Gesammelte Mathematische Werke, three volumes, Brunswick, 1930-1932.
This use of nominal definition (including contextual definition -- see the article Incomplete symbol) in connection with a logistic system is extraneous to the system in the sense that it may theoretically be dispensed with, and all formulas written in full. Practically, however, it may be necessary for the sake of brevity or perspicuity, or for facility in formal work.
Such methods of introducing new concepts, functions, etc. as definition by abstraction (q. v.), definition by recursion (q. v.), definition by composition (see Recursiveness) may be dealt with by reducing them to nominal definitions; i.e., by finding a nominal definition such that the definiens (and therefore also the definiendum) turns out, under an intended interpretation of the logistic system, to mean the concept, function, etc. which is to be introduced.
In addition to syntactical or nominal definition we may distinguish another kind of definition, which is applicable only in connection with interpreted logistic systems, and which we shall call semantical definition. This consists in introducing a new symbol or notation by assigning a meaning to it. In an interpreted logistic system, a nominal definition carries with it implicitly a semantical definition, in that it is intended to give to the definiendum the meaning expressed by the definiens; but two different nominal definitions may correspond to the same semantical definition. Consider, for example, the two following schemata of nominal definition in the propositional calculus (Logic, formal, § 1):
[A] ⊃ [B] → ∼A ∨ B.As nominal definitions these are inconsistent, since they represent [A] ⊃ [B] as standing for different formulas: either one, but not both, could be used in a development of the propositional calculus. But the corresponding semantical definitions would be identical if -- as would be possible -- our interpretation of the propositional calculus were such that the two definientia had the same meaning for any particular A and B.
[A] ⊃ [B] → ∼[A ∼B].
In the formal development of a logistic system, since no reference may be made to an intended interpretation, semantical definitions are precluded, and must be replaced by corresponding nominal definitions.
Of quite a different kind are so-called real definitions, which are not conventions for introducing new symbols or notations -- as syntactical and semantical definitions are -- but are propositions of equivalence (material, formal, etc.) between two abstract entities (propositions, concepts, etc.) of which one is called the definiendum and the other the definiens. Not all such propositions of equivalence, however, are real definitions, but only those in which the definiens embodies the "essential nature" (essentia, ουσια) of the definiendum. The notion of a real definition thus has all the vagueness of the quoted phrase, but the following may be given as an example. If all the notations appearing, including ⊃x, have their usual meanings (regarded as given in advance), the proposition expressed by
(F)(G)[[F(x) ⊃x G(x)] ≡ (x)[∼F(x) ∨ G(x)]]is a real definition of formal implication -- to be contrasted with the nominal definition of the ¦notation for formal implication which is given in the article Logic, formal, § 3. This formula, expressing a real definition of formal implication, might appear, e.g., as a primitive formula in a logistic system.
(A situation often arising in practice is that a word -- or symbol or notation -- which already has a vague meaning is to be given a new exact meaning, which is vaguely, or as nearly as possible, the same as the old. This is done by a nominal or semantical definition rather than a real definition; nevertheless it is usual in such a case to speak either of defining the word or of defining the associated notion.)
Sometimes, however, the distinction between nominal definitions and real definitions is made on the basis that the latter convey an assertion of existence, of the defimendum, or rather, where the definiendum is a concept, of things falling thereunder (Saccheri, 1697); or the distinction may be made on the basis that real definitions involve the possibility of what is defined (Leibniz, 1684). Ockham makes the distinction rather on the basis that real definitions state the whole nature of a thing and nominal definitions state the meaning of a word or phrase, but adds that non-existents (as chimaera) and such parts of speech as verbs, adverbs, and conjunctions may therefore have only nominal definition. -- A.C.
Nominal: Is discourse (language, speech, oratio) by which the meaning of a term is explained.
Positive: That which reveals the essence of a thing in positive terms, e.g., man is a rational animal.
Negative: That which states the nature of a thing in negative terms, e.g. God is not mortal, not corporeal, etc. Cf. La Logique de Port-Royal, Pt. I, ch. XII.
(a) By many writers the term covers the view that God has no immediate relation with the world, God indeed is responsible for the world but for reasons unknown or conjectured God has no commerce with it; accordingly, the supplications and hopes of men are illusory and fruitless. This doctrine is sometimes referred to as the "absentee landlord" view. Thomas Hardy's famous poem "God Forgotten" is an illustration. Deism, it is clear, is a form of theism,
(b) Deism is a term referring collectively and somewhat loosely to a group of religious thinkers of the 17th (and 18th) century in England and France who in attempting to justify religion, particularly Christianity, began by establishing the harmony of reason and revelation and developed what, in their time, was regarded as extreme views: assaults upon traditional supernaturalism, external revelation and dogmas implying mysteries, and concluding that revelation is superfluous, that reason is the touchstone to religious validity, that religion and ethics are natural phenomena, that the traditional God need hardly be appealed to since man finds in nature the necessary guides for moral and religious living. Not all deists, so called, went toward the more extreme expressions. Among the more important English deists were Toland, Collins, Tindal, Chubb and Morgan. Voltaire (1694-1778) influenced by English thought is the notable example of deism in France. On the whole the term represents a tendency rather than a school. -- V.F.
