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Single Idea 13342

[filed under theme 5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence ]

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.

Gist of Idea

Carnap defined consequence by contradiction, but this is unintuitive and changes with substitution

Source

comment on Rudolph Carnap (The Logical Syntax of Language [1934], p.88-) by Alfred Tarski - The Concept of Logical Consequence p.414

Book Ref

Tarski,Alfred: 'Logic, Semantics, Meta-mathematics' [Hackett 1956], 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.

The 28 ideas with the same theme [defining when one idea logically follows another]:

12373 Something holds universally when it is proved of an arbitrary and primitive case [Aristotle]
23173 If a syllogism admits one absurdity, others must follow [Aquinas]
13342 Carnap defined consequence by contradiction, but this is unintuitive and changes with substitution [Tarski on Carnap]
18812 Split out the logical vocabulary, make an assignment to the rest. It's logical if premises and conclusion match [Tarski, by Rumfitt]
13681 Logical consequence is marked by being preserved under all nonlogical substitutions [Quine, by Sider]
13827 Logical consequence isn't a black box (Tarski's approach); we should explain how arguments work [Prawitz]
14181 Validity is where either the situation or the interpretation blocks true premises and false conclusion [Etchemendy, by Read]
14180 Etchemendy says fix the situation and vary the interpretation, or fix interpretations with varying situations [Etchemendy, by Read]
10260 Logical consequence is defined by the impossibility of P and ¬q [Field,H, by Shapiro]
17286 Logical consequence is verification by a possible world within a truth-set [Fine,K]
10300 Logical consequence can be defined in terms of the logical terminology [Shapiro]
14188 Not all arguments are valid because of form; validity is just true premises and false conclusion being impossible [Read]
14182 If the logic of 'taller of' rests just on meaning, then logic may be the study of merely formal consequence [Read]
14183 Maybe arguments are only valid when suppressed premises are all stated - but why? [Read]
13679 Maybe logical consequence is more a matter of provability than of truth-preservation [Sider]
13682 Maybe logical consequence is impossibility of the premises being true and the consequent false [Sider]
13680 Maybe logical consequence is a primitive notion [Sider]
13678 The most popular account of logical consequence is the semantic or model-theoretic one [Sider]
10984 Logical consequence isn't just a matter of form; it depends on connections like round-square [Read]
10970 A theory of logical consequence is a conceptual analysis, and a set of validity techniques [Read]
15029 Modal accounts of logical consequence are simple necessity, or essential use of logical words [Sider]
18755 Validity is explained as truth in all models, because that relies on the logical terms [McGee]
11061 Intensional consequence is based on the content of the concepts [Hanna]
13288 Consequence is truth-preserving, either despite substitutions, or in all interpretations [Koslicki]
18813 Logical consequence is a relation that can extended into further statements [Rumfitt]
12195 Soundness in argument varies with context, and may be achieved very informally indeed [Rumfitt]
12199 There is a modal element in consequence, in assessing reasoning from suppositions [Rumfitt]
12201 We reject deductions by bad consequence, so logical consequence can't be deduction [Rumfitt]