104 research outputs found
Computer Science and Metaphysics: A Cross-Fertilization
Computational philosophy is the use of mechanized computational techniques to
unearth philosophical insights that are either difficult or impossible to find
using traditional philosophical methods. Computational metaphysics is
computational philosophy with a focus on metaphysics. In this paper, we (a)
develop results in modal metaphysics whose discovery was computer assisted, and
(b) conclude that these results work not only to the obvious benefit of
philosophy but also, less obviously, to the benefit of computer science, since
the new computational techniques that led to these results may be more broadly
applicable within computer science. The paper includes a description of our
background methodology and how it evolved, and a discussion of our new results.Comment: 39 pages, 3 figure
Mechanizing Principia Logico-Metaphysica in Functional Type Theory
Principia Logico-Metaphysica contains a foundational logical theory for
metaphysics, mathematics, and the sciences. It includes a canonical development
of Abstract Object Theory [AOT], a metaphysical theory (inspired by ideas of
Ernst Mally, formalized by Zalta) that distinguishes between ordinary and
abstract objects.
This article reports on recent work in which AOT has been successfully
represented and partly automated in the proof assistant system Isabelle/HOL.
Initial experiments within this framework reveal a crucial but overlooked fact:
a deeply-rooted and known paradox is reintroduced in AOT when the logic of
complex terms is simply adjoined to AOT's specially-formulated comprehension
principle for relations. This result constitutes a new and important paradox,
given how much expressive and analytic power is contributed by having the two
kinds of complex terms in the system. Its discovery is the highlight of our
joint project and provides strong evidence for a new kind of scientific
practice in philosophy, namely, computational metaphysics.
Our results were made technically possible by a suitable adaptation of
Benzm\"uller's metalogical approach to universal reasoning by semantically
embedding theories in classical higher-order logic. This approach enables one
to reuse state-of-the-art higher-order proof assistants, such as Isabelle/HOL,
for mechanizing and experimentally exploring challenging logics and theories
such as AOT. Our results also provide a fresh perspective on the question of
whether relational type theory or functional type theory better serves as a
foundation for logic and metaphysics.Comment: 14 pages, 6 figures; preprint of article with same title to appear in
The Review of Symbolic Logi
Revisiting the ‘Wrong Kind of Object’ Problem
Any uniform semantic treatment of fictional names (e.g.,‘Frodo’) across parafictional statements (e.g., ‘In The Lord of the Rings, Frodo was born in the Shire’) and metafictional statements (e.g., ‘Frodo was invented by Tolkien’) runs into a variation of the ‘wrong kind of object’ problem. The problem arises when an analysis of one of these statements inappropriately attributes a property to an object. For example, it would be problematic if an analysis implied that flesh and blood individuals are invented by someone, and similarly problematic if an analysis implied that abstract objects are born in a certain region. Abstract object theory has provided a solution to this conundrum by distinguishing two modes of predication: encoding and exemplifying. Recently Klauk has argued that the problem reappears for the analysis of explicit parafictional statements in this theory. In this paper we formalize the objection and show that one can distinguish three issues in connection with the ‘wrong kind of object’ problem. We then address them in turn.
Diamonds are Forever
We defend the thesis that every necessarily true proposition is always true. Since not every proposition that is always true is necessarily true, our thesis is at odds with theories of modality and time, such as those of Kit Fine and David Kaplan, which posit a fundamental symmetry between modal and tense operators. According to such theories, just as it is a contingent matter what is true at a given time, it is likewise a temporary matter what is true at a given possible world; so a proposition that is now true at all worlds, and thus necessarily true, may yet at some past or future time be false in the actual world, and thus not always true. We reconstruct and criticize several lines of argument in favor of this picture, and then argue against the picture on the grounds that it is inconsistent with certain sorts of contingency in the structure of time
Mechanizing Principia Logico-Metaphysica in Functional Type Theory
Principia Logico-Metaphysica proposes a foundational logical theory for metaphysics, mathematics, and the sciences. It contains a canonical development of Abstract Object Theory [AOT], a metaphysical theory (inspired by ideas of Ernst Mally, formalized by Zalta) that differentiates between ordinary and abstract objects.
This article reports on recent work in which AOT has been successfully represented and partly automated in the proof assistant system Isabelle/HOL.v
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