Living
Ontologists (a list of authors with an interest in ontology, with
synthetic bibliographies)
INTRODUCTION
"Lesniewski defined ontology, one of his three foundational systems, as 'a certain kind of modernized 'traditional logic' [On the foundations of mathematics (FM), p. 176]. In this respect it is worth bearing in mind that in the 1937-38 academic year Lesniewski taught a course called "Traditional 'formal logic' and traditional 'set theory' on the ground of ontology"; cf. Srzednicki and Stachniak, S. Lesniewski's Systems. Protothetic, 1988, p. 180.
On this
see Kotarbinski Gnosiology. The scientific
approach to the theory of knowledge, 1966, pp. 253-54 [the Polish original was published in 1929], which Lesniewski praised in [FM]: see in particular pp. 373 ff. Kotarbinski noted that Lesniewski "calls his system 'ontology' in harmony with certain terms used earlier (as in the 'ontological principle of contradiction')", and in strict relation to the Greek root of 'ontology' as the participle of the verb 'to be'. Lesniewski's 'ontology' is therefore "closely connected with traditional Aristotelian
formal logic, of which it is an extension and an improvement, while on the other hand it is a terminal point in the attempt to construct a calculus of names in the area of logistic ... If in spite of these reasons we do not use the word 'ontology' here as a name for the calculus of names, this is only because of the fear of a misunderstanding. Misunderstanding could arise from the fact that this name has its roots already in another role, i.e., it has been long agreed to call 'ontology' the enquiry 'on the general
principles of existence' conducted in the spirit of certain parts of Aristotelian 'metaphysical' books. It has to be admitted however, that if the Aristotelian definition of the main theory (prote filosofia) discussed in those books is interpreted in the spirit of a 'general theory of objects', then both the word and its meaning, can be applied to the calculus of names of Lesniewski", Kotarbinski 1966, pp. 373-374. Lesniewski commented on Kotarbinski's remarks thus: "I used the name 'ontology'
to characterize
the theory I was developing, without offence to my 'linguistic instincts' because I was formulating in that theory a certain kind of 'general principles of existence"' [FM, 374].
Given these premises, we gain clearer understanding of his interest in the principles of non-contradiction [PC] and excluded middle [EM], as well as his references to the theory of conversion (p. 68 ff), of the suppositio (p. 18) and of the validity of the syllogism (p. 71 ff). This inquiry was encouraged by his interest in the history of logic and in the formal treatment of the problems of classical philosophy by the Lvov-Warsaw school. Jan Łukasiewicz's (1886-1939)
research into the history of propositional
calculus, the Aristotelian syllogistic and the principle of non-contradiction are well known. (...) Twardowski, the founder of the school, was also interested in traditional logic. As a lecturer at the University of Lvov, for many years he taught a course on Attempts to reform traditional logic, in which he outlined the theories of Bolzano, Brentano, Boole and Schröder; cf. Dambska François Brentano et la pensée philosophique en Pologne: Casimir Twardowski et son École, Grazer
philosophischen
Studien, 5, 1978, p. 123.";
From: Roberto Poli and Massimo Libardi - Logic, theory of science, and metaphysics according to Stanislaw Lesniewski - Grazer Philosophische Studien 57, 1999 pp. 187-188.
"In the period between the two world wars, Stanislaw Lesniewski (1886-1939), one of the founders and a prominent member of the Warsaw School of Logic, created a system of the foundations of mathematics comprising three deductive theories: Protothetic, Ontology, and Mereology. The point of departure for the construction of this system was his study of logical paradoxes and, in this context, a distinction between the distributive and collective interpretations of a
class. This distinction between the two interpretations was reflected in the development of two deductive theories, the theory of collective classes, which he eventually called Mereology, and the theory of distributive classes, called Ontology. Finally, in order to combine Mereology and Ontology into a logically rigorous system, he constructed Protothetic — the system of "First principles." Lesniewski's ambition was "not to add one more calculus to the variety already invented, nor even to prove
general metatheorems about alternative formal calculi, in the interests of "comparative logic"; it was instead to perfect a universally valid classical system of logic and foundations of mathematics, in which he could rigorously formulate generalizations expressible only in the metalanguages of systems poorer in means of expression, [... ] and on which he could rely as a true instrument of deduction and scientific investigation (Luschei, The logical systems of Lesniewski, 1962, p. 24)."This
program was initiated by Lesniewski in 1914 with his studies on a general theory of sets (later to be named 'Mereology'). The first version of Mereology appeared in print in 1916 under the title Foundations of a General Theory of Sets. I (in Polish).
In 1919, Lesniewski joined the University of Warsaw as a professor of the philosophy of mathematics. He met a group of gifted mathematicians, Zygmunt Janiszewski, Stefan Mazurkiewicz, Waclaw Sierpidski, whose research interests, like those of Lesniewski, were focused on the foundations of mathematics. In 1920 this group, joined by Jan Łukasiewicz, founded the mathematical journal Fundamenta Mathematicae with Mazurkiewicz and Sierpiriski as editors, and Lesniewski
and Łukasiewicz as members of the editorial board. The name, scope, and membership of the editorial board of the journal adequately reflected the research activities of the Warsaw schools of mathematics and logic during the first decade of the journal's existence.
The construction of Ontology in the period between 1919-1921, marked the next step in the formation of Lesniewski's system of the foundations of mathematics, although it was not until 1930 that Ontology appeared in print (cf. Lesniewski, 1930).
The construction of Protothetic began in 1922 and went quickly through numerous improvements and modifications, to be concluded in 1923. By then, Lesniewski's system of the foundations of mathematics was formally ready and, to quote Jordan, it was "the most thorough, original, and philosophically significant attempt to provide a logically secure foundation for the whole of mathematics" (cf. Jordan, 1945).
Even such a critic of the importance of Lesniewski's contribution to modern logic as Grzegorczyk admitted that "Lesniewski's treatment of logic was in his times the most exact; it was simpler than Principia [Mathematica] and had it been published simultaneously with the second edition of the Principia, it would have played a considerable part in the development of logic" (Grzegorczyk, 1955, p. 78)."
