Logic and Foundations of Mathematics Commons^™

Intuitionism, Justification Logic, And Doxastic Reasoning, Vincent A. Peluce

Dissertations, Theses, and Capstone Projects

In this Dissertation, we examine a handful of related themes in the philosophy of logic and mathematics. We take as a starting point the deeply philosophical, and—as we argue, deeply Kantian—views of L.E.J. Brouwer, the founder of intuitionism. We examine his famous first act of intuitionism. Therein, he put forth both a critical and a constructive idea. This critical idea involved digging a philosophical rift between what he thought of himself as doing and what he thought of his contemporaries, specifically Hilbert, as doing. He sought to completely separate mathematics from mathematical language, and thereby logic. In chapter 3, we …

Avoiding Pragmatic Oddity: A Bottom-Up Defeasible Deontic Logic, Guido Governatori, Silvano Colombo Tosatto, Antonio Rotolo

Centre for Computational Law (2022-2025)

This paper presents an extension of Defeasible Deontic Logic to deal with the Pragmatic Oddity problem. The logic applies three general principles: (i) the Pragmatic Oddity problem must be solved within a general logical treatment of contrary-to-duty (CTD) reasoning; (ii) non-monotonic methods must be adopted to handle CTD reasoning; (iii) logical models of CTD reasoning must be computationally feasible and, if possible, efficient. The proposed extension of Defeasible Deontic Logic elaborates a preliminary version of the model proposed by Governatori and Rotolo [15]. The previous solution was based on particular characteristics of the (constructive, top-down) proof theory of the logic. …

A Thesis, Or Digressions On Sculptural Practice: In Which, Concepts & Influences Thereof Are Explained, Set Forth, Catalogued, Or Divulged By Way Of Commentaries To A Poem, First Conceived By The Artist, Fed Through Chatg.P.T., And Re-Edited By The Artist, To Which Are Added, Annotated References, Impressions And Ruminations Thereof, Also Including Private Thoughts & Personal Accounts Of The Artist, Jaimie An

Masters Theses

This thesis is an exercise in, perhaps a futile, attempt to trace just some of the ideas, stories, and musings I might meander through in my process. It’s not quite a map, nor is it a neat catalogue; it is a haphazard collection of tickets and receipts from a travel abroad, carelessly tossed in a carry-on, only to be stashed upon returning home. These ideas are derived from much greater thinkers and authors than myself; I am a mere collector or a translator, if that, and not a very good one, for much is lost. I do not claim comprehensive …

Canonical Extensions Of Quantale Enriched Categories, Alexander Kurz

MPP Research Seminar

No abstract provided.

Towards Erasing The Distinction Between The Computational And Syntactic Accounts Of Scientific Theories, Timothy Luft

Theses

One of the main goals of philosophy of science is to give a proper account of scientific theories and their structure. One way that accounts of the structure of scientific theories can be distinguished is by the mathematical or logical structures that they involve. For instance, syntactic accounts of scientific theories hold that theories are axioms in a logical framework, whereas semantic accounts are more liberal in the range of mathematical and logical structures they take as pertinent to the structure of scientific theories. Paul Thagard (1988) offers a computational account of scientific theories, which holds that theories are complex …

“What Line Can’T Be Measured With A Ruler?” Riddles And Concept-Formation In Mathematics And Aesthetics, William H. Brenner, Samuel J. Wheeler

Philosophy Faculty Publications

We analyze two problems in mathematics – the first (stated in our title) is extracted from Wittgenstein’s “Philosophy for Mathematicians”; the second (“What set of numbers is non-denumerable?”) is taken from Cantor. We then consider, by way of comparison, a problem in musical aesthetics concerning a Brahms variation on a theme by Haydn. Our aim is twofold: first, to bring out and elucidate the essentially riddle-like character of these problems; second, to show that the comparison with riddles does not reduce their solution to an exercise in bare subjectivity

Deontic Meta-Rules, Francesco Olivieri, Guido Governatori, Matteo Cristani, Antonino Rotolo, Abdul Sattar

Centre for Computational Law (2022-2025)

The use of meta-rules in logic, i.e., rules whose content includes other rules, has recently gained attention in the setting of non-monotonic reasoning: a first logical formalisation and efficient algorithms to compute the (meta)-extensions of such theories were proposed in Olivieri et al. (2021, Computing defeasible meta-logic. In JELIA 2021, LNCS, vol. 12678, pp. 69-84. Springer.). This work extends such a logical framework by considering the deontic aspect. The resulting logic will not just be able to model policies but also tackle well-known aspects that occur in numerous legal systems. The use of Defeasible Logic to model meta-rules in the …

Spatial Relations Between Conscious And Unconscious Thought, John Shannon Hendrix

Architecture, Art, and Historic Preservation Faculty Publications

No abstract provided.

Alternative Ontology For Ante Rem Structuralism Based On Huayan Buddhist Metaphysics, Chul Soon Hwang

CMC Senior Theses

Ante rem structuralism is a version of mathematical structuralism presented by Shapiro (1997) that asserts the existence of mathematical objects. It stands out amongst other structuralist views in that it secures a face value semantics for mathematical statements. In this paper, I propose an alternative ontology where structures are fully explained by relations. I argue that this alternative ontology avoids arguments against ante rem structuralism’s endorsement of indiscernible entities while retaining the convenience of a face value semantics for mathematical expressions.

This ontology is based on mereological nihilism and the Huayan Buddhist argument that an object can be fully described …

Reflections On Williamson On Logic And Validity, Graham Priest

Publications and Research

Over many years now, Tim Williamson and I have engaged in debates over fundamental issues concerning logic. On some things, we have disagreed strongly; on others, we have agreed.