This article is about the ontological dispute between finitists, who claim that only finitely many numbers exist, and infinitists, who claim that infinitely many numbers exist. Van Bendegem set out to solve the 'general problem' for finitism: how can one recast finite fragments of classical mathematics in finitist terms? To solve this problem Van Bendegem comes up with a new brand of finitism, namely so-called 'apophatic finitism'. In this article it will be argued that apophatic finitism is unable to represent (...) the negative ontological commitments of infinitism or, in other words, that which does not exist according to infinitism. However, there is a brand of infinitism, so-called 'apophatic infinitism', that is able to represent both the positive and the negative ontological commitments of apophatic finitism. Unfortunately, apophatic finitism cannot adopt that way without losing the ability to represent the positive ontological commitments of infinitism. (shrink)

This paper argues that two widely accepted principles about the indicative conditional jointly presuppose the falsity of one of the most prominent arguments against epistemological iteration principles. The first principle about the indicative conditional, which has close ties both to the Ramsey test and the “or‐to‐if” inference, says that knowing a material conditional suffices for knowing the corresponding indicative. The second principle says that conditional contradictions cannot be true when their antecedents are epistemically possible. Taken together, these principles entail that (...) it is impossible to be in a certain kind of epistemic state: namely, a state of ignorance about which of two partially overlapping bodies of knowledge corresponds to one's actual one. However, some of the more popular “margin for error” style arguments against epistemological iteration principles suggest that such states are not only possible, but commonplace. I argue that the tension between these views runs deep, arising just as much for non‐factive attitudes like belief, presupposition, and certainty. I also argue that this is worse news for those who accept the principles about the indicative conditional than it is for those who reject epistemological iteration principles. (shrink)

Although much has been written about the truth-conditions of de re attitude reports, little attention has been paid to certain ‘ultra-liberal’ uses of those reports. We believe that if these uses are legitimate, then a number of interesting consequences for various theses in philosophical semantics follow. The majority of the paper involves describing these consequences. In short, we argue that, if true, ultra-liberal reports: bring counterexamples to a popular approach to de re attitude ascriptions, which we will call ‘descriptivism’; and (...) combine with independently plausible principles about the logic of belief to imply that subjects can achieve omniscience about what exists from the armchair. Although we are not committed to the view that ultra-liberal reports are false, in the final part of the paper we discuss the prospects of pursuing a line according to which the acceptability of such reports ought not be taken at face value. We conclude by arguing that those who are sympathetic with this move might have reason to doubt the truth of an even broader class of acceptable de re attitude reports, namely those that have been taken to undermine orthodox accounts of de re attitude ascriptions. (shrink)

The history behind the ‘Madagascar’ example of Gareth Evans is traced, suggesting that the decisive reference-shift occurred in the 16th, not the 17, century. The difference between this example and the ‘Gödel’ example of Saul Kripke is explained in terms of the distinction between de re and de dicto beliefs and intentions.

I use the principle of truth-maker maximalism to provide a new solution to the semantic paradoxes. According to the solution, AUS, its undecidable whether paradoxical sentences are grounded or ungrounded. From this it follows that their alethic status is undecidable. We cannot assert, in principle, whether paradoxical sentences are true, false, either true or false, neither true nor false, both true and false, and so on. AUS involves no ad hoc modification of logic, denial of the T-schema's validity, or obvious (...) revenge. (shrink)

Kripke’s examples of allegedly contingent a priori sentences include ‘Stick S is exactly one meter long’, where the reference of ‘meter’ is fixed by the description ‘the length of stick S’. In response to skepticism concerning apriority Kripke replaced the meter sentence with a more sophisticated variant, arguing that the modified example is more immune to such skepticism. The case for apriority is examined. A distinction is drawn between apriority and a broader notion, “qua-priority,” of a truth whose epistemic justification (...) is dependent on no experience other than that required to justify belief of the deliverances of pure semantics. It is argued that Kripke’s examples are neither a priori nor qua-priori. (shrink)

The principle of universal instantiation plays a pivotal role both in the derivation of intensional paradoxes such as Prior’s paradox and Kaplan’s paradox and the debate between necessitism and contingentism. We outline a distinctively free logical approach to the intensional paradoxes and note how the free logical outlook allows one to distinguish two different, though allied themes in higher-order necessitism. We examine the costs of this solution and compare it with the more familiar ramificationist approaches to higher-order logic. Our assessment (...) of both approaches is largely pessimistic, and we remain reluctantly inclined to take Prior’s and Kaplan’s derivations at face value. (shrink)

This dissertation is an investigation into the relation between mind and language from different perspectives, split up into three interrelated but still, for the most part, self-standing parts. Parts I and II are concerned with the question how thought is affected by language while Part III investigates the scope covered by mind and language respectively. Part I provides a reconstruction of Ludwig Wittgenstein’s famous Private Language Argument in order to apply the rationale behind this line of argument to the relation (...) between mind and language. This argumentative strategy yields the conclusion that reasoning – an important type of thought – is constitutively dependent on language possession and is therefore not available to non-linguistic creatures. This result is achieved by considering the preconditions for reasoning – given that it is a rule-governed activity – and eliminating competitors to language for providing reasoners with what it takes to reason. Part II provides a critical outlook on the wide and highly heterogeneous field of linguistic relativity theories. It is argued that no kind of linguistic relativity whatsoever follows from the conclusion of Part I – i.e., the claim that reasoning is constitutively dependent on having a language. While Part II does not provide a conclusive argument against the linguistic relativity hypothesis, it is argued that endorsement of linguistic relativity theories often rests on a mistaken assumption to the effect that language and culture are interwoven in a way which makes it impossible to separate culture and language, as well as their respective studies. This assumption is undermined by providing examples of languages which clearly predate their culture or do not even have a culture at all. So, the assumption that language and culture are inextricably intertwined is refuted by way of counterexample. Part III provides an in-depth examination of the Principle of Expressibility – prominently endorsed and formulated by John Searle – which claims that whatever can be thought can also be said. The domains of what can be thought and of what can be said are considered in set theoretic terms in order to determine whether one is contained in the other, so that everything we can think can also be adequately communicated. After thorough study of interpretative issues regarding the Principle of Expressibility and consideration of the most pressing potential counterexamples to the principle, we can conclude that we have good reason to believe in the truth of the Principle of Expressibility. In conclusion, the achieved results are related back to prominent positions in the discussion about thought and language which already make their appearance in the very beginning of this investigation. The final chapter of this dissertation reminds us that eminent figures in philosophy have often taken a wrongheaded perspective on the relation between language and thought, so that language has frequently appeared to be an impediment to thought. We can, however, confidently conclude that language, on the contrary, is by far our most apt means for thought and that reasoning would not even be possible without the resources language provides. (shrink)

Several writers have assumed that when in “Outline of a Theory of Truth” I wrote that “the orthodox approach” – that is, Tarski’s account of the truth definition – admits descending chains, I was relying on a simple compactness theorem argument, and that non-standard models must result. However, I was actually relying on a paper on ‘pseudo-well-orderings’ by Harrison. The descending hierarchy of languages I define is a standard model. Yablo’s Paradox later emerged as a key to interpreting the result.

In this paper I look at Fred Dretske’s account of information and knowledge as developed in Knowledge and The Flow of Information. In particular, I translate Dretske’s probabilistic definition of information to a modal logical framework and subsequently use this to explicate the conception of information and its flow which is central to his account, including the notions of channel conditions and relevant alternatives. Some key products of this task are an analysis of the issue of information closure and an (...) investigation into some of the logical properties of Dretske’s account of information flow. (shrink)