Mahdollisten maailmojen. semantiikan synty ja kehitys. Mahdollisten maailmojen KIRJALLISUUTTA 2 KIRJALLISUUTTA 1 KIRJALLISUUTTA 3 KIRJALLISUUTTA 4

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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 KIRJALLISUUTTA 1 Copeland, B.J. (ed.) Logic and Reality: Essays on the Legacy of Arthur Prior. Oxford: Clarendon Press. Copeland, B.Jack 1999, hakusana Arthur Prior, Stanford Encyclopedia of Philosophy, internet-osoitteessa KIRJALLISUUTTA 2 Prior, Arthur N., 1957, Time and Modality, Oxford University Press, Oxford. Prior, Arthur N., 1967, Past, Present and Future, Clarendon Press, Oxford. 3 4 KIRJALLISUUTTA 3 KIRJALLISUUTTA 4 Prior, Arthur N., Papers on Time and Tense, Clarendon Press, Oxford. (New Edition, Hasle Per et al. (eds.), Oxford University Press, Oxford 2003.) Prior, Arthur N. 1977, Worlds, Times and Selves. London: Duckworth. (Edited by Fine, K.) 5 6 1

2 KIRJALLISUUTTA 5 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. KIRJALLISUUTTA 6 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. 7 8 KIRJALLISUUTTA 7 KIRJALLISUUTTA 8 Wright, G. H. von, 1951a, Deontic Logic, Mind 60, Wright, G. H. von, 1951b, An Essay in Modal Logic, North-Holland Puhlishing Company, Amsterdam. von Wright, G. H. 1952, On the Logic of some Axiological and Epistemological Concepts, Ajatus 17. (Tuomo Aho, The Birth of General Modal Logic, MS 2003.) Wright G. H. von 2002, Elämäni niin kuin sen muistan, Otava, Helsinki Georg Henrik von Wright ( ) von Wright 2 Aikaisemmin tapasin sanoa, että sain keskimäärin joka vuosi yhden uuden idean, jota pystyin kehittelemään eteenpäin loogisanalyyttisessa filosofoinnissani. (von Wright 2002, 336.) Vieraili uudelleen Cambridgessa, ystävystyi Wittgensteinin kanssa. Kutsuttiin Cambridgeen Wittgensteinin seuraajaksi. Palasi Suomeen hoitamaan virkaansa. von Wrightin ja Hintikan kautta suomalainen filosofia loi pysyvät kontaktit englanninkieliseen filosofiaan

3 von Wright luvun alussa alettiin toimittaa nidettä The Library of Living Philosophers sarjaan. Nide ilmestyi vuonna Sarjaan The Library of Living Philosophers pääsyä on usein pidetty Nobelin palkinnon veroisena huomionosoituksena filosofian alalla. Logiikan uudet tuulet von Wright askarteli Cambridgen kaudellaan logiikan filosofian klassisten kysymysten parissa. Merkittävin näistä oli loogisen totuuden ongelma, uutena aluevaltauksena kiinnostus modaalikäsitteisiin von Wrightin 4 pääteemaa modaalilogiikassa 1 Julkaisi 1951 kaksi tärkeää julkaisua modaalilogiikan tiimoilta: 1. Suppean monografian An Essay in Modal Logic (North-Holland Puhlishing Company, Amsterdam). 2. Mind-lehdessä artikkelin Deontic Logic, jonka ansiosta häntä pidetään modernin deonttisen logiikan perustajana. (Lisää deonttisesta logiikasta myöhemmin.) 1. perustavanlaatuinen analogia modaalioperaattoreiden ja kvanttoreiden välillä 2. tämän analogian käyttö aikaisempien, kvantifikaatioteoriaan liittyneiden ja distributiivisiin normaalimuotoihin perustuneiden, tulosten laajentamiseen koskemaan myös modaalilogiikan systeemeitä von Wrightin 4 pääteemaa modaalilogiikassa 2 von Wrightin 4 pääteemaa modaalilogiikassa 3 3. distributiivisten normaalimuotojen käyttö loogisen totuuden määrittelemiseen modaalilogiikassa 4. modaalikäsitteiden eri tulkintojen tutkiminen modaliteettien yleisen teorian kehittämiseksi Ks. tarkemmin: Føllesdal Dagfinn 1989, von Wright s Modal Logic, teoksessa Schilpp & Hahn (eds.) 1989,

