So-called 'Frege cases' pose a challenge for anyone who would hope to treat the contents of beliefs (and similar mental states) as Russellian propositions: It is then impossible to explain people's behavior in Frege cases without invoking non-intentional features of their mental states, and doing that seems to undermine the intentionality of psychological explanation. In the present paper, I develop this sort of objection in what seems to me to be its strongest form, but then offer a response to it. (...) I grant that psychological explanation must invoke non-intentional features of mental states, but it is of crucial importance which such features must be referenced. -/- It emerges from a careful reading of Frege's own view that we need only invoke what I call 'formal' relations between mental states. I then claim that referencing such 'formal' relations within psychological explanation does not undermine its intentionality in the way that invoking, say, neurological features would. The central worry about this view is that either (a) 'formal' relations bring narrow content in through back door or (b) 'formal' relations end up doing all the explanatory work. Various forms of each worry are discussed. The crucial point, ultimately, is that the present strategy for responding to Frege cases is not available either to the 'psycho-Fregean', who would identify the content of a belief with its truth-value, nor even to someone who would identify the content of a belief with a set of possible worlds. It requires the sort of rich semantic structure that is distinctive of Russellian propositions. There is therefore no reason to suppose that the invocation of 'formal' relations threatens to deprive content of any work to do. (shrink)

Identity, we're told, is the binary relation that every object bears to itself, and to itself only. But how can a relation be binary if it never relates two objects? This puzzled Russell and led Wittgenstein to declare that identity is not a relation between objects. The now standard view is that Wittgenstein's position is untenable, and that worries regarding the relational status of identity are the result of confusion. I argue that the rejection of identity as a binary relation (...) is perfectly tenable. To this end, I outline and defend a logical framework that is not committed to an objectual identity relation but is nevertheless expressively equivalent to first-order logic with identity. After it has thus been shown that there is no indispensability argument for objectual identity, I argue that we have good reasons for doubting the existence of such a relation, and rebut a number of attempts at discrediting these reasons. (shrink)

Are Fregean thoughts compositionally complex and composed of senses? We argue that, in Begriffsschrift, Frege took 'conceptual contents' to be unstructured, but that he quickly moved away from this position, holding just two years later that conceptual contents divide of themselves into 'function' and 'argument'. This second position is shown to be unstable, however, by Frege's famous substitution puzzle. For Frege, the crucial question the puzzle raises is why "The Morning Star is a planet" and "The Evening Star is a (...) planet" have different contents, but his second position predicts that they should have the same content. Frege's response to this antinomy is of course to distinguish sense from reference, but what has not previously been noticed is that this response also requires thoughts to be compositionally complex, composed of senses. That, however, raises the question just how thoughts are composed from senses. We reconstruct a Fregean answer, one that turns on an insistence that this question must be understood as semantic rather than metaphysical. It is not a question about the intrinsic nature of residents of the third realm but a question about how thoughts are expressed by sentences. (shrink)

The 'substitution argument' purports to demonstrate the falsity of Russellian accounts of belief-ascription by observing that, e.g., these two sentences: (LC) Lois believes that Clark can fly. (LS) Lois believes that Superman can fly. could have different truth-values. But what is the basis for that claim? It seems widely to be supposed, especially by Russellians, that it is simply an 'intuition', one that could then be 'explained away'. And this supposition plays an especially important role in Jennifer Saul's defense of (...) Russellianism, based upon the existence of an allegedly similar contrast between these two sentences: (PC) Superman is more popular than Clark. (PS) Superman is more popular than Superman. The latter contrast looks pragmatic. But then, Saul asks, why shouldn't we then say the same about the former? The answer to this question is that the two cases simply are not similar. In the case of (PC) and (PS), we have only the facts that these strike us differently, and that people will sometimes say things like (PC), whereas they will never say things like (PS). By contrast, there is an argument to be given that (LS) can be true even if (LC) is false, and this argument does not appeal to anyone's 'intuitions'. The main goal of the paper is to present such a version of the substitution argument, building upon the treatment of the Fregan argument against Russellian accounts of belief itself in "Solving Frege's Puzzle". A subsidiary goal is to contribute to the growing literature arguing that 'intuitions' simply do not play the sort of role in philosophical inquiry that so-called 'experimental philosophers' have supposed they do. (shrink)

In §8 of his Begriffsschrift (1879), Gottlob Frege discusses issues related to identity. Frege begins his most famous essay, “On Sense and Denotation” (1892), published 13 years later, by criticizing the view advocated in §8. He returns to these issues in the concluding paragraph. Controversies continue over these important passages. We offer an interpretation and discuss some alternatives. We defend that in the Begriffsschrift, Frege does not hold that identity is a relation between signs. §8 of the Begriffsschrift is motivated (...) by the conflict between two different criteria for sameness of conceptual content of sentences. To resolve that conflict, Frege introduces ‘≡’ in §8 and, thus, circumstances with names as constituents. To the same end, in “On Sense and Denotation,” Frege introduces senses and Thoughts and abandons both ‘≡’ and circumstances. He solves what we call the Co-instantiation problem, and disregards, but does not solve, the Name problem. (shrink)

