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Single Idea 12376
[filed under theme 5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
]
Full Idea
Demonstrations by reduction to the impossible assume that everything is asserted or denied.
Gist of Idea
Demonstrations by reductio assume excluded middle
Source
Aristotle (Posterior Analytics [c.327 BCE], 77a23)
Book Ref
Aristotle: 'Posterior Analytics (2nd ed)', ed/tr. Barnes,Jonathan [OUP 1993], p.17
A Reaction
This sounds like the lynchpin of classical logic.
The
27 ideas
with the same theme
[system of logic accepted as the modern norm]:
12376
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Demonstrations by reductio assume excluded middle
[Aristotle]
|
13337
|
A language: primitive terms, then definition rules, then sentences, then axioms, and finally inference rules
[Tarski]
|
9002
|
Elementary logic requires truth-functions, quantifiers (and variables), identity, and also sets of variables
[Quine]
|
9820
|
In classical logic, logical truths are valid formulas; in higher-order logics they are purely logical
[Dummett]
|
3098
|
Deductive logic is the only logic there is
[Harman]
|
13346
|
Truth is the basic notion in classical logic
[Bostock]
|
13545
|
Elementary logic cannot distinguish clearly between the finite and the infinite
[Bostock]
|
13822
|
Fictional characters wreck elementary logic, as they have contradictions and no excluded middle
[Bostock]
|
12430
|
Classical logic is our preconditions for assessing empirical evidence
[Kitcher]
|
12431
|
I believe classical logic because I was taught it and use it, but it could be undermined
[Kitcher]
|
9463
|
Classical logic is bivalent, has excluded middle, and only quantifies over existent objects
[Jacquette]
|
23548
|
Indeterminacy is in conflict with classical logic
[Fine,K]
|
15405
|
Classical logic neglects the non-mathematical, such as temporality or modality
[Burgess]
|
15421
|
Classical logic neglects counterfactuals, temporality and modality, because maths doesn't use them
[Burgess]
|
15427
|
The Cut Rule expresses the classical idea that entailment is transitive
[Burgess]
|
18784
|
In classical logic the connectives can be related elegantly, as in De Morgan's laws
[Mares]
|
18793
|
Material implication (and classical logic) considers nothing but truth values for implications
[Mares]
|
10972
|
The non-emptiness of the domain is characteristic of classical logic
[Read]
|
15020
|
Classical logic is good for mathematics and science, but less good for natural language
[Sider]
|
4705
|
Logical relativism appears if we allow more than one legitimate logical system
[O'Grady]
|
8951
|
Classical logic is: excluded middle, non-contradiction, contradictions imply all, disjunctive syllogism
[Fisher]
|
15326
|
Doubt is thrown on classical logic by the way it so easily produces the liar paradox
[Horsten]
|
16333
|
The underestimated costs of giving up classical logic are found in mathematical reasoning
[Halbach]
|
13849
|
Classical logic rests on truth and models, where constructivist logic rests on defence and refutation
[Engelbretsen/Sayward]
|
18804
|
The case for classical logic rests on its rules, much more than on the Principle of Bivalence
[Rumfitt]
|
18805
|
Classical logic rules cannot be proved, but various lines of attack can be repelled
[Rumfitt]
|
18827
|
If truth-tables specify the connectives, classical logic must rely on Bivalence
[Rumfitt]
|