4 An Essay in Modal Logic One should, however, not fail to observe that there are essential similarities between alethic, epistemic, and deontic modalities on the one hand and quantifiers on the other hand.... The logic of the words possible, impossible, and necessary, in other words, is very much similar to the logic of the words some, no, and all. An Essay in Modal Logic It is indeed not surprising that this should be the case. For, popularly speaking, the possible is that which is true under some circumstances, the impossible that which is true under no circumstances, and the necessary that which is true under all circumstances. (1951b, 2, 19) Tuomo Aho 1 Tuomo Aho 2 As far as I know, this is the first complete occurrence of the idea that modalities ought to be treated entirely abstractly. What is essential in the logic of modality is just a structure that can then possibly be applied to indefinitely many of our every-day concepts Instead of particular readings, we might symbolize the modality itself simply with an abstract box ~ (though von Wright himself does not do so). Aho Tuomo, The Birth of General Modal Logic, an unpublished manuscript von Wrightin merkityksestä modaalilogiikassa 1 von Wrightin merkityksestä modaalilogiikassa 2 During this period [in Cambridge] he... also pursued a new interest in modal and deontic logic - a subject he virtually invented. P.M.S. Hacker, von Wright s obituary (The Guardian, July 4, 2003) perhaps it is G. H. von Wright who should be named the second most important author (next to C.I. Lewis) in the syntactic tradition because

5 von Wrightin merkityksestä modaalilogiikassa 3... [t]hese two works [von Wright 1951a and 1951b] marked the beginning of much work in epistemic, doxastic, and deontic logic. Some studies of the same kind had already been published,, but Von Wright s work becomes seminal, especially in deontic logic. von Wrightin merkityksestä modaalilogiikassa 4 Bull, Robert A. & Krister Segerberg, Basic Modal Logic, in Gabbay, D. & F. Guenthner (eds.), Handbook of Philosophical Logic vol. II: Extensions of Classical Logic, D. Reidel Publishing Company, Dordrecht Boston Lancaster, 1984, Norm and Action Norm and Action Kirjassaan Norm and Action vuodelta 1963 von Wright liitti normaalimuotonsa tilakuvauksiin ja mahdollisiin maailmoihin: If there are n logically independent propositions there are evidently 2n possible ways in which they can be true and/or false together. Any such distribution of truth-values over the n propositions will be called a truthcombination Norm and Action Given n atomic formulae, one can form 2n different conjunction-formulae such that every one of the atomic formulae or its negation-formula is a constituent in the conjunction.... It is easily understood in which sense these 2n different conjunction-formulae Norm and Action may be said to correspond to the 2n different truth-combinations in the propositions expressed by the atomic formulae. The conjunction-formulae are sometimes called state-descriptions. The conjunctions themselves can be called possible worlds (in the field or space of the propositions expressed by the atomic formulae)

6 Norm and Action The (perfect) disjunctive normal form of a formula is a disjunction of (none or) some or all of the state-descriptions formed of its atomic constituents. If it is the disjunction of them all the formula expresses the tautology of the propositions expressed by its atomic constituents. Norm and Action This illustrates a sense in which a tautology can be said to be true in all possible worlds. If again the disjunctive normal form is 0-termed the formula expresses the contradiction of the propositions expressed by its atomic constituents Norm and Action Oskar Becker 1952 A contradiction is true in no possible world. Propositions which are true in some possible world(s) but not in all are called contingent. (1963, 19, 21 22) Untersuchungen über den Modalkalkül (1952) [Investigations into Modal Calculus]: Becker ehdotti leibnizlaista semantiikkaa modaalioperaattoreille. oma nimitys: modaalikalkyylin statistinen tulkinta : Becker 2 Becker 3 Leibniz has already supplied a statistical theory of modalities, in his theory of possible worlds in the understanding of God, of which only one is put into being by God through his free will. The necessary truths are true in all possible worlds, the necessary falsehoods (impossibilities) are not true in any possible world What is possible is found in at least one world, and what is unnecessary is not found in all possible worlds, i.e. not found in at least one. (1952: 18)