Through his paper On the syllogism, no. IV in the Transactions of the Cambridge Philosophical Society, vol. 10 (read April 23, 1860), De Morgan is to be regarded as the founder of the logic of relations. -- A. C.
Sophia Elizabeth De Morgan, Memoir of Augustus De Morgan. London, 1882.
∼[p ∨ q] ≡ [∼p ∼q],or the two corresponding dually related theorems of the algebra of classes,
∼[pq] ≡ [∼p v ∼q],
−(a ∪ b) = −a ∩ −b,In the propositional calculus these laws (together with the law of double negation) make it possible to define conjunction in terms of negation and (inclusive) disjunction, or, alternatively, disjunction in terms of negation and conjunction. Similarly in the algebra of classes logical product may be defined in terms of logical sum and complementation, or logical sum in terms of logical product and complementation.
−(a ∩ b) = −a ∪ −b.
As pointed out by Lukasiewicz, these laws of the propositional calculus were known already (in verbal form) to Ockham. The attachment of De Morgan's name to the corresponding laws of the algebra of classes appears to be historically more correct.
Sometimes referred to as generalizations or analogues of De Morgan's laws are the two dually related theorems of the functional calculus of first order,
∼(Ex)F(x) ≡ (x)∼F(x),and similar theorems in higher functional calculi. These make possible the definition of the existential quantifier in terms of the universal quantifier (or inversely). -- A.C.
∼(x)F(x) ≡ (Ex)∼F(x),
In common usage, "'denotation'' has a less special meaning, denote being approximately synonymous with designate (q.v.). A proper name may be said to denote that of which it is a name. Or, e.g., in the equation 2 + 2=4, the sign + may be said to denote addition and the sign = to denote equality (even without necessarily intending to construe these signs as proper names).
Concerning Frege's distinction between sense and denotation see the article Descriptions. -- A.C.
Denotation is a semantical concept, see Semiotic 2. -- R.C.
Applied Hegel's idealism to literary criticism. Gave a new interpretation to poets' sentiments and ideals, and linked them to the civil history of Italy. New Italian idealism of about 1900 was based on his thought. -- L.V.
In Principia Mathematica descriptions (or notations serving the same purpose in context) are introduced is incomplete symbols (q. v.). Russell maintains that descriptions not only may but must be thus construed as incomplete symbols -- briefly, for the following reasons. The alternative is to construe a description as a proper name, so that, e.g., the description the author of Waverley denotes the man Scott and is therefore synonymous with the name Scott. But then the sentences "Scott is the author of Waverley" and "Scott is Scott" ought to be synonymous -- which they clearly are not (although both are true). Moreover, such a desription as the King of France cannot be a proper name, since there is no King of France whom it may denote; nevertheless, a sentence such as "The King of France is bald" should be construed to have a meaning, since it may be falsely asserted or believed by one who falsely asserts or believes that there is a King of France.
Frege meets the same difficulties, without construing descriptions as incomplete symbols, by distinguishing two kinds of meaning, the sense (Sinn) and the denotation (Bedeutung) of an expression (formula, phrase, sentence, etc.). Scott and the author of Waverley have the same denotation, namely the man Scott, but not the same sense. The King of France has a sense but no denotation; so likewise the sentence, The King of France is bald. Two expressions having the same sense must have the same denotation if they have a denotation. When a constituent part of an expression is replaced by another part having the same sense, the sense of the whole is not altered. When a constituent part of an expression is replaced by another having the same denotation, the denotation of the whole (if any) is not altered, but the sense may be. The denotation of an (unasserted) declarative sentence (if any) is a truth-value, whereas the sense is the thought or content of the sentence. But where a sentence is used in indirect discourse (as in saying that so-and-so says that . . ., believes that . . ., is glad that . . ., etc.) the meaning is different in such a context the denotation of the sentence is that which would be its sense in direct discourse. (In quoting some one in indirect discourse, one reproduces neither the literal wording nor the truth-value, but the sense, of what he said.)
Frege held it to be desirable in a formalized logistic system that every formula should have not only a sense but also a denotation -- as can be arranged by arbitrary semantical conventions where necessary. When this is done, Frege's sense of a sentence nearly coincides with proposition (in sense (b) of the article of that title herein). -- Alonzo Church
G. Frege, Über Sinn und Bedeutung. Zeitschrift für Philosophie und philosophische Kritik, n. s., vol. 100 (1892), pp. 25-50. B. Russell, On denoting, Mind, n. s.. vol. 14 (1905). pp. 479-493.
Cf.
Ontologically, its materialism means that matter, nature, the observable world is taken "without reservations," as real in its own right, neither deriving its reality from any supernatural or transcendental source, nor dependent for its existence on the mind of man. It is considered scientifically evident that matter is prior to mind both temporally and logically in the sense that mind never appears except as an outgrowth of matter, and must be explained accordingly. Space and time are \iewed as forms of the existence of matter.
