Abstract
The controversy over universals has been revived, the parties being the same that clashed in Antiquity and the Middle Ages: realism, conceptualism, nominalism. The difference is that the universals referred to at present are neither “forms” nor “essences of things”, nor are they Platonic ideas of concrete objects, but abstract entities of a special kind: sets of individuals, sets of sets of individuals, sets of sets of sets of individuals, etc., interpreted as objects which are essentially non-perceivable, extra-temporal and extra-spatial. Just as centuries ago, the realistic standpoint is that universals exist; the conceptualistic standpoint is that they exist in mente, but not extra mentem; and the nominalistic standpoint, in opposition to the other two trends, is that the existence of universals is firmly rejected. Conceptualism has few adherents at present; but the other two movements are very strong.
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S. Lesniewski, ‘O podstawach matematyki’ (On the Foundations of Mathematics), Przeglqd Filozoficzny, Vol. 30, No. 2-3, 1927 (especially pp. 166–9 and 186-202), and Vol. 31, No. 3, 1928 (especially pp. 261-3). Similar ideas are to be found in S. Leonard and N. Goodman, ‘The Calculus of Individuals and Its Uses’, Journal of Symbolic Logic, Vol. 5, 1940; in N. Goodman, The Structure of Appearance, Cambridge, Mass., 1951; and in J. Słupecki, ‘Towards a Generalized Mereology of Lesniewski’, Studia Logica, VIII, 1958. (English-language readers will find a more comprehensive discussion of Leśniewski’s ideas in E. C. Luschei, The Logical Systems of Leśniewski, North-Holland 1962, — Tr.)
T. Kotarbinski, ‘The Reistic, or Concretistic, Approach’, p. 45 in the present book. It may be helpful to explain that reism is based on Leśniewski’s ontology and uses the concepts characteristic of that system. In that ontology the only primitive term is ‘est’ (‘is’), introduced by the axiom II A, B (A est B ≡ ≡ (IIx (x est A → x est B) ∧ΣX (X est A)AIIX, y (x est A ∧y est A → x est y))). The term ex (“exists”) is defined thus: IIA (ex A ≡ Σx (x est A)). This obviously yields the theorem: II,4, B (A est B → ex A), by which a statement of the type A est B has en existential consequence ex A which applies to the designatum of A.
T. Kotarbiéski, The Development Stages of Concretism, in the Supplement to Gnosiology, Pergamon Press 1966, pp. 429–37.
T. Kotarbiéski, Gnosiology, ed. cit., p. 51.
T. Kotarbiéski, Wybór pism (Selected Works), Vol. II, Warszawa 1958, p. 75.
Ut supra, pp. 109–10. Both (c) and (a) have two formulations each: both cases formulations which form a given pair are treated as synonymous. These will be marked (a1), (a2), (c1), (c2).
T. Kotarbinski, Gnosiology, ed. cit., p. 7. See also his Selected Works (cf. footnote5), Vol. II, pp. 232–3. (It is to be noted that the ‘term’ used in Gnosiology corresponds to the term ‘name’ often used in the present book. It would appear that neither is a completely satisfactory rendering of the Polish term ‘nazwa’, simply because of a certain vagueness of the latter. — Tr.)
From K. Ajdukiewicz’s review of the first Polish edition of Gnosiology, included in the Supplement to the English-language version. The formulation mentioned here is on p. 519 of the latter version. (Tr.)
T. Kotarbinski, Selected Works, Vol. II, pp. 232–3.
T. Kotarbinski, Gnosiology, pp. 9 and 406; see also his Selected Works, Vol. II, pp. 74 and 232-3.
This interpretation is partly based on the formulations found in Gnosiology, p. 9, and in the paper ‘The Reistic, or Concretistic, Approach’, also in the present book. It is to be noted that at the time when the Polish version of Gnosiology first appeared partial definitions were not yet known. Yet partial definitions should also be taken into consideration; this is justified by the present-day approach and at the same time would not appear to be at variance with the intenttions of the reists.
