The Epistemology of Natural Deduction

• Author / Creator

  Masoud, Seyed Hassan

• 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.

• Subjects / Keywords

  • Natural Deduction
  • Epistemic Rigor
  • Formal Rigor

• Graduation date

  Spring 2015

• Type of Item

  Thesis

• Degree

  Doctor of Philosophy

• DOI

  https://doi.org/10.7939/R3PC2TH7N

• License

  This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.