The term dialectical expresses the dynamic interconnectedness of things, the universality of change and its radical character everything possessing any sort of reality is in process of self-transformation, owing to the fact that its content is made up of opposing factors or forces the internal movement of which interconnects everything, changes each thing into something else. Mechanism in the sense of non-dialectical materialism as well as metaphysics in the sense of idealistic ontology are thus rejected.
The position taken is that investigation reveals basic, recurrent patterns of change, expressible as laws of materialist dialectics, which are seen as relevant to every level of existence, and, because validated by past evidence, as indispensable hypotheses in guiding further investigation. These are
These laws, connecting ontology with logic, are contrasted to the formalistic laws of identity, difference and excluded middle of which they are considered qualitatively enriched reconstructions. Against the ontology of the separateness and self-identity of each thing, the dialectical laws emphasize the interconnectedness of all things and self-development of each thing. An A all parts of which are always becoming non-A may thus be called non-A as well as A. The formula, A is A and cannot be non-A, becomes, A is A and also non-A, that is, at or during the same instant: there is no instant, it is held, during which nothing happens. The view taken is that these considerations apply as much to thought and concepts, as to things, that thought is a process, that ideas gain their logical content through interconnectedness with other ideas, out of and into which they develop.
Consequently, the dialectical method means basically that all things must be investigated in terms of their histories; the important consideration is not the state in which the object appears at the moment, but the rate, direction and probable outcome of the changes which are taking place as a result of the conflict of forces, internal and external. The necessity of observation and prediction in every field is thus ontologically grounded, according to dialectical materialism, which not only rejects a priorism, holding that "nature is the test of dialectics" (Engels: Anti-Dühring), but claims to express with much more fidelity than formal logic, with its emphasis on unmoving form rather than changing content, the basis of the method modern science actually uses. There is an equal rejection of theory without practice and practice without theory.
One may assert that the human brain, capable of forming ideas, does so not prior to or independently of the rest of the natural world, but in relation to it, moved and stimulated by its manifold content. Ideas reflect things, but the reflection, like everything else, is dialectical, not inert, but active. Ideas grow out of and lead back to things, sometimes very circuitously; things may be reflected fancifully, by abstraction or in new combinations as well as directly. While there is a perfectly objective reality to reflect, the reflection is never perfect: truth is absolute, but knowledge relative.
The social theory, termed historical materialism, represents the application of the general principles of materialist dialectics to human society, by which they were first suggested. The fundamental changes and stages which society has passed through in the course of its complex evolution are traced primarily to the influence of changes taking place in its economic base. This base has two aspects: material forces of production (technics, instrumentalities) and economic relations (prevailing system of ownership, exchange, distribution). Growing out of this base is a social superstructure of laws, governments, arts, sciences, religions, philosophies and the like. The view taken is that society evolved as it did primarily because fundamental changes in the economic base resulting from conflicts of of interest in respect to productive forces, and involving radical changes in economic relations, have compelled accommodating changes in the social superstructure. Causal action is traced both ways between base and superstructure, but when any "higher" institution threatens the position of those who hold controlling economic power at the base, the test of their power is victory in the ensuing contest. The role of the individual in history is acknowledged, but is seen in relation to the movement of underlying forces. Cf. Plekhanov, Role of the Individual m History.
The general direction of social evolution, on this view is from classless, collectivist forms (primitive communism) to class forms (slave-master, serf-lord, worker-capitalist) to classless, socialist, communist forms on the modern level of highly complex technics. Classes are defined as groups having antagonistic economic relationships to the means of production. The resultant conflict of interests is called the class struggle, which, involving the means and way of life, is carried on in all fields, often unconsciously.
It is held that society has not accomplished many basic transformations peacefully, that fundamental changes in the economic system or the social superstructure, such as that from medieval serf-lord to modern worker-capitalist economy, have usually involved violence wherein the class struggle passes into the acute stage of revolution because the existing law articulates and the state power protects the obsolete forms and minority-interest classes which must be superseded. The evolution of capitalism is considered to have reached the point where the accelerating abundance of which its technics are capable is frustrated by economic relationships such as those involved in individual ownership of productive means, hiring and firing of workers in the light of private profits and socially unplanned production for a money market. It is held that only technics collectively owned and production socially planned can provide employment and abundance of goods for everyone. The view taken is that peaceful attainment of them is possible, but will probably be violently resisted by priveleged minorities, provoking a contest of force in which the working class majority will eventually triumph the world over.
The working class, in coming to power, is seen to establish its own state form, based upon the dictatorship of the proletariat, which is maintained so long as a state is necessary, and which is considered to extend democracy to the majority by establishing collective ownership of the means of production. This first stage is defined as socialism, the economic principle of which is, "from each according to ability, to each according to work performed". The second stage is defined as communism, the economic principle of which is, "from each according to ability, to each according to need" (Marx "Gotha Program"). In its fullest sense, on a world wide scale, this stage is considered to include an economy of abundance made possible by social utilization of unrestricted production, a disappearance of the antagonism between town and country and that between mental and physical labor, and, because irreconcilable class conflicts will ha\e ceased to exist, a "withering away" (Engels: Anti-Dühring) of the state as an apparatus of force. What will remain will be a state-less '"administration of things."
