Theory and History of Ontology
by Raul Corazzon | e-mail: rc@
ontology.co
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In 1970 Boguslaw Wolniewicz published a Polish translation of Ludwig Wittgenstein Tractatus logico-philosophicus.
Wolniewicz, Boguslaw. 1968. "A Difference between Russell's and Wittgenstein's Logical Atomism." In Akten Des Xiv. Internationalen Kongresses Für Philosophie. Wien, 2. - 9. September 1968 - Vol. Ii, 263-267. Wien: Herder.
Reprinted in: Logic and metaphysics (1999) - pp. 193-197
———. 1969. "A Note on Black's 'Companion'." Mind no. 78:141.
Reprinted in: Logic and metaphysics (1999) - p. 229.
"It is a mistake to suppose that in Wittgenstein's "Tractatus" the meaning of Urbild has any connexion with that of picture. "
———. 1969. "A Parallelism between Wittgensteinian and Aristotelian Ontologies." In Boston Studies in the Philosophy of Science. Vol. Iv, edited by Cohen, Robert S. and Wartofsky, Marx W., 208-217. Dordrecht: Reidel Publishing Company.
Proceedings of the Boston Colloquium for the philosophy of science 1966/1968.
Reprinted in: Logic and metaphysics (1999) - pp. 198-207
———. 1970. "Four Notion of Independence." Theoria no. 36:161-164.
Reprinted in: Logic and metaphysics (1999) - pp. 127-130.
WFour (binary) relations of independence I(p,q) between propositions are distinguished: the Wittgensteinian I sub-w, the statistical I sub-s, the modal I sub-m, and the deductive I sub-d. The validity of the following theorem is argued for: I sub-w(p,q) implies I sub-s(p,q) implies I sub-m(p,q) implies Isub-d(p,q). "
———. 1971. "Wittgensteinian Foundations of Non-Fregean Logic." In Contemporary East European Philosophy. Vol. 3, edited by D'Angelo, Edward, DeGrood, David and Riepe, Dale, 231-243. Bridgeport: Spartacus Books.
———. 1972. "The Notion of Fact as a Modal Operator." Teorema:59-66.
Reprinted in: Logic and metaphysics (1999) - pp. 218-224
"The notion of fact /fp = "it is a fact that p"/ is characterized axiomatically, and the ensuing modal systems shown to be equivalent to tT, S4 and S5 respectively."
———. 1973. "Zur Semantik Des Satzkalküls: Frege Und Wittgenstein." In Der Mensch - Subjekt Und Objekt (Festchrift Für Adam Schaff), edited by Borbé, Tasso. Wien: Europaverl.
———. 1977. "Sachlage Und Elementarsätz." In Wittgenstein and His Impact on Contemporary Thought. Proceedings of the Second International Wittgenstein Symposium, 29th August to 4th September 1977, Kirchberg/Wechsel (Austria), edited by Leinfellner, Elisabeth, 174-176. Wien: Hölder-Pichler-Tempsky.
———. 1978. "Situations as the Reference of Propositions." Dialectics and Humanism no. 5:171-182.
"The reference of propositions is determined for a class of languages to be called the "Wittgensteinian" ones. A meaningful proposition presents a possible situation. Every consistent conjunction of elementary propositions presents an elementary situation. The smallest elementary situations are the "Sachverhalte"; the greatest are possible worlds. The situation presented by a proposition is to be distinguished from that verifying it, but the greatest situation presented is identical with the smallest verifying. The reference of compound propositions is then determined as a function of their components."
———. 1978. "Objectives of Propositions." Bulletin of the Section of Logic no. 7:143-147.
"The paper sketches out a semantics for propositions based upon the Wittgensteinian notion of a possible situation. The objective of a proposition is defined as the smallest situation verifying it. Two propositions are assumed to have the same objective iff they are strictly equivalent. Formulas are given which determine the objectives of conjunction and disjunction as functions of the objectives of their components. finally a link with possible-world semantics is established."
