Archiv der Kategorie: Logik

Günther: Das generelle Problem der logischen Allgemeingültigkeit eines formalisierten Ausdrucks

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“Aus dem bisher Gesagten geht hervor, daß das generelle Problem der logischen Allgemeingültigkeit eines formalisierten Ausdrucks, d.h. also die Frage, unter welchen Bedingungen eine Formel im Hinblick auf jeden möglichen Individuenbereich den Character rein formaler Wahrheit besitzt, schon im engeren Prädikatenkalkül nicht endgültig lösbar ist.” (p. 364) #Günther #Allgemeingültigkeit #Wahrheit #Prädikatenkalkül

Günther, Gotthard, Die aristotelische Logik des Seins und die nicht-aristotelische Logik der Reflexion, in: Zeitschrift für philosophische Forschung 12 (1958), 360–407.

Günther: Zeno on Being and Time

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“Zeno’s paradox stemmed from the fact that Being stands for the class of all ortho-objects designated by a single value. Time, on the other hand, belongs to the first class of pseudo-objects which require designation by a duality of values. When Zeno confronted Being and Time, he effected, formally speaking, a confrontation between value-singularity and value-duality. It is obvious that no two-valued system can display all the features which Zeno’s problem implies. The introduction of a third value is the first step to bring Time within the range of logical analysis.” (p. 402) #Günther #Zeno #Being #Time

Günther, Gotthard, Time, Timeless Logic and Self-Referential Systems, in: Annals of the New York Academy of Sciences 138 (1967), 396–406.

Günther: The Kenogrammatic Theory of Logic

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“The kenogrammatic theory of logic offers such a locus; and thus Time is rendered noneliminable. But the introduction of a third value and a concomitant ontological locus gives us only a new ontology – not yet a logic to think about it in terms of designation and nondesignation. The theory of Time, therefore, requires a wider basis than three-place kenogrammatic structures provide.” (402sq.) #Günther #KenogrammaticTheoryOfLogic #time

Günther, Gotthard, Time, Timeless Logic and Self-Referential Systems, in: Annals of the New York Academy of Sciences 138 (1967), 396–406.

Günther: The Problem of Time

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“The problem whether Time can or cannot be eliminated reveals itself now as a spurious alternative. Behind it looms the larger issue of two-valued classic and many-valued transclassic logic. In Aristotelian logic, the progressive elimination of Time is, indeed, an inescapable postulate. It does not provide Time with an ontological locus of its own.” (p. 402) #Günther #time #logic

Günther, Gotthard, Time, Timeless Logic and Self-Referential Systems, in: Annals of the New York Academy of Sciences 138 (1967), 396–406.

Yourgrau: The Complete Set of Mathematical Truths

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„The complete set of mathematical truths will never be captured by any finite or recursive list of axioms that is fully formal. Thus, no mechanical device, no computer, will ever be able to exhaust the truths of mathematics. It follows immediately, as Gödel was quick to point out, that if we are able somehow to grasp the complete truth in this domain, then we, or our minds, are not machines or computers. (Enthusiasts of artificial intelligence were not amused.)“ (p. 3) #Yourgrau #Gödel #MathematicalTruth

Yourgrau, Palle, A World Without Time. The Forgotten Legacy of Gödel and Einstein. New York: Basic Books 2005.