I challenge a claim that seems to be made when nominalists offer reformulations of the content of mathematical beliefs, namely that these reformulations are accessible to everyone. By doing so, I argue that these theories cannot account for the mathematical knowledge that ordinary people have. In the first part of the paper I look at reformulations that employ the concept of proof, such as those of Mary Leng and Ottavio Bueno. I argue that ordinary people don’t have many beliefs about (...) proofs, and that they are not in a position to acquire knowledge about proofs autonomously. The second part of the paper is concerned with other reformulations of content, such as those of Hartry Field and Stephen Yablo. There too, the problem is that people are not able to acquire knowledge of the reformulated propositions autonomously. Ordinary people simply do not have beliefs with the kind of content that the nominalists need, for their theory to account for the mathematical knowledge of ordinary people. All in all then, the conclusion is that a large number of theories that suggest reformulations of mathematical content yield contents that are inaccessible for most people. Thus, these theories are limited, in that they cannot account for the mathematical knowledge of ordinary people. (shrink)

I outline Brandom’s theory of de re and de dicto belief ascriptions, which plays a central role in Brandom’s overall theory of linguistic communication, and show that this theory offers a surprising, new response to Burge’s (Midwest Stud 6:73–121, 1979) argument for social externalism. However, while this response is in principle available from the perspective of Brandom’s theory of belief ascription in abstraction from his wider theoretical enterprise, it ceases to be available from this perspective in the wider context of (...) his inferential role semantics and his doctrines of scorekeeping and of the expressive role of belief ascriptions in discourse. In this wider context, Brandom’s theory of belief ascriptions implies that Burge’s argument trivially fails to have the disquieting implications for psychological explanations that it is widely taken to have. Yet since this is not trivially so, Brandom’s theory apparently provides a false picture of our practice of interpreting belief ascriptions. I then argue that Brandom might as well accept the alternative picture of interpreting belief ascriptions that Burge’s argument presupposes: even in the context of his overall project, Brandom’s take on our practice of interpreting them does not afford belief ascriptions with the discursive significance Brandom claims they have. (shrink)

The question of whether content externalism poses a threat to the traditional view of self-knowledge has been much debated. Compatibilists have tried to diffuse the threat by appealing to the self-verifying character of reflexive judgments about our own thoughts, while incompatibilists have strenuously objected that this does not suffice. In my paper I argue that this debate is fundamentally misconceived since it is based, on both sides, on the problematic notion of ‘knowledge of content’. What this shows, I argue, is (...) not that content externalism is unobjectionable, but that the real challenge to content externalism is not an epistemological one. The real difficulty concerns the content externalist’s seemingly necessary commitment to the idea that individuals have an incomplete grasp of the concepts that go into their own thoughts. This idea poses a threat not to self-knowledge, I argue, but rather to our first- and second-order reasoning abilities. (shrink)

Frege’s ‘differential dubitability’ test is a test for differences in cognitive value: if one can rationally believe that p while simultaneously doubting that q, then the contents p and q amount to different ‘cognitive values’. If subject S is rational, does her simultaneous adoption of different attitudes towards p and q require that the difference between p and q(as cognitive values) be transparent to her? It is natural to think so. But I argue that, if attitude anti-individualism is true, then (...) rational differential dubitability does not presuppose that differences in cognitive value be transparent. The significance of this argument lies in what it tells us, both about the notion of cognitive value (and its relation to the differential dubitability test), but also about the prospects for a Burge-type position which aims to combine attitude anti-individualism with a (perhaps qualified) reliance on the differential dubitability test. (shrink)

Kripshe treats ‘god’ as an empty natural kind term such as ‘unicorn’. She applies Saul Kripke's fresh views about empty natural kinds to ‘god’. Metaphysically, says Kripshe, there are no possible worlds in which there are gods. Gods could not have existed, given that they do not actually exist and never did. Epistemologically, godlessness is an a posteriori discovery. Kripshe dismisses the gods in the same breath that she dismisses mermaids. Semantically, the perspective Kripshe finds most perspicacious, no counterfactual situation (...) is properly describable as one in which there are gods. Perhaps it is not quite a necessary truth that there are no gods. According to Saul Kripke, failed natural kind terms are ill-defined. Incorporating ill-defined terms into declarative sentences yields only mock propositions. Just as the meteorologist has no professional interest in mock thunder, the logician has no professional interest in mock propositions. Kripshe disagrees with agnostics who assign a low probability to ‘There is at least one god’. The bearers of probabilities must be propositions. Despite this deference to science, Kripshe agrees with the a priori atheist that, necessarily, no future experience could constitute an encounter with a god. Divine revelation is impossible. Kripshe's a posteriori necessary atheism compares favorably to familiar forms of atheism and to non-cognitivists. It reveals interesting challenges to a coherent formulation of atheism. (shrink)

Among the topics to whose discussion Diego Marconi has contributed outstandingly over the years, two of the most notable are the nature of lexical competence and the status of the law of non-contradiction. The topics are linked by the popular idea that adherence to basic logical laws is a necessary condition of understanding logical words, in particular that adherence to the law of non-contradiction is a necessary condition of understanding words for negation. For example, it may be proposed...

Les conditions de possession permettant l’individuation des concepts, bien que peu étudiées, constituent l’un des lieux fondamentaux de la polémique opposant les points de vue frégéen et anti-individualiste. Dans cet article, je décris une théorie compatibiliste de la valeur cognitive qui réunit des conditions de possession anti-individualistes et individualistes. Je soutiens que cette approche générale de la compatibilité des explications frégéenne et anti-individualiste de la possession de concepts suffit à mettre en doute l’idée voulant que la déférence et la transparence (...) sont des caractéristiques fondamentales de la valeur cognitive. (shrink)