Foundations of Deduction's Pedigree: A Non-Inferential Account
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Date
2010-01-05T20:52:01Z
Authors
Seitz, Jeremy
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Publisher
University of Waterloo
Abstract
In this thesis I discuss the problems associated with the epistemological task of arriving at basic logical knowledge. This is knowledge that the primitive rules of inference we use in deductive reasoning are correct. Knowledge of correctness, like all knowledge, is available to us either as the product of inference, or it is available non-inferentially. Success in the campaign to justify the correctness of these rules is mired by opposing views on how to do this properly. Inferential justifications of rules of inference, which are based on reasons, lead to regressive or circular results. Non-inferential justifications, based on something other than reasons, at first do not seem to fare any better: without a basis for these justifications, they appear arbitrary and unfounded.
The works of Boghossian and Dummett who argue for an inferentialist approach, and Hale who supports non-inferentialism are carefully examined in this thesis. I conclude by finding superiority in Hale's suggestion that a particular set of basic logical constants are indispensable to deductive reasoning. I suggest that we endorse a principle which states that rules are not premises, and are therefore to be excluded from expression as statements in a deductive argument. I argue that the quality of being indispensable is sufficient for a basic rule of deduction to be countenanced as default-justified, and therefore need not be expressed in argument. By a rule's evading expression in argument, it avoids circular reasoning in deductive arguments about its own correctness.
Another important outcome that emerges from my research is the finding that non-inferential knowledge is ontologically prior to the inferential sort. This is because plausible inferential knowledge of basic logical constants shall always be justified by circular reasoning that already assumes the correctness of the rule to be vindicated. This initial assumption is tantamount to non-inferential knowledge, and therefore this latter is more primitive-in fact the only primitive-species of basic logical knowledge.
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Keywords
Epistemology, Philosophy of Logic, Rules of Inference, Modus Ponens, Inferentialism, Non-inferentialism, Theories of Justification, Tortoise & Achilles, Michael Dummett, Bob Hale