Quotes about container
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Friedrich List photo
Ludwig Wittgenstein photo
Bertrand Russell photo
Alfred Tarski photo

“For reasons mentioned at the beginning of this section, we cannot offer here a precise structural definition of semantical category and will content ourselves with the following approximate formulation: two expressions belong to the same semantical category if (I) there is a sentential function which contains one of these expressions, and if (2) no sentential function which contains one of these expressions ceases to be a sentential function if this expression is replaced in it by the other. It follows from this that the relation of belonging to the same category is reflective, symmetrical and transitive. By applying the principle of abstraction, all the expressions of the language which are parts of sentential functions can be divided into mutually exclusive classes, for two expressions are put into one and the same class if and only if they belong to the same semantical category, and each of these classes is called a semantical category. Among the simplest examples of semantical categories it suffices to mention the category of the sentential functions, together with the categories which include respectively the names of individuals, of classes of individuals, of two-termed relations between individuals, and so on. Variables (or expressions with variables) which represent names of the given categories likewise belong to the same category.”

Alfred Tarski (1901–1983) Polish-American logician

Source: The Semantic Conception of Truth (1952), p. 45; as cited in: Schaff (1962) pp. 36-37.

Gottlob Frege photo
Rajneesh photo
Bertrand Russell photo

“If a "religion" is defined to be a system of ideas that contains unprovable statements, then Gödel taught us that mathematics is not only a religion, it is the only religion that can prove itself to be one.”

Bertrand Russell (1872–1970) logician, one of the first analytic philosophers and political activist

John D. Barrow, Between Inner and Outer Space: Essays on Science, Art and Philosophy (Oxford University Press, 2000, ISBN 0-192-88041-1, Part 4, ch. 13: Why is the Universe Mathematical? (p. 88). Also found in Barrow's "The Mathematical Universe" http://www.lasalle.edu/~didio/courses/hon462/hon462_assets/mathematical_universe.htm (1989) and The Artful Universe Expanded (Oxford University Press, 2005, ISBN 0-192-80569-X, ch. 5, Player Piano: Hearing by Numbers, p. 250
Misattributed

Romain Rolland photo
Socrates photo

“How grievously I was disappointed! …I found my philosopher altogether forsaking mind and any other principle of order, but having recourse to air, and ether, and water, and other eccentricities. I might compare him to a person that began by maintaining generally that mind is the cause of the actions of Socrates, but who, when endeavored to explain the causes of my several actions in detail, went on to show that I sit here because my body is made up of bones and muscles; and the bones he would say, are hard and have ligaments which divide them, and the muscles are elastic, and they cover the bones, which also have a covering or environment of flesh and skin which contains them; and as the bones are lifted at their joints by the contraction or relaxation of the muscles, I am able to bend my limbs, and this is why I an sitting here in a curved posture… and he would have a similar explanation of my talking to you, which he would attribute to sound, and air, and hearing, and he would assign ten thousand other causes of the same sort, forgetting to mention the true cause, which is that Athenians have thought fit to condemn me, and accordingly I have thought it better and more right to remain here and undergo my sentence; for I am inclined to think that these muscles and bones of mine would have gone off to Megara or Boeotia… if they had been guided only by their idea of what was best, and if I had not chosen as the better and nobler part… to undergo any punishment that the State inflicts.”

Socrates (-470–-399 BC) classical Greek Athenian philosopher

Plato, Phaedo