In this paper, I argue from a metasemantic principle to the existence of analytic sentences. According to the metasemantic principle, an external feature is relevant to determining which concept one expresses with an expression only if one is disposed to treat this feature as relevant. This entails that if one isn’t disposed to treat external features as relevant to determining which concept one expresses, and one still expresses a given concept, then something other than external features must determine that one (...) does. I argue that, in such cases, what determines that one expresses the concept also puts one in a position to know that certain sentences are true—these sentences are thus analytic relative to this determination basis. Finally, I argue that there are such cases: some sentences are analytic relative to what determines that we express certain key concepts, and these sentences include ones that have always been thought to be the best candidates for being analytic, namely, stipulative truths, and first principles of mathematics. (shrink)

In this paper, I introduce and defend a notion of analyticity for formal languages. I first uncover a crucial flaw in Timothy Williamson’s famous argument template against analyticity, when it is applied to sentences of formal mathematical languages. Williamson’s argument targets the popular idea that a necessary condition for analyticity is that whoever understands an analytic sentence assents to it. Williamson argues that for any given candidate analytic sentence, there can be people who understand that sentence and yet who fail (...) to assent to it. I argue that, on the most natural understanding of the notion of assent when it is applied to sentences of formal mathematical languages, Williamson’s argument fails. Formal analyticity is the notion of analyticity that is based on this natural understanding of assent. I go on to develop the notion of formal analyticity and defend the claim that there are formally analytic sentences and rules of inference. I conclude by showing the potential payoffs of recognizing formal analyticity. (shrink)

Many philosophers have discussed the ability of thinkers to think thoughts that the thinker cannot justify because the thoughts involve concepts that the thinker incompletely understands. A standard example of this phenomenon involves the concept of the derivative in the early days of the calculus: Newton and Leibniz incompletely understood the derivative concept and, hence, as Berkeley noted, they could not justify their thoughts involving it. Later, Weierstrass justified their thoughts by giving a correct explication of the derivative concept. This (...) paper discusses various accounts of how a thinker manages to think with a concept that they incompletely understand and finds them wanting in the case at hand. Part of the overlooked complexity is that there are many derivative concepts, and it is unclear in virtue of what a thinker would be thinking with one of them rather than another. After critical evaluation of standard accounts, this paper suggests a novel account of how one should think about the derivative concepts with which Newton and Leibniz thought and how Weierstrass could have managed to justify their thoughts even if their thoughts did not involve the same derivative concept as Weierstrass’s. (shrink)

Tyler Burge has in many writings distinguished between mental content externalism based on incorrect understanding and mental content externalism based on partial but not incorrect understanding. Both and have far-reaching implications for analyses of communication and concept possession in various expert-layperson relations, but Burge and his critics have mainly focused on . This article first argues that escapes the most influential objection to . I then raise an objection against Burge’s argument for . The objection focuses on Burge’s claim that (...) a person with a partial understanding of a term in our community expresses our standard concept because he is willing to defer to our standard understanding, while his “Putnamian” twin in a counterfactual community does not. The problem with Burge’s argument for this claim is that he does not consider the possibility that the person in our community and the twin would defer to the same understanding if they were presented with the same alternatives. Drawing from widespread dispositional assumptions about meaning, I argue that Burge must accept that they express the same concept if they would defer to the same understanding. The article closes with an examination on various ways the externalist may attempt to avoid this problem and concludes that none of them succeeds. (shrink)

Moral discourse allows for speakers to disagree in many ways: about right and wrong acts, about moral theory, about the rational and conative significance of moral failings. Yet speakers’ eccentricities do not prevent them from engaging in moral conversation or from having (genuine, not equivocal) moral disagreement. Thus differences between speakers are compatible with possession of moral concepts. This paper examines various kinds of moral disagreements and argues that they provide evidence against conceptual-role and informational atomist approaches to understanding our (...) moral concepts. Conceptual role approaches fail because they cannot account for shared concepts among speakers with different commitments to the practical and conative ramifications of moral judgments. Informational atomist views fail because speakers need not be locked on to the same moral properties to share moral concepts. (shrink)

Informal rigour is the process by which we come to understand particular mathematical structures and then manifest this rigour through axiomatisations. Structural relativity is the idea that the kinds of structures we isolate are dependent upon the logic we employ. We bring together these ideas by considering the level of informal rigour exhibited by our set-theoretic discourse, and argue that different foundational programmes should countenance different underlying logics (intermediate between first- and second-order) for formulating set theory. By bringing considerations of (...) perturbations in modal space to bear on the debate, we will suggest that a promising option for representing current set-theoretic thought is given by formulating set theory using quasi-weak second-order logic. These observations indicate that the usual division of structures into \particular (e.g. the natural number structure) and general (e.g. the group structure) is perhaps too coarse grained; we should also make a distinction between intentionally and unintentionally general structures. (shrink)