———. 1978. "Wittgenstein Und Der Positivismus." In Wittgenstein, the Vienna Circle and Critical Rationalism. Proceedings of the Third International Wittgenstein Symposium, 13th to 19th August 1978, Kirchberg Am Wechsel (Austria), edited by Bergehel, Hal, Hübner, Adolf and Eckehart, Köhler, 75-77. Wien: Hölder-Pichler-Tempsky.
———. 1978. "Les Situations Comme Corrélats Semantiques Des Enoncés." Studia Filozoficzne no. 2:27-41.
———. 1979. "A Wittgensteinian Semantics for Propositions." In Intention and Intentionality. Essay in Honour of G. E. M. Anscombe, edited by Diamond, Cora and Teichman, Jenny, 165-178. Ithaca: Cornell University Press.
"More than once Professor Anscombe has expressed doubt concerning the semantic efficacy of the idea of an 'elementary proposition' as conceived in the Tractatus. Wittgenstein himself eventually discarded it, together with the whole philosophy of language of which it had been an essential part. None the less the idea is still with us, and it seems to cover theoretical potentialities yet to be explored. This paper is a tentative move in that direction.
According to Professor Anscombe, (*) Wittgenstein's 'elementary propositions' may be characterized by the following five theses:
(1) They are a class of mutually independent propositions.
(2) They are essentially positive.
(2) They are such that for each of them there are no two ways of being true or false, but only one.
(4) They are such that there is in them no distinction between an internal and an external negation.
(5) They are concatenations of names, which are absolutely simple signs.
We shall not investigate whether this is an adequate axiomatic for the notion under consideration. We suppose it is. In any case it is possible to modify it in one way or another, and for the resulting notion still to preserve a family resemblance with the original idea. One such modification is sketched out below."
———. 1979. "Some Formal Properties of Objectives." Bulletin of the Section of Logic no. 8:16-20.
"The objectives of propositions as defined in an earlier paper are shown here to form a distributive lattice."
———. 1980. "On the Lattice of Elementary Situations." Bulletin of the Section of Logic no. 9:115-121.
———. 1980. "On the Verifiers of Disjunction." Bulletin of the Section of Logic no. 9:57-59.
———. 1981. "The Boolean Algebra of Objectives." Bulletin of the Section of Logic no. 10:17-23.
"This concludes a series of papers constructing a semantics for propositional languages based on the notion of a possible "situation". Objectives of propositions are the situations described by them. The set of objectives is defined and shown to be a boolean algebra isomorphic to that formed by sets of possible worlds."
———. 1982. "A Formal Ontology of Situations." Studia Logica no. 41:381-413.
"A generalized Wittgensteinian semantics for propositional languages is presented, based on a lattice of elementary situations. Of these, maximal ones are possible worlds, constituting a logical space; minimal ones are logical atoms, partitioned into its dimensions. A verifier of a proposition is an elementary situation such that if real it makes true. The reference (or objective) of a proposition is a situation, which is the set of all its minimal verifiers. (Maximal ones constitute its locus.) Situations are shown to form a Boolean algebra, and the Boolean set algebra of loci is its representation. Wittgenstein's is a special case, admitting binary dimensions only."
Contents:
0. Preliminaries;
1. Elementary Situations
1.1.The Axioms; 1.2.Some Consequences; 1.3. W-Independence; 1.4.States of Affairs;
2. Sets of Elementary Situations
2.1.The Semigroup of SE"-Sets; 2.2.The Lattice of Minimal SE"-Sets; 2.3.Q-Spaces and V-Sets; 2.4.V-Equivalence and Q-Equivalence; 2.4.V-Classes and V-Sets;
3. Objectives of Propositions
3.1. Verifiers of Propositions; 3.2. Verifying and Forcing; 3.3. Situations and Logical Loci; 3.4. Loci and Objectives of Compound Propositions 3.5. The Boolean Algebra of Situations;
4. References
———. 1982. "Ludwig Fleck and Polish Philosophy." Dialectics and Humanism no. 9:25-28.
———. 1982. "A Closure System for Elementary Situations." Bulletin of the Section of Logic no. 11:134-139.
———. 1982. "On Logical Space." Bulletin of the Section of Logic no. 11:84-88.
———. 1983. "Logical Space and Metaphysical Systems." Studia Logica no. 42:269-284.
