Tarski/Field: According to him the following two sentences are a contradiction because he needs quantities for his definition of implication: a) "snow is white" does not imply logically "grass is green". - b) There are no mathematical entities (m.e.) like quantities. - ((s) Therefore, Field must be independent of Tarski.) Solution Field: Implication as a basic concept.
Tarski/Truth: unlike disquotational truth: only for a fragment. - Unrestricted quantifiers and semantic concepts must be excluded. Problem: we cannot create infinite conjunctions and disjunctions with that. - (Tarski-Truth is not suitable for generalization).
DeflationsimVsTarski/QuineVsTarski. - Otherwise, we must give up an explicit definition. - Deflationism: uses a generalized version of the truth-schema. - TarskiVsDeflationism: pro compositionality. (Also Davidson) - Tarski: needs recursion to characterize e.g."or".
Composition principle/Field: E.g. A sentence consisting of a one-digit predicate and a referencing name is true, iff the predicate is true of what the name denotes. - This goes beyond logical rules because it introduces reference and denotation. - Tarski: needs this for a satisfying Truth-concept. Deflationism: it is not important for it. - (> Compositionality).
Truth-Theory/Tarski: Thesis: we do not get an adequate Truth-theory if we take only all instances of the schema as axioms. - This does not give us the generalizations we need, e.g. that the modus ponens receives the truth.
Deflationism/Tarski/Field. Actually, Tarski's approach is also deflationistic.
Horwich I 477
FieldVsTarski/Soames: hides speech behavior. - Field: introduces primitive reference, and so on. -> language independence. - SoamesVsField: his physicalist must reduce every single one of the semantic concepts. - For example, he cannot characterize negation as a symbol by truth, because that would be circular. E.g. he cannot take negation as the basic concept, because then there would be no facts about speakers (no semantic facts about use) that explain the semantic properties. - FieldVsTarski: one would have to be able to replace the semantic terms by physical terms._____________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.
Realism, Mathematics and Modality Oxford New York 1989
Truth and the Absence of Fact Oxford New York 2001
Science without numbers Princeton New Jersey 1980
P. Horwich (Ed.)
Theories of Truth Aldershot 1994