Sunday, March 15, 2009

Polish Prof. Boguslaw Wolniewicz on the Formal Ontology of Situations

Polish Prof. Boguslaw Wolniewicz on the Formal Ontology of Situations

"The theory presented below was developed in an effort to clarify the metaphysics of Wittgenstein's Tractatus. The result obtained, however, is not strictly the formal twin of his variant of Logical Atomism. but something more, general, of which the latter is lust a special case. One might call it an ontology of situations. Some basic ideas of that ontology stern from Stenius Wittgenstein's Tractatus, Oxford, 1968 and Suszko Ontology in the Tractatus of L. Wittgenstein - Notre Dame Journal of Formal Logic, 1968.
Let L be a classic propositional language. Propositions of L are supposed to have their semantic counterparts in the realm of possibility, or as Wittgenstein put it: in logical space. These counterparts are situations, and S is to be the totality of them. The situation described by a proposition a is S(a). With Meinong we call it the objective of a."
From: Boguslaw Wolniewicz - A formal ontology of situations - Studia Logica 41: 381-413 (1982). pp. 381-382.

"Different ontologies adopt different notions of existence as basic. Aristotle's paradigm of existence is given by the equivalence:
(A) to be = to be a substance.
On the other hand, the paradigm of existence adopted in Wittgenstein's Tractatus is given by the parallel equivalence:
(W) to be = to be a fact.
Now, an Aristotelian substance is the denotation of an individual name, whereas a Wittgensteinian fact is the denotation of a true proposition. It seems therefore that the notions of existence derived from these two paradigms should be quite different, and one might readily expect that the metaphysical systems erected upon them will display wide structural discrepancies.
It turns out, however, that in spite of this basic difference there runs between these two systems a deep and striking parallelism. This parallelism is so close indeed that it makes possible the construction of a vocabulary which would transform characteristic propositions of Wittgenstein's ontology into Aristotelian ones, and conversely. To show in some detail the workings of that transformation will be the subject of this paper.
The vocabulary mentioned is based on the following four fundamental correlations:

1) primary substances (substantiae primae)
2) prime matter (materia prima)
3) form (forma)
4) self-subsistence of primary substances (esse per se)

1) atomic facts
2) objects
3) confiugration
4) independence of atomic facts

Aristotle's ontology is an ontology of substances, Wittgenstein's ontology is an ontology of facts. But concerning the respective items of each of the pairs (1)-(4) both ontologies lay down conditions which in view of our vocabulary appear to be identical. To show this let us confront, to begin with, the items of pair (1): substances and facts.
(The interpretation of Aristotle adopted in this paper is the standard one, to be found in any competent textbook of the history of philosophy. Therefore, with but one exception, no references to Aristotle's works will be given here.)Relatively to the system involved substances and facts are of the same ontological status. Aristotle's world is the totality of substances (summa rerum), Wittgenstein's world is the totality of facts (die Gesamtheit der Tatsachen). For Aristotle whatever exists in the basic sense of the word is a primary substance, for Wittgenstein - an atomic fact. Moreover, both ontologies are MODAL ones, allowing for different modes of being (modi essendi); and both take as basic the notion of `contingent being' (esse contingens), opposed to necessary being on the one hand, and to the possibility of being on the other. Both substances and facts are entities which actually exist, but might have not existed. The equality of ontological status between substances and facts is corroborated by the circumstance that both are PARTICULARS, there being - as the saying goes - no multiplicity of entities which FALL UNDER them.
Substances and facts stand also in the same relation to the ontological categories of pairs (2) and (3). Both are always COMPOUND entities, a substance consisting of matter and form, and a fact consisting of objects and the way of their configuration. But in neither of the two systems is this compoundness to be understood literally as composition of physically separable parts or pieces. The compoundness (compositio) of a substance consists in its being formed stuff (materia informata), and the compoundness of a fact in its being a configuration of objects.
In view of correlation (4) we have also an equality of relation which a substance bears to other substances, and a fact to other facts. Self-subsistence is the characteristic attribute of primary substances: substantia prima = ens per se. If we take this to mean that each substance exists independently of the existence or non-existence of any other substance we get immediately the exact counterpart of Wittgenstein's principle of logical atomism stating the mutual independence of atomic facts. It should be noted that thus understood the attribute of self-subsistence or independence is a relative one, belonging to a substance - or to a fact - only in virtue of its relation to other substances - or facts.
From a Wittgensteinian point of view Aristotle's substances are not things, but hypostases of facts, and thus their names are not logically proper names, but name-like equivalents of propositions. (By that term we mean roughly either a noun clause of the form `that p', or any symbol which might be regarded as a definitional abbreviation of such clause.) Surely, from the Aristotelian point of view it might be easily retorted here that just the opposite is the case: substances are not `reified' facts, but on the contrary - facts are 'dereified' substances. Without passing judgement on these mutual objections let us note in passing that their symmetric character seems to be itself an additional manifestation of the parallelism discussed."
From: Boguslaw Wolniewicz - 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. Dordrecht: Reidel Publishing Company 1969. pp. 208-210 (notes omitted).

SELECTED PUBLICATIONS (Works in Polish are not enclosed)
In 1970 Boguslaw Wolniewicz published a Polish translation of Ludwig Wittgenstein Tractatus logico-philosophicus.