The general theory of historical materialism claims to be a methodological basis for all specific social sciences, as well as for aesthetics and ethics. Cf. Trotsky: Literature and Revolution.
Art, to dialectical materialism, is an activity of human beings which embodies a reflection of the reality surrounding them, a reflection which may be conscious, unconscious, reconstructive or deliberately fantastic, and which possesses positive aesthetic value in terms of rhythm, figure, color, image and the like. Art is good to the extent that it is a faithful and aesthetic reflection of the reality dealt with. Accordingly, proletarian or socialist realism (q.v.) is not photographic, static, but dialectical, conscious that any given period or subject is moving into its future, that class society is becoming classless society. This realism is optimistic, involving a "revolutionary romanticism".
Bibliography:
(b) objectively: see Distinction. -- V.J.B.
Contrasted with Intuitive, and applied to knowledge; also to transitions of thought. Our knowledge of, e.g., the nature of time, is discursive or conceptual if we are able to state what time is; otherwise it is only intuitive. Transitions of thought mediated by verbal or conceptual steps would be called discursive and said to be "reasoning". Immediate transitions, or transitions mediated in subconscious ways, would be called intuitive. --
C.J.D.
(b) In logic: Disparate terms have been variously defined by logicians:
Absolute: There is an absolute distinction between two things when neither one is a mode of the other, e.g. that between a stone and gold. A modal distinction is a distinction between a thing and its mode, e.g. that between a body and its shape.
Adequate: A distinction between two whole beings, e.g. between the sun and the moon. An inadequate distinction is a distinction between a whole being and its part, e.g. between the hand and one of its fingers.
Of the reasoning reason (rationis ratiocinantts) . A distinction in which our mind conceives things as distinct when there is no foundation in reality for making such a distinction, the whole distinction is dependent upon the one reasoning. E.g. when in one and the same thing we conceive the nature of subject and predicate as diverse attributes, as when we say: man is man, or when we conceive the same thing through synonymous concepts, as if we say: man is a rational animal, as though we are distinguishing man from rational animal.
Of the reasoned reason (rationis ratiocinatae): A distinction in which our mind conceives as distinct things that are not really distinct, when there is some foundation in reality for making such a distinction, e.g. perfections of God.
Real: A distinction belonging to a thing independently of the operation of the intellect, as that between the soul and body of man. A mental distinction (distinctio rationis) is one belonging to things through the operation of the intellect conceiving as distinct those things which are not really distinct, e.g. that between the attributes of God. -- H.G.
(a) In general impractical, philosophical theorists, uninterested in other views than their own; dogmatists.
(b) In particular: a group of French political philosophers of the early nineteenth century. --
V.J.B.
a. State of mind characterized by human conflict.
b. Literary genre in which conflicts are portrayed on the stage. -- L.V.
(a) In metaphysics: Theory which admits in any given domain, two independent and mutually irreducible substances e.g. the Platonic dualism of the sensible and intelligible worlds, the Cartesian dinlism of thinking and extended substances, the Leibnizian dualism of the actual and possible worlds, the Kantian dualism of the noumenal and the phenomenal. The term dualism first appeared in Thomas Hyde, Historia religionis veterum Persarum (1700) ch. IX, p. 164, where it applied to religious dualism of good and evil and is similarly employed by Bayle m his Dictionary article "Zoroaster" and by Leibniz in Theodicee. C. Wolff is responsible for its use in the psycho-physical sense, (cf. A. Lalande, Vocabulaire de la Philosophie. Vol. I, p. 180, note by R. Eucken.)
(b) In epistemology: Epistemological dualism is the theory that in perception, memory and other types of non-inferential cognition, there is a numerical duality of the content or dntum immediately present to the knowing mind
and (sense datum, memory image, etc.) and the real object known (the thing perceived or remembered) (cf. A. O. Lovejoy, The Revolt Against Dualism, pp. 15-6). Epistemological monism, on the contrary identifies the immediate datum and the cognitive object either by assimilating the content to the object (epistemological realism) or the object to the content (epistemological idealism). -- L.W.
Though Socrates, Plato and Aristotle had propounded doctrines of virtues, they were concerned essentially with Good rather than with rightness of action as such. The Stoics were the first to develop and popularize the notion that man has a duty to live virtuously, reasonably and fittingly, regardless of considerations of human happiness. Certain elements in Rabbinical legalism and the Christian Gospel strained in the same direction, notably the concept of the supreme and absolute law of God. But it was Kant who pressed the logic of duty to its final conclusion. The supreme law of duty, the categorical imperative (q.v.), is revealed intuitively by the pure rational will and strives to determine the moral agent to obey only that law which can be willed universally without contradiction, regardless of consequences.
Naturalistic interpretations of duty tend to discredit such an intuitionistic basis and seek instead to account for duty and conscience as outgrowths of training, tradition and social custom. -- O.F.K.
Diallelon: A vicious circle (q. v.) in definition. -- A. C.
Diallelus: A vicious circle (q. v.) in proof. -- A.C.
Dialogic method: The presentation of a thesis or argument in dialogue form. --
C.A.B.
