“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.”

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

Adopted from Wikiquote. Last update Jan. 30, 2022. History

Help us to complete the source, original and additional information

Do you have more details about the quote "For reasons mentioned at the beginning of this section, we cannot offer here a precise structural definition of semanti…" by Alfred Tarski?

Alfred Tarski6

Polish-American logician 1901–1983

Rudolf Carnap (1891–1970) German philosopher

Source: Carnap’s intellectual biography (1963), p. 62

“In an isolated system, which cannot exchange energy and matter with the surroundings, this tendency is expressed in terms of a function of the macroscopic state of the system: the entropy.”

Ilya Prigogine (1917–2003) physical chemist

Part 2; Cited in: Evgenii Rudnyi (2013).
Thermodynamics of Evolution (1972)

“Those skilled in mathematical analysis know that its object is not simply to calculate numbers, but that it is also employed to find the relations between magnitudes which cannot be expressed in numbers and between functions whose law is not capable of algebraic expression.”

Antoine Augustin Cournot Researches into the Mathematical Principles of the Theory of Wealth

Source: Researches into the Mathematical Principles of the Theory of Wealth, 1897, p. 3 ; Cited in: Robert Edouard Moritz. Memorabilia mathematica; or, The philomath's quotation-book https://archive.org/stream/memorabiliamathe00moriiala#page/198/mode/2up, (1914) p. 33: About the nature of mathematics

“I could give here several other ways of tracing and conceiving a series of curved lines, each curve more complex than any preceding one, but I think the best way to group together all such curves and them classify them in order, is by recognizing the fact that all points of those curves which we may call "geometric," that is, those which admit of precise and exact measurement, must bear a definite relation to all points of a straight line, and that this relation must be expressed by a single equation. If this equation contains no term of higher degree than the rectangle of two unknown quantities, or the square of one, the curve belongs to the first and simplest class, which contains only the circle, the parabola, the hyperbola, and the ellipse; but when the equation contains one or more terms of the third or fourth degree in one or both of the two unknown quantities (for it requires two unknown quantities to express the relation between two points) the curve belongs to the second class; and if the equation contains a term of the fifth or sixth degree in either or both of the unknown quantities the curve belongs to the third class, and so on indefinitely.”

René Descartes book La Géométrie

Second Book
La Géométrie (1637)

“Beauty is power and elegance, right action, form fitting function, intelligence, and reasonability. And very often expressed in curves.”

Kim Stanley Robinson Mars trilogy

Source: Red Mars

“I must avert here once again to my view of the opposition that exists between individuality and personality, notwithstanding the fact that the one demands the other. Individuality is, if I may so express it, the container or thing which contains, personality the content or thing contained, or I might say that my personality is in a certain sense my comprehension, that which I comprehend or embrace within myself — which is in a certain way the whole Universe — and that my individuality is my extension; the one my infinite, the other my finite.”

Miguel de Unamuno (1864–1936) 19th-20th century Spanish writer and philosopher

The Tragic Sense of Life (1913), VIII : From God to God

“[...] engine is the material expression of any indefinite function of any degree of generality and complexity.”

Ada Lovelace (1815–1852) English mathematician, considered the first computer programmer

As quoted by Rosen, Kenneth H. (2013). Discrete Mathematics and Its Applications, McGraw-Hill, ISBN 9780071315012. p.29.

“Simple-minded beyond the experience of Wall Street or State Street, he resorted, like most men of the same intellectual calibre, to commonplaces when at a loss for expression: "Let us have peace!" or, "The best way to treat a bad law is to execute it"; or a score of such reversible sentences generally to be gauged by their sententiousness.”

Henry Adams (1838–1918) journalist, historian, academic, novelist

The Education of Henry Adams (1907)

“According to Husserl, that 'act of meaning', or the use of a given phrase as an expression of a certain language, consists in the fact that a sensory content appears in consciousness, by means of which one might think visually about that phrase, should that content be joined by an appropriate intention directed to that phrase. But when a given phrase is used as an expression belonging to a certain language, then that sensory content is joined by another intention, not necessarily a representative one, which is however in principle directed to something other than that phrase itself. Together with the sensory content in question, that intention makes up a uniform experience, but neither the experiencing of that sensory content, nor that intention is a complete, independent experience. Both the one and the other are non-independent parts of the experience as a whole. The meaning of a given expression (as a type) would be, according to Husserl, the type under which that intention joined to the sensory content must fall if the given phrase is to be used as an expression belonging precisely to that language”

Kazimierz Ajdukiewicz (1890–1963) Philosopher, logician

Kazimierz Ajdukiewicz, On the Meaning of Expressions, Lwow 1931. (original title: O znaczeniii wyrazen.) p. 19-20; as cited in: Schaff (1962;299)

“The expression that there is nothing to express, nothing with which to express, nothing from which to express, no power to express, no desire to express, together with the obligation to express.”

Samuel Beckett book Three Dialogues

Also quoted in "Conversations with Samuel Beckett and Bram van Velde by Charles Juliet" by Nicholas Lezard, in The Guardian (23 January 2010) http://www.theguardian.com/books/2010/jan/23/conversations-samuel-beckett-van-velde <br class="br">Three Dialogues (1949)

Help us to complete the source, original and additional information

Alfred Tarski6

Related quotes

Related topics