Combining Texts

Ideas for 'The Rationality of Science', 'On the General Idea of Proof Theory' and 'Against the Professors (six books)'

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3 ideas

5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence

13827	Logical consequence isn't a black box (Tarski's approach); we should explain how arguments work [Prawitz]
	Full Idea: Defining logical consequence in the way Tarski does is a rather meagre result, treating an argument as a black box, observing input and output, while disregarding inner structure. We should define logical consequence on the basis of valid arguments.
	From: Dag Prawitz (On the General Idea of Proof Theory [1974], §2)

5. Theory of Logic / E. Structures of Logic / 1. Logical Form

6020	'Man is a rational mortal animal' is equivalent to 'if something is a man, that thing is a rational mortal animal' [Sext.Empiricus]
	Full Idea: Definitions are identical to universal propositions in meaning, and only differ in syntax, for whoever says 'Man is a rational mortal animal' says the same thing in meaning as whoever says 'If something is a man, that thing is a rational mortal animal'.
	From: Sextus Empiricus (Against the Professors (six books) [c.180], 11.8)
	A reaction: How strikingly like Bertrand Russell's interest and solutions. Sextus shows a straightforward interest in logical form, of a kind we associate with the twentieth century. Did Sextus Empiricus invent quantification?

5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models

13826	Model theory looks at valid sentences and consequence, but not how we know these things [Prawitz]
	Full Idea: In model theory, which has dominated the last decades, one concentrates on logically valid sentences, and what follows logically from what, but one disregards questions concerning how we know these things.
	From: Dag Prawitz (On the General Idea of Proof Theory [1974], §1)