Dialogism: Inference from one premiss of a (categorical) syllogism to the disjunction of the
conclusion and the negation of the other premiss is a dialogism. Or, more generally, if the inference from A and B to C is a valid inference, that from A to C ∨ ∼B may be called a dialogism. -- A. C.
Dianoetic Virtues: (Gr. aretai dianoetikai) In Aristotle's ethics the virtues or excellences of the dianoia; intellectual virtues. The dianoetic virtues are distinguished from the moral virtues in having for their end the explicit apprehension of rational principles, whereas the moral virtues are concerned with the rational control of the sensitive and appetitive life. See Aristotelianism; Dianoia; Nous; Phronesis. -- G.R.M.
Dianoia: (Gr. dianoia) The faculty or exercise of thinking, as exhibited especially in the discriminating and conjoining or disjoining of concepts; the discursive understanding (Aristotle). -- G.R.M.
Diaspora: Literally the Greek word signifies a scattering or dispersion. Name given to the countries through which the Jews were dispersed after being exiled or deported from their homeland and also to the Jews living in those lands. Also applied to converts from Judaism to Christianity of the early Church living outside of Palestine. -- J.J.R.
Dichotomy: (Gr. dicha, in two; temno, to cut) Literally, a division into two parts. In a specific example the view that man consists of soul and body. The earlier view of the Old Testament writers; also, a view found in certain expressions of St. Paul. See also Trichotomy. -- V.F.
Dictum de omni et nullo: The leading principles of the syllogisms in Barbara and Celarent, variously formulated, and attributed to Aristotle. "Whatever is affirmed (denied) of an entire class or kind may be affirmed (denied) of any part." The four moods of the first figure were held to be directly validated by this dictum, and this was given as the motive for the traditional reductions of the last three syllogistic figures to the first. See also Aristotle's dictum. -- A.C.
Didactics: (Gr. didaktikos, taught) The branch of education concerned with methods of teaching and instruction. In theology and religion didactics in contradistinction to catechetics, is instiuction in fundamentals of religious doctrine. -- L.W.
Diderot, Denis: (1713-1784) He was editor-in-chiet ot trie French Encyclopaedia and as such had a far reaching influence in the Enlightenment. His own views changed from an initial deism to a form of materialism and ended in a pantheistic naturalism. He displayed a keen interest in science and may be viewed as a forerunner of positivism. He issued severe polemics against the Christian religion.
Difference: (in Scholasticism) Common: That which makes a distinction (or division) by some separable accident, as when we say that this person is sitting and that one standing. By this difference a person can differ not only from another but also from himself, as one who is now old differs from himself as he was when young. -- H.G.
Dilemma: See Proof by cases, and Logic, formal, § 2.
Dilettantism: Opposite of professionalism. If contributed to art appreciation because it opposed the too intellectual rules of traditional taste, particularly in Rome, 2nd century; in France and England, 18th century. -- L.V.
Dilthey, Wilhelm: (1833-1911) A devoted student of biography, he constructed a new methodology and a new interpretation of the study of society and culture. He formulated the doctrine of Verstehungs-psychologie, which is basic to the study of social ends and values. He was the founder of Lebensphilosophie. Being the first humanistic philosopher historian of his age, he led in the comprehensive research in the history of intellectual development. Main works:
Dimension: (scientific) 1. Any linear series or order of elements. 2. Any quantity of a given kind, capable of increase or decrease over a certain range, a variable. 3. In the physical system: mass, length and time. -- A.C.B.
Dimensions of Consciousness: (Lat. dimensus, pp. of dimentire, to measure off) Pervasive and mutually irreducible features of conscious processes such as quality, intensity, extent, duration and intentionality. (Cf. E. B. Titchencr, Lectures on the Elementary Psychology of Feeling and Attention, Lect. IV; E. G. Boring, The Physical Dimensions of Consciousness, Ch. 3.) -- L.W.
Ding an sich: (Ger. thing in itself) A Kantian term referring to what lies beyond human experience and observation. "Things in themselves" are transcendent, not transcendental or applicable to any human experience. The "thing in itself" exists independent and apart from all knowledge. It has an independent reality apart from the subjectivity of human knowledge. -- H.H.
Diogenes Laertius: (also B.C.) A late biographical doxographer, to whom is owed most of the biographical and source material of Pre-Socratic philosophy. Cf. R. Hope, Diog. Laertius -- E.H.
Dionysian: The art impulse in which life is relived, in which life's joys and pains are re-experienced. The dynamic and passionate of the will of life and power. (Nietzsche.) -- H.H.
Diorism: The Greek term in Plato's usage signifies division, distinction; in that of Aristotle, distinction, definition, which is also the meaning today. In mathematics, a statement of the
conditions needed in order to solve a problem. -- J.J.R.
Direct knowledge: A thing is said to be known directly when our cognition terminates in and refers immediately to the thing itself; a thing is known reflexly, when our cognition terminates in and refers immediately to the image or concept of the thing previously known. E.g. I know man directly upon seeing him, but upon seeing his image, I know him reflexly, because then I know him through the cognition of the image. --
H.G.
Direct theories of knowing: Any theories of knowledge which maintain that objects are known directly without the intermediary of percepts, images or ideas. -- A.C.B.