The roots of Protothetic can already be found in Lesniewski's early writings between 1912 and 1914. The "deductions" in his 1916 work on the general theory of sets are based on his logical intuitions which eventually were captured in the axioms and directives of Protothetic and Ontology. "
From the Editor's Foreword to: S. Lesniewski's Systems. Protothetic - Edited by Jan Srzednicki Jan and Zbigniew Stachniak - ;Dordrecht, Kluwer, 1998, pp. VII-VIII.
APPLICATIONS OF LESNIEWSKI'S ONTOLOGY
Tadeusz Kotarbinski (1) made the following comment on Lesniewski's ontology: « It must be however admitted if the Aristotelian definition of the supreme theory... be interpreted in the spirit of a "general theory of objects", then both the word ["ontology" — J. W.] and its meaning are applicable to the calculus of terms as expounded by Lesniewski ».
Lesniewski (2) himself fully shared this opinion : «I used the name "ontology" to characterize the theory which I was developing without offence to my "linguistic instincts" because I was formulating in that theory a certain kind of "general principles of existence"» (3).
Both quotations suggest looking at Lesniewski's ontology (hereafter LO) for insights for philosophical ontology. This is precisely what I would like to do in this paper (4).
That Lesniewski's logical systems have interesting applications in philosophy has already been pointed out by several authors. For example:
— Lejewski's (5) works about multicategorial and unicategorial languages and ontologies. In particular, Lejewski shows how Lesniewski's ideas help in speaking on non- existents without falling into Platonism or Meinongianism;
— Simon's (6) study on parts and wholes ;
— Lejewski's and Wolenski's (7) attempts to interpret Kotarbinski's reism by means of LO (8) ;
— Waragai's (9) formalization of fundamental ontological principles in the framework of LO ;
— Henry's (10) uses of LO in his reconstructions of medieval logic and semantics.
My concern here is more general. I will try to show how to attack the concept of being by means of Lesniewski's logic. Before going on to do this, however, I would like to make some comments on the relation of Lesniewski's logic to nominalism. The first impression is that mereology is particularly important in this respect. Certainly, this is correct, because mereology formalizes the part/whole relation which is crucial for nominalism. The usual interpretation of mereology
provides a formalization of the theory of physical parts in Brentano's sense. Simons (11) shows that one can also obtain a nice mereological interpretation of «being a part in the metaphysical sense». Now there remains the problem of mereology which would be suitable for a theory of logical parts. This is probably equivalent to finding a mereology similar in its expressive power to set theory.
At first glance, both first-order logic and Lo seem to be equally good as logical bases for nominalism. However, this is not the case because, although first-order quantifiers range over individuals, the standard semantics for elementary quantification theory must appeal to sets and relations Lesniewski's Logic and the Concept of Being as referents of predicates. On the other hand, if we take Lejewski's (12) ontological tables as semantic models of nominal phrases in
LO, we easily see that all nominal expressions exclusively refer to individual things. Moreover, the identity predicate is definable in elementary ontology, though it must be added as a new primitive to elementary logic or defined by second-order means. Finally, looking at nominalism through «Lesniewskian glasses» we can see that the metaphysical nature of individuals is not especially important for nominalism. Now it is not especially surprising that Quine's ontology is sometimes qualified as nominalistic
Platonism. It is only strange for anybody who thinks about nominalism as a kind of materialism. What Lo shows is that nominalism consists in abandoning general objects, essences common to many individuals and the like. I am not claiming that the marriage of nominalism and Lo secures victory for the former. My intention rather, is to show that Lo helps nominalists much more than does first-order logic."
1. T. Kotarbinski, Gniosology, The Scientific Approach to the Theory of Knowledge, tr. by O. Wojtasiewicz, Pergamon Press Ossolineum, Oxford-Wroclaw, pp. 210-211.
2. S. Lesniewski, «O podstawach matematyki» [On the Foundations of Mathematics], Przeglad filozoficzny 34, 142-170 ; Eng. tr. in Lesniewski, Collected Works, ed. by S. J. Surma, J. T. Srzednicki, D. I. Barnett and V. F. Rickey, Kluwer, Dordrecht, 1992, p. 374.
3. This translation seems inadequate. It should rather be «general principles of being» (in the Polish original, we have «ogolne zasady bytu», not «ogolne zasady istnienia»). Lesniewski clearly distinguished « being » [byt] from « existence » [istnienie].
4. The same also concerns Lesniewski's mereology.
5. Czeslaw Lejewski «A System of Logic, for Bicategorial Ontology», Journal of Philosophical Logic, 3, 1976, 99-117, «Ontology and Logic», in Philosophy of Logic, ed. by S. Korner, University of California Press, Berkeley and Los Angeles, pp. 1-28.
6. Peter Simons, Parts, Clarendon Press, Oxford, 1987.
7. Czelsaw Lejewski : «Outline of Ontology», Bulletin of the John Rylands, University Library of Manchester, v. 59, n° 1, pp. 127-147, 1976, «On the Dramatic Stage in the Development of Kotarbinski's Pansomatism», in Ontologie und Logik / Ontology and Logic, ed by P. Weingartner and E. Morscher, Duncker und Humblot, Berlin, pp. 197-214, 1979. J. Wolenski, «Reism and Lesniewski's Ontology», History and Philosophy of Logic, 7, pp.
167-172, 1986.
8. Of course, Kotarbinski himself applied LO to his ontology.
9. «Ontological Law of Contradiction and its Logical Structure», The Annals of the Japan Association for Philosophy of Science, v. 6, n° 1, pp. 43-58, 1980.
10. D. Henry, Medieval Logic and Metaphysics, Hutchinson, London, 1958. î.
11. P. Simons, Parts, Clarendon Press, Oxford, 1987.
12. « On Lesniewski's Ontology », Ratio, 1, pp. 150-176, 1958.
From: Jan Wolenski - Lesniewski's logic and the concept of Being- Recherches sur la Philosophie et le Langage (1995) pp. 94-96.
