MAKINGS AND THEIR USE IN ANALYSIS
OF LOGICALAND OTHER MODALITIES
Department of Logic, N. Copernicus University of Toru_
Department of Logic, Jagiellonian University of Krakуw
e-mail: [email protected]
1. Classification of modalities.
Modalities are modifiers. For example, alethic modalities are modifiers of truth components, or — more generally — semantical, logical and ontological components of a judgement and objects involved in it.
Let us consider two conjugate classifications of modalities:
A. Based on a grammatical difference:
Noun-like (like possibility, etc.) vs. Adjective-like (possible, etc.)
B. Based on an ontological principle:
Logical modalities vs. Superlogical modalities.
LOGICAL modalities are used for collection and comparison: possible, necessarily, contingently, etc.
They are adjective-like and, in their depth, they are quantifiers (cf. relational semantics).
SUPERLOGICAL modalities are used for expression and modification of very general conditions. They can be divided into several groups including:
A priori modalities, concerning what can be thought, used to delineate the realm of reason. Examples are thinkable, understandable, reasonable, controvertible.
Ontological modalities, useful for describing the general and basic conditions for some families of objects or complexes. They are, inter alia, used for delineation of the ontological space of all possibilities, the most general field we can deal with.
Examples are: possibility, necessity, contingency, and exclusion taken in the sense of a condition; compossibility, coexistence, and eminent existence in the sense of Leibniz, (formal) possibility in the sense of Wittgenstein’ Tractatus; combinable, synthetizable and analyzable; and several common philosophical modalities de re: by necessity, essentially, by its very nature, etc.
Ontological MAKINGS are as follows: making possible, making impossible, etc.
Metaphysical modalities, concerning facts and existence, what is real or actual: real, existing, actual, factual, true, false, to be a fact, to be true. Metaphysical MAKINGS: making true, making fact, making real, making actual, etc.
Makings form a basic and very challenging family of modalities.
2. 1 A bit of grammar.
English. In English makings are of the form Gerund + Noun: Making N, for suitable N. For example:
Making Possible x makes y possible MP(x, y)
Making Impossible x makes y impossible MI(x, y);
Introduced by Russell and investigated by his followers:
Making True x makes y true MT(x, y);
Making Real x makes y real MR(x, y)
Making Actual x makes y actual MAc(x, y)
Making Fact x makes y to be a fact MF(x, y)
Making Thought x makes y to be a thought MTh(x, y) – thinking
Making Act x makes y to be an act MA(x, y) – acting.
To sum up, English form of makings is very general and formal. It can be done for any noun, without any clear limitation.
Polish. Polish form for makings is more particular and subtle:
They are so-called prefixed verbs, made of verbs (u-V-ć) or nouns (u‑N-ć), called by me urabiacze.
Urabiacze result by two operations: perfecting one u- and neutralizing one -ć
Examples: umożliwić, uniemożliwić, uprawdziwić, urealnić, ufaktyczni_, umy_li_, uczyni_, etc.
2.2 A bit of ontologic.
(1) Making possible and making impossible are two basic makers.
(2) Making possible is, in a sense, ambiguous:
Strong variant: MP(x, y) means x makes y and y is possible, or x makes y to be possible:
(MPM) MP(x, y) M(x, y)M(y).
Weak variant: MP(x, y) means P(x, y): x makes a necessary condition for y, or x excludes a barer for y.
Hereafter MP is the common, general form of making possible (and other makers as well):
MP = M + P.
(3) The strong variant M( , ) offers a way to define other makers:
(MPF) MF(x, y) M(x, y)F(y)
(MPT) MT(x, y) M(x, y)T(y)
(MPTh) MTh(x, y) M(x, y)Th(y)
(MPA) MA(x, y) M(x, y)A(y) etc.
(4) The weak version P( , ) is the weakest of all makers:
(MPP) MP(x, y) P(x, y), or even MP(x, y) P(x, M(y))
(MFP) MF(x, y) P(x, y), or even MF(x, y) P(x, F(y))
(MTP) MT(x, y) P(x, y), or even MT(x, y) P(x, T(y)) etc.
M MP P
(5) The only case of makings fully investigated up now is the case of MT.
It includes two parts:
Russellian — Facts are left-side arguments of MT, They are truth makers, i. e.,
(BR) MT(x, y) F(x);
Fregean and Tarskian — Making true means verification (satisfaction), i. e.,
(F-T) MT(x, y): x ╞ y,
fulfilling usual compossibility principles.
Logical custom: Differentiate between MT-arguments: MT(N, A), or MT(X, A).
By the above analysis, in particular by (1), the general theory of makings must be based on (and, in fact, is a part of) ontology.
2.3 Use of makings
In the rest of my lecture, after outlining a general ontology of analysis and synthesis – called combination ontology – I will study two types of application of the above apparatus:
A. For making a very general combination semantics for logical and other modalities;
B. For more scrupulous discussion of facts as truth makers.
Connection with Leibnizian and Wittgensteinian ontologies is also discussed.
 Perzanowski J., Some ontological and semantical puzzles of Wittgenstein’s Tractatus, In: Aesthetics, Proceedings of the 8th International Wittgenstein Symposium, Kirchberg am Wechsel, 15th to 21th August 1983, Hцlder- Pichler-Tempsky, Wien 1984, pp. 224 – 230.
 Perzanowski J., Logiki modalne a filozofia, Wyd. Uniwersytetu Jagiellońskiego, Krakуw,1989, pp. 159. Slighty modified version reprinted in , pp. 262 – 346.
 Perzanowski J., ed., Jak filozofować?, PWN, Warszawa, 1989, pp. 400.
 Perzanowski J., Towards Post-Tractatus Ontology, In: Wittgenstein – Towards a Re-valuation, Proceedings of the 14th International Wittgenstein Symposium, Kirchberg am Wechsel, 13th to 20th August 1989, Hцlder-Pichler-Tempsky, Wien 1990, pp. 185 – 199.
 Perzanowski J., Combination Semantics: An Outline, [in:] M. Balat and J. Deledalle-Rhodes, eds., Signs of Humanity, Mouton de Gruyter, 1992, pp. 437 – 442.
 Świrydowicz K., Logiczne teorie obowiązku warunkowego, wyd. UAM, Poznań, 1995, pp. 235