Combining Texts

All the ideas for 'Good and Evil', 'The Logical Syntax of Language' and 'The Philosophy of Logic'

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6 ideas

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

13342	Carnap defined consequence by contradiction, but this is unintuitive and changes with substitution [Tarski on Carnap]
	Full Idea: Carnap proposed to define consequence as 'sentence X follows from the sentences K iff the sentences K and the negation of X are contradictory', but 1) this is intuitively impossible, and 2) consequence would be changed by substituting objects.
	From: comment on Rudolph Carnap (The Logical Syntax of Language [1934], p.88-) by Alfred Tarski - The Concept of Logical Consequence p.414
	A reaction: This seems to be the first step in the ongoing explicit discussion of the nature of logical consequence, which is now seen by many as the central concept of logic. Tarski brings his new tool of 'satisfaction' to bear.

5. Theory of Logic / C. Ontology of Logic / 4. Logic by Convention

13251	Each person is free to build their own logic, just by specifying a syntax [Carnap]
	Full Idea: In logic, there are no morals. Everyone is at liberty to build his own logic, i.e. his own form of language. All that is required is that he must state his methods clearly, and give syntactical rules instead of philosophical arguments.
	From: Rudolph Carnap (The Logical Syntax of Language [1934], §17), quoted by JC Beall / G Restall - Logical Pluralism 7.3
	A reaction: This is understandable, but strikes me as close to daft relativism. If I specify a silly logic, I presume its silliness will be obvious. By what criteria? I say the world dictates the true logic, but this is a minority view.

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity

18200	Very large sets should be studied in an 'if-then' spirit [Putnam]
	Full Idea: Sets of a very high type or very high cardinality (higher than the continuum, for example), should today be investigated in an 'if-then' spirit.
	From: Hilary Putnam (The Philosophy of Logic [1971], p.347), quoted by Penelope Maddy - Naturalism in Mathematics
	A reaction: Quine says the large sets should be regarded as 'uninterpreted'.

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics

18199	Indispensability strongly supports predicative sets, and somewhat supports impredicative sets [Putnam]
	Full Idea: We may say that indispensability is a pretty strong argument for the existence of at least predicative sets, and a pretty strong, but not as strong, argument for the existence of impredicative sets.
	From: Hilary Putnam (The Philosophy of Logic [1971], p.346), quoted by Penelope Maddy - Naturalism in Mathematics II.2

8857	We must quantify over numbers for science; but that commits us to their existence [Putnam]
	Full Idea: Quantification over mathematical entities is indispensable for science..., therefore we should accept such quantification; but this commits us to accepting the existence of the mathematical entities in question.
	From: Hilary Putnam (The Philosophy of Logic [1971], p.57), quoted by Stephen Yablo - Apriority and Existence
	A reaction: I'm not surprised that Hartry Field launched his Fictionalist view of mathematics in response to such a counterintuitive claim. I take it we use numbers to slice up reality the way we use latitude to slice up the globe. No commitment to lines!

22. Metaethics / C. The Good / 1. Goodness / a. Form of the Good

22489	'Good' is an attributive adjective like 'large', not predicative like 'red' [Geach, by Foot]
	Full Idea: Geach puts 'good' in the class of attributive adjectives, such as 'large' and 'small', contrasting such adjectives with 'predicative' adjectives such as 'red'.
	From: report of Peter Geach (Good and Evil [1956]) by Philippa Foot - Natural Goodness Intro
	A reaction: [In Analysis 17, and 'Theories of Ethics' ed Foot] Thus any object can simply be red, but something can only be large or small 'for a rat' or 'for a car'. Hence nothing is just good, but always a good so-and-so. This is Aristotelian, and Foot loves it.