THE LESNIEWSKI COLLECTION
The Ballieu Library and the Philosophy Department of the University of Melbourne have formed the Lesniewski Collection. This Collection comprises all materials published by Stanislaw Lesniewski during his lifetime, and some unpublished materials in their original languages.
ENGLISH TRANSLATIONS
Introductory remarks to the continuation of my article
Grundzüge
eines neuen Systems der Grundlagen der Mathematik
. In
Polish logic
1920-1939.
Edited by Mccall Storrs. Oxford: Clarendon Press 1967. pp.
116-169
On definitions in the so-called theory of deduction. In
Polish logic
1920-1939.
Edited by Mccall Storrs. Oxford: Clarendon Press 1967. pp.
170-187
"On the foundations of mathematics,"
Topoi.An International Review of
Philosophy
2: 7-52 (1983).
S. Lesniewski's Lecture Notes in logic.
Edited by Srzednicki Jan
and Stachniak Zbigniew. Dordrecht: Kluwer 1988.
Contents:
Translators' Foreword IX
PART ONE: FOUNDATIONS OF MATHEMATICS
1. From the foundations of Protothetic 3
2. Definitions and these of Lesniewski's Ontology 29
3. Class theory 59
PART TWO: PEANO ARITHMETIC AND WHITEHEAD'S THEORY OF EVENTS
4. Primitive terms of arithmetic 129
5. Inductive definitions 153
6. Whitehead's theory of events 171
List of seminars and courses delivered by Lesniewski at Warsaw University
between 1919 and 1939 179
Bibliography 181
Collected works.
Dordrecht: Kluwer 1992.
Contents:
Introduction by The Editors VII-XVI
A contribution to the analysis of existential propositions (1911) 1
An attempt at a proof of the ontological principle of contradiction (1912)
20
The critique of the logical principle of the Excluded Middle (1913) 47
Is all truth only true eternally or it is also true without a beginning?
(1913) 86
Is the class of classes not subordinated to themselves, subordinated to
itself? (1914) 115
Foundations of the General Theory of Sets. I (1916) 129
On the foundations of mathematics 1927-1931 (The series consists of the
following papers): 174
I. Introduction (1927) 174
II. On Russell' 'antinomy' concerning 'The Class of Classes which are not
elements of themselves' (1927) 197
III. On various ways of understanding the words 'Class' and 'Collection'
(1927) 207
IV. On 'Foundations of the General Theory of Sets. I.' (1928) 227
V. Further theorems and definitions of the 'General Theory of Sets' from the
period up to the year 1920 inclusive (1929) 264
VI. The axiomatization of the 'General Theory of Sets' from the year 1918
(1930) 315
VII. The axiomatization of the 'General Theory of Sets' from the year 1920
(1930) 321
VIII. On certain conditions established by Kuratowski and Tarski which are
sufficient and necessary for P to be the Class of objects a (1930) 327
IX. Further theorems of the 'General Theory of Sets' from the years
1921-1923 (1930) 332
X. The axiomatization of the 'General Theory of Sets' from the year 1921
(1931) 350
XI. On 'Singular' propositions of the type 'A e b' (1931) 364
On functions whose fields, with respect to these functions are groups (1929)
383
On functions whose fields, with respect to these functions are Abelian
groups (1929) 399
Fundamentals of a new system of the foundations of mathematics (1929) 410
On the foundations of Ontology (1930) 606
On definitions in the so-called theory of deduction (1931) 629
Introductory remarks to the continuation of my article 'Grundzüge eines
neuen Systems der Grundlagen der Mathematik' (1938) 649
An annotated Lesniewski Bibliography [up to 1978] by Frederick V. Rickey 711
(*)
Index 787-794
On this edition see the review by Peter Simons:
Discovering Lesniewski
- History and
Philosophy of Logic, 15 (1994) pp. 227-235.
EXCERPTS FROM HIS PUBLICATIONS (in preparation)
SELECTED BIBLIOGRAPHY (in progress)
S. Lesniewski's Systems. Ontology and Mereology. Edited by
Srzednicki Jan, Rickey Frederick V., and Czelakowski J. The Hague: Martinus
Nijhoff 1984. Contents: Editorial Note 7; 1. Z. Kruszewski: Ontology
without axioms (1925) 9; 2. B. Sobocinski: Lesniewski's analysis of
Russell's Paradox (1949) 11; 3. C. Lejewski: Logic and existence (\1954) 45;
4. J. Slupecki: S. Lesniewski's Calculus of Names (1955) 59; 5. C. Lejewski:
On Lesniewski's Ontology (1958) 123; 6. J. Canty: Ontology: Lesniewski's
logical language (1969) 149; 7. B. Iwanus: On Lesniewski's elementary
Ontology (1973) 165; 8. B. Sobocinski: Studies in Lesniewski's Mereology
(1954) 217; 9. E. Clay: On the definition of mereological class (1966) 229;
10. C. Lejewski: Consistency of Lesniewski's Mereology (1969) 231; 11. E.
Clay: The dependence of a mereological axiom (1970) 239; 12. E. Clay -
Relation of Lesniewski's Mereology to Boolean algebra (1974) 241;
Protothetic bibliography 253; Index of Names 261.
"Stanislaw Lesniewski aujourd'hui," Recherches sur la Philosophie et
le Langage 16 (1995). Contents: Denis Miéville et Denis Vernant:
Présentation 5; Bibliographie de Stanislaw Lesniewski 21; Czeslaw Lejewski:
Remembering Stanislaw Lesniewski 25; Denis Miéville: Stanislaw Lesniewski et
l'importance d' une logique développementale 93; Jan Wolenski: Lesniewski's
logic and the concept of Being 93; Peter Simons: Lesniewski and ontological
commitment 103; Georges Kalinowski: Les démonstrations de la non-existence
des objets généraux chez Lesniewski 121; Frédéric Nef: Sémantique et
ontologie: réflexions sur la théorie des objets et les propriétés 179; Denis
Vernant: Logique et pragmatique: la genèse du concept d'assertion 179; Alain
Lecomte: Une descendance des systèmes de Lesniewski. Le calcul de Lambek (de
la grammaire logique aux grammaires de logiques des types) 207; Alain
Berrendonner: Anaphore associatie et méréologie 237; Jacques Roualt:
Représentations centrées objets, formalisation en linguistique et systèmes
de Lesniewski 257; Mounia Fredj: Implémentation des principes méréologiques
275; Olivier Houdé: Le "langage méréologique" ajoute-t-il quelque chose aux
descriptions psychologiques 297; List des numéros déjaà publiés 321;
Adresses des auteurs 330.
