Abstract
The issue of existence has been one of Karel Lambert’s main philosophical concerns for more than two .decades. It constitutes the central motivating factor not only for his pioneering development of free logic but also for his less formal philosophical works.1 Moreover it was his Gastvortrag on existence once given at the Department of Philosophy of the University of Regensburg, West Germany, in the early 70ies that marks the beginning of our friendship, although, as Joe never failed to mention when introducing me to one of his colleagues, a critical remark of mine ‘destroyed’ his then theory of inexistent, fictional objects. Therefore it will certainly not be inappropriate if my contribution to this Festschrift centers around the very issue of existence.
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Notes
Cf. especially ‘On Logic and Existence’, Notre Dame Journal of Formal Logic 6, 1965, 135–141; ‘Impossible Objects’, Inquiry 17, 1974, 303-314; ‘On the Philosophical Foundations of Free Logic’, Inquiry 24, 1981, 147-203; and the monograph Meinong and the Principle of Independence, Cambridge University Press, [Cambridge] 1983.
In Karel Lambert (ed.), Philosophical Problems in Logic, Reidel, Dordrecht, 1969.
The idea is to let the universe of (epistemic) discourse just be some non-empty set of entities called ‘possible individuals’ whereas the so-called ‘actually existing individuals’ simply form a subset (not even necessarily a genuine one) of the former set. My reasons for following this strategy especially in the context of epistemic logic have been stated in ‘Knowledge, Belief, Existence, and Quantifiers — A Note on Hintikka’, Grazer Philosophische Studien 2 1976, 55-65; cf. also section 8.2 of my book Glauben, Wissen und Wahrscheinlichkeit, Wien, 1980.
The following abbreviations are used: AV = Vorausedition zur Reihe VI — Philosophische Schriften — in der Ausgabe der Akademie der Wissenschaften …, ed. by the Leibniz-Forschungsstelle, University of Münster, Münster, 1982ff.; C = L. Couturat (ed.), Opuscules et fragments inédits de Leibniz, Paris, 1903; GI = F. Schupp (ed.): Generales Inquisitiones de Analyst Notionum et Veritatum, Meiner Verlag, Hamburg; 1982; GP = C. J. Gerhardt (ed.), Die philosophischen Schriften von G. W. Leibniz, 7 vol., Berlin, 1875-1890; P = G. H. R. Parkinson (ed.), Leibniz: Logical Papers, Clarendon Press, Oxford, 1966.
Cf., e.g., §1 Gl: “ANot-A is a contradictory terra. That which does not contain a contradictory term, i.e. Anot-A, is possible. That which is not Y not-Y is possible” (P, 54).
As is done in my ‘Leibniz’s Calculus of Strict Implication’ in J. Srednicki (ed), Initiatives in Logic, Nijhoff, Dordrecht, 1987, pp. 1–35.
A proof of completeness may be found in my ‘Leibniz und die Boolesche Algebra’, Studia Leibnitiana 16, 1984, 187–203.
Unfortunately, in Parkinson’s translation this sentence which states that if the particular negative proposition is false, then ANot-B is impossible, i.e. [!] Acontains B, has been omitted.
The word ‘true’ seems to indicate that Leibniz here wants to express something like the rule of detachment; he goes on to explain; however: “By a false letter I understand either a false term (i.e. one which is impossible, or, is a non-entity) or a false proposition …”. Thus, if the letters Aand Bare taken to stand for concepts, the quoted sentence does express Ax6, while the equally admissable interpretation of Aand Bas propositions leads to the rule of modus ponens.
Cf. my ‘Unbestimmte Begriffe’ bei Leibniz’, Studia Leibnitiana 16, 1984,1-26.
C, 235; cf. also the famous passage from the Nouveaux Essais where Leibniz uses the expressions ‘extension’ and ‘intension’; GP, 5, 469.
E.g. in B. Mates, The Philosophy of Leibniz, Oxford University Press, Oxford, 1986.
Cf., e.g., 530 and 534, #7.
Except for the Dissertatio de Arte Combinatoria of 1666 and for one early fragment of around 1676 (C, 321-4), Leibniz always followed the convention of expressing the universal affirmative proposition ‘Omne Aest B’ simply as ‘Aest B’, i.e. AcB.Thus, e.g., in the Specimen Calculi universalis of 1679 he declared “Auniversal affirmative proposition will be expressed here as follows: ais b, or, (every) man is an animal. We shall, therefore, always understand the sign of universality to be prefixed” (P, 33). He stuck to this convention throughout his later logical writings.
Cf. Englebretsen, ‘A Note on Leibniz’s Wild Quantity Thesis’, Studia Leibnitiana 20 1988, 87–9.
Cf. §48 Gl: “ ‘AYcontains B’ is the particular affirmative proposition with respect to A”
§23 GI referred to here by Leibniz contains the rule of introducing a concept variable functioning as an existential quantifier: “For any definite letter there can be substituted an indefinite letter not yet used”. (P, 57)
Cf. C, 229-231, esp. the proof of ‘Axiom 7’. A detailed discussion of this passage may be found in my “Non est’ non est ‘est non”, Studia Leibnitiana 18, 1986, 1-37.
Some alternative definitions are discussed in section 3.3 of my book Das System der Leibnizschen Logik, de Gruyter, Berlin, 1990.
Here as well as in some further details I deviate from Parkinson’s translation which has ‘exists’ for Leibniz’s ‘est’. The point is that Leibniz goes on to distinguish the “essential” from the “existential” meaning of ‘Aest’ as ‘Aest Ens possibile’ vs. ‘A est Ens existens’. Therefore only the latter may justifiably be translated as ‘Aexists’!
Cf., e.g., AV, 79: “The universal negative proposition ‘No Bis C’ is reduced to this universal affirmative one: ‘Every Bis not-C’”.
In later works Leibniz preferred the following variant where ‘c’ is eliminated, according to Th6, in favour of ‘=’: “Univ. aff. ‘A= AB’, part. neg.’ Anot = AB’, Univ. neg. ‘A = Anon-B’, part. neg. ‘Anot = Anon-B”’ (C, 236), i.e.: Schema 3 U.A. A= AB A=A∼BU.N. P.A. (A=A∼B) (A=AB) P.N.
In ‘Zur Einbettung der Syllogistik in Leibnizens ‘Allgemeinen Kalkül’’, Studio Leibnitiana Sonderheft 15 1988, 38-71, I have defined a schema to be homogeneous if the formalisations of the 4 categoricals “follow the same logical idea”, i.e. if they obey to the laws of obversion and opposition.
Of course, Th14 I(A) → (P(A) →Ac0) holds as well.
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Lenzen, W. (1991). Leibniz on Ens and Existence. In: Spohn, W., Van Fraassen, B.C., Skyrms, B. (eds) Existence and Explanation. The University of Western Ontario Series in Philosophy of Science, vol 49. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3244-2_6
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