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Ideas for 'works', 'Mere Possibilities' and 'The Concept of Logical Consequence'

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5 ideas

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

18812	Split out the logical vocabulary, make an assignment to the rest. It's logical if premises and conclusion match [Tarski, by Rumfitt]
	Full Idea: Tarski made a division of logical and non-logical vocabulary. He then defined a model as a non-logical assignment satisfying the corresponding sentential function. Then a conclusion follows logically if every model of the premises models the conclusion.
	From: report of Alfred Tarski (The Concept of Logical Consequence [1936]) by Ian Rumfitt - The Boundary Stones of Thought 3.2
	A reaction: [compressed] This is Tarski's account of logical consequence, which follows on from his account of truth. 'Logical validity' is then 'true in every model'. Rumfitt doubts whether Tarski has given the meaning of 'logical consequence'.

5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=

13344	X follows from sentences K iff every model of K also models X [Tarski]
	Full Idea: The sentence X follows logically from the sentences of the class K if and only if every model of the class K is also a model of the sentence X.
	From: Alfred Tarski (The Concept of Logical Consequence [1936], p.417)
	A reaction: [see Idea 13343 for his account of a 'model'] He is offering to define logical consequence in general, but this definition fits what we now call 'semantic consequence', written |=. This it is standard practice to read |= as 'models'.

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

16464	We regiment to get semantic structure, for evaluating arguments, and understanding complexities [Stalnaker]
	Full Idea: The point of regimentation is to give a perspicuous representation of the semantic structure of an expression, making it easier to evaluate the validity of arguments and to interpret complex statements.
	From: Robert C. Stalnaker (Mere Possibilities [2012], 4.2)
	A reaction: This is an authoritative summary from an expert of why all philosophers must take an interest in logical form.

5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / e. or

16465	In 'S was F or some other than S was F', the disjuncts need S, but the whole disjunction doesn't [Stalnaker]
	Full Idea: In 'either Socrates was a philosopher or someone other than Socrates was a philosopher', both propositions expressed by the disjuncts depend for their existence on the existence of Socrates, but the whole disjunction does not.
	From: Robert C. Stalnaker (Mere Possibilities [2012], 4.2)
	A reaction: Nice example, just the sort of thing we pay philosophers to come up with. He is claiming that propositions can exist in possible worlds in which the individuals mentioned do not exist.

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

13343	A 'model' is a sequence of objects which satisfies a complete set of sentential functions [Tarski]
	Full Idea: An arbitrary sequence of objects which satisfies every sentential function of the sentences L' will be called a 'model' or realization of the class L of sentences. There can also be a model of a single sentence is this way.
	From: Alfred Tarski (The Concept of Logical Consequence [1936], p.417)
	A reaction: [L' is L with the constants replaced by variables] Tarski is the originator of model theory, which is central to modern logic. The word 'realization' is a helpful indicator of what he has in mind. A model begins to look like a possible world.