7 Arthur N. Prior ( ) Prior appears to have been the first to use a binary relation in an explicitly modal context Prior 2 in fact, a bimodal context and the first to employ an accessibility-like interpretation of the relation. In the course of reexpressing propositions of his tense-modal logics in the form of quantifications over times, Prior introduced a relation holding between an earlier and a later point of time. (Copeland) Prior 3 Prior 4 Arthur Prior used a binary relation in an explicitly modal context in a congress held in Wellington, New Zealand in He used it in connection with his tense logic. The idea that alethic modalities can be analyzed in terms of quantification over possible states of affairs was present in a book manuscript (entitled The Craft of Modal Logic) that he had completed as early as WWW-site The Craft 1 Ks. lisää Priorista: The WWW-site for Prior studies Perhaps it was clear to Prior at the time of the Wellington address that, in principle, a parallel approach might be applied to alethic modal logic. Certainly, the idea that the modalities may be analysed in terms of quantification over possible states of affairs is present in a book manuscript, never published,

8 The Craft 2... which Prior completed in 1951, entitled The Craft of Formal Logic. Prior wrote in The Craft : For the similarity in behaviour between signs of modality and signs of quantity, various explanations may be offered. It may be, for example, that signs of modality are just ordinary quantifiers... The Craft 3... operating upon a peculiar subjectmatter, namely possible states of affairs. It would not be quite accurate to describe theories of this sort as reducing modality to quantity. They do reduce modal distinctions to distinctions of quantity, but the variables to which the quantifiers are attached retain something modal in their signification The Craft 4... they signify possibilities, chances, possible states of affairs, possible combinations of truth-values, or the like. (pp ) Important influences on Prior here were the Tractatus account of tautology and contradiction,... The Craft 5... and the writings of C. S. Peirce (in his unpublished manuscript Computations and Speculations, Prior referred to the passages from Peirce that were quoted above); Prior also mentioned John Wallis a professor of geometry at Oxford in the 17th century in this connection. (Copeland) Copeland Copeland Early in 1951 Prior read von Wright's article Deontic Logic, and the penultimate chapter of The Craft contains a cameo discussion of this topic. Von Wright's influence is also clear in the paper Prior read in August of that same year to the AAP Conference in Sydney, entitled The Ethical Copula.... Here Prior discusses and defends the parallel von Wright drew in Deontic Logic between moral words and modal words. No doubt Prior found in deontic logic a significant connection between his existing interest in ethics and his fastdeveloping interest in modal logic

9 Copeland Prior's reading of von Wright reinforced in his mind an idea that he had come across in Peter of Spain, Isaac Watts and the Port Royal Logic, an idea that was to be of considerable importance for his own future work. What von Wright calls the alethic modes - necessity, possibility, impossibility and contingency - Copeland are members of an extended group of concepts that includes the epistemic modes ( it is known that, it is not known to be false that, etc.), the doxastic modes (for example it is believed that ), and the deontic modes (such as it is permitted that and it is obligatory that ) Copeland Copeland In The Craft Prior also lists Watts' it is written that and it is said that, noting that "one could think of innumerable others" (p.749). Later von Wright was to draw attention to what may be called the agentive modes: the agent brings it about that, the agent makes it true that, and the like (von Wright 1963).... Prior introduces the collective term quasi-modals for the non-alethic modes (p.749) and remarks, accurately, that "there is a hint of a large field here" (p.752). He was later to refer to his own tense operators as quasi-modal operators (1968: 138) Copeland Copeland By the time he wrote Formal Logic he was advocating the study of "the general modal form It is -- that p ; as a distinct propositional form", observing that "this field has not been much cultivated" (1955a: 218).... Between them Prior and von Wright pioneered the now much investigated field of general intensional logic, as it may be called, in which the syntax, and latterly the semantics, developed for the study of the alethic modalities is used in the analysis of a wide range of quasimodal concepts

10 Copeland Seuraavaksi Von Wright's deontic logic and Prior's tense logic were the first major successes in this field. Another has been the logic of action or the logic of the agentive modes. (Copeland 1999.) Klassinen kausi: Kanger, Prior, Hintikka, Kripke, Montague,