|Quine, Willard Van Orman
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|Proxy Function||VI 43
Proxy function/Quine: every explicit and reversibly unambiguous transformation f - E.g. if Px originally meant that x was a P, we therefore re-interpret Px so that it means that x is now f of a P -according for multi-digit predicates - the predicates then apply to the correlates fx instead to x - all sentences stay as they are - observation sentences remain correlated to the same stimuli - but the objects of the theory have changed dramatically - ((s) Example There is a Gödel number of x.)
Ontology/Loewenheim/Proxy function/Quine: the different ontologies resulting from both are unambiguously correlatable - and as a whole empirically indistinguishable. - E.g. Tabhita: only Geach’s cat or cosmos minus cat - distinction: relativistic: by the role that one plays relatively around the other - even link to trained stimuli remains intact - the nodes where we assume the objects are neutral.
Definition proxy function/Proxy function/Quine/Lauener: a function that assigns to each object of the original theory such a one from the new theory. - E.g. The Goedel number of - to reduce one theory to another. Proxy function/(s): maintains number of digits of the predicates (fulfillment of n-tuples of arguments by n-tuples of values). - Thus it averts the trivialization of a reduction to a theory of natural numbers (> Loewenheim).
Proxy function/PF/Reduction/Quine: must not be reversibly unambiguous. - E.g. irreversible proxy function which reduces a theory of expressions and fractions: Expressions by Goedel numbers, fractions with diagonal process. - Then the same number can stand for a fraction or an expression. - That’s ok, because fractures and expressions are so different that the question of identity does not arise, therefore, the original theory does not benefit from the differences. -> multi-sorted logic - if, in contrast, all elements of the initial theory are distinguishable. (E.g. pure arithmetic of rational or real numbers) you need a reversibly unambiguous proxy function.
Apparent class/Quine: given by open formula - E.g. proxy function can be construed as apparent class, if it is a function as an open formula with two free variables. - (> apparent quantification).
Wort und Gegenstand Stuttgart 1980
Theorien und Dinge Frankfurt 1985
Grundzüge der Logik Frankfurt 1978
Mengenlehre und ihre Logik Wiesbaden 1967
Die Wurzeln der Referenz Frankfurt 1989
Unterwegs zur Wahrheit Paderborn 1995
From a logical point of view Cambridge, Mass. 1953
Bezeichnung und Referenz
Zur Philosophie der idealen Sprache, J. Sinnreich (Hg), München 1982
Philosophie der Logik Bamberg 2005
Ontologische Relativität Frankfurt 2003