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Ideas for 'On the Philosophy of Logic', 'Introduction to Philosophical Papers I' and 'The Rise of Analytic Philosophy 1879-1930'

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5 ideas

5. Theory of Logic / A. Overview of Logic / 6. Classical Logic

8951	Classical logic is: excluded middle, non-contradiction, contradictions imply all, disjunctive syllogism [Fisher]
	Full Idea: For simplicity, we can say that 'classical logic' amounts to the truth of four sentences: 1) either p or not-p; 2) it is not the case that both p and not-p; 3) from p and not-p, infer q; 4) from p or q and not-p, infer q.
	From: Jennifer Fisher (On the Philosophy of Logic [2008], 12.I)
	A reaction: [She says there are many ways of specifying classical logic] Intuition suggests that 2 and 4 are rather hard to dispute, while 1 is ignoring some grey areas, and 3 is totally ridiculous. There is, of course, plenty of support for 3!

5. Theory of Logic / B. Logical Consequence / 3. Deductive Consequence |-

22279	Frege's sign |--- meant judgements, but the modern |- turnstile means inference, with intecedents [Potter]
	Full Idea: Natural deduction systems generally depend on conditional proof, but for Frege everything is asserted unconditionally. The modern turnstile |- is allowed to have antecedents, and hence to represent inference rather than Frege's judgement sign |---.
	From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 03 'Axioms')
	A reaction: [compressed] Shockingly, Frege's approach seems more psychological than the modern approach. I would say that the whole point of logic is that it has to be conditional, because the truth of the antecedents is irrelevant.

5. Theory of Logic / C. Ontology of Logic / 2. Platonism in Logic

8950	Logic formalizes how we should reason, but it shouldn't determine whether we are realists [Fisher]
	Full Idea: Even if one is inclined to be a realist about everything, it is hard to see why our logic should be the determiner. Logic is supposed to formalize how we ought to reason, but whether or not we should be realists is a matter of philosophy, not logic.
	From: Jennifer Fisher (On the Philosophy of Logic [2008], 09.I)
	A reaction: Nice to hear a logician saying this. I do not see why talk in terms of an object is a commitment to its existence. We can discuss the philosopher's stone, or Arthur's sword, or the Loch Ness monster, or gravitinos, with degrees of commitment.

5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism

22291	Deductivism can't explain how the world supports unconditional conclusions [Potter]
	Full Idea: Deductivism is a good account of large parts of mathematics, but stumbles where mathematics is directly applicable to the world. It fails to explain how we detach the antecedent so as to arrive at unconditional conclusions.
	From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 12 'Deduc')
	A reaction: I suppose the reply would be that we have designed deductive structures which fit our understanding of reality - so it is all deductive, but selected pragmatically.

5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth

22295	Modern logical truths are true under all interpretations of the non-logical words [Potter]
	Full Idea: In the modern definition, a 'logical truth' is true under every interpretation of the non-logical words it contains.
	From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 19 'Frege's')
	A reaction: What if the non-logical words are nonsense, or are used inconsistently ('good'), or ambiguously ('bank'), or vaguely ('bald'), or with unsure reference ('the greatest philosopher' becomes 'Bentham')? What qualifies as an 'interpretation'?