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The Epistemology of Natural Deduction Open Access


Other title
Formal Rigor
Natural Deduction
Epistemic Rigor
Type of item
Degree grantor
University of Alberta
Author or creator
Masoud, Seyed Hassan
Supervisor and department
Bernard Linsky (Philosophy)
Examining committee member and department
Richard Zach (Philosophy, U of Calgary)
Allen Hazen (Philosophy)
Jeffry Pelletier (Philosophy)
Bruce Hunter (Philosophy)
Michael Dawson (Psychology)
Department of Philosophy

Date accepted
Graduation date
Doctor of Philosophy
Degree level
Natural deduction and the axiom method, as two derivation methods of formal deductive logic, are extensionally equivalent in the sense that they prove the same theorems and they derive the same premise-conclusion arguments: one has a derivation of a given conclusion from a given premise set if and only if the other does. They differ significantly, however, from an epistemo-logical point of view. Being based on the notion of hypothetical reasoning, providing the most logically detailed steps within a derivation, and being tied closely to the conception of logic as attempting to model mathematical reasoning are some features that give natural deduction systems an epistemic flavor the axiom-based systems, to a large extent, lack. This work investigates these features through a comparison of the two sorts of deduction systems. Analyzing the historical background of the advent and flourishing of the two methods, looking at the real examples of mathematical reasoning, and taking into account the way a rational agent carries out a logical derivation, give historical, experiential, and phenomenological dimensions to the work. All these features turn around the epistemic insight that deductive reasoning is a way of coming to know whether and how a given conclusion logically follows from a given set of premises. The general results include finding the main characteristic feature of natural deduction as having a method of making a hypothesis and deriving some conclusions from it in combination with previous premises if any. Also the notion of epistemic rigor is defined which proves to be useful in investigating the significant advantages of natural deduction. Epistemic rigor can be measured by looking at the simplicity and purity of the rules of inference. Another distinctive feature of natural deduction is the two-dimensionality of its derivations which is due to the fact that the formulas that occur within the scope of an assumption are not at the same level as other formulas outside the scope of that assumption. Furthermore, it is shown that, to a large extent, the best way of formalizing mathematical proofs is using natural deduction. The whole work is done within the framework of an epistemic approach to logic which characterizes logic as the science of reasoning.
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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