S. Lesniewski's Systems. Protothetic. Edited by Srzednicki Jan
and Stachniak Zbigniew. Dordrecht: Kluwer 1998. Contents: Editor's
Foreword VII; 1. Peter M. Simons: Nominalism in Poland (1983) 1; 2. V.
Frederick Rickey: A survey of Lesniewski's logic (1977) 23; 3. Alfred
Tajtelbaum-Tarski: On the primitive term of logistic (1923) 43; 4. Boleslaw
Sobocinski: An investigation in Protothetics (1949) 69; 5. Jerzy Slupecki:
St. Lesniewski's Protothetics (1953) 85; 6. Boleslaw Sobocinski: On the
single axiom of Protothetic (1960) 153; 7. V. Frederick Rickey: Axiomatic
inscriptional syntax. Part II. The syntax of Protothetic (1973) 217; VIII.
Audoënus Le Blanc: investigations in Protothetic (1985) 289; Protothetic
bibliography 299; Author Index 309.
Ajdukiewicz Kazimierz. Syntactic connection. In Polish logic
1920-1939. Edited by McCall Storrs. Oxford: Clarendon Press 1967. pp.
207-231 Originally published in German as: Die syntaktische Konnexität
- Studia Philosophica, 1, 1935, pp. 1-27.
Betti Arianna, "Logica ed esistenza in Stanislaw Leniewski", Università
degli Studi di Firenze, 1995. Tesi di laurea (Relatore: Ettore Casari).
Betti Arianna. De Veritate: another chapter. The
Bolzano-Lesniewski connection. In The Lvov-Warsaw School and contemporary
philosophy. Edited by Kijania-Placek Katarzyna and Wolenski Jan.
Dordrecht: Kluwer 1998. pp. 115-137
Betti Arianna, "Il rasoio di Lesniewski," Rivista di Filosofia:
87-112 (1998).
Betti Arianna. Sempiternal truth. The Bolzano-Twardowski-Lesniewski
axis. In The Lvov-Warsaw School. The new generation. Edited by
Jadacki Jacek Jusliuz and Pasniczek Jacek. Amsterdam: Rodopi 2006. pp.
371-399
Canty John Thomas, "Lesniewski's terminological explanations as
recursive concepts," Notre Dame Journal of Formal Logic 10: 337-369
(1969). "The terminological concepts for the system of Ontology extended
by the axiom of infinity are shown to be definable within that system. in
1929 Lesniewski first published terminological explanations for his system
of logic, where he used certain concepts from his system of Mereology along
with others such as equiformity. In this paper the terminological concepts
are given entirely within the system of Ontology extended by the axiom of
infinity. Since the definitions given are recursive, the incompleteness of
this extension of Ontology is readily established."
Chrudzimski Arkadiusz. The young Lesniewski on existentials
propositions. In Actions, products, and things: Brentano and Polish
philosophy. Edited by Chrudzimski Arkadiusz and Łukasiewicz Dariusz.
Frankfurt: Ontos Verlag 2006. pp. 107-120
Clay Robert F., "The consistency of Lesniewski's Mereology relative to
the Real Number System," Journal of Symbolic Logic 33: 251-257
(1968).
Clay Robert F., "Introduction to Lesniewski's logical systems,"
Annali dell'Istituto di Discipline Filosofiche dell'Università di Bologna:
5-31 (1980).
Cocchiarella Nino, "A conceptualist interpretation of Lesniewski's
ontology," History and Philosophy of Logic 22: 29-43 (2001). "A
first-order formulation of Lesniewski"s Ontology is formulated and shown to
be interpretable within a free first-order logic of identity extended to
include nominal quantification over proper and common-name concepts. The
latter theory is then shown to be interpretable in monadic second-order
predicate logic, which shows that the first-order part of Lesniewski"s
Ontology is decidable."
Davis Charles C., "A note on the axiom of choice in Lesniewski's
Ontology," Notre Dame Journal of Formal Logic 17: 35-43 (1976).
Gobber Giovanni, "Alle origini della grammatica categoriale: Husserl,
Lesniewski, Ajdukiewicz," Rivista di Filosofia Neo-Scolastica 76:
258-295 (1985).
Gombocz Wolfgang, "Lesniewski und Mally," Notre Dame Journal of
Formal Logic 20: 934-946 (1979).
Grzegorczyk Andrzej, "The systems of Lesniewski in relation to
contemporary logical research," Studia Logica 3: 77-95 (1955).
Henry Desmond Paul, "Lesniewski's Ontology and some medieval logicians,"
Notre Dame Journal of Formal Logic 10: 324-326 (1969). "In the
issue of this journal dated October 1966 (Vol. VII, No. 4, pp. 361-364)
Professor John Trentman suggested limitations on my claim that Lesniewski's
Ontology is of use in furnishing formal analyses of medieval logical
theories, his grounds being that certain medieval theories deny what is
called the "two-name theory of predication" allegedly common to Ockham and
Ontology. Hence while the work of Ockhamists would be analysable with
reference to Ontology, that of those "Thomists" who deny the two-name theory
would not. Professor Trentman then goes on to suggest that for such
"Thomist" analyses to take place, "something like Frege's functional
analysis of predication", is needed to show the "disparity of semantic
category that holds between the subject and the predicate", thereby implying
that no such form is available in Ontology, and that the allegations about
the inadequacy of the two-name theory could have escaped my notice.
Neither of these implications is tenable. Ignoring the second of them, I can
deal with the first by exemplifying the manner in which the Ontology in
question deals with the relations between names and verbs (i.e. functors
which when completed with nominal arguments form propositions)."