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. Wien: Herder 1968. pp. 263-267Reprinted in: Logic and metaphysics (1999) - pp.193-197

"A note on Black's 'Companion'," Mind 78: 141 (1969).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. "

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. Dordrecht: Reidel Publishing Company 1969. pp. 208-217Proceedings of the Boston Colloquium for the philosophy of science 1966/1968.Reprinted in: Logic and metaphysics (1999) - pp.198-207

"Four notion of independence," Theoria 36: 161-164 (1970).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). "

Wittgensteinian foundations of non-Fregean logic. In Contemporary East European philosophy. Vol. 3. Edited by D'Angelo Edward, DeGrood David, and Riepe Dale. Bridgeport: Spartacus Books 1971. pp. 231-243

"The notion of fact as a modal operator," Teorema: 59-66 (1972).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."

Zur Semantik des Satzkalküls: Frege und Wittgenstein. In Der Mensch - Subjekt und Objekt (Festchrift für Adam Schaff). Edited by Borbé Tasso. Wien: Europaverl. 1973. pp.

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. Wien: Hölder-Pichler-Tempsky 1977. pp. 174-176

"Objectives of propositions," Bulletin of the Section of Logic 7: 143-147 (1978)."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."

"Situations as the reference of propositions," Dialectics and Humanism 5: 171-182 (1978)."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."

"Les situations comme corrélats semantiques des enoncés," Studia Filozoficzne 2: 27-41 (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. Wien: Hölder-Pichler-Tempsky 1978. pp. 75-77

"Some formal properties of objectives," Bulletin of the Section of Logic 8: 16-20 (1979)."The objectives of propositions as defined in an earlier paper are shown here to form a distributive lattice."

A Wittgensteinian semantics for propositions. In Intention and intentionality. Essay in honour of G. E. M. Anscombe. Edited by Diamond Cora and Teichman Jenny. Ithaca: Cornell University Press 1979. pp. 165-178"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."

"On the lattice of elementary situations," Bulletin of the Section of Logic 9: 115-121 (1980).

"On the verifiers of disjunction," Bulletin of the Section of Logic 9: 57-59 (1980).

"The Boolean algebra of objectives," Bulletin of the Section of Logic 10: 17-23 (1981)."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."

"A closure system for elementary situations," Bulletin of the Section of Logic 11: 134-139 (1982).

"On logical space," Bulletin of the Section of Logic 11: 84-88 (1982).

"Ludwig Fleck and Polish philosophy," Dialectics and Humanism 9: 25-28 (1982).

"A formal ontology of situations," Studia Logica 41: 381-413 (1982)."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 Situations1.1.The Axioms; 1.2.Some Consequences; 1.3. W-Independence; 1.4.States of Affairs;2. Sets of Elementary Situations2.1.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 Propositions3.1. 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

"Truth arguments and independence," Bulletin of the Section of Logic 12: 21-28 (1983).

"Logical space and metaphysical systems," Studia Logica 42: 269-284 (1983)."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."

"An algebra of subsets for join-semilatttices with unit," Bulletin of the Section of Logic 13: 21-24 (1984).

"A topology for logical space," Bulletin of the Section of Logic 13: 255-259 (1984).

"Suszko: a reminiscence," Studia Logica 43: 317-321 (1984).Reprinted in: Logic and metaphysics (1999) - pp.302-306

"Die Grundwerte einer wissenschaftlichen Weltauffassaung," Conceptus 19: 3-8 (1985)."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. "

"Discreteness of logical space," Bulletin of the Section of Logic 15: 132-136 (1986).

"Entailments and independence in join-semilattices," Bulletin of the Section of Logic 18: 2-5 (1989)."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."

"On atomic join-semilattices," Bulletin of the Section of Logic 18: 105-111 (1989).Reprinted in: Logic and metaphysics (1999) - pp. 307-312.
The essence of Logical Atomism: Hume and Wittgenstein. In Wittgenstein. Eine Neubewertung. Akten 14. Internationale Wittgenstein-Symposium. Vol. 1. Wien: Hölder-Pichler-Tempsky 1990. pp. 106-111

"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. Dordrecht: Kluwer 1990. pp. 199-204Reprinted in: Logic and metaphysics (1999) - pp.265-271

Elzenberg's logic of values. In Logic counts. Edited by Zarnecka-Bialy Ewa. Dordrecht: Kluwe 1990. pp. 63-70Reprinted 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.

"A sequel to Hawranek/Zygmunt," Bulletin of the Section of Logic 20: 143-144 (1991).

Needs and value. In Logic and ethics. Edited by Geach Peter. Dordrecht: Kluwer 1991. pp.

On the discontinuity of Wittgenstein's philosophy. In Peter Geach: philosophical encounters. Edited by Lewis Harry. Dordrecht: Kluwer 1991. pp. 77-81Reprinted in: Logic and metaphysics (1999) - pp. 13-17.

"A question of logic in the philosophy of religion," Bulletin of the Section of Logic 22: 33-36 (1993).

On the synthetic a priori. In Philosophical logic in Poland. Edited by Wolenski Jan. Dordrecht: Kluwer 1994. pp. 327-336

Logic and metaphysics. Studies in Wittgenstein's ontology of facts. Warsaw: Polskie Towarzystwo Semiotyczne 1999.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.

"Atoms in semantic frames," Logica Trianguli 4: 69-86 (2000)."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"."

"Extending atomistic frames," Logica Trianguli 5 (2001)."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."

Tractatus 5.541 - 5.542. In Satz un Sachverhalt. Edited by Neumaier Otto. Sankt Augustin: Academia Verlag 2001. pp. 185-190"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."

"Extending atomistic frames: part II," Logica Trianguli 6: 69-88 (2003)."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")."

"On a minimality condition," Bulletin of the Section of Logic 34: 227-228 (2005).

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