|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.|
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That "and" has become the word for the conjunction by contingent circumstances has no consequences on the status of the true statement that p is implied by p and q. What a set of sentences means depends on conventions. What follows from a set of premises does not depend on them (formal).
Logic/Nagel: logical judgments are based on our comprehension, but they are not a judgment about our ability of comprehension -
Das letzte Wort Stuttgart 1999
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Die Grenzen der Objektivität Stuttgart 1991