall argue, would be vulnerable to the objections McDowell brings against him. But I shall also argue that there is a way of developing it which is not vulnerable to these objections. The view I shall defend here is not one I am entirely comfortable attributing to Evans—nor one I am particularly comfortable claiming as my own. Because Evans does not say very much about the nature of non-conceptual content, nor about the relation between perceptual states and beliefs, the text is simply too thin to support the attribution to him of any specific, developed version of the view that perceptual content is non-conceptual. There is textual evidence that elements of the view I am about to develop were accepted by Evans, and I shall discuss these

The Consistency of predicative fragments of frege’s grundgesetze der arithmetik

As is well-known, the formal system in which Frege works in his Grundgesetze der Arithmetik is formally inconsistent, Russell’s Paradox being derivable in it.This system is, except for minor differences, full second-order logic, augmented by a single non-logical axiom, Frege’s Axiom V. It has been known for some time now that the first-order fragment of the theory is consistent. The present paper establishes that both the simple and the ramified predicative second-order fragments are consistent, and that Robinson arithmetic, Q, is relatively interpretable in the simple predicative fragment. The philosophical significance of the result is discussed

Finitude and Hume’s Principle

The paper formulates and proves a strengthening of ‘Frege’s Theorem’, which states that axioms for second-order arithmetic are derivable in second-order logic from Hume’s Principle, which itself says that the number of Fs is the same as the number ofGs just in case the Fs and Gs are equinumerous. The improvement consists in restricting this claim to finite concepts, so that nothing is claimed about the circumstances under which infinite concepts have the same number. ‘Finite Hume’s Principle’ also suffices for the derivation of axioms for arithmetic and, indeed, is equivalent to a version of them, in the presence of Frege’s definitions of the primitive expressions of the language of arithmetic. The philosophical significance of this result is also discussed.

Cardinality, Counting, and Equinumerosity

Frege, famously, held that there is a close connection between our concept of cardinal number and the notion of one-one correspondence, a connection enshrined in Hume’s Principle. Husserl, and later Parsons, objected that there is no such close connection, that our most primitive conception of cardinality arises from our grasp of the practice of counting. Some empirical work on children’s development of a concept of number has sometimes been thought to point in the same direction. I argue, however, that Frege was close to right, that our concept of cardinal number is closely connected with a notion like that of one-one correspondence, a more primitive notion we might call just as many.

Truth and disquotation

Hartry Field has suggested that we should adopt at least a methodological deflationism: “[W]e should assume full-fledged deflationism as a working hypothesis. That way, if full-fledged deflationism should turn out to be inadequate, we will at least have a clearer sense than we now have of just where it is that inflationist assumptions ... are needed”. I argue here that we do not need to be methodological deflationists. More pre-cisely, I argue that we have no need for a disquotational truth-predicate; that the word ‘true’, in ordinary language, is not a disquotational truth-predicate; and that it is not at all clear that it is even possible to introduce a disquotational truth-predicate into ordinary language. If so, then we have no clear sense how it is even possible to be a methodological deflationist. My goal here is not to convince a committed deflationist to abandon his or her position. My goal, rather, is to argue, contrary to what many seem to think, that reflection on the apparently trivial character of T-sentences should not incline us to deflationism.

Tarski, Truth, and Semantics

No one denies that Tarski made a major contribution to one particular problem about truth, namely, the resolution of the semantic paradoxes—although, of course, there is disagreement about whether he provided the correct solution. But some philosophers have suggested that Tarski also made a significant contribution to another project, that of providing semantic theories for natural languages. Hartry Field (2001), for example, credits Tarski with transforming the problem of reducing truth to physicalistically acceptable notions into that of reducing “primitive denotation”. And Donald Davidson (1984c) founded an entire approach to semantics by arguing that a theory of meaning for a language may take the form of a Tarskian definition of truth. But, according to John Etchemendy Etchemendy (1988),1 in so far as Tarski’s work does contribute to empirical semantics, this “is little more than a fortuitous accident”. There are both conceptual and historical issues here. The conceptual question is whether reading Tarski’s work on truth as it must be read, if it is to have any relevance to semantics, requires misunderstanding the character of his mathematical work. The historical question is whether Tarski intended his work to be so read. Etchemendy’s view is that Tarski was primarily concerned to resolve the semantic paradoxes. Yet

CONSISTENCY AND THE THEORY OF TRUTH

What is the logical strength of theories of truth? That is: If you take a theory

Meaning and Truth‐Conditions: A Reply to Kemp

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Ramified Frege Arithmetic

and add a theory of truth to it, how strong is the resulting theory, as compared to

The Development of Arithmetic in Frege's Grundgesetze der Arithmetik

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