Henry Desmond Paul. Medieval logic and metaphysics. London:
Hutchinson 1972.
Ishimoto Arata. Logicism revisited in the propositional fragment of
Lesniewski's Ontology. In Philosophy of mathematics today. Edited by
Agazzi Evandro and Darvas György. Dordrecht: Kluwer
1997. pp. 219-232
Iwanus Boguslaw, "An extension of the traditional logic containing the
elementary ontology and the algebra of classes," Studia Logica 25:
97-135 (1969). "The paper deals with the axiomatic Calculus of Names (S
sub 2) which is an extension of the system S sub 1 presented in my paper
"Remarks about syllogistic with negative terms" (Studia logica, vol. XXIV).
The primitive terms of S sub 2 are the function of a categorical
universal-affirmative proposition, the complement of a set, and the empty
set. In S sub 2 one is given the definitions of addition and multiplication
of sets, the universal set and the relation epsilon (... is ...) which
corresponds semantically to the primitive term of Lesniewski's Ontology. It
is proved that the elementary ontology and the elementary algebra of classes
are fragments of s sub 2."
Iwanus Boguslaw, "Remarks about syllogistic with negative terms,"
Studia Logica 24: 131-137 (1969). "The article presents a system S of
syllogistic based on three axioms. The functor "a" / every...is.../ and the
sign of nominal negation are primitive terms of system S. The known
axiomatic systems of syllogistic with negative terms constructed by I.
Thomas, A. Wedberg and C. A. Meredith are fragments of system S. It seems
that the axioms of system S better characterize the categorical propositions
containing negative terms since this characterization excludes some
non-intuitive interpretations of such propositions, admissible in the above
mentioned systems. It is also mentioned that there exists an extension of
system S containing the elementary algebra of classes and the elementary
Ontology of Lesniewski."
Kearns John, "The contribution of Lesniewski," Notre Dame Journal of
Formal Logic 8: 61-93 (1967).
Kearns John, "Two views of variables," Notre Dame Journal of Formal
Logic 10: 163-180 (1969). "This paper argues that there are two
fundamental ways to regard variables in formalized languages. One way,
associated with Russell and Quine, regards variables as autonomous
referential expressions. On this view, quantification is the fundamental
device for indicating ontological commitments. The second way to regard
variables is linked to Frege and Lesniewski; variables are regarded as
replacements for constant expressions. Such a view leads to an understanding
of quantifiers in terms of substitution instances of the quantified
expressions. It is argued that the second way of regarding variables is
preferable to the first way, and that no logical results need be given up if
this way is adopted."
Kotarbinski Tadeusz. Gnosiology. The scientific approach to the
theory of knowledge. Oxford: Pergamon Press 1966. Original Polish
edition 1929; second revised edition 1961. Translated from the Polish by
Olgierd Wojtasiewicz; translation edited by G. Bidwell and C. Pinder
Küng Guido, "The meaning of quantifiers in the logic of Lesniewski,"
Studia Logica 26: 309-322 (1977).
Küng Guido, "La logique est-elle une discipline des mathématiques out
fait-elle partie de l'ontologie?," Dialectica 39: 243-258 (1985).
"Heinrich Scholz and J. M. Bochenski have claimed that the laws of formal
logic are the most general laws about things, properties, relations,
states-of-affairs, etc. Others have mixed up logic and set theory. But
Lesniewski's interpretation of the quantifiers shows that properly speaking
logic belongs neither to ontology nor to mathematics."
Lejewski Czeslaw, "Logic and existence," British Journal for the
Philosophy of Science 5: 104-119 (1954). "I wish to conclude with a
brief summary of the results. The aim of the paper was to analyse rather
than criticize. I started by examining two inferences which appeared to
disprove the validity of the rules of universal instantiation and
existential generalization in application to reasoning with empty
noun-expressions. Then I distinguished two different interpretations of the
quantifiers and argued that under what I called the unrestricted
interpretation the two inferences were correct. Further arguments in favour
of the unrestricted interpretation of the quantifiers were brought in, and
in particular it was found that by adopting the unrestricted interpretation
it was possible to separate the notion of existence from the idea of
quantification. With the aid of the functor of inclusion two functors were
defined of which one expressed the notion of existence as underlying the
theory of restricted quantification while the other approximated the term
exist(s) as used in ordinary language. It may be useful to supplement
this summary by indicating some aspects of the problem of existence which
have not been included in the discussion. I analyzed the theory of
quantification so far as it was applied in connection with variables for
which noun-expressions could be substituted and my enquiry into the meaning
of exist (s) ' was limited to cases where this functor was used with
noun-expressions designating concrete objects or with noun-expressions that
were empty. It remains to explore, among other things, in what sense the
quantifiers can be used to bind predicate variables and what we mean when we
say that colours exist or that numbers exist. These are far more difficult
problems, which may call for a separate paper or rather for a number of
separate papers."
Lejewski Czeslaw, "On implicational definitions," Studia Logica
8: 189-206 (1958).
Lejewski Czeslaw, "On Lesniewski's Ontology," Ratio 1: 150-176
(1958).
Lejewski Czeslaw, "A re-examination of the Russellian theory of
descriptions," Philosophy 35: 14-29 (1960).
Lejewski Czeslaw, "A single axiom for the mereological notion of proper
part," Notre Dame Journal of Formal Logic 4: 279-285 (1967).
Lejewski Czeslaw, "Consistency of Lesniewski's Mereology," Journal of
Symbolic Logic 34: 321-328 (1969). "Lesniewski's Mereology
presupposes his Ontology, which in turn presupposes his Protothetic. A proof
is outlined to show that if we interpret name-variables as
proposition-variables and if at the same time we interpret the ontological
'epsilon' as the functor of conjunction and the mereological 'el' as the
functor of assertion then the axioms and directives of Ontology and
Mereology become repectively theses and directives of Protothetic."
Lejewski Czeslaw, "A system of logic for bicategorial ontology,"
Journal of Philosophical Logic 3: 265-283 (1974).
