|Equivalence: Relation between sentences. It exists if both sides have the same truth value, so that they are both true or both false._____________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. |
Equivalence/Platonism/Nominalism/Field: Question: in what sense are Platonist (E.g. "Direction 1 = direction 2") and nominalistic statements (c1 is parallel to c2) equivalent?
Problem: if there are no directions, the second cannot be a consequence of the first. - They are only equivalent within a directional theory.
Solution/Field: one can regard the equivalences as important, even if the theories are wrong.
Problem: for the importance one should be able to accept truth.
Solution: conservative extension (does not apply to the ontology) - this is harmless for consequences that do not mention directions.
Definition cognitively equivalent/Field: equivalent by logic plus the meaning of true.
Disquotational true/Deflationism: means that the propositions in the Talski scheme should be cognitively equivalent. - ((s) Plus meaning of true here: the same understanding of true.
Extensional equivalence/Field: Problem: if we assume extensional equivalence and abstract it from the size, there are infinitely many entities to which a simple theory, such as the chemical valences applies: For example, the number 3 not only applies to molecules but also to larger aggregates etc.
Cognitive equivalent/deflationism/utterance/truth/(s)> Redundancy theory/Field: an utterance u and the assertion that u is true (as the speaker understands it) are cognitively equivalent.
N.B.: the assertion that an utterance is true, has an existential obligation (ontological obligation): there must be something that is true. While the utterance u itself does not provide an ontological obligation. Therefore, the two are not completely cognitively equivalent.
Relatively cognitively equivalent: here: u and the assertion of the truth of u are cognitively equivalent relative to the existence of u.
E.g. "Thatcher is so that she is self-identical and snow is white" is cognitively equivalent to "snow is white" relative to the existence of Thatcher - the verification conditions are the same.
N.B.: we do not need any truth conditions.
Material Equivalence/Field: means that A > B is equivalent to ~ A v B.
Problem: most authors do not believe the conclusion of e.g. "Clinton will not die in office" on "When Clinton dies in office, Danny de Vito becomes President". Therefore equivalence does not seem to exist.
Solution/Lewis: the truth conditions for indicative conditionals must be radically index-dependent to maintain the surface logic.
Lewis: thesis: the surface logic should not be respected.
Lewis: Thesis: E.g. Clinton/Vito: truth-maintaining despite absurdity. - Solution: probability function: P (Vito I Clinton).
In the case of the indicative conditional, the premise is always presupposed - Adams: intuitively, conclusions with conditionals are correct. - Problem: then they will say less about the world._____________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