"The paper applies the theory presented in "A formal ontology of situations" (Studia Logica, vol. 41 (1982), no. 4) to obtain a typology of metaphysical systems by interpreting them as different ontologies of situations.
Four are treated in some detail: Hume's diachronic atomism, Laplacean determinism, Hume's synchronic atomism, and Wittgenstein's logical atomism. Moreover, the relation of that theory to the "situation semantics" of Perry and Barwise is discussed."
———. 1983. "Truth Arguments and Independence." Bulletin of the Section of Logic no. 12:21-28.
———. 1984. "An Algebra of Subsets for Join-Semilatttices with Unit." Bulletin of the Section of Logic no. 13:21-24.
———. 1984. "A Topology for Logical Space." Bulletin of the Section of Logic no. 13:255-259.
———. 1984. "Suszko: A Reminiscence." Studia Logica no. 43:317-321.
Reprinted in: Logic and metaphysics (1999) - pp. 302-306
———. 1985. "Die Grundwerte Einer Wissenschaftlichen Weltauffassaung." Conceptus no. 19:3-8.
"The scientific world-view is one of the fundamentals of our culture. It can be characterized in part by its specific system of values. A world-view is regarded as a scientific one if "truth" is one of its primary values, that is, as a value which is not a means, but an end in itself. Truth is served in particular by the two instrumental values of conceptual clarity and openness to critique. Their standing is (at present) low, for two reasons. (1) Unclear thinking not only promotes social idols; its consequences are also often difficult to see clearly and immediately. (2) In any case truth is of no interest (in a biological sense) to human beings; therefore, critique can at best be a socially tolerated activity. On the other hand, truth is not only a value, but also a force which in the long run cannot be held back; this fact gives some hope to adherents of the scientific world-view. "
———. 1986. "Discreteness of Logical Space." Bulletin of the Section of Logic no. 15:132-136.
———. 1989. "Entailments and Independence in Join-Semilattices." Bulletin of the Section of Logic no. 18:2-5.
"The paper generalizes Wittgenstein's notion of independence. in a join-semilattice of elementary situations the atoms are the Sachverhalte, and maximal ideals are possible worlds. A subset of that semilattice is independent iff it is free of "ontic ties". This is shown to be equivalent to independence in von Neumann's sense."
———. 1989. "On Atomic Join-Semilattices." Bulletin of the Section of Logic no. 18:105-111.
Reprinted in: Logic and metaphysics (1999) - pp. 307-312.
———. 1990. "A Question About Join-Semilattices." Bulletin of the Section of Logic:108.
———. 1990. "Concerning Reism in Kotarbinski." In Kotarbinski: Logic. Semantics and Ontology, edited by Wolenski, Jan, 199-204. Dordrecht: Kluwer.
Reprinted in: Logic and metaphysics (1999) - pp. 265-271
———. 1990. "Elzenberg's Logic of Values." In Logic Counts, edited by Ewa, Zarnecka-Bialy, 63-70. Dordrecht: Kluwe.
Reprinted in: Logic and metaphysics (1999) - pp. 286-292 (with the title: Elzenberg's axiology"
"1. Values are what our value-Judgements refer to, and the passing of Judgements is one of our vital activities, like sleeping and breathing. We constantly appraise things as good or bad, pretty or ugly, as noble or base, well-made or misshapen. No wonder that both the act of appraisal and that which it refers to - i.e. the real or spurious values - have been always the source of philosophical reflexion. In systematic form such reflexion is what we call axiology.
In Polish philosophy it was Henryk Elzenberg (1887-1967) who reflected upon matters of axiology most deeply and incisively.
(...)
3. Leibniz had said somewhere: "There are two mazes in which the human mind is most likely to get lost: one is the concept of continuity, the other is that of liberty". This admits of generalization: all concepts are mazes, viz mazes of logical relations between the propositions that involve them.
One such maze is the concept of 'value'. Possibly, it is even the same as one of the two mentioned by Leibniz, only entered - so to say - by another door. For it would be in full accord with Elzenberg's position - and with that of Kant too - to adopt the following characteristic: values are what controls the actions of free agents. Thus the concepts of value and of liberty should constitute one conceptual maze, or - which comes to the same - two mazes communicating with each other.
