Mahdollisten maailmojen. semantiikan synty ja kehitys. ((p q) r) (r ( p q)) is written CCApqNrCrKNpNq. Mahdollisten maailmojen. Puolalainen notaatio 2

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1 Mahdollisten maailmojen semantiikan synty ja kehitys (Fte264/265, Kf330n) FT Ilpo Halonen to klo S20A sh luento Mahdollisten maailmojen semantiikan synty ja kehitys Kurssimateriaali löytyy myös internetistä osoitteesta sekä Philosophica-kirjastosta. Materiaali on pääosin pdf-muodossa. Tarvittavan ilmaisen Adobe Reader - ohjelman voi ladata osoitteesta 2 Puolalainen notaatio 1 p is written Np p q is written Kpq p q is written Apq p q is written Cpq p q is written Epq Puolalainen notaatio 2 ((p q) r) (r ( p q)) is written CCApqNrCrKNpNq 3 4 KIRJALLISUUTTA 1 KIRJALLISUUTTA 2 Hintikka Jaakko 1957a, Quantifiers in deontic logic, Societas Scientarum Fennica, Commentationes, Humanarum Literarum 23, no. 4. Helsinki. Hintikka, Jaakko, 1957b, Modality as Referential Multiplicity, Ajatus 20, Lindström Sten 2001, Quine s Interpretation Problem and the Early Development of Possible Worlds Semantics, in Carlson Erik and Rysiek Sliwinski (eds.), Omniumgatherum. Philosophical essays dedicated to Jan Österberg on the occasion of his sixtieth birthday, Uppsala philosophical studies 50, 2001, (Myös internet-osoitteessa philos/personal/lindstrom/sl.quine.pdf) 5 6 1

2 KIRJALLISUUTTA 3 Montague, R., 1974, Formal Philosophy: Selected Papers of Richard Montague, Yale University Press, New Haven. KIRJALLISUUTTA 4 Rantala Veikko 2003, Possible Worlds, teoksessa Haaparanta Leila & Ilkka Niiniluoto (eds.), Analytic Philosophy in Finland, Poznan Studies in the Philosophy of the Sciences and the Humanities Volume 80, 2003, (Myös internet-osoitteessa siis koko kirja! content/rodopi/pozs) 7 8 KIRJALLISUUTTA 5 KIRJALLISUUTTA 6 Rantala Veikko & Ari Virtanen 1996, Kuka keksikään Kripke-semantiikan?, kirjassa Koskinen, Ismo et al. (toim.), Luonto toisena, toinen luontona. Kirjoituksia Lauri Mehtosen 50- vuotispäivän kunniaksi, Filosofisia tutkimuksia Tampereen yliopistosta 60, Tampere. Rantala Veikko & Ari Virtanen 2004, Johdatus modaalilogiikkaan, Gaudeamus, Helsinki. Schilpp, Paul Arthur & Lewis Edwin Hahn (eds.), 1989, The Philosophy of Georg Henrik von Wright, The Library of Living Philosophers XIX, Open Court, la Salle, Illlinois Richard Montague ( ) At UCLA in May 1955, Montague gave a talk entitled Logical Necessity, Physical Necessity, Ethics, and Quantifiers (LNPNEQ). Montague s handwritten notes for the talk survive.11 This manuscript overlaps yet is not identical with its published successor, Montague (1960) Stig Kanger ( ) Kangerin yleinen modaliteettien teoria ilmestyi vuonna 1957 Tukholman yliopiston julkaisemassa Kangerin 47- sivuisessa väitöskirjassa Provability in Logic