Lejewski Czeslaw, "Outline of Ontology," Bulletin of the John Rylands
University Library of Manchester 59: 127-147 (1976).
Lejewski Czeslaw. On the dramatic stage in the development of
Kotarbisnki's pansomatism. In Ontologie und Logik. Ontology and Logic.
Berlin: Duncker & Humblot 1979. pp. 197-214 Proceedings of an
International Colloquium (Salzburg, 21-24 September 1976) Discussion pp.
215-218
Lejewski Czeslaw. Logic and ontology. In Modern logic. A survey.
Edited by Hintikka Jaakko. Dordrecht: Reidel 1981. pp. 379-398
Lejewski Czeslaw, "A note on Lesniewski's axiom system for the
mereological notion of ingredient or element," Topoi 3: 63-72 (1983).
Lejewski Czeslaw, "Accomodating the informal notion of class within the
framework of Lesniewski's Ontology," Dialectica 39: 217-241 (1985).
"Interpreted distributively the sentence 'Indiana is a member of the class
of American federal states' means the same as 'Indiana is an American
federal state'. In accordance with the collective sense of class
expressions the sentence can be understood as implying that Indiana is a
part of the country whose capital city is Washington. Neither interpretation
appears to accommodate all the intuitions connected with the informal notion
of class. A closer accommodation can be achieved, it seems, if class
expressions are interpreted as verb-like expressions of a certain kind as
available within the framework of Lesniewski's Ontology."
Lejewski Czeslaw, "Logic and non-existence," Grazer Philosophische
Studien 25/26: 209-234 (1986). "An attempt is made in the present
essay to accommodate various senses of the notion of existence and of that
of non-existence within the framework of logic. With this aim in view a
system of Lesniewski's Ontology, referred to as System S, is outlined.
Equipped with appropriate definitions and illustrated with a selection of
theses it offers a logical theory of existence and non-existence. The
usefulness of the theory is then tested by interpreting in its terms some of
the principal notions and assertions of Meinong's ontology. A few brief
comments on the notion of 'possible object' and on 'semantics' of fiction
conclude the essay."
Lejewski Czeslaw, "Ricordando Stanislaw Lesniewski," Quaderni del
Centro Studi per la Filosofia Mitteleuropea 1989 (1): 5-47 (1989).
Edited by Massimo Libardi
Lejewski Czeslaw, "Formalization of functionally complete propositional
calculus with the functor of implication as the only primitive term,"
Studia Logica 48: 479-494 (1989). "The most difficult problem that
Lesniewski came across in constructing his system of the foundations of
mathematics was the problem of 'defining definitions', as he used to put it.
He solved it to his satisfaction only when he had completed the
formalization of his protothetic and ontology. By formalization of a
deductive system one ought to understand in this context the statement, as
precise and unambiguous as possible, of the conditions an expression has to
satisfy if it is added to the system as a new thesis. Now, some
protothetical theses, and some ontological ones, included in the respective
systems, happen to be definitions. In the present essay I employ
Lesniewski's method of terminological explanations for the purpose of
formalizing Łukasiewicz's system of implicational calculus of propositions,
which system, without having recourse to quantification, I first extended
some time ago into a functionally complete system. This I achieved by
allowing for a rule of 'implicational definition', which enabled me to
define any proposition forming functor for any finite number of
propositional arguments."
Lepage François, "Partial monotonic Protpthetics," Studia Logica
66: 147-163 (2000). "This paper has four parts. In the first part, I
present Lesacuteniewski's protothetics and the complete system provided for
that logic by Henkin. The second part presents a generalized notion of
partial functions in propositional type theory. In the third part, these
partial functions are used to define partial interpretations for
protothetics. Finally, I present in the fourth part a complete system for
partial protothetics. Completeness is proved by Henkin's method using
saturated sets instead of maximally saturated sets. This technique provides
a canonical representation of a partial semantic space and it is suggested
that this space can be interpreted as an epistemic state of a non-omniscient
agent."
Luschei Eugene. The logical systems of Lesniewski. Amsterdam :
North-Holland 1962.
Miéville Denis. Un développement des systèmes logiques de Stanislaw
Lesniewski: protothétique, ontologie, méréologie. Berne: Peter Lang
1984.
Miéville Denis, "Un aperçu des caractéristiques et de l'esprit des
systèmes logiques de Stanislaw Lesniewski," Dialectica 39: 166-179
(1985). "This article provides an introduction to the deductive theories,
which are so little known, of S. Lesniewski. The reasons that led this
Polish logician to develop a theory of collective classes as well as the
logical theories that underlie it are set forth here, and the main
characteristics of Lesniewski's three systems -- mereology, protothetics and
ontology -- are presented. Some epistemological considerations are included
in this study."
Miéville Denis, "Introduction à l'oeuvre de S. Lesniewski. Fascicule I -
La Protothétique," Travaux de Logique (Neuchâtel) (2001).
Miéville Denis, "Introduction à l'oeuvre de S. Lesniewski. Fascicule II
- L'Ontologie," Travaux de Logique (Neuchâtel) (2004).
Miéville Denis, "Introduction à l'oeuvre de S. Lesniewski. Fascicule III
- La Méréologie," Travaux de Logique (Neuchâtel) (2005).
Miéville Denis, "Introduction à l'oeuvre de S. Lesniewski. Fascicule IV
- L'oeuvre de jeunesse," Travaux de Logique (Neuchâtel) (2006).
Poli Roberto and Libardi Massimo, "Logic, theory of science, and
metaphysics according to Stanislaw Lesniewski," Grazer Philosophische
Studien 57: 183-219 (1999). "Due to the current availability of the
English translation of almost all of Lesniewski's works it is now possible
to give a clear and detailed picture of his ideas. Lesniewski's system of
the foundation of mathematics is discussed. In a brief outline of his three
systems Mereology, Ontology and Protothetics his positions concerning the
problems of the forms of expression, proper names, synonymity, analytic and
synthetic propositions, existential propositions, the concept of logic, and
his views of theory of science and metaphysics are sketched. The influence
of Mill, Łukasiewicz, Austrian philosophy and especially Petrazycki on his
thinking is evaluated and an interpretation is suggested setting him
squarely in a tradition of classical Aristotelian logic."
