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| 13338 | '"It is snowing" is true if and only if it is snowing' is a partial definition of the concept of truth |
| Full Idea: Statements of the form '"it is snowing" is true if and only if it is snowing' and '"the world war will begin in 1963" is true if and only if the world war will being in 1963' can be regarded as partial definitions of the concept of truth. | |||
| From: Alfred Tarski (The Establishment of Scientific Semantics [1936], p.404) | |||
| A reaction: The key word here is 'partial'. Truth is defined, presumably, when every such translation from the object language has been articulated, which is presumably impossible, given the infinity of concatenated phrases possible in a sentence. |
| 13337 | A language: primitive terms, then definition rules, then sentences, then axioms, and finally inference rules |
| 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. | |||
| From: Alfred Tarski (The Establishment of Scientific Semantics [1936], 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 |
| Full Idea: Semantics is the totality of considerations concerning concepts which express connections between expressions of a language and objects and states of affairs referred to by these expressions. Examples are denotation, satisfaction, definition and truth. | |||
| From: Alfred Tarski (The Establishment of Scientific Semantics [1936], p.401) | |||
| A reaction: Interestingly, he notes that it 'is not commonly recognised' that truth is part of semantics. Nowadays truth seems to be the central concept in most semantics. |
| 13336 | A language containing its own semantics is inconsistent - but we can use a second language |
| Full Idea: People have not been aware that the language about which we speak need by no means coincide with the language in which we speak. ..But the language which contains its own semantics must inevitably be inconsistent. | |||
| From: Alfred Tarski (The Establishment of Scientific Semantics [1936], p.402) | |||
| A reaction: It seems that Tarski was driven to propose the metalanguage approach mainly by the Liar Paradox. |
| 13339 | A sentence is satisfied when we can assert the sentence when the variables are assigned |
| Full Idea: Here is a partial definition of the concept of satisfaction: John and Peter satisfy the sentential function 'X and Y are brothers' if and only if John and Peter are brothers. | |||
| From: Alfred Tarski (The Establishment of Scientific Semantics [1936], p.405) | |||
| A reaction: Satisfaction applies to open sentences and truth to closed sentences (with named objects). He uses the notion of total satisfaction to define truth. The example is a partial definition, not just an illustration. |
| 13340 | Satisfaction is the easiest semantical concept to define, and the others will reduce to it |
| Full Idea: It has been found useful in defining semantical concepts to deal first with the concept of satisfaction; both because the definition of this concept presents relatively few difficulties, and because the other semantical concepts are easily reduced to it. | |||
| From: Alfred Tarski (The Establishment of Scientific Semantics [1936], p.406) | |||
| A reaction: See Idea 13339 for his explanation of satisfaction. We just say that a open sentence is 'acceptable' or 'assertible' (or even 'true') when particular values are assigned to the variables. Then sentence is then 'satisfied'. |
| 13341 | Using the definition of truth, we can prove theories consistent within sound logics |
| Full Idea: Using the definition of truth we are in a position to carry out the proof of consistency for deductive theories in which only (materially) true sentences are (formally) provable. | |||
| From: Alfred Tarski (The Establishment of Scientific Semantics [1936], p.407) | |||
| A reaction: This is evidently what Tarski saw as the most important first fruit of his new semantic theory of truth. |