Timothy Williamson has argued that in the debate on modal ontology, the familiar distinction between actualism and possibilism should be replaced by a distinction between positions he calls contingentism and necessitism. He has also argued in favor of necessitism, using results on quantified modal logic with plurally interpreted second-order quantifiers showing that necessitists can draw distinctions contingentists cannot draw. Some of these results are similar to well-known results on the relative expressivity of quantified modal logics with so-called inner and outer (...) quantifiers. The present paper deals with these issues in the context of quantified modal logics with generalized quantifiers. Its main aim is to establish two results for such a logic: Firstly, contingentists can draw the distinctions necessitists can draw if and only if the logic with inner quantifiers is at least as expressive as the logic with outer quantifiers, and necessitists can draw the distinctions contingentists can draw if and only if the logic with outer quantifiers is at least as expressive as the logic with inner quantifiers. Secondly, the former two items are the case if and only if all of the generalized quantifiers are first-order definable, and the latter two items are the case if and only if first-order logic with these generalized quantifiers relativizes. (shrink)

A satisfactory solution to the problem of consciousness would take the form of a simple yet fully general model that specifies the precise conditions under which any given state of consciousness occurs. Science has uncovered numerous correlations between consciousness and neural activity, but it has not yet come anywhere close to this. We are still looking for the Newtonian laws of consciousness. -/- One of the main difficulties with consciousness is that we lack a language in which to formulate illuminating (...) generalizations about it. Philosophers and scientists talk about "what it’s like", sensations, feelings, and perceptual states such as seeing and hearing. This language does not allow a precise articulation of the internal structures of conscious states and their inter-relations. It is inadequate to capture relations of the kind we are looking for between conscious states and physical states. -/- In this thesis I refine and defend a theory of consciousness which promises to solve this regimentation problem: the representational theory of consciousness. I argue that the representational theory can solve the regimentation problem and smooth out other important obstacles to a fruitful study of consciousness. I also make a case for the theory independently of its payoffs, and I discuss the leading opposing theories at some length. (shrink)

Following Henkin's discovery of partially-ordered (branching) quantification (POQ) with standard quantifiers in 1959, philosophers of language have attempted to extend his definition to POQ with generalized quantifiers. In this paper I propose a general definition of POQ with 1-place generalized quantifiers of the simplest kind: namely, predicative, or "cardinality" quantifiers, e.g., "most", "few", "finitely many", "exactly α", where α is any cardinal, etc. The definition is obtained in a series of generalizations, extending the original, Henkin definition first to a general (...) definition of monotone-increasing (M↑) POQ and then to a general definition of generalized POQ, regardless of monotonicity. The extension is based on (i) Barwise's 1979 analysis of the basic case of M↑ POQ and (ii) my 1990 analysis of the basic case of generalized POQ. POQ is a non-compositional Ist-order structure, hence the problem of extending the definition of the basic case to a general definition is not trivial. The paper concludes with a sample of applications to natural and mathematical languages. (shrink)

Context is essential in virtually all human activities. Yet some logical notions seem to be context-free. For example, the nature of the universal quantifier, the very meaning of “all”, seems to be independent of the context. At the same time, there are many quantifier expressions, and some are context-independent, while others are not. Similarly, purely logical consequence seems to be context-independent. Yet often we encounter strong inferences, good enough for practical purposes, but not valid. The two types of examples suggest (...) a general problem: how to characterise the context-free logical concepts in their natural environment, that is, in the field of their context-dependent associates. A general Thesis on Quantifiers is formulated: among all quantifiers, the context-free ones are just those definable by the universal quantifier. The issue of inferences is treated following the approach introduced by Richard L. Epstein: valid ones are an extreme case, the result of the disappearance of context-dependence. This idea can be applied to an analysis of a form of abduction, called “reductive inference” in Polish literature on logic. A tentative Thesis on Inferences identifies the validity of a strong inference that is context-independent. (shrink)

Ontological pluralism is the view that there are different fundamental ways of being. Recent defenders of this view—such as Kris McDaniel and Jason Turner—have taken these ways of being to be best captured by semantically primitive quantifier expressions ranging over different domains. They have thus endorsed, what I shall call, quantificational pluralism. I argue that this focus on quantification is a mistake. For, on this view, a quantificational structure—or a quantifier for short—will be whatever part or aspect of reality’s structure (...) that a quantifier expression carves out and reflects. But if quantificational pluralism is true, then a quantifier should be more natural than its corresponding domain; and since it does not appear to be the case that a quantifier is more natural than its corresponding domain, quantificational pluralism does not appear to be true. Thus, I claim, an ontological pluralist should not be a quantificational pluralist. (shrink)

According to one prominent strand of mainstream logic and metaphysics, identity is indistinguishability. Priest has recently argued that this permits counterexamples to the transitivity and substitutivity of identity within dialetheic metaphysics, even in paradigmatically extensional contexts. This paper investigates two alternative regimentations of indistinguishability. Although classically equivalent to the standard regimentation on which Priest focuses, these alternatives are strictly stronger than it in dialetheic settings. Both regimentations are transitive, and one satisfies substitutivity. It is argued that both regimentations provide better (...) candidates to occupy the core theoretical role of numerical identity than does the standard regimentation. (shrink)

The goal of this paper is to present a new reconstruction of Aristotle's assertoric logic as he develops it in Prior Analytics, A1-7. This reconstruction will be much closer to Aristotle's original...

We often speak as if there are merely possible people—for example, when we make such claims as that most possible people are never going to be born. Yet most metaphysicians deny that anything is both possibly a person and never born. Since our unreflective talk of merely possible people serves to draw non-trivial distinctions, these metaphysicians owe us some paraphrase by which we can draw those distinctions without committing ourselves to there being merely possible people. We show that such paraphrases (...) are unavailable if we limit ourselves to the expressive resources of even highly infinitary first-order modal languages. We then argue that such paraphrases are available in higher-order modal languages only given certain strong assumptions concerning the metaphysics of properties. We then consider alternative paraphrase strategies, and argue that none of them are tenable. If talk of merely possible people cannot be paraphrased, then it must be taken at face value, in which case it is necessary what individuals there are. Therefore, if it is contingent what individuals there are, then the demands of paraphrase place tight constraints on the metaphysics of properties: either (i) it is necessary what properties there are, or (ii) necessarily equivalent properties are identical, and having properties does not entail even possibly being anything at all. (shrink)

This paper aims to shed new light on certain philosophical theories of perceptual experience by examining the semantics of perceptual ascriptions such as “Jones sees an apple.” I start with the assumption, recently defended elsewhere, that perceptual ascriptions lend themselves to intensional readings. In the first part of the paper, I defend three theses regarding such readings: I) intensional readings of perceptual ascriptions ascribe phenomenal properties, II) perceptual verbs are not ambiguous between intensional and extensional readings, and III) intensional perceptual (...) ascriptions have a relational form. The second part of the paper describes the implications of I-III for theories of perceptual experience. I argue that I-III support and reconcile the three main views of perceptual experience, relationalism, disjunctivism, and representationalism. However, I-III leave open at least one important point of contention: particularism, the view that we experience external objects. I conclude by exploring the implications of accepting or denying particularism given I-III. (shrink)

With this paper I aim to demonstrate that a look beyond the Aristotelian square of opposition, and a related non-conservative view on logical determiners, contributes to both the understanding of Aristotelian syllogistics as well as to the study of quantificational structures in natural language.