Frege’s views on identity continue to provoke scholars, and rightly so. In particular his view in Begriffsschrift of 1879, and its relation to his view in ‘Über Sinn und Bedeutung’ of 1892 deserve careful attention. The issues involved have a wider significance than Frege’s specific views on identity in different periods, though these are important enough. They concern also the move from what I call below ‘thin’ semantics, which is exhausted in signs being assigned content, to a ‘thick’ semantics, in (...) which ‘modes of determining their content’, or Sinne are also concerned. (shrink)

In this essay, I first solve solve a conundrum and then deal with criteria of identity, Leibniz's definition of identity and Frege's adoption of it in his (failed) attempt to define the cardinality operator contextually in terms of Hume's Principle in Die Grundlagen der Arithmetik. I argue that Frege could have omitted the intermediate step of tentatively defining the cardinality operator in the context of an equation of the form ‘NxF(x) = NxG(x)'. Frege considers Leibniz's definition of identity to be (...) purely logical, although without saying why it is in line with his logicist project. I argue that the universal criterion of identity that Frege takes from Leibniz's definition and the specific criterion of identity for cardinal numbers embodied in Hume’s Principle (namely equinumerosity) work hand in hand in the tentative contextual definition of the cardinality operator. Yet the interplay between the two criteria is powerless to prevent the emergence of the Julius Caesar problem, let alone suggests how it could be solved. The final explicit definition of the cardinality operator that Frege sets up still rests on the identity criterion of equinumerosity since cardinal numbers are defined as equivalence classes of that relation. (shrink)

The authors believe that the questions raised at the beginning of Frege’s On Sense and Reference – ‘Is [identity] a relation? A relation between objects, or between names or signs of objects?’ – set the course for a long-lasting but not at all satisfying discussion. For the disputants tend to advocate, either a ‘name-view’ of identity in a straightforward but rudimentary and logically untenable form, or else a version of an ‘object-view’ that makes all too light of the analysandum–analysans distinction (...) and hence is damned to analytical barrenness. In contrast, by unfolding the underlying idea of the original ‘name-view’, the authors offer three alternative and mutually compatible interpretations of identity that may best be characterized as the ‘name-based’, the ‘hybrid’ and the ‘sense-based’ variant of a ‘concept-view of identity’. At the same time, however, these interpretations may well be considered variants of a non-barren ‘object-view’. (shrink)

The article presents Frege's distinction between Sense and Reference. After a short introduction, it explains the puzzle which gave rise to the distinction; Frege's earlier solution, and his reasons for its later repudiation. The distinction, which embodies Frege's second solution, is then discussed in two phases. The first, which is restricted to proper names, sets out its most basic features. The second discusses 'empty' names; indirect speech, and the distinction for predicates and for complete sentences. Finally, two criticisms, by Russell (...) and by Kripke, are briefly set out. (shrink)

The ongoing debate about whether Frege has ever abandoned the metalinguistic solution to Frege’s Puzzle not only is important by itself, but has serious ramifications. In this article, I show that Frege did abandon the metalinguistic solution and his objection to it is as follows. Though the co-reference relation between two signs is mediated by the connection of each of the two signs with the same designated thing, the connection is nevertheless arbitrary because it could be established even if one (...) of the two signs is distinguished from the other only as object not as sign. As a result, if by “a = b” we assert a co-reference relation, we would express no proper knowledge. (shrink)

Robert Stalnaker has argued that mathematical information is information about the sentences and expressions of mathematics. I argue that this metalinguistic account is open to a variant of Alonzo Church's translation objection and that Stalnaker's attempt to get around this objection is not successful. If correct, this tells not only against Stalnaker's account of mathematical truths, but against any metalinguistic account of truths that are both necessary and informative.

Frege's puzzle about identity sentences has long challenged many philosophers to find a solution to it but also led other philosophers to object that the evidential datum it is grounded on is false. The present work is an elaboration of this second kind of reaction: it explains why Frege's puzzle seems to resist the traditional objection, giving voice to different and more elaborated presentations of the evidential datum, faithful to the spirit but not to the letter of Frege's puzzle. The (...) final outcome is negative, no satisfactory formulation of the evidential datum is found and Frege's puzzle is challenged until a better formulation of it is found. (shrink)

The ongoing debate about whether Frege has ever abandoned the metalinguistic solution to Frege’s Puzzle not only is important by itself, but has serious ramifications. In this article, I show that Frege did abandon the metalinguistic solution and his objection to it is as follows. Though the co-reference relation between two signs is mediated by the connection of each of the two signs with the same designated thing, the connection is nevertheless arbitrary because it could be established even if one (...) of the two signs is distinguished from the other only as object not as sign. As a result, if by “a = b” we assert a co-reference relation, we would express no proper knowledge. (shrink)

In Begriffsschrift, Frege presented a formal system and used it to formulate logical definitions of arithmetical notions and to deduce some noteworthy theorems by means of logical axioms and inference rules. From a contemporary perspective, Begriffsschrift’s deductions are, in general, straightforward; it is assumed that all of them can be reproduced in a second-order formal system. Some deductions in this work present—according to this perspective—oddities that have led many scholars to consider it to be Frege’s inaccuracies which should be amended. (...) In this paper, we continue with the analysis of Begriffsschrift’s logic undertaken in an earlier work and argue that its deductive system must not be reconstructed as a second-order calculus. This leads us to argue that Begriffsschrift’s deductions do not need any correction but, on the contrary, can be explained in coherence with a global reading of this work and, in particular, with its fundamental distinction between function and argument. (shrink)