Prakel Judith, "A Lesniewskian re-examination of Goodman's nominalistic
rejection of classes," Topoi 2: 87-98 (1983).
Prior Arthur Norman. Existence in Lesniewski and in Russell. In
Formal systems and recursive functions. Edited by Crossley John N. and
Dummett Michael. Amsterdam: North Holland Publishing Company 1965. pp.
149-155 Proceedings of the Eighth Logic Colloquium. Oxford, July 1963
Rickey Frederick V., "A survey of Lesniewski's logic," Studia Logica
36: 407-426 (1977).
Rickey Frederick V., "Interpretations of Lesniewski's Ontology,"
Dialectica 39: 181-192 (1985). "This article proposes to clarity the
problem of interpreting Lesniewski's ontology. A distinction is made between
two kinds of interpretation: substitutional and "natural". Substitutional
interpretation is shown to involve difficulties and limitations. A "natural"
ontology, the major principles of which are presented here, is shown to be
of considerable interest."
Simons Peter, "On understanding Lesniewski," History and Philosophy
of Logic 3: 165-191 (1982). Reprinted in: Peter Simons -
Philosophy and logic in Central Europe from Bolzano to Tarski. Selected
essays - Dordrecht, Kluwer 1992 pp. 227-258
Simons Peter, "A Lesniewskian language for the nominalistic theory of
substance and accident," Topoi 2: 99-110 (1983).
Simons Peter, "A Brentanian basis for Lesniewskian logic," Logique et
Analyse 27: 297-398 (1984). Reprinted in: Peter Simons -
Philosophy and logic in Central Europe from Bolzano to Tarski. Selected
essays - Dordrecht, Kluwer 1992 pp. 259-269
Simons Peter. Lesniewski's logic and its relation to classical and free
logics. In Foundations of logic and linguistic. Problems and their
solutions: a selection of contributed papers from the VIIth International
congress of logic, methodology, and philosophy of science, held in Salzburg
from the 11th-16th July, 1983 . Edited by Dorn Georg and Weingartner
Paul. New York: Plenum Press 1985. pp. 369-402 Reprinted in: Peter Simons
- Philosophy and logic in Central Europe from Bolzano to Tarski. Selected
essays - Dordrecht, Kluwer 1992 pp. 271-293
Simons Peter, "A semantics for Ontology," Dialectica 39: 193-216
(1985). "This article proposes to clarify the problem of interpreting
Lesniewski's Ontology. A distinction is made between the two kinds of
interpretation: substitutional and "natural". Substitutional interpretation
is shown to involve difficulties and limitations. A "natural" Ontology, the
major principles of which are presented here, is shown to be of considerable
interest."
Simons Peter, "Lesniewskian term logic," Lingua e Stile 27: 25-45
(1992). "Students of traditional logic, by which I mean the central core
of categorical syllogistic with whatever further forms were studied at the
time, were drilled in putting the sentences occurring in arguments into
«correct logical form», and present-day students do no different when
replacing their natural language sentences by the formulas or semiformulas
of predicate logic. Both procedures involve doing some violence to natural
modes of expression. A sentence like Whoever flies saves time must be
replaced by something like Every flier is a time-saver by traditional
logicians and by For all x: if x flies then x saves time by modern
logicians. As this makes clear, different logical systems may compete in
offering prepared forms proximate to a natural specimen, so there may be a
real choice as to which system is preferable for a given purpose. This is
familiar to observers of modern logic since there are competing logics of
definite descriptions, modality, and so on. Of course, if we confine
attention just to the opposition between categorical syllogistic and
predicate logic, there seems to be no contest. Predicate logic is
expressively much the more powerful system, and as these two are the only
two logical systems to have enjoyed widespread acceptance as tools for
analysing validity of natural arguments, it might seem that only predicate
logic remains as a general vehicle for workaday argument assessment. But the
large number of introductory logic textbooks which still contain material on
categorical syllogistic bears witness to the fact that, within its more
limited sphere, the traditional logic of terms is widely felt to be a more
natural and useful alternative to monadic predicate logic. Historical
interest alone could not compensate for the inconveniences of introducing
two quite different systems, with their different sentential analyses, laws,
and terminology, to cover the same ground. It is apparent that one
disadvantage of predicate logic for these purposes is its use of bound
individual variables, which natural languages do not have, and which they
can simulate and match only by rather tortuous use of pronouns and
pronominal phases. Of course this helps to account for the greater
perspicuity of predicate logic once we leave the simplest sentences behind,
but at the most elementary level it is a hindrance. The singular
term/predicate analysis of simple predications compels common noun phrases
and adjectives used attributively to appear as syntactically inseparable
parts of predicates, which correspond most closely to verb phrases in
natural language. Again, this is not a huge sacrifice, but it is pervasive,
is felt to be unnatural, and contributes to beginners' difficulties in
learning logic. So it is worth considering from a practical and
pedagogical point of view whether, in order to gain the considerable
benefits conferred by predicate logic - quantification, multiple generality,
relational predicates - it is necessary to put up with the disagreeable
features of standard predicate logic. I shall argue that it is not, and that
a more natural and flexible medium for which to prepare natural language
sentences and arguments is provided by the term logic invented around 1920
by Stanislaw Lesniewski (1886-1939) and usually known as Ontology. (*)"
(*) The possible confusion of the system of logic with the branch of
metaphysics of the same name is not a danger in this context, and in any
case I will write the name of the system with a capital letter. Sometimes
Ontology is called the Calculus of Names, but this is misleading, since much
more than names are involved. It would be nice to have a better name for
Ontology.
Simons Peter, "Discovering Lesniewski: Collected Works,"
History and Philosophy of Logic 15: 227-235 (1994). "This discussion
review examines the English edition of Lesniewski's collected works. Points
emphasized include: the early (pre-symbolic) period, the quality of
translation and typesettings, and the scandalously outdated bibliography."
