Q

Quadrivium: (Lat. quatuor, and viae, four ways) The second, and more advanced group of liberal arts studies in the middle ages, arithmetic, geometry, astronomy and music. -- V.J.B.

See Trivium for the other three of the seven liberal arts, first proposed for education by Plato, Republic, III.

Quaestio: (Scholastic) A subdivision or chapter of some treatise. Later, the special form, imitating or actually reproducing a discussion, to which a thesis is proposed, then the arguments against it are listed, next the objections or argumenta contra are exposed, and the question is solved in the so-called corpus articuli, usually introduced by the standing phrase respondeo dicendum, finally the objections against the thesis and the response or solution are taken up one by one and answered. This is the quaestio disputata. The quaestio quodlibetalis stems from disputations in which all kind of problems were brought up and the leader had to arrange them somehow and to answer all of them. -- R.A.

Quakerism: The name given to that Christian group officially known at the Society of Friends founded by George Fox (1624-1691). Central principles include: guidance by an inner light, freedom from institutional or outward sanctions, the sanctity of silence, the simplicity of living; and, commitment to peaceful social relations. Three American groups are: orthodox, Hicksites (liberal) and Wilburites (formalists). -- V.F.

Quale: (Pl. qualia) (Lat from qualis, of what kind) A quality considered as an independent entity rather than as a quality of a thing. A quale is usually conceded as a universal essence (like redness, sweetness, etc.) but the term may also be applied to individual qualities (this red, this sweet taste). -- L.W.

Qualities, extensional: Qualities which characterize certain complex wholes composed of point-instants related to each other in virtue of their different positional qualities. (Broad ) -- H.H.

Qualities, immaterial: Instances of non-positional qualities that are not characterized by any determinable form of quality of spatial position. (Broad.) -- H.H.

Qualities, material: Instances of non-positiond qualities characterized by the determinable qualities of spatial position. (Broad.) -- H.H.

Qualities, non-positional: Qualities like color, temperature, etc. to which no spatial or temporal position can be assigned. (Broad.) -- H.H.

Qualities, positional: Temporal and spatial positions. (Broad .) -- H.H.

Qualities, structural: Positional and extensional qualities classed together. (Broad.) -- H.H.

Quality: The four traditional kinds of categorical propositions (see logic, formal, § 4) were distinguished according to quality as affirmative or negative, and according to quantity as particular, singular, or universal. See the articles Affirmative Proposition and Particular Proposition. -- A.C.

Quantifier: Universal quantifier is the name given to the notation (x) prefixed to a logical formula A (containing the free varible x) to express that A holds for all values of x -- usually, for all values of x within a certain range or domain of values, which either is implicit in the context, or is indicated by the notation through some convention. The same name is also given to variant or alternative notations employed for the same purpose. And of course the same name is given when the particular variable appearing is some other letter than x.

Similarly, existential quantifier is the name given to the notation (Ex) prefixed to a logical formula A (containing the free variable x) to express that A holds for some (i.e., at least one) value of x -- usually, for some value of x within a certain range or domain. The E which forms part of the notation is often inverted, and various alternative notitions also occur.

It may also be allowed to prefix the quantifiers (x) and (Ex) to a formula (sentence) A not containing x as a free variable, (x)A and (Ex)A then having each the same meaning as A.

See logic, formal, § 3. -- A. C.

W. V. Quine, Elementary Logic, Boston and New York, 1941.

Quantity: In Aristotle and Kant (q.v.), one of the categories (q.v.) of judgment. See Quality.

Quaternio terminorum: In the categorical syllogism (logic, formal, § 5), the major and minor premisses must have a term in common, the middle term. Violation of this rule is the fallacy of quaternio terminorum, or of four terms. It is most apt to arise through equivocation (q.v.), an ambiguous word or phrase playing the role of the middle term, with one meaning in the major premiss and another meaning in the minor premiss; and in this case the fallacy is called the fallacy of ambiguous middle. -- A.C.

Quantum: An indivisible unit, or atom, of any physical quantity. Quantum mechanics (q.v.) is based on the existence of quanta of energy, the magnitude of the quantum of radiant energy (light) of a given frequency -- or of the energy of a particle oscillating with given frequency -- being equal to Planck's constant (q.v.) multiplied by the fiequency. -- A.C.

Quantum mechanics: An important physical theory, a modification of classical mechanics, which has arisen from the study of atomic structure and phenomena of emission and absorption of light by matter, embracing the matrix mechanics of Heisenberg, the wave mechanics of Schrödinger, and the transformation theory of Jordan and Dirac. The wave mechanics introduces a duality between waves and particles, according to which an electron, or a photon (quantum of light), is to be considered in some of its aspects as a wave, in others as a particle. See further quantum and uncertainty principle. -- A.C.

F. A. Lindemann, The Physical Significance of the Quantum Theory, Oxford, 1932. J. Frenkel, Wave Mechanics, Elementary Theory, Oxford 1937. Louis de Broglie, Matter and Light, The New Physics, translated by W. H. Johnston, New York, 1939.

Quiddity: (Lat quidditas, whatness) Essence; that which is described in a definition. -- V.J.B.

Quieting: The pacification of mind is the initial point of departure as well as the endpoint of a vital series. (Avenarius.) -- H.H.

Quintessence: (Lat. quinta essentia, the fifth essence) the purest, most highly concentrated form of a nature or essence; originally, in Aristotelianism, the fifth element, found in celestial bodies, distinguished from the four earthly elements. -- V.J.B.

Quotation marks, syntactical use of: See Notations, logical.