The Question Hume Didn't Ask: Why Should We Accept Deductive Inferences?

In Carlo Cellucci & Paolo Pecere (eds.), Demonstrative and Non-Demonstrative Reasoning in Mathematics and Natural Science, pp. 137-165. Edizioni dell'Università di Cassino (2006)
Abstract
Towards the middle of the eighteenth century Hume asked: Why should we accept non-deductive inferences? Strangely enough he didn’t ask the corresponding question: Why should we accept deductive inferences? This was not due to an oversight but rather to the belief, widespread even today, that there is a basic difference between deductive and non-deductive inferences: while non-deductive inferences cannot be justified, deductive inferences can be justified. Though widespread even today, such belief has been challenged by a number of people, from Sextus Empiricus to Lewis Carroll. However, although their arguments raise doubts about the possibility of justifying deductive inferences, many people still believe that, while non-deductive inferences cannot be justified, deductive inferences can be justified. The question of the justification of deductive inferences is all the more important as it is strictly connected with the question: What is a deductive inference? and a non-deductive inference? This paper provides a new answer to these questions.
Keywords Justification of Deduction  Justification of Induction  Non-Deductive Inferences
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    Carlo Cellucci (2008). The Nature of Mathematical Explanation. Studies in History and Philosophy of Science Part A 39 (2):202-210.
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