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Single Idea 13545
[filed under theme 5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
]
Full Idea
In very general terms, we cannot express the distinction between what is finite and what is infinite without moving essentially beyond the resources available in elementary logic.
Gist of Idea
Elementary logic cannot distinguish clearly between the finite and the infinite
Source
David Bostock (Intermediate Logic [1997], 4.8)
Book Ref
Bostock,David: 'Intermediate Logic' [OUP 1997], p.184
A Reaction
This observation concludes a discussion of Compactness in logic.
The
27 ideas
with the same theme
[system of logic accepted as the modern norm]:
12376
|
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]
|