|Logic: logic is the doctrine of the admissibility or inadmissibility of relations between statements and thus the validity of the compositions of these statements. In particular, the question is whether conclusions can be obtained from certain presuppositions such as premises or antecedents. Logical formulas are not interpreted at first. Only the interpretation, i. e. the insertion of values, e.g. objects instead of the free variables, makes the question of their truth meaningful._____________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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Semantic anti-realism/evidence: in contrast to Putnam might be satisfied now with a "one-way": (EC, epistemic limitation):
(EC) If P is true, then there is evidence that it is so.
Evidence/WrightVsPutnam: truth is limited by evidence. This leads to a revision of the logic.
If there is no evidence, Putnam must actually allow by contraposition of EC that it is not the case that P is true, from which follows per negation equivalence that the negation of P must be regarded as true.
Semantic Anti-Realism: refuses to concede the unlimited validity of the principle of bivalence (true/false).
Semantic Anti-Realism/Wright: there is this scope for reconciliation: who represents EC, is obliged by the negation equivalence, to permit (A):
A If no evidence for P is present, then there is evidence for its negation. (s) VsAbsurd.
Wright: this is synonymous to an admission that there is evidence, in principle, both for the confirmation as well as for the rejection of P: But that conceals a suppressed premise:
B Either there is evidence for P or there is none.
A case of the excluded third.
Classic, is the conditional (A) an equivalent of the disjunction (C):
C Either there is evidence for P or there is evidence for its negation. ((s) Not at undecidability).
Problem: that it is precisely the case of the excluded third, that is not to be assertible (not assertible): It would not be sufficient to simply reject the principle of the bivalence (true/false). If (B) Either there is evidence for P or there is no unlimited assertible, the embarrassment will occur: the logic must be revised for all cases where evidence is not guaranteed.
Revision of Logic/Wright: may be required when the Liar or anything alike comes into play. Here one can assume a "weak" biconditional:
Definition biconditional, weak: A <> B is weakly valid if it is impossible that one of the two statements may be true, if the other is not, even if A, under certain circumstances has a different valuation from B or no truth value, while B has one.
Definition biconditional, strong: A <> B is highly valid if A and B always get necessarily the same valuation.
Then it also apllies for discourse areas in which the disquotation scheme and the equivalence scheme are called into doubt that both are still weakly valid.
Revision of Logic/Negation: within an apparatus with more than two truth values there can be no objection against the introduction of an operator "Neg", which is subject to the determination that Neg A is false if A is true, but is true in all other cases.
Then, if A <> B is weakly valid, that also aplies to Neg A <> Neg B. Then there is no obstacle against the derivation of the negation equivalence:
Neg (P) is true <> Neg ("P" is true).
WrightVs: however, this will not succeed. Not even as an assertion of weak validity when "assertible" is used for "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.
Wahrheit und Objektivität Frankfurt 2001
G. H. von Wright
Erklären und Verstehen Hamburg 2008