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Single Idea 13681
[filed under theme 5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
]
Full Idea
Quine's view of logical consequence is that it is when there is no way of uniformly substituting nonlogical expressions in the premises and consequences so that the premises all remain true but the consequence now becomes false.
Gist of Idea
Logical consequence is marked by being preserved under all nonlogical substitutions
Source
report of Willard Quine (Carnap and Logical Truth [1954], p.103) by Theodore Sider - Logic for Philosophy 1.5
Book Ref
Sider,Theodore: 'Logic for Philosophy' [OUP 2010], p.9
A Reaction
One might just say that the consequence holds if you insert consistent variables for the nonlogical terms, which looks like Aristotle's view of the matter.
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]
|
14180
|
Etchemendy says fix the situation and vary the interpretation, or fix interpretations with varying situations
[Etchemendy, by Read]
|
14181
|
Validity is where either the situation or the interpretation blocks true premises and false conclusion
[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]
|
13680
|
Maybe logical consequence is a primitive notion
[Sider]
|
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]
|
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]
|