Grammar, Ambiguity, and Descriptions: A Study in the Semantics of Definite Descriptions

The semantics of definite descriptions has been a central topic in philosophy of language ever since Russell’s landmark paper ‘On Denoting’(1905). Russell argued that definite descriptions should not be seen as referential expressions, but instead as quantificational expressions. In other words, a sentential utterance containing a definite description should be understood as expressing a general/object-independent proposition. A problem arises with the view once we consider the fact that definite descriptions are used frequently and consistently to refer to particular individuals. Through this observation, Donnellan (1966) argued that definite descriptions would be better understood as having two distinct uses, one referential and one attributive/quantificational. We can call this the ambiguity problem in definite descriptions. The following thesis will argue that the ambiguity problem disappears once we take seriously the grammar that underpins sentential utterances containing definite descriptions, and that the semantics of the definite article is determined in part by the grammatical topology of determiner phrases and in part by what grammatical environments determiner phrases can be felicitously placed. The thesis, therefore, is that the semantics of definite descriptions is grounded in grammatical facts

Mechanised metamathematics : an investigation of first-order logic and set theory in constructive type theory

In this thesis, we investigate several key results in the canon of metamathematics, applying the contemporary perspective of formalisation in constructive type theory and mechanisation in the Coq proof assistant. Concretely, we consider the central completeness, undecidability, and incompleteness theorems of first-order logic as well as properties of the axiom of choice and the continuum hypothesis in axiomatic set theory. Due to their fundamental role in the foundations of mathematics and their technical intricacies, these results have a long tradition in the codification as standard literature and, in more recent investigations, increasingly serve as a benchmark for computer mechanisation. With the present thesis, we continue this tradition by uniformly analysing the aforementioned cornerstones of metamathematics in the formal framework of constructive type theory. This programme offers novel insights into the constructive content of completeness, a synthetic approach to undecidability and incompleteness that largely eliminates the notorious tedium obscuring the essence of their proofs, as well as natural representations of set theory in the form of a second-order axiomatisation and of a fully type-theoretic account. The mechanisation concerning first-order logic is organised as a comprehensive Coq library open to usage and contribution by external users.In dieser Doktorarbeit werden einige Schlüsselergebnisse aus dem Kanon der Metamathematik untersucht, unter Verwendung der zeitgenössischen Perspektive von Formalisierung in konstruktiver Typtheorie und Mechanisierung mit Hilfe des Beweisassistenten Coq. Konkret werden die zentralen Vollständigkeits-, Unentscheidbarkeits- und Unvollständigkeitsergebnisse der Logik erster Ordnung sowie Eigenschaften des Auswahlaxioms und der Kontinuumshypothese in axiomatischer Mengenlehre betrachtet. Aufgrund ihrer fundamentalen Rolle in der Fundierung der Mathematik und ihrer technischen Schwierigkeiten, besitzen diese Ergebnisse eine lange Tradition der Kodifizierung als Standardliteratur und, besonders in jüngeren Untersuchungen, eine zunehmende Bedeutung als Maßstab für Mechanisierung mit Computern. Mit der vorliegenden Doktorarbeit wird diese Tradition fortgeführt, indem die zuvorgenannten Grundpfeiler der Methamatematik uniform im formalen Rahmen der konstruktiven Typtheorie analysiert werden. Dieses Programm ermöglicht neue Einsichten in den konstruktiven Gehalt von Vollständigkeit, einen synthetischen Ansatz für Unentscheidbarkeit und Unvollständigkeit, der großteils den berüchtigten, die Essenz der Beweise verdeckenden, technischen Aufwand eliminiert, sowie natürliche Repräsentationen von Mengentheorie in Form einer Axiomatisierung zweiter Ordnung und einer vollkommen typtheoretischen Darstellung. Die Mechanisierung zur Logik erster Ordnung ist als eine umfassende Coq-Bibliothek organisiert, die offen für Nutzung und Beiträge externer Anwender ist

Higher Theory and the Three Problems of Physics

According to the Butterfield--Isham proposal, to understand quantum gravity we must revise the way we view the universe of mathematics. However, this paper demonstrates that the current elaborations of this programme neglect quantum interactions. The paper then introduces the Faddeev--Mickelsson anomaly which obstructs the renormalization of Yang--Mills theory, suggesting that to theorise on many-particle systems requires a many-topos view of mathematics itself: higher theory. As our main contribution, the topos theoretic framework is used to conceptualise the fact that there are principally three different quantisation problems, the differences of which have been ignored not just by topos physicists but by most philosophers of science. We further argue that if higher theory proves out to be necessary for understanding quantum gravity, its implications to philosophy will be foundational: higher theory challenges the propositional concept of truth and thus the very meaning of theorising in science.Comment: 23 pages, 1 table

Essencialismo, modalidade e Teoria da Referência Direta

Orientador: Marco Antonio Caron RuffinoDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciências HumanasResumo: É questionável se a teoria semântica de Kripke isoladamente considerada - ou qualquer outra versão da teoria da referência direta - acarreta fortes alegações/reivindicações metafísicas. Neste trabalho, eu analiso tais alegações a partir de (i) acompanhar de perto a argumentação de Kripke, e (ii) usar da interpretação de Salmon de como podemos construir a perspectiva kripkeana sem excluir o papel do a priori do esquema, (iii) estar particularmente atenta a alegações metafísicas que envolvem termos gerais como termos de espécies naturais, e finalmente (iv) opor as propostas de Fine e Salmon a fim de entender as limitações de uma aproximação modal à noção de essência. Meu objetivo é contribuir para o debate sobre os limites entre semântica e metafísica dentro da teoria da referência direta e como entender descobertas científicas dentro deste contextoAbstract: It is doubtful whether Kripke¿s semantical theory alone - or any other version of direct reference theory alone - entails strong essentialist claims. In this work, I analyze such claims through (i) following Kripke¿s argumentation closely, and (ii) using Salmon¿s interpretation of how we could build Kripke¿s perspective without excluding the a priori role from the scheme, (iii) being particularly attentive to essentialist claims that involve general terms such as natural kind terms, and finally (iv) opposing Fine¿s proposal to Salmon¿s in order to understand the limitations of a modal approach to essence. My goal is to contribute to the debate around the boundaries between semantics and metaphysics in the direct reference theory and how to understand scientific discoveries within this contextMestradoFilosofiaMestra em Filosofia2016/25913-7FAPES