Formulations (3), (4) and (5) are, for the sake of simplicity, given only for statements of the type ‘A is B’. However, since in ontology all simple statements are definitionally reducible to statements of that type, and since all compound statements are combinations of simple ones, the same formulations can easily be made to cover all other statements.
Note that, if this analysis is correct, then of the two statements, (a 1 and (C1), which in the reistic theory are considered to be synonymous with (a 2) or (c2) (cf. footnote6 above), (a 2) alone evokes no doubts or objections. In the case of (c2), it seems to differ in content from (a1) and (c1); in particular, it does not state — not directly anyway — that translatability into the language of things is a necessary condition of the meaningfulness of the statements under consideration. It points rather to the motives which account for the adoption of that assumption.
T. Kotarbiéski, Gnosiology, ed. cit., p. 434.
T. Kotarbiéski, ‘Uwagi na temat reizmu’ (Comments on Reism), Ruch Filozoficzny, Nos 1-10, 1930-1 (quoted from the text reprinted in Selected Works, Vol. II, pp. 108-9).
The last issue is certainly the most controversial of all. It does seem, however, that making the semantic role of the terms ‘is’ and ‘exists’ depend on the methodological properties of the statements in which those terms are used is fairly natural. Moreover, this is not specifically linked to the reistic standpoint. For instance, this assumption is adopted by K. Ajdukiewicz in his paper ‘W sprawie pojęcia istnienia’ (On the Concept of Existence), 1951, reprinted in Język i po,znanie (Language and Cognition), Vol. II, 1965. It is also in harmony with the tendencies discussed by R. Carnap in ‘Empiricism, Semantics and Ontology’, Revue Internationale de Philosophie, II, 1950, and with H. Reichenbach’s views as formulated in Experience and Prediction, 5th ed., Chicago 1957, Sec. 24 et passim.
Cf. K. Ajdukiewicz, ‘W sprawie uniwersaliów’ (Concerning Universals), Przeglqd Filozoficzny 1934 (reprinted in Język i poznanie (Language and Cognition), Vol. I, Warsaw 1960.
Cf. footnote16 above. To avoid misunderstandings it should be said that the primary meaning of the copula ‘is’ is interpreted here as in Sec. 3, formulation (2), above, but with the understanding that the term ‘name’ is interpreted more broadly.
In ‘The Development Stages of Concretisim’ (first published in Polish in 1958; for an English-language version see the Supplement to Gnosiology, ed. cit.), T. Kotarbinski even shifts his main emphasis from theorems to a programme. He maintains that the reistic doctrine in its earlier stages was hypothetical in nature and concludes that “in its. mature form concretism absolutely insists on its programme only.” (Cf. Gnosiology, p. 435) This is certainly a much more cautious formulation, and far less open to objections and criticism than the previous one. It does not, however, reject the previous concept of meaningfulness (see the paper under consideration in fine) and thus does not remove the essential obstacle, i.e., the conflict with mathematics and the exact sciences.
The Development Stages of Concretism, loc. cit.
Cf. the two papers on concretism in the Supplement to Gnosiology, ed. cit.
If a language L assumes set theory, and if an expression M is a predicate in L, then as we know, we may rightly conclude in L that there is an infinite hierarchy of sets: the set of M’s, the set of the sets of the sets of M’s, etc., ad infinitum.
Cf. A. Mostowski, ‘Thirty Years of Foundational Mathematics’, Acta Philosophica Fennica, XVII, 1965, p. 7, and H. Mehlberg’s paper in Logic and Language, Dordrecht 1963, pp. 79 and 84.
Cf. G. Berkeley, A Treatise concerning the Principles of Human Knowledge, Dublin 1710.
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Kotarbinska, J. (1979). Puzzles of Existence. In: Pelc, J. (eds) Semiotics in Poland 1984–1969. Synthese Library, vol 119. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-9777-6_21
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