Marion Jean-Luc. Sur l'ontologie grise de Descartes. Science cartesienne et savoir aristotelicien dans les Regulae. Paris: Vrin 1975.
Revised edition 1981
Marion Jean-Luc. Sur la théologie blanche de Descartes: Analogie, création des verités eternelles, fondément. Paris:
Presses Universitaires de France 1981.
Revised edition 1991
Marion Jean-Luc. Sur le prisme métaphysique de Descartes. Constitution et limites de l'onto-théo-logie dans la pensée cartésienne.
Paris: Presses Universitaires de France 1986.
English translation by Jeffrey L. Kosky: On Descartes' metaphysical prism. The constitution and the limits of Onto-theo-logy in Cartesian thought, Chicago,
University of Chicago Press, 1999.
Mertz Donald W. Moderate realism and its logic. New Haven: Yale University Press 1996.
Mertz Donald W. Essays on realist instance ontology and its logic. Predication, structure, and identity. Frankfurt: Ontos Verlag 2006.
Articles
Mertz Donald W., "The logic of instance ontology," Journal of Philosophical Logic 28: 81-111 (1999).
Abstract: "An ontology's theory of ontic predication has implications
for the concomitant predicate logic. Remarkable in its analytic power
for both ontology and logic is the here developed Particularized
Predicate Logic (PPL), the logic inherent in the realist version of the
doctrine of unit or individuated predicates. PPL, as axiomatized and
proven consistent below, is a three-sorted impredicative intensional
logic with identity, having variables ranging over individuals x,
intensions R, and instances of intensions Ri. The power of PPL is
illustrated by its clarification of the self-referential nature of
impredicative definitions and its distinguishing between legitimate and
illegitimate forms. With a well-motivated refinement on the axiom of
comprehension, PPL is, in effect, a higher-order logic without a forced
stratification of predicates into types or the use of other ad hoc
restrictions. The Russell-Priest characterization of the classic
self-referential paradoxes is used to show how PPL diagnosis and solves
these antimonies. A direct application of PPL is made to Grelling's
Paradox. Also shown is how PPL can distinguish between identity and
indiscernibility."
Mertz Donald W., "Individuation and instance ontology," Australasian Journal of Philosophy 79: 45-61 (2001).
"A critique of James Moreland's defense of bare particulars serves as a
context for providing an alternative and sustainable account of
individuation based upon the linking-'combinatorial'-nature of ontic
predication. Displayed most clearly in polyadic predicates, an ontic
predicate is assayed as a simple particular with two abstractable
aspects: a repeatable intension and an unrepeatable unifying agency
among a subject n-tuple. The assumption that predicate instances are
complex is shown to imply either a Bradley-type regress or impossible
'bare-linkings'. An analogy is given to explicate how an entity can be
simple but found two distinct aspects."
Nef Frédéric. Logique et langage. Éssais de sémantique intensionelle. Paris: Hemés 1988.
Nef Frédéric. L'objet quelconque. Recherches sur l'ontologie de l'objet. Paris: Vrin 2000.
Nef Frédéric. Qu'est-ce que la métaphysique? Paris : Gallimard 2004.
Nef Frédéric. Les propriétés des choses. Expérience et logique. Paris: Vrin 2006.
Articles
Nef Frédéric, "Ontologie de l'objet, théorie des propriétés et théorie des ensembles: quelques problèmes
et perspectives," Revue Internationale de Philosophie 61: 181-208 (2006).
Omyla Mieczyslaw, "Translatability in non-Fregean theories," Studia Logica 35: 127-138 (1976).
Omyla Mieczyslaw, "Boolean theories with quantifiers," Bulletin of the Section of Logic 7: 76-83 (1978).
Omyla Mieczyslaw, "Basic intuitions of non-Fregean logic," Bulletin of the Section of Logic 11: 40-47 (1982).
Omyla Mieczyslaw. The logic of situations. In Language
and ontology. Proceedings of the 6th International Wittgenstein
Symposium. 23rd to 30th August 1981 Kirchber am Wechsel (Austria). Edited by Leinfellner Werner, Kraemer Eric, and Schamk Jeffrey. Wien:
Hölder-Pichler-Tempsky 1982. pp. 195-198
"Professor Roman Suszko introduced a broad class of languages into the
literature of logic. In honour of Wittgenstein Suszko named these
languages W-languages. Syntax, semantics and consequence operations in
these languages are based on the famous ontological principle: whatever
exists is either a situation, or an object, or a function. The
distinguishing property of W-languages is that they contain sentential
and nominal variables, identity connectives and identity predicates.