Discourse: Orderly communication of thought, or the power to think logically. --
C.A.B.
Discovery: (Lat. discooperire, to discover) 1. The act of becoming aware of something previously existing but unknown. 2. The act of insight (usually more or less sudden) by which a scientific hypothesis or explanatory conception comes into consciousness. -- A.C.B.
Discrepancy: A difference from that which was expected or is required by some datum. -- C.A.B.
Discrete: A class is said to have discrete order (e.g. the whole numbers), if (1) it satisfies Dedekind's postulate (q.v.) and (2) every element (except the first if any) has a next predecessor and also (except the last if any) a next successor. Contrasted with "dense" or "compact" order, such as that of the rational numbers, in which no element is next to any other. -- C.J.D.
Discretion: (Lat. discretum, pp. of discernere, to discern) The mental capacity for critical discrimination especially in matters of ethics and conduct. -- L.W.
Discrimination: (Lat. discriminare, to separate) (a) subjectively: the rational power to distinguish between objects, real or logical, and betwen moral right and wrong. In Aristotelianism there is also a function of internal sense (Gr. kritikon, sensory discrimination; Lat. vis aestimativa or cogitativa) by which men and the higher animals distinguish the good from the bad in their sense experience,
Discursive Cognition: (Lat. discurrere, to run about) Discursive, as opposed to intuitive cognition, is attained by a series of inferences rather than by direct insight. See Intuitive Cognition. -- L.W.
Disjunction: See Logic, formal, § 1.
Disjunctive: A sentence of either of the forms A ∨ B, A + B (or a proposition expressed by such a sentence) -- see Logic, formal, § 1 -- may be called a disjunctive sentence (or proposition). -- A. C.
Disjunctive syllogism: See Logic, formal, § 2.
Disparate: (Lat. dis + par. equal) (a) In psychology and epistemology: a term descriptive of the qualitative heterogeneity between sensations of different senses. Sensations of the same sense (e.g. a red and a green color patch) are dissimilar (see Similarity; Resemblance), sensations of different senses (e.g. a red patch and a cold surface) are disparate. The criterion of psychological disparity between two sensations is the absence of intermediate sensations by which it is possible to pass continuously from the one to the other. (Wundt, Physiol. Psychol., 4th ed., I, 286.) The disparity of the fields the several senses divides them into so many watertight compartments and thus raise the epistemological problem of correlation between the disparate data of different senses. See Correlation.
Disparity: See Disparate.
Disputatio: (Scholastic) Out of the quaestiones disputatae developed gradually a rigid form of scholastic disputation. The defensor theseos proposed his thesis and explained or proved it in syllogistic form. The opponentes argued against the thesis and its demonstration by repeating first the proposition and the syllogism proving it, then either by denying the validity of one or the other premises (nego maiorem, minorem) or by making distinctions restricting the proposition (distinguo maiorem, minorem). In the disputations of students under the direction of a magister the latter used to summarize the disputation and to "determine the question". -- R.A.
Disputation: (a) A dispute, or the act of disputing, (b) A formal exercise in which some set topic is debated. -- C.A.B.
Dissimilarity: Difference, unlikeness, heterogeneity. -- C.A.B.
Dissociation: (Lat. dis + socius, a companion) The operation of mind by which the elements of a complex are discriminated. Dissociative discrimination is facilitated when elements which are commonly conjoined are found in new combinations. James calls this the law of "dissociation by varying concomitants." (Principles of Psychology, I, 506.) --
I.W.
Dissociation of Personality: A disorder of personality consisting in the loss of the normally stable and constant integration of the self. Two types of disintegration of personality are distinguishable: (a) The ideas and states dissociated from the central core of the self may float about as detached and depersonalized states. See Deperonalization. (b) The dissociated ideas and
states may cohere into a secondary or split-off consciousness. -- L.W.
Distinction: (in Scholasticism) Consists in this, that one thing is not another.
Distinctness: (Ger. Deutlichkeit) In Husserl: Explicit articulatedness with respect to syntactical components. (See Confused). Distinctness is compatible with emptiness or obscurity of material content. See Descartes, Leibniz. -- D.C.
Distribution (of terms): In the four traditional Aristotelian propositional forms, the subjects of universal propositions and the predicates of negative propositions are distributed, the other terms are undistributed. -- C.A.B.
Distributive Justice: Justice as exhibited in the distribution of honor, money, rights and privileges among the members of a community; characterized by Aristotle as requiring equality of proportion between persons and rewards. See Corrective Justice. -- G.R.M.
Distributive law is a name given to a number of laws of the same or similar form appearing in various disciplines -- compare associative law. A distributive law of multiplication over addition appears in arithmetic:
x X (y + z) = (x X y) + (x X z).
This distributive law holds also in the theory of real numbers, and in many other mathematical disciplines involving two operations called multiplication and addition. In the propositional calculus there are four distributive laws (two dually related pairs):
p[p ∨ r] ≡ [pq ∨ pr].
Also four corresponding laws in the algebra of classes. -- A.C.
[p ∨ qr] ≡ [p ∨ q][p ∨ r].
p[p + r] ≡ [pq + pr].
