Reactions: logic and the excluded middle
In mathematics one uses various kinds of argumentations. Some are well-known logical rules, such as the syllogism: all men are mortal, Socrates is a man, therefore Socrates is mortal. Others are not formalised in strict rules and rely on ‘good understanding’. Mathematicians usually agree on what they consider legitimate arguments in a mathematical proof. But is this sufficient? Does this mean that the argumentations mathematicians have employed for centuries are correct?
KeywordsClassical Logic Intuitionistic Logic Double Negation Classical Propositional Logic Incompleteness Theorem
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