P. Lorenzen – författare

Wer gegenwiirtig nach der Geschichte unseres wissenschaft­ lichen Denkens fragt, geriit bald in mancherlei Zwiespalt. Ja, ungekliirt Zwiespiiltiges mag ihn schon zum Fragen gedrangt haben. Der Triumph des Fortschritts der Naturwissenschaften ist noch tiberall zu vernehmen; untiberhorbar - zumal in Europa - dringt aber unheilvolles Klagen tiber die alles verschlingende Technik dazwischen. In eigenartiger Entsprechung hierzu hat das historische BewuBtsein unaufhaltsam von unserem Denken Besitz ergriffen. Kunst, Religion und Moral, alles ist historisch relativiert, die Geschichtsbetrachtung selbst nicht minder - dagegen steht aber noch eine vollig unhistorische Denkweise der Mathematiker und Naturwissenschaftler. Man schlage etwa die Fachzeitschriften dieser exakten Wissenschaften auf: Was vor 30 Jahren revolutio­ nar war, heiBt heute "klassisch", es interessieren nur Fragestellun­ gen, die nach solchen "klassischen" Ergebnissen aufgeworfen werden. DaB die exakte Naturwissenschaft mindestens 2500 Jahre alt ist (Geometriel), ist aus dem BewuBtsein verdrangt. Es muBte schon ein Zufall sein, wenn man einmal einen Hinweis darauf findet, daB die Physik wenigstens 300 Jahre alt ist. Man wende nicht ein, daB in jedem Physiklehrbuch der Name "NEWTON" vorkommt, sogar das "Archimedische" Prinzip. Von dem Geiste ARCHIMEDES' oder NEWTONS steckt in den modernen Buchern kaum etwas darin: sie werden aufgefaBt als Physiker im heutigen Sinne, als ob sie dasselbe gewollt hatten wie wir heute - nur wuBten sie noch nicht so viel, und deshalb haben solche Entdeckungen "von fruher" als historische Merkwurdigkeiten ihren Platz in Physikbuchern.

"Logic", one of the central words in Western intellectual history, compre­ hends in its meaning such diverse things as the Aristotelian syllogistic, the scholastic art of disputation, the transcendental logic of the Kantian critique, the dialectical logic of Hegel, and the mathematical logic of the Principia Mathematica of Whitehead and Russell. The term "Formal Logic", following Kant is generally used to distinguish formal logical reasonings, precisely as formal, from the remaining universal truths based on reason. (Cf. SCHOLZ, 1931). A text-book example of a formal-logical inference which from "Some men are philosophers" and "All philosophers are wise" concludes that "Some men are wise" is called formal, because the validity of this inference depends only on the form ofthe given sentences -in particular it does not depend on the truth or falsity of these sentences. (On the dependence of logic on natural language, English, for example, compare Section 1 and 8). The form of a sentence like "Some men are philosophers", is that which remains preserved when the given predicates, here "men" and "philosophers" are replaced by arbitrary ones. The form itself can thus be represented by replacing the given predicates by variables. Variables are signs devoid of meaning, which may serve merely to indicate the place where meaningful constants (here the predicates) are to be inserted. As variables we shall use - as did Aristotle - letters, say P, Q and R, as variables for predicates.

"Logic", one of the central words in Western intellectual history, compre­ hends in its meaning such diverse things as the Aristotelian syllogistic, the scholastic art of disputation, the transcendental logic of the Kantian critique, the dialectical logic of Hegel, and the mathematical logic of the Principia Mathematica of Whitehead and Russell. The term "Formal Logic", following Kant is generally used to distinguish formal logical reasonings, precisely as formal, from the remaining universal truths based on reason. (Cf. SCHOLZ, 1931). A text-book example of a formal-logical inference which from "Some men are philosophers" and "All philosophers are wise" concludes that "Some men are wise" is called formal, because the validity of this inference depends only on the form ofthe given sentences -in particular it does not depend on the truth or falsity of these sentences. (On the dependence of logic on natural language, English, for example, compare Section 1 and 8). The form of a sentence like "Some men are philosophers", is that which remains preserved when the given predicates, here "men" and "philosophers" are replaced by arbitrary ones. The form itself can thus be represented by replacing the given predicates by variables. Variables are signs devoid of meaning, which may serve merely to indicate the place where meaningful constants (here the predicates) are to be inserted. As variables we shall use - as did Aristotle - letters, say P, Q and R, as variables for predicates.