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5. Theory of Logic / A. Overview of Logic / 6. Classical Logic

[system of logic accepted as the modern norm]

26 ideas
Demonstrations by reductio assume excluded middle [Aristotle]
A language: primitive terms, then definition rules, then sentences, then axioms, and finally inference rules [Tarski]
Elementary logic requires truth-functions, quantifiers (and variables), identity, and also sets of variables [Quine]
In classical logic, logical truths are valid formulas; in higher-order logics they are purely logical [Dummett]
Deductive logic is the only logic there is [Harman]
Truth is the basic notion in classical logic [Bostock]
Elementary logic cannot distinguish clearly between the finite and the infinite [Bostock]
Fictional characters wreck elementary logic, as they have contradictions and no excluded middle [Bostock]
Classical logic is our preconditions for assessing empirical evidence [Kitcher]
I believe classical logic because I was taught it and use it, but it could be undermined [Kitcher]
Classical logic is bivalent, has excluded middle, and only quantifies over existent objects [Jacquette]
Classical logic neglects the non-mathematical, such as temporality or modality [Burgess]
Classical logic neglects counterfactuals, temporality and modality, because maths doesn't use them [Burgess]
The Cut Rule expresses the classical idea that entailment is transitive [Burgess]
In classical logic the connectives can be related elegantly, as in De Morgan's laws [Mares]
Material implication (and classical logic) considers nothing but truth values for implications [Mares]
The non-emptiness of the domain is characteristic of classical logic [Read]
Classical logic is good for mathematics and science, but less good for natural language [Sider]
Logical relativism appears if we allow more than one legitimate logical system [O'Grady]
Classical logic is: excluded middle, non-contradiction, contradictions imply all, disjunctive syllogism [Fisher]
Doubt is thrown on classical logic by the way it so easily produces the liar paradox [Horsten]
The underestimated costs of giving up classical logic are found in mathematical reasoning [Halbach]
Classical logic rests on truth and models, where constructivist logic rests on defence and refutation [Engelbretsen/Sayward]
The case for classical logic rests on its rules, much more than on the Principle of Bivalence [Rumfitt]
Classical logic rules cannot be proved, but various lines of attack can be repelled [Rumfitt]
If truth-tables specify the connectives, classical logic must rely on Bivalence [Rumfitt]