Construct · 4 fields · 7 citations
One name. Different field. Different construct. One map.
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An assignment that gives every formula of a language one of the truth values, true or false, so that the value of a compound statement is fixed by the values of its parts. George Boole's 1854 An Investigation of the Laws of Thought first treated logical statements with the numbers 1 and 0 and computed the truth of combined statements by algebra. Alfred Tarski's 1935 Der Wahrheitsbegriff in den formalisierten Sprachen gave the modern account, in which a valuation fixes the truth of each sentence relative to an interpretation. The referent is a mapping from sentences to true or false, and it is not a measuring function on a field, a money figure put on an asset, or a person's act of prizing.[1][2]
A function on a field or ring that measures the size or divisibility of each element, arranged so that the value of a product is the sum of the values and the value of a sum is at least the smaller of the two. Josef Kürschák's 1913 Über Limesbildung und allgemeine Körpertheorie introduced the term, in German Bewertung, for a real-valued measure of magnitude on a field, and Wolfgang Krull's 1932 Allgemeine Bewertungstheorie generalised it to values in any ordered group, founding valuation theory. A familiar case is the p-adic valuation, which records how many times a prime divides a number. The referent is an algebraic measuring function, and it has nothing to do with truth values in logic, a price placed on an asset, or a philosopher's account of valuing.[3][4]
The estimate of what an asset is worth, formed by projecting the income it is expected to produce and discounting those future amounts back to a present figure. Irving Fisher's 1930 The Theory of Interest set out the discounting of expected future income as the way to value capital, and John Burr Williams's 1938 The Theory of Investment Value built the dividend-discount and discounted-cash-flow method still used to value a firm or a share. The referent is a monetary appraisal of an asset, expressed in currency, and it is unrelated to a truth assignment, a measuring function on a field, or the philosophical act of prizing.[5][6]
The activity of appraising and prizing, by which a person or group judges something to be good, desirable, or worth pursuing. John Dewey's 1939 Theory of Valuation argued that valuation is observable behaviour: the prizing of ends and the appraising of means against their actual consequences, rather than a report of a fixed inner feeling. The referent is a value judgment, or the process that forms it, studied in ethics and value theory, and it is distinct from a truth assignment in logic, a measuring function in algebra, or a money figure placed on an asset.[7]
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