Abstract
The philosophical systems, in which one speaks about ontologically varied objects, in which — if they are not contradictory — some formal ontology occurs in a hidden way, are an inspiration, like natural language, for seeking such formal constructions in which some distinctions among objects are possible. There is a need to capture the main semantic idea which underlies research of this kind.
This is an English version of my paper: 1988, ‘Cztery typy predykacji’ (Four types of predication), Studia filozoficzne 6–7, 117–126.
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Notes
C. Lejewski distinguishes in his works three classical types of logical languages: Aristotelian language (the name category forms here referential names), Frege-Russellian language (singular referential names) and Legniewskis language (referential names — general and singular, and non-referential — empty names). See for instance: Lejewski, C.: 1965, A Theory of Non-Reflexive Identity and Its Ontological Ramifications. In: Weingartner, P. ( Ed.) Grundfragen der Wissenschaften and ihre Wurzeln in der Metaphysik, Salzburg-München, pp. 65–102.
Kotarbinski, T.: 1961, Z zagadnied klasyfikacji nazw. In: Kotarbitiski, T., Elementy teorii poznania, logiki formalnej i metodologii nauk, 2nd Ed., Ossolineum. English: On the classification of names. In: Kotarbiríski, T., Gnosiology, Pergamon Press, Oxford, 1966. The notion of individual name depends on an assumed individual theory.
Quine in his logical system treats names such as clever, town as singular ones — they refer (indirectly according to us) to classes. See Quine, W. V. 0.: 1955, Mathematical Logic, 2nd Ed., Cambridge, Massachusetts, §22.
Cf. Ajdukiewicz, K.: 1934, W sprawie uniwersaliów, Przeglad Filozoficzny 37, 219–234. English: On the Problem of Universals. In: K. Ajdukiewicz, The Scientific World-Perspective and Other Essays 1931–1963, Ed. by Jerzy Giedymin, Reidel, Dordrecht, 1978, pp. 95–110. The distinguishing of these name subcategories is especially important for languages using articles. Let us take for example the propositions: Socrates is a man, Socrates is the husband of Xanthippe and the lion is an animal. The first and third are equivalents to the above analyzed propositions. Ascribing to the word is the category n/s/n, the definite article as functor would be of category n/o, the indefinite article of category n/u.
As is known, Aristotle in his syllogistic restricted the names to the general referential ones. See Lukasiewicz, J.: 1951, Aristotles Syllogistic from the Standpoint of Modern Formal Logic, Oxford, 4f.
Lejewski, C.: 1978, Idealization of Ordinary Language for the Purposes of Logic. In: D. T. Alleton, E. Carney, and D. Holdcroft (Eds.) Function and Context in Linguistic Analysis, Cambridge, pp. 94–110.
Iwanus, B.: 1976, W sprawie tzw. nazw pustych Acta Universitas Wratislaviensis 290 (Logika 5), 73–90.
By elementary ontology we mean the fragment of ontology in which the quantifiers bind only nominal variables.
One of theses of this calculus is:s really-exists or s intentionally-exists. One can show that a thesis of this calculus is also if s really-exists, then it is not true, that s intentionally-exists. An attempt at a construction of a name calculus which realizes this predication type, built according to the spirit of Legniewskis ontology, is introduced in my dissertation: Z badari nad zastosowaniami systemów Lesniewskiego (Investigations on applications of Le(niewskis systems), (Jagiellonian University, Cracow 1984). A fragment of this construction was used by the author in 1986: Zur logischen Analyse der langen Namen in der deutschen Sprache, In: Termini-ExistenzModalitäten (Philosophische Beiträge 4, Humboldt-Universität zu Berlin), pp. 45–57.
See Küng, G.: 1963, Ontologie und logistische Analyse der Sprache: Eine Untersuchung zur zeitgenössischen Universaliendiskussion, Springer-Verlag, Wien, p. 84ff. (English: Ontology and the Logistic Analysis of Language: An Enquiry into the Contemporary Views on Universals, D. Reidel, Dordrecht, 1963 ). See also his: 1977, Nominalistische Logik heute, Allgemeine Zeitschrift für Philosophy 2, 29–52.
We obtain also the same result by interpreting homo est animal by homo-esse est animal-esse (est is here of (s/n)\s/(s/n) category). Cf. Kling, G.: Nominalistische Logik heutechrw(133), p. 46.
In the classical predicate calculus a exists means Ex(x = a), which is tersely expressed in Quines well-known thesis: to be is to be the value of a bound variable.
The set theoretical interpretation of the proposition homo est animal would be the class of homo is included in the class of animal.
See Frege, G.: Über Sinn und Bedeutung. In: G. Frege, Funktion, Begriff, Bedeutung, 6th Ed., Ed. by G. Patzig, Göttingen, 1986, pp. 40–65.
As synonym of this term Frege used also the word singular name (Einzelname). See Frege, G.: Ausführungen über Sinn und Bedeutung. In: G. Frege, Nachgelassene Schriften, Vol. I, Ed. by Hans Hermes, Friedrich Kambartel, and Friedrich Kaulbach, F. Meiner Verlag, Hamburg, 1969, pp. 128–136.
See Camap, R.: 1968, Einführung in die symbolische Logik, Springer-Verlag, Wien-New York, 3rd Ed., p. 40. (English: Introduction to Symbolic Logic and Its Applications, New York, 1958 ).
An n-ary relation is the intension of an n-ary predicate. Ibid., p. 40, p. 90f.
Lejewski, C.: A Theory of Non-Reflexive Identitychrw(133).
In the framework of TNI a does not exists is expressed as: (a = a). The special case of a rule of extensionality, assumed in this system is (a)
Lambert, K. and Scharle, T.: 1967, A Translation Theorem for Two Systems of Free Logic Logique et Analyse 39–40, 328–341.
Ibid., p. 332ff.
Kearns, J. T.: 1968, A Universally Valid System of Predicate Calculus with No Existential Presuppositions Logique et Analyse 41, 367–389. This system is constructed similarly to Lejewskis TNI.
Plus and minus are here the predicate-forming functors. We have here the theses: r, Exists(x) Exists
Certain ontological distinctions in classical philosophy were mentioned earlier, when we presented classical predication theory.
The term object occurs here in the narrower meaning of presented object. The pair object—presentation corresponds with the pair real object—presented object, by a wider understanding of object. See Twardowski, K.: 1894, Zur Lehre vom Inhalt and Gegenstand der Vorstellungen, Hölder, Wien, §4.
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Wojciechowski, E. (1994). Types of Predication. In: Woleński, J. (eds) Philosophical Logic in Poland. Synthese Library, vol 228. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8273-5_20
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