|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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|Hoyningen-Huene II 148f
A: No one can read this book in three days. - B: A hard-working student can read this book in three days.
Whether there are hard-working students is something that cannot be captured with the statement logic. The inconsistency of the example can only be detected with the predicate logic. Other inconsistencies cannot be captured by the means of logic at all: A: Hans is a giant. - B: Hans is a dwarf.
Re III 62f
Difference compact/non-compact: classical logic is a logic of the 1st level. A categorical set of axioms for arithmetic must be a second-level logic. (Quantifiers also for properties).
Logic 1./2. level are not to be distinguished syntactically, but semantically!
E.g. Napoleon all properties: are not syntactically to be distinguished, whether logic 1st or 2nd level.
VsClassical Logic: This reduction, of course, fails. For "nothing is round and square" is necessarily true, but its non-logical components cannot be interpreted in any way that makes this statement false.
Allowing variable areas of definition for classical representation was a catastrophe. The modality has returned. We can make a substitution, but we cannot really change the range.
If an object is round, it follows that it is not square. But this conclusion is not valid thanks to the form, but thanks to the content.
It was a mistake to express the truth-preservation criterion as "it is impossible that the premisses are true and the conclusion false". Because it is not so obvious that there is a need to conclude from A to B. Provided he is cowardly, it follows that he is either cowardly or - what one wants. But simply from the fact that he is cowardly does not follow that if he is not cowardly - what one wants.
Re III 151
Logic 1st level: individuals, 2nd level variables for predicates, distribution of the predicates by quantifiers - 1st level allows restricted vocabulary of the 2nd level: existence and universal quantifier! f
Re III 161
Free logic: no existence assumptions - no conclusion from the absence of the truth value to falsehood - global evaluation.
Me I 26
Justification of Logic/Menne: the so-called logical principles of identity, of consistency, and the excluded middle are not sufficient to derive the logic. In addition, ten theorems and rules of the propositional logic are needed, just to derive the syllogistic exactly. These axioms do not represent obvious ontological principles - Kant: transcendental justification of logic. It must be valid a priori.
The justification from the language: oversees that there is no explicit logic at all if the language itself already contained logic. Precisely because language does not always proceed logically, the logic is needed for the standardization of language. - Menne: there must be a recursive procedure for justification._____________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.
Me I Albert Menne Folgerichtig Denken Darmstadt 1988
HH II Hoyningen-Huene Formale Logik, Stuttgart 1998
Re III Stephen Read Philosophie der Logik Hamburg 1997
Sal IV Wesley C. Salmon Logik Stuttgart 1983
Sai V R.M.Sainsbury Paradoxien Stuttgart 2001