To get a survey of such logical maze the first thing is to fix the ontological category of the concept in question. Thus, in our case, we ask what kind of entities are those 'values' supposed to be. (Ontological categories are the most general classes of entities, the summa genera A term even more general has to cover literally everything: like 'entity' or 'something'. For everything is an entity, just as everything is a something.)
Different ontologies admit different sets of categories. The categories most frequently referred to are those of 'objects', 'properties', and 'relations'; the more exotic ones are those of an 'event', a 'set', a 'function', or a 'situation'. One point, however, is of paramount importance: the categories admitted In one ontology have to be mutually disjoint". p. 63; 66.
———. 1990. "The Essence of Logical Atomism: Hume and Wittgenstein." In Wittgenstein. Eine Neubewertung. Akten 14. Internationale Wittgenstein-Symposium. Vol. 1, 106-111. Wien: Hölder-Pichler-Tempsky.
———. 1991. "Needs and Value." In Logic and Ethics, edited by Geach, Peter Thomas, 289-302. Dordrecht: Kluwer.
———. 1991. "A Sequel to Hawranek/Zygmunt." Bulletin of the Section of Logic no. 20:143-144.
———. 1991. "On the Discontinuity of Wittgenstein's Philosophy." In Peter Geach: Philosophical Encounters, edited by Lewis, Harry A., 77-81. Dordrecht: Kluwer.
Reprinted in: Logic and metaphysics (1999) - pp. 13-17.
"How is Wittgenstein's later philosophy related to his earlier one?
Despite much discussion there is little clarity on that. So let us give it again some consideration.
(...)
Philosophy of language oscillates between the two poles of metaphysics and psychologism; (...) . The main representative of the former trend is Frege, and the Tractatus follows closely in his wake. The Philosophical Investigations, on the other hand, are the expression of a dramatic departure from Frege and towards psychologism. Language is now viewed by Wittgenstein not in its logical capacity as the medium of thought and the bearer of truth-value, but instrumentally as a means of communication. Its relation to reality fades out, and its connexion with feeling, thinking, and doing comes massively to the fore.
Psychologism and positivism go hand in hand. Metaphysics, though not condemned as a vice as in pure positivism, is viewed as a malaise to be cured. Thus Wittgenstein's later philosophy turns into a kind of psychotherapy, exerting itself to bring metaphysics to a stop. What for? This is never made clear, as if it were a matter of course. But it is not." (pp. 80-81)
———. 1993. "A Question of Logic in the Philosophy of Religion." Bulletin of the Section of Logic no. 22:33-36.
———. 1994. "On the Synthetic a Priori." In Philosophical Logic in Poland, edited by Wolenski, Jan, 327-336. Dordrecht: Kluwer.
———. 1999. Logic and Metaphysics. Studies in Wittgenstein's Ontology of Facts. Warsaw: Polskie Towarzystwo Semiotyczne.
Contents: Preface 11; Discontinuity of Wittgenstein's philosophy 13; 1. Elementary situations as a lattice of finite length 19; Elementary situations as a semilattice 73; 3. Independence 127; 4. Elementary situations generalized 137; 5. Auxiliary studies 193; 5.1 The Logical Atomisms of Russell and Wittgenstein 193; 5.2 A parallelism between Wittgenstein and Aristotle 198; 5.3 Frege's semantics 207; 5.4. The notion of fact as a modal operator 218; 5.5 "Tractatus" 5.541 - 5.542 224; 5.6 History of the concept of a Situation 229; 6. Offshoots 243 6.1 Languages and codes 243; 6.2 Logic and hermeneutics 254; 6.3 Kotarbinski's Reism 265; 6.4 On Bayle's critique of theodicy 271; 6.5 Elzenberg's axiology 286; 6.6 Needs and values 293; 6.7 Suszko: a reminiscence 302; Supplements 307; Indices: Index of subjects 317; Index of names 326; Index of Tractatus references 329.
———. 2000. "Atoms in Semantic Frames." Logica Trianguli no. 4:69-86.