Simons Peter, "Reasoning on a tight budget: Lesniewski's nominalistic
metalogic," Erkenntnis 56: 99-122 (2002).
Simons Peter. Things and truths: Brentano and Lesniewski, ontology amd
logic. In Actions, products, and things: Brentano and Polish philosophy.
Edited by Chrudzimski Arkadiusz and Łukasiewicz Dariusz. Frankfurt: Ontos
Verlag 2006. pp. 83-106
Sinisi Vito, "Nominalism and common names," Philosophical Review
71: 230-235 (1961). "Edwin Allaire, Gustav Bergmann and Reinhardt
Grossmann have objected to the nominalistic analysis of "this is red and
that is red" which treats "red" as a common name. Such an analysis, they
argued, must assimilate the copula in this sentence to the "is" of identity.
sinisi claims that this objection is mistaken. Using a logical system
developed by Stanislaw Lesniewski, he shows that it is possible to construe
"red" as a common name without taking the copula as the "is" of identity."
Sinisi Vito, "Lesniewski's analysis of Whitehead's theory of events,"
Notre Dame Journal of Formal Logic 7: 323-327 (1966).
Sinisi Vito, "Lesniewski and Frege on collective classes," Notre Dame
Journal of Formal Logic 10: 239-246 (1969). "Between 1927 and 1931
Lesniewski published a series of articles on the foundations of mathematics
in the Polish journal Przeglad Filozoficzny. 65% of the work is
devoted to various axiomatizations of Lesniewski's mereology (a theory of
collective classes) while the remainder takes up various related issues. In
the third part of this series Lesniewski informally sets forth his notion of
a collective class, criticizes certain descriptions of distributive classes,
and argues that there is no justification in Frege's statement that the
conception of a class as consisting of individuals, so that the individual
thing coincides with the unit class, cannot in any case be supported.
Lesniewski's refutation of Frege's statement appears to be unknown to
western logicians and philosophers. None of the recent books on Frege (e.g.,
Angelelli, Egidi, Sternfeld, Thiel, Walker) mentions it. Luschei, in his
The Logical Systems of Lesniewski, mentions it but does not present it.
My purpose here is to state and explain Lesniewski's refutation in the hope
that it will help stimulate interest in his work."
Sinisi Vito, "Lesniewski's analysis of Russell's antinomy," Notre
Dame Journal of Formal Logic 17: 19-34 (1976).
Sinisi Vito, "The development of Ontology," Topoi 2: 53-62
(1983).
Slupecki Jerzy, "St Lesniewski's Protothetics," Studia Logica 1:
44-111 (1953).
Slupecki Jerzy, "Lesniewsjki's Calculus of Names," Studia Logica
3: 7-70 (1955).
Slupecki Jerzy, "Towards a generalized mereology of Lesniewski.,"
Studia Logica 8: 131-154 (1958).
Sobocinski Boleslaw, "L'analyse de l'antinomie russellienne par
Lesniewski," Methodos (1949). Published in four parts: I - II -
III: vol. 1. (1949) pp. 94-107; 220-228; 308-316; IV: vol. 2 (1950) pp.
237-257.
Sobocinski Boleslaw, "On the single axioms of protothetic, I," Notre
Dame Journal of Formal Logic 1: 52-73 (1960).
Sobocinski Boleslaw, "On the single axioms of protothetic, II," Notre
Dame Journal of Formal Logic 2: 111-126 (1961).
Sobocinski Boleslaw, "On the single axioms of protothetic, III,"
Notre Dame Journal of Formal Logic 2: 129-148 (1961).
Sobocinski Boleslaw. Successive simplifications of the axiom-system of
Lesniewski's Ontology. In Polish logic 1920-1939. Edited by McCall
Storrs. Oxford: Clarendon Press 1967. pp. 188-200
Stachniak Zbigniew. Introduction to model theory for Lesniewski's
Ontology. Wroclaw: Wydawnictwo Uniwersytetu Wroclaskiego 1981.
Strawson Peter Frederick and Lejewski Czeslaw, "Symposium: proper
names," Proceedings of the Aristotelian Society Supplementary vol.
31: 191-236 (1957).
Surma Stanislaw. On the work and influence of Stanislaw Lesniewski. In
Logic Colloquium 76. Edited by Gandy Robin and Hyland John Martin.
Amsterdam: North-Holland 1977. pp. 191-220
Takano Mitio, "A semantical investigation into Lesniewski's axiom of his
ontology," Studia Logica 44: 71-77 (1985).
Trentman John, "Lesniewski's Ontology and some medieval logicians,"
Notre Dame Journal of Formal Logic 7: 361-364 (1966).
Vasyukov Vladimir, "A Lesniewskian guide to Husserl's and Meinong's
jungles," Axiomathes 4 (1): 59-74 (1993).
Wojciechowski Eugeniusz, "Zwischen der Syllogistik und den Systemen von
Lesniewski: Eine Rekonstruktion der Idee der Quantifizierung der Pradikate,"
Grazer Philosophische Studien 48: 165-200 (1994).
Wolenski Jan, "Reism and Lesniewski's Ontology," History and
Philosophy of Logic 7: 167-176 (1986).
Wolenski Jan. Logic and philosophy in the Lvov-Warsaw school.
Dordrecht: Kluwer 1989.
Wolenski Jan, "Lesniewski's logic and the concept of Being,"
Recherches sur la Philosophie et le Langage: 93-101 (1995). This
paper applies Lesniewski's logical ideas to an analysis of the concept of
being. The analysis follows the classical ontology which is based on a
distinction of two concepts of being : being in the distributive sense and
being in the collective sense. Now it is argued that Lesniewski's ontology
(calculus of names) is a much better device for analysizing being in the
distributive sense than the standard first-order predicate logic. Moreover,
basic intuition connected with the being in the collective sense are nicely
captured by mereology.
Zanasi Fausto, "Su alcuni aspetti della teoria della definizione nei
sistemi logici di S. Lesniewski," Annali dell'Istituto di Discipline
Filosofiche dell'Università di Bologna: 219-232 (1980).
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