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Articles 1 - 6 of 6
Full-Text Articles in Logic and Foundations of Mathematics
A Groundwork For A Logic Of Objects, David Winters
A Groundwork For A Logic Of Objects, David Winters
Electronic Thesis and Dissertation Repository
The history of philosophy is rich with theories about objects; theories of object kinds, their nature, the status of their existence, etc. In recent years philosophical logicians have attempted to formalize some of these theories, yielding many fruitful results. My thesis intends to add to this tradition in philosophical logic by developing a second-order logical system that may serve as a groundwork for a multitude of theories of objects (e.g. concrete and abstract objects, impossible objects, fictional objects, and others). Through the addition of what we may call sortal quantifiers (i.e. quantifiers that bind individual variables ranging over objects of …
Computing, Modelling, And Scientific Practice: Foundational Analyses And Limitations, Filippos A. Papagiannopoulos
Computing, Modelling, And Scientific Practice: Foundational Analyses And Limitations, Filippos A. Papagiannopoulos
Electronic Thesis and Dissertation Repository
This dissertation examines aspects of the interplay between computing and scientific practice. The appropriate foundational framework for such an endeavour is rather real computability than the classical computability theory. This is so because physical sciences, engineering, and applied mathematics mostly employ functions defined in continuous domains. But, contrary to the case of computation over natural numbers, there is no universally accepted framework for real computation; rather, there are two incompatible approaches --computable analysis and BSS model--, both claiming to formalise algorithmic computation and to offer foundations for scientific computing.
The dissertation consists of three parts. In the first part, we …
The Methodological Roles Of Tolerance And Conventionalism In The Philosophy Of Mathematics: Reconsidering Carnap's Logic Of Science, Emerson P. Doyle
The Methodological Roles Of Tolerance And Conventionalism In The Philosophy Of Mathematics: Reconsidering Carnap's Logic Of Science, Emerson P. Doyle
Electronic Thesis and Dissertation Repository
This dissertation makes two primary contributions. The first three chapters develop an interpretation of Carnap's Meta-Philosophical Program which places stress upon his methodological analysis of the sciences over and above the Principle of Tolerance. Most importantly, I suggest, is that Carnap sees philosophy as contiguous with science—as a part of the scientific enterprise—so utilizing the very same methods and subject to the same limitations. I argue that the methodological reforms he suggests for philosophy amount to philosophy as the explication of the concepts of science (including mathematics) through the construction and use of suitably robust meta-logical languages. My primary …
Structures In Real Theory Application: A Study In Feasible Epistemology, Robert H. C. Moir
Structures In Real Theory Application: A Study In Feasible Epistemology, Robert H. C. Moir
Electronic Thesis and Dissertation Repository
This thesis considers the following problem: What methods should the epistemology of science use to gain insight into the structure and behaviour of scientific knowledge and method in actual scientific practice? After arguing that the elucidation of epistemological and methodological phenomena in science requires a method that is rooted in formal methods, I consider two alternative methods for epistemology of science. One approach is the classical approaches of the syntactic and semantic views of theories. I show that typical approaches of this sort are inadequate and inaccurate in their representation of scientific knowledge by showing how they fail to account …
The Reasonable Effectiveness Of Mathematics In The Natural Sciences, Nicolas Fillion
The Reasonable Effectiveness Of Mathematics In The Natural Sciences, Nicolas Fillion
Electronic Thesis and Dissertation Repository
One of the most unsettling problems in the history of philosophy examines how mathematics can be used to adequately represent the world. An influential thesis, stated by Eugene Wigner in his paper entitled "The Unreasonable Effectiveness of Mathematics in the Natural Sciences," claims that "the miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve." Contrary to this view, this thesis delineates and implements a strategy to show that the applicability of mathematics is very reasonable indeed.
I distinguish three forms of the …
Anti-Foundational Categorical Structuralism, Darren Mcdonald
Anti-Foundational Categorical Structuralism, Darren Mcdonald
Electronic Thesis and Dissertation Repository
The aim of this dissertation is to outline and defend the view here dubbed “anti-foundational categorical structuralism” (henceforth AFCS). The program put forth is intended to provide an answer the question “what is mathematics?”. The answer here on offer adopts the structuralist view of mathematics, in that mathematics is taken to be “the science of structure” expressed in the language of category theory, which is argued to accurately capture the notion of a “structural property”. In characterizing mathematical theorems as both conditional and schematic in form, the program is forced to give up claims to securing the truth of its …