more from this thinker     |     more from this text

Single Idea 13337

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

Full Idea

For a language, we must enumerate the primitive terms, and the rules of definition for new terms. Then we must distinguish the sentences, and separate out the axioms from amng them, and finally add rules of inference.

Gist of Idea

A language: primitive terms, then definition rules, then sentences, then axioms, and finally inference rules

Source

Alfred Tarski (The Establishment of Scientific Semantics [1936], p.402)

Book Ref

Tarski,Alfred: 'Logic, Semantics, Meta-mathematics' [Hackett 1956], p.402

A Reaction

[compressed] This lays down the standard modern procedure for defining a logical language. Once all of this is in place, we then add a semantics and we are in business. Natural deduction tries to do without the axioms.

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]