The intended interpretation of W-languages is such that sentential
variables range over the universum of situations, nominal variables
range over the universum of objects. All other symbols in these
languages except sentential and nominal variables are interpreted as
symbols of some functions both defined over the universum of situations
and the universum of objects. Identity connectives correspond to
identity relations between situations, and identity predicates
correspond to identity relations between objects. It is obvious that
the ordinary predicate calculus with identity is a part W-language
excluding sentential variables, but the most often used sentential
languages are the part of W-languages without nominal variables and
identity predicates. In this paper, I will discuss only W-languages
containing sentential variables, connectives and possibly quantifiers
binding sentential variables." p. 195
Omyla Mieczyslaw, "Non-Fregean logic and ontology of situations," Ruch Filozoficzny 47: 27-30 (1989).
Omyla Mieczyslaw, "The principles of non-Fregean semantics for sentences," Journal of Symbolic Logic 55: 422-423 (1990).
Omyla Mieczyslaw. Non-Fregean semantics for sentences. In Philosophical logic in Poland. Edited by Wolenski Jan. Dordrecht:
Kluwer 1994. pp. 153-165
"In this paper I intend to present the general and formal principles of
non-Fregean semantics for sentences and to derive the simplest
consequences of these principles. The semantic principles constitue
foundation of non-Fregean sentential calculus and its formal semantics
and the philosophical interpretations of it. Non-Fregean sentential
calculus is the basic part of non-Fregean logic. Non-Fregean logic is a
generalization of classical logic. It was conceived by Roman Suszko
under the influence of Wittgensteinian's Tractatus Logico-Philosophicus.
The term "non-Fregean" indicates that the set of semantic correlate of
sentences need not contain of just two elements, as it assumed by Frege
in Über Sinn und Bedeuting (1892). Frege accepted the following semantic principle:
(A.F.) all true sentences have the same common referent, and similarly all false sentences also have the one common referent.
J. Łukasiewicz interpreted the common referent of true sentences as
"Being" and analogically the common referent of all false sentences as
"Unbeing". Suszko called the principle (A.F) the "semantical version of
the Frege an axiom".
In Abolition of the Frgean Axiom (1975)
Suszko wrote: "If one accepts the Fregean Axiom then one is compelled
to be an absolute monist in the sense that there exists only one and
necessary fact".
According to Suszko (A. F.) has a counterpart in the language of
classical logic which is a formula asserting that the universe of
sentential variables is a two-element set. This formula is not
expressed that fact in the language of non-Fregean logic.
In SCI and modal systems
(1972) Suszko presents the properties of his logic as follows: "...
nonFregean logic is the realization of the Fregean program in pure
logic, logically bi-valent and extensional with two modifications: (1)
keep formulas (sentences) and termes (names) as disjoint syntactic
categories, having sense and denotations,as well, and (2) drop the
desperate assumption that all true or false senetences have the same
denotation (not sense that is proposition)"." pp. 153-154.
Omyla Mieczyslaw. A formal ontology of situations. In Formal ontology. Edited by Poli Roberto and Simons Peter. Dordrecht:
Kluwer 1996. pp. 173-187
"The theoretical foundation for this paper is the system of a
non-Fregean logic created by Roman Suszko under the influence of
Wittgenstein's Tractatus Logico-Philosophicus. In fact, we use just a fragment of it called here a non-Fregean sentential logic.
Our basic term is that of a 'situation'. We do not answer the question
what situations are. We simply assume that sentences present
situations, and we provide a criterion determining when two sentences
of some fixed language present the same situation.
The lay-out of this paper is the following. First we set out certain
philosophical consequences of the assumption adopted in classical logic
that the only connectives of the language in question are the
truth-functional ones. Then we sketch out briefly the axiomatics of
non-Fregean sentential logic, and of a formal semantics of the
algebraic type for it.
Next, for an arbitrary model for a non-Fregean sentential logic, we
pick out from the formulae true in that model a theory to be called the
'ontology of situations determined by the model in question' - in
contradistinction to all sentences holding contingently in that model,
i.e. not determined by its algebra. In the ontology of situations
determined by a model we point out those propositions which pertain to
possible worlds." p. 173
Philosophical Interpretations of non-Fregean Sentential Logic
According to the principles of non-Fregean semantics as presented in
Omyla 1975, all sentences of an interpreted language have their
references. However, not in every such language are we in a position to
put forward universal and existential theorems with regard to the
structure of the universe of those references. To be in such position
the language in question must contain as its sublanguage the language
of non-Fregean sentential logic, or at least a significant part of it.