[p ∨ [q ≡ r] ≡ [p ∨ q] ≡ [p ∨ r]].
Disvalue: Bad. Evil. Opposed to value or goodness. -- A.J.B.
Divisibility: The property in virtue of which a whole (whether physical, psychical or mathematical) may be divided into parts which do not thereby necessarily sever their relation with the whole. Divisibility usually implies not merely analysis or distinction of parts, but actual or potential resolution into parts. From the beginning philosophers have raised the question whether substances are infinitely or finitely divisible. Ancient materialism conceived of the physical atom as an indivisible substance. Descartes, however, and after him Leibniz, maintained the infinite divisibility of substance. The issue became the basis of Kant's cosmological antinomy (Crit. of pure Reason), from which he concluded that the issue was insoluble in metaphysical terms. In recent decades the question has had to take account of (1) researches in the physical atom, before which the older conception of physical substance has steadily retreated; and (2) the attempt to formulate a satisfactory definition of infinity (q.v.). -- O.F.K.
Division: (Lat. dividere, to divide) The logical process of indicating the species within a genus, the sub-species within the species, and so on a classificatory scheme constructed on the principle of genus and species. -- A.C.B.
Divisionism: Principle of obtaining the effects of light in painting by juxtaposing instead of mixing tints. -- L.V.
Docta ignorantia: Liteially, learned ignorance, refers to men's knowledge of God which unavoidably includes a negative element, since He immeasurably surpasses the knowledge of Him gleaned from this phenomenal world, yet for man this is truly a real learning. Title given to one of his philosophical treatises by Nicholas of Cusa (1401-1464) who understood it in the sense of an insight into the incomprehensibility of the infinite. --
J.J.R.
Doctrinaires:
Dogma: The Greek term signified a public ordinance of decree, also an opinion. A present meaning: an established, or generally admitted, philosophic opinion explicitly formulated, in a depreciative sense; one accepted on authority without the support of demonstration or experience. Kant calls a directly synthetical proposition grounded on concepts a dogma which he distinguishes from a mathema, which is a similar proposition effected by a construction of concepts. In the history of Christianity dogmas
have come to mean definition of revealed truths proposed by the supreme authority of the Church as articles of faith which must be accepted by all its members. -- J.J.R.
Dogmatism: (Gr. dogma, opinion) A term used by many and various philosophers to characterize their opponents' view more or less derogatorily since the word cannot rid itself of certain linguistic and other associations. The Skeptics among Greek philosophers, doubting all, called dogmatism every assertion of a positive nature. More discriminately, dogmatism may be applied to presumptuous statements or such that lack a sufficiently rational ground, while in the popular mind the word still has the affiliation with the rigor of church dogma which, having a certain finality about it, appeals to faith rather than reason. Since Kant, dogmatism has a specific connotation in that it refers to metaphysical statements made without previous analysis of their justification on the basis of the nature and aptitudes of reason, exactly what Kant thought to remedy through his criticism. By this animadversion are scored especially all 17th and 18th century metaphysical systems as well as later ones which cling to a priori principles not rationally founded. Now also applied to principles of a generalized character maintained without regard to empirical conditions. -- K.F.L.
Donatists: Followers of Bishop Donatus, leader of a Christian sect which originated in North Africa in the beginning of the fourth century. They taught the invalidity of sacraments administered by an unworthy minister and that known sinners should be denied membership in the Church. Their most powerful opponent was Saint Augustine. --
J.J.R.
Donum superadditum: A theological term denoting a gratuitous gift of God superadded to the natural gifts which accompany human nature; hence a supernatural gift, like divine grace. -- J.J.R.
Double-Aspect Theory: Theory that the mind and the body of an individual are two distinguishable but inseparable aspects of a single underlying substance or process. Spinoza, as a consequence of his metaphysical doctrine trnt "thinking substance and extended substance are one and the same thing" (Ethics, Part II, prop. 7) was committed to the Two-Aspect Theory of the body-mind relation. Cf. C. Lloyd Morgan (Life, Mind and Spirit, p. 46); S. Alexander (Space, Time and Deity) and C. H. Strong are recent advocates of a two-aspect Theory. -- L.W.
Double negation, law of: The theorem of the propositional calculus,
&sim:∼p ≡ p.
-- A.C.
Doubt: (Fr. doute, from Lat. dubito, to be uncertain) Partial disbelief. The denial of a proposition offered or formerly held as true. The withdrawal of belief. In psychology: suspended judgment; the state of hesitation between contradictory propositions. Philosophical doubt has been distinguished as definitive or provisional. Definitive doubt is scepticism (which see). Provisional doubt is the rule proposed by the Cartesian method (q.v.) of voluntary suspension of judgment in order to reach a more dependible conclusion. Opposite of certainty. -- J.K.F.
Doxa: The positional character common to all modes of beliewng: not only to believing in simple positive certainty (protodoxa, Ger. Urdoxa), but to modifications of the latter, such as doubting, disbelieving, affirming, denying, and assuming. Doxa in Husseil's sense includes episteme. It is present not only in syntactical-categorial judging, but in simple pre-categorial perceiving. Moreover, it is present in passive as well as in active synthesis. Non-doxic positionality is present in valuing and willing. -- D.C.
