Aboutness in Imagination

I present a formal theory of the logic and aboutness of imagination. Aboutness is understood as the relation between meaningful items and what they concern, as per Yablo and Fine’s works on the notion. Imagination is understood as per Chalmers’ positive conceivability: the intentional state of a subject who conceives that p by imagining a situation—a configuration of objects and properties—verifying p. So far aboutness theory has been developed mainly for linguistic representation, but it is natural to extend it to intentional states. The proposed framework combines a modal semantics with a mereology of contents: imagination operators are understood as variably strict quantifiers over worlds with a content-preservation constraint

Mereology and uncertainty

Mereology as an art of composing complex concepts out of simpler parts is suited well to the task of reasoning under uncertainty: whereas it is most often difficult to ascertain whether a given thing is an element of a concept, it is possible to decide with belief degree close to certainty that the class of things is an ingredient of an other class, which is sufficient for carrying out the reasoning whose conclusions are taken as true under given conditions. We present in this work a scheme for reasoning based on mereology in which mereology in the classical sense is fuzzified in analogy to the concept fuzzification in the sense of L. A. Zadeh. In this process, mereology becomes rough mereology

Disjunctive Parts

Fine (2017a) sets out a theory of content based on truthmaker semantics which distinguishes two kinds of consequence between contents. There is entailment, corresponding to the relationship between disjunct and disjunction, and there is containment, corresponding to the relationship between conjunctions and their conjuncts. Fine associates these with two notions of parthood: disjunctive and conjunctive. Conjunctive parthood is a very useful notion, allowing us to analyse partial content and partial truth. In this chapter, I extend the notion of disjunctive parthood in terms of a structural relation of refinement, which stands to disjunctive parthood much as mereological parthood stands to conjunctive parthood. Philosophically, this relation may be modelled on the determinable- determinate relation, or on a fact-to-fact notion of grounding. I discuss its connection to two other Finean notions: vagueness (understood via precisification) and arbitrary objects. I then investigate what a logic of truthmaking with refinement might look like. I argue that (i) parthood naturally gives rise to a relevant conditional; (ii) refinement underlies a relevant notion of disjunction; and so (iii) truthmaker semantics with refinement is a natural home for relevant logic. The resulting formal models draw on Fine’s (1974) semantics for relevant logics. Finally, I use this understanding of relevant semantics to investigate the status of the mingle axiom

Bolzano’s early quest for a priori synthetic principles:Mereological aspects of the analytic-synthetic distinction in Kant and the early Bolzano

The aim of the present study is to gain insight into the development of the ideas of Bolzano, often described as the grandfather of analytic philosophy, out of the German philosophy of the eighteenth century. It provides an analysis of Wolff's influential mathematical method and argues that the notion of construction plays an important role in Wolff's account of definitions and geometric demonstrations. Investigation of Wolff's work, however, reveals that he does not provide a philosophical account for the role of construction in the mathematical method. As a result, Kant's philosophy of mathematics can be understood as filling the gap in Wolff's mathematical method rather than as a replacement. Contrary to existing studies, the present study substantiates the following claim: the Kantian idea that mathematical knowledge extends (synthetic) rather than clarifies our knowledge (analytic) plays a crucial role in the work of the early Bolzano. An unexpected outcome of this study is that so called mereological distinctions (part-whole relations) are fundamental to the philosophy of mathematics of both Kant and the early Bolzano. Detailed investigation of Bolzano's manuscripts and notes reveals that part-whole relations play a central role in his conception of general mathematics. According to a reconstruction of his theory of numbers, Bolzano regards arithmetic as synthetic because it relies on the laws of associativity and commutativity as synthetic principles

\u27You\u27 Will Always Have \u27Me\u27: A Compositional Theory of Person

This dissertation investigates the morpho-syntactic makeup of personful expressionsin natural language; special focus is given to referential uses of personal pronouns. The central thesis guiding the inquiry is that utterance contexts, which serve to fix the semantic values of person indexicals, are specifically a kind of centered situation. This treatment of contexts puts restrictions on what kinds of person features are definable, and the resulting inventory of such features (in conjunction with independently-motivated pragmatic constraints on the use of referential expressions) provides a novel explanation for the typology of person systems