As we are not interested here in the universe of any particular
language, but only in that of a quite arbitrary one, let us consider
now some philosophical aspects of arbitrary models of that kind. Let M
= (U, F) be such a model. The elements of the universe of U do not
generally answer to the intuitions we have about the reference of
sentences, and about situations in particular. However, the algebraic
structure imposed on U by the theory TR(M) is the same as that of a
possible universe of situations, with regard to the operations
corresponding to logical constants. Moreover, the set F has the formal
properties of a possible (or 'admissible') set of situations obtaining
in that universe. This is so because sentential variables are at the
same time sentential formulae, and because the logical constants get in
the model M their intended interpretation. Thus for any model M = (U,
F) its algebra U is a formal representation of some universe of
situations, and the set F is a formal representation of some admissible
set of facts obtaining in some universe of situations. Not all the
generalized SCI-algebras represent some algebra of situations; for not
all of them contain a set F representing the facts, i.e. such that the
couple (U, F) is a model. This depends on how the operations in the
algebra U are defined. For the sake of simplicity the algebra of any
model M = (U, F) for the language of a non-Fregean sentential logic
will be called the algebra of situations occurring in the model M, and the designated set F will be called the set of facts obtaining
in M. Such a terminology is appropriate here for we are interested only
in the formal properties of those universe of situations which in view
of our semantic principles find expression in the logical syntax of the
language in question, and in consequence operation holding in it. By
the completeness theorem for non-Fregean logic it follows that for any
consistent theory T in L there is a model M such that T e TR(M). Hence
any theory in the language of non-Fregean sentential logic will be
called a theory of situations. The term 'ontology of situations' we take over from the title of Wolniewicz 1985 [Ontologia sytuacji: Ontology of situations
in Polish], but we understand it a bit differently. By an ontology of situations we
mean a theory describing the necessary facts of universe of situations
fixed beforehand. I.e. an ontology of situations is a set of formulae
holding in some fixed universe of situations, independently of which
situations there are facts. To be more accurate, by an ontology of
situations we mean a set of formulae with the following three
properties:
( 1) An ontology of situations is a theory having in its vocabulary
just one kind of variable - e. the sentential one. Under the intended
interpretation they range over a universe of situations. (Like in modem
set theory there are variables of just one kind, i.e. those ranging
over sets.)
(2) An ontology of situations is formulated in a language containing
logical symbols only, i. e. logical constants and variables. To justify
that postulate let us note that such a basic theory should not
presuppose any other terminology except the logical one. At most it
might adopt some specific ontological terms as primitive,
characterizing them axiomatically. However, we shall deal here only
with such ontologies of situations which are expressed exclusively in
logical terms." pp. 180-181.
Omyla Mieczyslaw, "Possible worlds in the language of non-Fregean logic," Studies in Logic, Grammar and Rhetoric 6: 7-15 (2003).
"The term "possible world" is used usually in the metalanguage of modal
logic, and it is applied to the interpretation of modal connectives.
Surprisingly, as it has been shown in Suszko Ontology in the Tractatus L. Wittgenstein (1968)
certain versions of that notion can be defined in the language of
non-Fregean logic exclusively, by means of sentential variables and
logical constants. This is so, because some of the non-Fregean theories
contain theories of modality, as shown in Suszko Identity Connective and Modality (1971).
Intuitively, possible worlds are maximal (with respect to an order of
situations) and consistent situations, while the real world may be
understand as a situation, which is a possible world and the fact.
Non-Fregean theories are theories based on the non-Fregean logic.
Non-Fregean logic is the logical calculus created by Polish logician
Roman Suszko in the sixties. The idea of that calculus was conceived
under the influence of Wittgenstein's Tractatus. According to
Wittgenstein, declarative sentences of any language describe
situations."
Pasniczek Jacek. The logic of intentional objects. A Meinongian version of Classical logic. Dordrecht: Kluwer 1997.
Articles
Pasniczek Jacek. The Meinongian logic vs. the Classical logic. In Theories of Objects: Meinong and Twardowski. Edited by Pasniczek Jacek.
Lublin: Wydawnictvo Uniwersytetu Marii Curie-Sklodoskiej 1992. pp. 105-112
Pasniczek Jacek, "The simplest Meinongian logic," Logique et Analyse 143-144: 329-342 (1993).
"The Meinongian logic is a logic which accommodates main principles of
Meinong's theory of objects. This principles give rise to a very
extensive ontology which contains various kind of nonexistent entities
(e.g., incomplete and impossible ones). In the paper quite a simple
Meinongian logic is developed. This logic has the following features:
1) it is extensional, 2) it differs slightly from the classical
first-order logic, 3) it is a first-order system, 4) it is closer to
the natural language than classical logic, 5) it is much more simple
than Meinongian systems created by T. Parsons and E. Zalta."
Pasniczek Jacek, "Ways of reference to Meinongian objects. Ontological commitment of Meinongian theories," Logic and Logical Philosophy
2: 69-86 (1994).
Pasniczek Jacek, "Lesniewski's Ontology vs. Meinongian ontology ((Toward a Meinongian calculus of names)," Axiomathes: 279-286 (1996).
Petitot Jean. Morphogenèse du Sens. Pour un schématisme de la structure. Paris: Presses Universitaires de France 1985.
English translation by Franson Manjali - Morphogenesis of meaning - Bern, Peter Lang, 2003
Petitot Jean. Naturalizing phenomenology. Issues in contemporary phenomenology and cognitive science.
Edited by Petitot Jean et al. Stanford: Stanford University Press 1999.
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