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Single Idea 9002

[filed under theme 5. Theory of Logic / A. Overview of Logic / 6. Classical Logic ]

Full Idea

Elementary logic, as commonly systematized nowadays, comprises truth-function theory (involving 'or', 'and', 'not' etc.), quantifiers (and their variables), and identity theory ('='). In addition, set theory requires classes among values of variables.

Gist of Idea

Elementary logic requires truth-functions, quantifiers (and variables), identity, and also sets of variables

Source

Willard Quine (Carnap and Logical Truth [1954], II)

Book Ref

Quine,Willard: 'Ways of Paradox and other essays' [Harvard 1976], p.110

A Reaction

Quine is famous for trying to squeeze properties out of the picture, which would then block higher-order logics (which quantify over properties). Quine's list gives a nice programme for a student of the philosophy of logic to understand.

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]