"Elaborating on Wittgenstein's ontology of facts, semantic frames are described axiomatically as based on the notion of an elementary situation being the verifier of a proposition. Conditions are investigated then for suchframes to be atomic, i.e. to have lattice-theoretic counterparts of his "Sachverhalte"."
———. 2001. "Extending Atomistic Frames." Logica Trianguli no. 5.
"A "semantic frame" is bounded join-semilattice of elementary situations, with its maximal ideals to represent possible worlds and mapped into the complete sets of propositions determined by a given abstract logic ( L, Cn). A frame is Humean if the elementary situations are separated by its possible worlds, and it is atomistic if the semilattice is so. One frame is the extension of another if the latter is an {0,1}-subsemilattice of the former satisfying certain conditions discussed."
———. 2001. "Tractatus 5.541 - 5.542." In Satz Un Sachverhalt, edited by Neumaier, Otto, 185-190. Sankt Augustin: Academia Verlag.
"In Wittgenstein's "Tractatus", thesis 5 is the Principle of Extensionality: all propositions are truth-functions of their clauses. This, however, has been often thrown into doubt. There are - it is said - compound propositions whose truth-value does not depend on that of their clauses. The usual example given are the so-called intensional contexts, like "John thinks that p", or "John says that p". And indeed, the truth-value of "p" is patently immaterial here to that of the whole proposition which it is part of.
Wittgenstein's retort are the following much discussed theses, adduced here in a translation of our own:
5.54 In the general propositional form, propositions occur in one another only as bases of truth-operations.
5.541 At first sight it seems that a proposition might occur in another also in a different way.
Particularly in certain propositional forms of psychology, like "A believes that p is the case", "A thinks p", etc.
For taken superficially, proposition p seems here to stand to the object A in some sort of relation.
(And in modem epistemology - Russell, Moore, etc. - these have actually been construed that way.)
5.542 However, "A believes that p", "A thinks p", "A says p" are clearly of the form " 'p' says p "; and this is not correlating a fact with an object, but a correlation of facts by correlating their objects.
The objection is met here in two steps. Firstly, it is pointed out that a proposition of the form "John says that p" is actually of the form "'p' says that p". The idea is this: the proposition "John says that Jill has a cat" means: John produces the sentence "Jill has a cat", the latter saying by itself that Jill has a cat. In such a way propositions get independent of the persons producing them, and communicate some objective content. It is surely not by John's looks that we come to know about Jill's cat, but merely by his words. Whom they stem from, is irrelevant.
In his second step Wittgenstein follows Frege's interpretation of indirect speech, but with modifications. He points out that the formula " 'p' says that p " is equivalent to some compound proposition in which neither the proposition "p" as a syntactic unit, nor anything equivalent to it, does occur although there occur all the logically relevant constituents of "p" separately.
(...)
The distinction between abstract and concrete states of affairs is not drawn explicitly in the "Tractatus". But it fits well thesis 5.156, if we expand that thesis by a few words of comment, added here in brackets:
5.156(d) A proposition may well be en incomplete image of a particular (concrete) situation, but it is always the complete image (of an abstract one).
The circumstance that in 5.156 not "states of affairs", but "situations" are mentioned, is of no consequence in our context. We assume that states of affairs are just atomic situations, and so the distinction between "concrete" and "abstract" applies to both."
———. 2003. "Extending Atomistic Frames: Part Ii." Logica Trianguli no. 6:69-88.
"The paper concludes an earlier one (Logica Trianguli, 5) on extensions of atomistic semantic frames. Three kinds of extension are considered: the adjunctive, the conjunctive, and the disjunctive one. Some theorems are proved on extending "Humean" frames, i.e. such that the elementary situations constituting their universa are separated by the maximally coherent sets of them ("realizations")."
———. 2005. "On a Minimality Condition." Bulletin of the Section of Logic no. 34:227-228.
On the website "Theory and History of Ontology" (www.ontology.co)
Kazimierz Twardowski on the Content and Object of Presentations
Stanislaw Lesniewski's Logical Systems: Protothetic, Ontology, Mereology
Tadeusz Kotarbinski from Ontological Reism to Semantical Concretism
Roman Suszko and the Non-Fregean Logics
Roman Ingarden: Ontology as a Science on the Possible Ways of Existence