3 Kanger 2 Kirjan esipuheessa Kanger toteaa, että [m]ost of the investigations contained in this essay were made for a course in logic, which I gave during the spring term of 1955 at the University of Stockholm. Kanger 3 Hänen kirjasensa joka ei ole juuri enempää kuin luentomoniste on vaikealukuinen, ja työ jäi yleisesti ottaen huomiotta. Kangerin tärkeää panosta modaalilogiikan semantiikalle on paljon vääristelty Kanger 4 Kaplan: Kanger... introduced a relation between worlds and explicitly stated completeness theorems for M, S4 and S5 (Kaplan, 1966, 122). Føllesdal (tietämättä Montaguen luennosta 1955): Kanger [1957a] proposed the first fully model theoretic interpretation of modal logic. (Føllesdal, 1994, 886.) Kanger 5 Føllesdal jatkaa: Moreover, he [Kanger] introduced a fundamental new idea, which... at that time was an innovation:... Kanger regarded the notion of a possible world as a relative notion. One world may be possible relative to some other worlds, and not possible relative to further worlds. (ibid., 886.) Kanger 6 Jaakko Hintikka (s. 1929) While Kanger did state a soundness theorem for the systems M, S4 and S5 (1957a: 40), he stated no modal completeness theorems and his work left questions of completeness open, even in the case of propositional modal systems. (Copeland) Keskeiset kirjat: 1962, Knowledge and Belief. An Introduction to the Logic of the Two Notions, Cornell University Press, Ithaca NY. 1969, Models for Modalities, Reidel, Dordrecht

4 Hintikka 1957a 1...we often find it extremely useful to try to chart the different courses the events may take even if we don t know which one of the different charts we are ultimately going to make use of.... This analogy is worth elaborating. The concern of a general staff is not limited to what there will actually be... Hintikka 1957a 2... Its business is not just to predict the course of a planned campaign, but rather to be prepared for all the contingencies that may crop up during it. Most of the maps prepared by the general staff represent situations that will never take place Hintikka 1957a 3...There are for the most parts some actual units for which the marks on the map stand, and the mutual positions of the units are such that the situation could conceivably arise.... Hintikka 1957a 4... But the location of the units on the maps may be different from the locations the units have or ever will have. Some of the marks may stand for units which have not yet been formed; other maps may be prepared for situations in which some of the existing units have been destroyed. All these features have their analogues in modal logic Hintikka 1957a 5 Hintikka 1957a 6 In this example Hintikka informally speaks of the same units as occurring in different situations ( cross-world identification of individuals ) and of individuals coming into existence or disappearing as one goes from one situation to another ( varying domains ). (Sten Lindström) We may perhaps say that when we are doing modal logic, we are doing more than one thing at one and the same time. We use certain symbols constants and variables to refer to the actually existing objects of our domain of discourse

5 Hintikka 1957a 7 But we are also using them to refer to the elements of certain other states of affairs that need not be realized. Or, which amounts to the same, we are employing these symbols to build up maps or models for the purpose of sketching certain situations that will perhaps never take place.... Hintikka 1957a 7... If we could confine our attention to one of these possible states of affairs at a time, the occurrences of our symbols would be purely referential. The interconnections between the different models interfere with this Hintikka 1957a 8 Hintikka 1957a 9... But since the symbols are purely referential within each particular model, the deviation from pure referentiality is not strong enough to destroy the possibility of employing quantifiers with pretty much the same rules as in the ordinary quantification theory.... If I had to characterize the situation briefly, I should say that the occurrences of our terms in modal contexts are not usually purely referential, but rather that they are multiply referential Hintikka 1957a 10 This idea of referential multiplicity is perhaps the basic intuitive idea behind the possible worlds interpretation of modal notions and of indexical semantics in general. It seems that Hintikka here gives one of the earliest, or perhaps the earliest, clear expression of the idea.... Hintikka 1957a Hintikka s semantics for quantified modal logic is informally interpreted in such a way that the quantifiers range over genuine individuals. Thus, Hintikka has a notion of cross-world identification: one and the same individual may occur in different worlds

6 Hintikka 1957a 12...However, the semantics allows individuals to split from one world to another, i.e., the individuals a and b may be identical in one world w 0 but they may fail to be identical in some alternative world to w Hintikka 1957a Thus, the principle: x y(x = y ~(x = y)), is not valid in Hintikka s semantics. (Sten Lindström) Hintikka 1957a 14 Seuraavaksi As a consequence, the unrestricted principle of indiscernibility of identicals does not hold in modal contexts according to Hintikka (c.f., Hintikka (1961) and later writings). Klassinen kausi jatkuu... Erityisesti: Saul Kripke (s. 1940) Kuka keksikään Kripkesemantiikan?