Drama:
Dravya: (Skr.) Substance, as a substratum of qualities (see guna), accidents, or modes. Various classes are established by Indian philosophers. --K.F.L.
Drawing: Essential element of painting, sculpture and architecture. The Florentine Renaissance and all classical epochs in general considered drawing the basis of the aforesaid arts which were called the arts of drawing. -- L.V.
Driesch, Hans Adolf Eduard: (1867-1940) An experimental biologist turned philosopher, he as a rationalist became the most prominent defender of a renovated vitalism. He excludes the physical-chemical level of reality from his vitalism. He asserts that every organism has its own entelechy. For what he terms phylogenetic development, a more inclusive vitalism of the whole evolutionary process, he postulates a super-personal phylogenetic entelechy. He offers an a priori justification of his vitalistic theory, and treats incisively the logic of the psychological. Main works:
-- H.H.
Dualism: (Lat. duo, two)
Duality: See Logic, formal, §§ 1, 3, 7, 8.
Ductio per contradictoriam propositionem sive per impossible: (Lat.) A logical argument in which the truth of a proposition is established by showing that its contradictory is untrue or impossible; an application of the principle of excluded middle. --
V.J.B.
Dühring, Eugen Karl: (1813-1901) Dühring, a German economist and philosopher, started on a legal career which lasted until 1859. He became docent at the University of Berlin and taught there until he lost his license in 1874. He was editor of Der moderne Volkergeist and of Personalist und Emancipator. Philosophically he belonged to the positivistic school. Dühring advocated not the elimination of capitalism, but of its abuses through the medium of a strong labor movement. His literary work is strongly tinged with anti-semitism, and he is probably better known for the attack which Marx and Engels made upon him than for his own work.
-- M.B.M.
Duns Scotus, John: (1266/74-1308) Doctor Subtilis, was born somewhere in the British Isles, studied at the Franciscan monastery at Dumfries and at Oxford before 1290. He studied at Pans for four years, then taught theology at Oxford from 1300-1302, at Pans from 1302-1303, when he was banished for his opposition to King Philip IV. He received his doctorate at Paris in 1305 and went to Cologne in 1307, where he died. He is the most distinguished medieval defender of the view that universals which have "haeccity" (q.v.) as well as quiddity. His realism was adopted by Charles Peirce (q.v.) works:
-- V.J.B.
Duration: A limited extent of existence in time, more or less long, from a fraction of second to countless ages. H. Bergson gives it a special interpretation in regarding it as "time perceived as indivisible", a living present; as such, duration becomes the very essence of creative change, of creative evolution and must be opposed to time as measurable. --
R.B.W.
Durkheim, Emile: (1858-1917) A French sociological positivist. He stressed the group mind, which for him is the point of reference for all human knowledge. The group mind has an impersonal, non-subjective character that is superior to the individual mind, and acts as a directive force for the individual agents that comprise society. He studied both religion and ethics from his positivistic point of view.
-- H.H.
Duty: (Ang-Fr. duete, what is due, Ger. Pflicht) Whatever is necessary or required; or whatever one is morally obliged to do, as opposed to what one may be pleased or inclined to do. Also, the moral obligation itself and the law or principle in which it is expressed.
In ethics, duty is commonly associated with conscience, reason, rightness, moral law, and virtue.
Dyad: (Gr. duas, two) A pair of units considered as one. In Pythagoreanism the dyad is the number two, thought of as a substantial essence, or physically, as a line, i.e. two points which do not coincide. -- V.J.B.
Dyadic: (Gr. duas, two) Term meaning duality. Human experience is said to be dyadic, i.e. man's nature is dual in conflicts between good intentions and bad accomplishments, in oppositional strains and stresses. The personality of God is held to be dyadic in the confronting of difficulties or frustrations to his good will. Reality is spoken of as dyadic when it is said to be characteristically dual, e.g. both One and Many, static and dynamic, free and determined, abstract and concrete, universal and particular. -- V.F.
Dyadic Relation: A two-termed relation (q.v.).
Dynamic Vitalism: See Vitalism.
Dynamis: (Gr. dynamis) In Aristotle's philosophy (1) a source of change or power to effect change; faculty; (2) more generally the capacity a thing has of passing to a different state; potentiality. See Aristotelianism; Energeia. -- G.R.M.
Dynamism: (Gr. dynamis, power) A term applied to a philosophical system which, in contrast to philosophy of mechanism (q.v.), adopts force rather than mass or motion as its basic explanatory concept. In this sense the Leibnizian philosophy is dynamism in contrast to the mechanism of Descartes' physics. -- L.W.
Dyophysites: A term applied to the Catholics,
who held that there are two natures in Christ,
the Divine and the human, by the Monophysites,
or the followers of Eutyches, who advanced the
formula, "one nature after the union." -- J.J.R.
Dysteleology: (Gr. dus, bad; telos, end or purpose) The term for the forbidding and frustrating aspects of life (such as unfavorable environmental factors, organic maladaptations, the struggle for existence, disease, death, etc.) which make difficult, if not impossible, the theory that there are good purposes predominantly at work
in the world. -- V.F.