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Single Idea 23173
[filed under theme 5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
]
Full Idea
In syllogistic arguments, granted one absurdity, others must follow too.
Gist of Idea
If a syllogism admits one absurdity, others must follow
Source
Thomas Aquinas (Summa Theologicae [1265], I-II Q19 6)
Book Ref
Aquinas,Thomas: 'On Law, Morality and Politics', ed/tr. Baumgarth,W. /Regan R. [Hackett 1988], p.9
A Reaction
This asserts the necessity of logical consequence, which he derives from Aristotle.
The
28 ideas
with the same theme
[defining when one idea logically follows another]:
12373
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Something holds universally when it is proved of an arbitrary and primitive case
[Aristotle]
|
23173
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If a syllogism admits one absurdity, others must follow
[Aquinas]
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13342
|
Carnap defined consequence by contradiction, but this is unintuitive and changes with substitution
[Tarski on Carnap]
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18812
|
Split out the logical vocabulary, make an assignment to the rest. It's logical if premises and conclusion match
[Tarski, by Rumfitt]
|
13681
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Logical consequence is marked by being preserved under all nonlogical substitutions
[Quine, by Sider]
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13827
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Logical consequence isn't a black box (Tarski's approach); we should explain how arguments work
[Prawitz]
|
14181
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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]
|
13678
|
The most popular account of logical consequence is the semantic or model-theoretic one
[Sider]
|
13679
|
Maybe logical consequence is more a matter of provability than of truth-preservation
[Sider]
|
13680
|
Maybe logical consequence is a primitive notion
[Sider]
|
13682
|
Maybe logical consequence is impossibility of the premises being true and the consequent false
[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]
|
12201
|
We reject deductions by bad consequence, so logical consequence can't be deduction
[Rumfitt]
|
12199
|
There is a modal element in consequence, in assessing reasoning from suppositions
[Rumfitt]
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