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Ideas for 'Parmenides', 'Identity and Existence in Logic' and 'The Logical Syntax of Language'

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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.

5. Theory of Logic / G. Quantification / 5. Second-Order Quantification

18763	Basic variables in second-order logic are taken to range over subsets of the individuals [Anderson,CA]
	Full Idea: Under its now standard principal interpretation, the monadic predicate variables in second-order logic range over subsets of the domain on individuals.
	From: C. Anthony Anderson (Identity and Existence in Logic [2014], 1.5)
	A reaction: This is an interpretation in which properties are just sets of things, which is fine if you are a logician, but not if you want to talk about anything important. Still, we must play the game. Boolos introduced plural quantification at this point.

5. Theory of Logic / G. Quantification / 7. Unorthodox Quantification

18771	Stop calling ∃ the 'existential' quantifier, read it as 'there is...', and range over all entities [Anderson,CA]
	Full Idea: Ontological quantifiers might just as well range over all the entities needed for the semantics. ...The minimal way would be to just stop calling '∃' an 'existential quantifier', and always read it as 'there is...' rather than 'there exists...'.
	From: C. Anthony Anderson (Identity and Existence in Logic [2014], 2.6)
	A reaction: There is no right answer here, but it seems to be the strategy adopted by most logicians, and the majority of modern metaphysicians. They just allow abstracta, and even fictions, to 'exist', while not being fussy what it means. Big mistake!

5. Theory of Logic / L. Paradox / 3. Antinomies

13986	Plato found antinomies in ideas, Kant in space and time, and Bradley in relations [Plato, by Ryle]
	Full Idea: Plato (in 'Parmenides') shows that the theory that 'Eide' are substances, and Kant that space and time are substances, and Bradley that relations are substances, all lead to aninomies.
	From: report of Plato (Parmenides [c.364 BCE]) by Gilbert Ryle - Are there propositions? 'Objections'

14150	Plato's 'Parmenides' is perhaps the best collection of antinomies ever made [Russell on Plato]
	Full Idea: Plato's 'Parmenides' is perhaps the best collection of antinomies ever made.
	From: comment on Plato (Parmenides [c.364 BCE]) by Bertrand Russell - The Principles of Mathematics §337