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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.
| 13335 | Semantics is the concepts of connections of language to reality, such as denotation, definition and truth [Tarski] |
| 13336 | A language containing its own semantics is inconsistent - but we can use a second language [Tarski] |
| 13337 | A language: primitive terms, then definition rules, then sentences, then axioms, and finally inference rules [Tarski] |
| 13338 | '"It is snowing" is true if and only if it is snowing' is a partial definition of the concept of truth [Tarski] |
| 13339 | A sentence is satisfied when we can assert the sentence when the variables are assigned [Tarski] |
| 13340 | Satisfaction is the easiest semantical concept to define, and the others will reduce to it [Tarski] |
| 13341 | Using the definition of truth, we can prove theories consistent within sound logics [Tarski] |