Modal Intensionalism

The traditional approach to modality analyzes necessity and possibility in terms of possible worlds. According to this approach, what is necessarily true is true in (or at) all possible worlds. In the first half of this paper, I argue that there is a genuine alternative approach to modality. The alternative approach does not appeal to possible worlds but properties that bear various relations of inclusion and exclusion to one another. In the second half of this paper, I flesh out the formal details of this approach with respect to the modal propositional calculi. The result is a completely un-Kripkean formal semantics. Along the way, I provide a novel property mereology.Master of Art

Numbers and Necessity

I offer a new account of property parthood, and on its basis, novel semantic approaches to first-order logic, modal propositional logic, and quantified modal logic. I also use it in my metaphysical accounts of sets and the natural numbers. Along the way, I analyze property parthood in terms of the mental conjunction of ideas. What results: idealist accounts of necessity and number with certain explanatory advantages over standard accounts.Doctor of Philosoph

Cognitive synonymy : a dead parrot?

Funding: This research is published within the project ‘The Logic of Conceivability’, funded by the European Research Council (ERC CoG), Grant Number 681404.Sentences φ and ψ are cognitive synonyms for one when they play the same role in one’s cognitive life. The notion is pervasive (Sect. 1), but elusive: it is bound to be hyperintensional (Sect. 2), but excessive fine-graining would trivialize it and there are reasons for some coarse-graining (Sect. 2.1). Conceptual limitations stand in the way of a natural algebra (Sect. 2.2), and it should be sensitive to subject matters (Sect. 2.3). A cognitively adequate individuation of content may be intransitive (Sect. 3) due to ‘dead parrot’ series: sequences of sentences φ1,…,φn where adjacent φi and φi+1 are cognitive synonyms while φ1 and φn are not (Sect. 3.1). Finding an intransitive account is hard: Fregean equipollence won’t do (Sect. 3.2) and a result by Leitgeb shows that it wouldn’t satisfy a minimal compositionality principle (Sect. 3.3). Sed contra, there are reasons for transitivity, too (Sect. 3.4). In Sect. 4, we come up with a formal semantics capturing this jumble of desiderata, thereby showing that the notion is coherent. In Sect. 5, we re-assess the desiderata in its light.Publisher PDFPeer reviewe

Kant on analytic judgements

In this thesis I will present and defend an interpretation of Kant’s remarks on analytic judgements in his critical-era texts. Specifically, I will argue that, of the four characterisations of this class of judgements which Kant presents in the Critique of Pure Reason, it is those in terms of (i) conceptual containment and (ii) the identity of concepts (both at A6-7 / B11) which are fundamental, mutually supportive and capable of explaining the other characterisations. In order to motivate this interpretation against long-standing objections, I follow de Jong (1995) and Anderson (2005, 2015) in urging that Kant’s talk of conceptual containment and identity should be understood on the model of similar locutions as they feature in the term logics of his rationalist predecessors, in particular those of Leibniz and Wolff. Furthermore, I will argue that in much the same way that the rationalist models of inter-conceptual containment and identity are used by Leibniz and Wolff to explain the truth of all propositions in purely intensional terms, Kant’s mirror-image account of analytic judgements renders the a prioricity of said judgements a function of just such intensional characteristics. In the second chapter, I will contextualise this interpretation within Kant’s broader account of theoretical judgement in the CPR by explaining the way in which he is able to commensurate this commitment to intensional containment and identity relations with his further commitment to the possibility of distinctively synthetic judgements. In the third and final chapter, I will propose that, for Kant, analyticity is an epistemological property of select judgements, not that which renders those judgements true. In other words, I will urge that for Kant analytic judgements are not true in virtue of concepts but, rather, that their truth is merely knowable a priori by means of the containment and exclusion relations which hold between their constituent concepts