Worlds and Objects of Epistemic Space : A study of Jaakko Hintikka's modal semantics

This study focuses on meaning and knowledge by assessing a distinctive view regarding their relation, namely the modal view of Jaakko Hintikka. The development of this view has not been previously scrutinized. By paying close attention to the texts of Hintikka, I show that, despite the extensive deployment of mathematical tools, the articulation of the view remained intuitive and vague. The study calls attention to several points at which Hintikka omits relevant details or disregards foundational questions. Attempts are made to articulate Hintikka’s certain ideas in a more specific manner, and new problems that result are identified. The central claim argued for is that Hintikka’s exposition was unsatisfactory in many respects and hence the view, as it stands, falls short in its explanatory scope compared to current theories in the intersection of logic, semantics, and epistemology. However, I argue that, despite its shortcomings, the prospects of the modal view are not exhausted. This is verified by introducing a new interpretation of the framework and by sketching new applications relevant in philosophy of language and in epistemology. It is also pointed out that certain early advances of the view closely resemble, and therefore anticipate, the central tenets of the currently influential two-dimensional approaches in logic and semantics.Tutkimus paneutuu merkityksen ja tiedon käsitteisiin tarkastelemalla Jaakko Hintikan työtä modaalisen semantiikan parissa. Tutkimus osoittaa, että Hintikka jätti modaalisen semantiikan kehitystyössään avoimeksi useita perustavia kysymyksiä ja yksityiskohtia. Tutkimuksessa pyritään artikuloimaan täsmällisemmin joitakin Hintikan näkemyksiä, ja tunnistetaan uusia syntyviä ongelmia. Keskeisenä väitteenä on, että Hintikan teoreettinen työ jäi monilta osin epätyydyttäväksi, ja siten hänen modaalinen näkemyksensä ei yllä selitysvoimaltaan ja sovelluspotentiaaliltaan samalle tasolle kuin nykyiset filosofiset teoriat, jotka operoivat logiikan, semantiikan ja epistemologian risteyskohdissa. Tästä huolimatta tutkimuksessa argumentoidaan, että Hintikan teoreettinen viitekehys tarjoaa myös uusia kiinnostavia näköaloja. Tämä todennetaan tarjoamalla Hintikan viitekehykselle uusi tulkinta, ja soveltamalla sitä uusiin kielifilosofisiin kysymyksiin. Tutkimus nostaa myös esiin kirjallisuudessa ohitetun tosiasian, että Hintikan työ ennakoi tärkeällä tavalla nykyisin vaikutusvaltaisia kaksi-dimensionaalisia lähestymistapoja logiikassa ja semantiikassa

Fictional Characters and Their Discontents: Prolegomena to Any Future Metaphysics of Fictional Entities

In recent metaphysics, the questions of whether fictional entities exist, what their nature is, and how to explain truths of statements such as “Sherlock Holmes lives at 221B Baker Street” and “Holmes was created by Arthur Conan Doyle” have been subject to much debate. The main aim of my thesis is to wrestle with key proponents of the abstractionist view that fictional entities are abstract objects that exist (van Inwagen 1977, 2018, Thomasson 1999 and Salmon 1998) as well as Walton’s (1990) pretense view, which denies the existence of such entities. In the process, I propose modifications to these views to deal with problems they face and show how the modifications better account for the philosophical data. Key abstractionists (van Inwagen 1977, Thomasson 1999) make a strict distinction between discourse within fiction, in which statements about literary characters cannot be literally true, and discourse about fiction, as it occurs in literary criticism, where statements about fictional characters can be literally true. Fictional objects are postulated to account for the truth of the latter. This runs into trouble because statements thought to be literally true are not literal. (Yagisawa 2001, Friend 2002) I provide a uniform analysis to account for the truth of statements involving fictional characters by appealing to a presupposition involving a metaphor in both contexts. The presupposition is that there is an x such that x is fictional; x is likened to a real person; and x is and ought to be treated/counted as a real person for all relevant intents and purposes. More generally, I adopt Everett and Schroeder’s (2015) realist view that fictional characters are ideas constituted by mental representations. This, to me, better accounts for how fictional characters are created within the world’s causal nexus (unlike non-spatiotemporal entities in abstractionism), among other things. One key challenge they face is to explain how ideas can possess properties such as being a detective. I present a fine-grained version of their view, according to which the mental representations constituting fictional entities encode mind-dependent properties. Moreover, I explain how reference to such representations is possible, using Bencivenga’s (1983) Neo-Kantian view of reference and Karttunen’s (1976) view on discourse referents. Finally, I suggest that the identity of fictional characters is interest-relative. The constant, and sometimes radical, change of properties that, fictional characters can undergo is taken to be a consequence of the fact that unified mental representations are bundles of simpler mental representations. As change occurs, simpler representations are replaced by others. A key theme that runs through the thesis is that neither fictionality nor pretense is relevant to the semantics of fictional sentences—a claim bolstered by Matravers’ (2014) arguments. Whether or not my account works, this claim, as well as the new philosophical data I bring up, are some of the challenges I pose to the heart of established views