Philosophy Dictionary of ArgumentsHome
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| Operators, logic: operators are symbols for performing a function, e.g. and; or; if; then; etc._____________Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments. | |||
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J. Bigelow on Operators - Dictionary of Arguments
I 145 Operator/Bigelow/Pargetter: an operator is something that does not occur in the normal language (everyday language). >Everyday language. In contrast, it occurs in equations. >Equations. For example, the plus sign: Plus/Plus sign/+/Bigelow/Pargetter: if it stands between two number names (!), (e.g."3" and "5", it makes a new term out of it, namely "(3 + 5)" which in turn refers to a number. >Names, >Reference, >Numbers. That is, plus makes a new name from two old names. Everyday language: it is not absolutly necessary to add operators to it. You can also have their tasks done by predicates. For example, instead of + we can accept a predicate R. >Predicates. I 146 Operator/Predicate/Bigelow/Pargetter: in general: for an n-digit operator, there will be a (n+1)-digit predicate: O (x1,... xn) = x (n+1), instead we can say: Ro(x1,…xn, x(n+1)). I 145 Operator/Bigelow/Pargetter: For example, plus, plus sign,"+": is applied to number names and provides new number names. Operator: corresponds semantically to a relation. >Relations. Relation/Bigelow/Pargetter: is used differently in semantics: instead of using a relation to determine the semantic value of a sentence, we use it to obtain the referent of a compound referential term. >Semantics, >Semantic value. Relation/syntactic rule: Ro(x1,… x(n+1)). Is true iff (x1,... x (n+1) stand in the required relation. On the other hand, Operator/syntactic rule: O (x1,... xn) refers to x(n+1) iff x1,…x(n+1) stand in the required relation I 146 Operator: an n-digit operator could be replaced by a predicate for a relation for a (n+1)-digit relation - but there are different syntactic rules: statement about relation true/false. >Truth values. Statement with operator: refers to - With probability: e.g. P (p v q) = P(p) + P(q) - P(p u q) is the compound expression and not a name, but a sentence. >Sentences. This converts it into a referring statement (this in turn is a name). +Plus sign: two-names-one-name-operator - P: sentence-to-name-operator. Operator/Probability/Bigelow/Pargetter: here "P" is an operator that can be applied to composite terms (possibly with "+"). This compound term (example P(p v q) = P(p) + P(q) - P (p u q) is not a name,... I 147 ...but a sentence. Operator/probability: thus P converts a sentence into a referring expression. (This is again a name.) Probability/Possibility/Necessity/Modality/Bigelow/Pargetter: "necessary" and would be > would be can be reinterpreted as probability operators. >Probability, >Possibility, >Necessity, >Modalities. For example, "it is likely to grade n that...". Such operators make sentences out of sentences. For example, operator P: for each sentence p P(p) will refer to the number n, iff it is likely to grade n that p is true._____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. Translations: Dictionary of Arguments The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition. |
Big I J. Bigelow, R. Pargetter Science and Necessity Cambridge 1990 |
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Ed. Martin Schulz, access date 2024-04-18