Stephen Yablo

According to neo-Fregean Platonism, abstraction principles—such as the principle that the direction of line a is identical to the direction of line b iff a and b are parallel—may in some cases be regarded as introducing new singular terms (e.g., “the direction of line a”) and as fixing the truth-conditions of genuine identity statements featuring them. If neo-Fregeanism is to vindicate Frege’s idea that a plausible philosophy of arithmetic can and should treat the natural numbers as a species of _object_, it must address the so-called “Caesar Problem”: the problem of explaining in general terms which objects given in other terms they are to be distinguished from. This chapter pilots a novel solution to the Caesar Problem via the notion of a _real definition_: a definition whose purpose is not to explain a meaning, but to characterize the essential nature of the thing introduced.

An untruth can still be true where thus and such is concerned; no surprise there. What is perhaps surprising is that an unfalsehood can be false, when conceived as addressed to a certain subject matter. So it is with “The King of France is bald,” according to Strawson, understood as a claim about the bald people. Could “Vulcan exists” be like this? Though not false, because the term lacks a referent, it is nevertheless false about the existing things; it misdescribes them as including Vulcan. This is a misdescription because for every existing _x_, _x_ is not Vulcan even if Vulcan exists. How can “_x_ is not Vulcan even if Vulcan exists” be evaluated, though, when the name is empty? Just use the Ramsey Test. When we imagine the oracle saying, “Vulcan exists,” and consider on that basis whether Vulcan is, say, Saturn, the answer is clear.

The philosopher Hilary Putnam uses model theory to cast doubt on our ability to engage semantically with an objective world. The role of mathematics for him is to prove this pessimistic conclusion. The present chapter, on the other hand, explores how models can _help_ us to engage semantically with the objective world. Mathematics functions here as an analogy. Among their many other accomplishments, numbers boost the language’s expressive power; they give us access to recondite physical facts. Models, among their many other accomplishments, do the same thing. This is the analogy this chapter attempts to develop.

Bayesian conditionalization is rigid: learning E fixes p(E) at 1 while preserving probabilities conditional on E. Non-rigid update is preferable when, in the course of learning that E is true, we change our views about how—by way of which truthmakers ϵ. A Jeffrey-style generalization of Bayes—active conditioning—is developed which gives learning events a handle on p(ϵ|E) and p(E) both. E brings a truthmaker-incorporating “probasition” to the table, rather than simply an intension. Confirmation relations go hyperintensional as a result. Eis true in the same worlds may not license the same updates, if their truth flows from different sources.

In this chapter, Stephen Yablo develops a theory of the concept of the relevance of a circumstance to an outcome. He takes as his starting point the minimal sufficiency model of relevance, according to which a circumstance is relevant to an outcome if it forms part of some circumstance that (i) suffices for that outcome and (ii) has no proper part which would also suffice for that outcome. But the minimal sufficiency model encounters problems when one considers infinitary cases. To solve these problems, Yablo appeals to the notion of ways in which a circumstance can obtain. This allows him to define a graded notion of sufficiency, such that a circumstance might have parts which are sufficient for an outcome without being as sufficient for that outcome. Incorporating the idea of graded sufficiency into the minimal sufficiency model gives us the idea that a circumstance is relevant to an outcome if it forms part of some circumstance that (i) suffices for that outcome and (ii) has no proper part which suffices for that outcome as fully.

David Lewis asked in “A problem about permission” about the effects on context, specifically on the “sphere of permissibility,” of allowing behavior that had previously been forbidden. The framework of truthmaker semantics sheds useful light on this problem. Update procedures are definable in the truthmaker framework that capture more than Lewis was able to just with worlds. Connections are drawn with epistemic modals, belief revision and the semantics of exceptives. We consider how a truthmaker account of permissive update might be integrated into a larger semantic/pragmatic account of deontic language. Bridge principles are articulated associating types of deontic act with distinct update rules. Distinct forms of permission trigger distinct procedures because they aim at spheres more or less strongly verifying ◊φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Diamond \varphi $$\end{document}, the claim that φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varphi $$\end{document} is permissible.

Analytic semantics got its start when Frege pointed out differences in cognitive content between sentences that in some good sense “say the same.” Frege put cognitive content (in the form of sense) at the heart of semantic content. Most prefer nowadays to see cognitive contents as generated by semantic contents in context; a sentence's cognitive significance is an aspect rather of the information imparted by its use. I argue for a particular version of this idea. Semantic contents generate cognitive contents by operating levers in a larger piece of machinery, involving also the presupposition P one is leaning on and the subject matter M under discussion. A sentence's cognitive content is what its literal-content-restricted-to-P-worlds says about M. It's by triggering different presuppositions and/or different subject matters that coreferential names make their distinctive mark on a sentence's felt information value.

Holmes exists is false. How can this be, when there is no one for the sentence to misdescribe? Part of the answer is that a sentence’s topic depends on context. The king of France is bald, normally unevaluable, is false qua description of the bald people. Likewise Holmes exists is false qua description of the things that exist; it misdescribes those things as having Holmes among them. This does not explain, though, how Holmes does not exist differs in cognitive content from, say, Vulcan does not exist. Our answer builds on an observation of Kripke’s: even if Holmes exists, he is not in this room, for we were all born too late.