Q

Quality and Quantity

Philosophical categories reflecting important sides of objective reality. The world consists not of ready, finished things, but represents a sum total of processes in which things are constantly changing, coming into being, and undergoing destruction. But from this it does not follow that they do not have a definite form of existence, are absolutely unstable, and are indistinguishable among themselves (see Relativism). However much an object changes, for a time it remains a given qualitatively definite object, and not another. The qualitative definiteness of objects and phenomena is what makes them stable, what differentiates them, and makes the world boundlessly diverse.

Quality is the essential definiteness of an object by virtue of which it is the given object and not another, and differs from other objects. The quality of an object is not reduced to its separate properties. It is bound up with the object as a whole, embraces it completely, and is inseparable from it. That is why the concept of quality is associated with the being of an object. While remaining itself, an object cannot lose its quality. But each object is bound by thousands of threads with other objects, is in diverse relations with them, and represents the unity of the singular, the particular, and the universal. Besides qualitative definiteness, all objects also possess quantitative definiteness: a definite magnitude, number, volume, speed of its processes, degree of development of properties, etc.

Quantity is that definiteness of a thing owing to which it can be (really or mentally) divided into homogeneous parts or assembled from these parts. Homogeneity (similarity, identity) of parts or objects is a distinctive feature of quantity. The differences between dissimilar objects are qualitative, the differences between similar objects are quantitative. In contrast to quality, quantity is not associated so closely with the being of an object; quantitative changes do not at once lead to the destruction or essential change of an object. Only after reaching a definite limit for each object do quantitative changes cause qualitative changes. In this sense quantitative relations differ from qualitative relations by an outward relation to the nature of the objects. That is why in the process of knowledge (for example, in mathematics) they can be separated from their content as something indifferent. The exceptionally wide applicability of mathematical theories to spheres of natural science and technology differing in their concrete content is explained by the fact that mathematics studies quantitative relations.

Quality cannot be reduced to quantity, as metaphysicians try to do. No object possesses only qualitative or only quantitative properties. Each object represents the unity of a definite quality and quantity (see Measure). Disturbance of the measure leads to a change of the given object or phenomenon, to its conversion into another object or phenomenon (see Transition from Quantity to Quality).

Quantification of the Predicate

Establishment of the volume of the predicate of a proposition. In traditional formal logic, judgements are divided according to the volume of the subject; two kinds of judgements are distinguished: universal (for example, "all squares are rectangles") and particular (for example, "some students are sportsmen").

W. Hamilton proposed also to take into account the volume of the predicate, for example, besides two kinds of affirmative judgements in which the predicate is taken not in its full volume and which Hamilton calls universal-particular and particular-particular, two more kinds are singled out: universal-universal (for example, "all equilateral triangles are equiangular triangles") and particular-universal (for example, "some trees are oaks") in which the predicate is taken in its full volume. Such quantification of the predicate makes it possible to consider the judgement as an equation.

In mathematical logic, quantification of the predicate is understood to mean the linking of variable predicates by quantifiers and the transition from functional calculus of the first order to functional calculus of the second order.

Quantifiers

Operations in mathematical logic which link subject variables, variable propositions or variable predicates of various logical functions, thus forming expressions which are completely and definitely characterised by their truth-value or falsehood. There are universal quantifiers (symbol ∀) and existential quantifiers (symbol ∃). For example, given the propositional function "X possesses the property of N", then a universal quantifier ∀x constructs the proposition "every X possesses the property of N", while the existential quantifier ∃x constructs the proposition "there exists X possessing the property of N".

Quantity

See Quality and Quantity.

Quantum Mechanics

The department of physics that studies the motions of small-scale particles. The foundations of quantum mechanics were laid in 1924 by Louis de Broglie, who discovered the wave-corpuscular nature of physical quantities. As a consistent system quantum mechanics was developed by Schrödinger, Heisenberg, and others in 1925-27.

The basic features of quantum mechanics as a physical theory (wave-corpuscular dualism, the uncertainty principle, etc.) derive from the existence of the quantum of action. In conditions when the quantum of action can be neglected, quantum mechanics turns into classical mechanics (see Correspondence Principle). Unlike classical mechanics, the behaviour of an individual particle in quantum mechanics is governed by probability, statistical laws. Consequently, in quantum mechanics the concept of trajectory of motion and the classical notions of causality are meaningless.

The unusual properties of small-scale particles are reflected in the so-called wave function, which provides a quantum-mechanical characteristic of a particle's state. This function is derived from the quantum-mechanical "wave equation", which is the fundamental law of motion of elementary particles. For small velocities this is Schrödinger's equation. For high velocities the law of motion of very small particles is expressed by Dirac's equation, which takes into account the requirements of relativity theory.

Quantum mechanics has contributed to the understanding of an extremely broad range of phenomena in physics, chemistry, and even biology: atomic structure, radioactivity, the periodic system of elements, etc. Insofar as quantum mechanics deals with matter at a deeper level than classical physics, it has posed such philosophical problems as the relationship between subject and object, knowledge and physical reality, chance and necessity, determinism and indeterminism, physical "observability" and mathematical formalism, etc.

Different philosophical approaches to these problems are directly manifested in the different interpretations of the basic features of quantum mechanics, the wave function in the first place. The essence of the wave function cannot in principle be expressed in the language of classical physics, insofar as it ascribes to particles simultaneously wave and corpuscular properties, which are mutually exclusive in the classical sense. In treating of microcosmic particles one must approach them from the point of view of materialist dialectics, which provides a key to the understanding of dialectical contradiction and dialectical synthesis, and especially one must expand our notions of space and time, thereby going beyond the confines of quantum mechanics.

In a period when physics was unable to do this, the Copenhagen school of quantum mechanics gained prominence, declaring the wave function to be merely "a record of our knowledge concerning the state of microcosmic particles" (see Bohr, Copenhagen School, Complementarity Principle). Some idealistically reasoning scientists went so far as to reject the objective nature of the microcosm and causality in it, tending to overemphasise the role of the observer and the instrument. Actually, though, the wave function is a reflection of the objective properties of microcosmic particles and it is entirely wrong to draw subjectivist conclusions from the unconventional nature of these properties. It is hardly accidental that with the development of modern physics, with its discovery of the reciprocal interchangeability of elementary particles, their structure and their inseparable connection with vacuum, which thereby confirmed the objective nature of the "paradoxes" of quantum mechanics, many outstanding scientists, such as Heisenberg and Bohr, gradually moved away from positivist methods.

Quantum of Action

A universal constant equal to 6.55×10⁻²⁷ erg/sec, denoted by h. A fundamental quantity in quantum mechanics, it was discovered by Planck in 1900. The quantum of action can be regarded as the boundary between small-scale and large-scale phenomena. The domain in which it can be neglected and assumed to be zero is the macroscopic domain. As contrasted, in the domain of microscopic events the quantum of action cannot, as a matter of principle, be assumed to tend to zero.

The basic importance of the quantum of action is that it establishes the connection between dialectically contradictory and mutually exclusive properties of microscopic particles. This connection is expressed in equations of Louis de Broglie (see also Wave-Corpuscular Dualism, the Uncertainty Principle).

Quietism

A passive contemplative attitude to life, renunciation of vigorous activity, the name of a trend in Catholicism which arose in the 17th century. Quietism is a consequence of fatalism and it is inherent to a certain extent in all religions. Marxist ethics, rejecting fatalism, holds that although man depends on circumstances, circumstances also depend on him. It condemns indifference, lack of initiative, and non-resistance to evil and urges man to work actively to realise the lofty ideals of communism.