PHILOSOPHY OF SCIENCE COLLOQUIUM, March

Department of HISTORY AND PHILOSOPHY OF SCIENCE Eotvos University, BudapestPazmany P. setany 1/A Budapest Phone/Fax: (36-1) 372 2924 Department's Home Page:http://hps.elte.huhttp://hps.elte.hu PHILOSOPHY OF SCIENCE COLLOQUIUM Room 6.54 (6th floor) Monday 4:00 PM March Program 4 March 4:00 PM 6th floor 6.54 Language: Hungarian O z s e b H o r a n y i Department of Communication Studies University of Pecs Leteznek-e propoziciok? Ugy latszik, hogy ez a logika tortenetenek tanusaga szerint regi kerdes manapsag, ebben a naturalizalt vilagban, ujra aktualissa valt. Az eloadas nem csak letezesuk mellett fog ervelni, de ervei sem lesznek mai keletuek. Legfokeppen a diszkusszio kedveert: hatha utobb mindannyian tisztabban latunk! 11 March 4:00 PM 6th floor 6.54 Language: English, except all participants speak Hungarian G a b o r E t e s i^{\star \dagger } (lecturer) and I s t v a n N e m e t i^{\dagger } \star Yukawa Institute, Kyoto University, Japan \dagger Alfred Renyi Institute of Mathematics, Budapest General relativistic- (and/or quantum-) computability; computing non-Turing-computable functions in Malament-Hogarth spacetimes It used to be a (meta) theorem of mathematical logic that mankind will never know that ZFC (which forms the foundation of mathematics) is consistent, assuming it is. We will argue that this meta-theorem is gone, it is no more provable. We will report on (convergent) results of various research groups at various parts of the world coming, independently, to the same conclusion which is, roughly, that Turing computability may not (after all) be the final limit of the capabilities of artificial computing devices. Some of the above mentioned researchers are e.g. Hogarth (Cambridge), Malament, Earman, ourselves, Kieu (Australia), F. Tipler, to mention only a few. We investigate the Church--Kalmar--Kreisel--Turing Theses concerning theoretical (necessary) limitations of future computers and of deductive sciences, in view of recent results of classical general relativity theory. We argue that (i) there are several distinguished Church--Turing-type Theses (not only one) and (ii) validity of some of these theses depend on the background physical theory we choose to use. In particular, if we choose classical general relativity theory as our background theory, then the above mentioned limitations (predicted by these Theses) become no more necessary, hence certain forms of the Church--Turing Thesis cease to be valid (in general relativity). (For other choices of the background theory the answer might be different.) We also look at various ``obstacles'' to computing a non-recursive function (by relying on relativistic phenomena) published in the literature and show that they can be avoided (by improving the ``design'' of our future computer). We also ask ourselves, how all this reflects on the arithmetical hierarchy and the analytical hierarchy of uncomputable functions. (We note that the goal of ``computing the uncomputable'' is distincly more modest than executing so called supertasks. Indeed, we do not claim possibility of the second.) A paper advocating carefully and it detail the view we adopt here -- that developments in the background physical theory can influence profoundly the fundamentals of the theories of computability and logic -- appeared in Bull. Symbolic Logic Vol. 6 No 3 (2000), pp.265-283 by Deutsch et al. Our paper on this subject is available on the following internet address: [http://ipsapp008.lwwonline.com/ips/frames/menu.asp?J=4779&S=36698&M…] A further useful reference is Hogarth, M.: ``Predictability, Computability, and Spacetime'', pp.1-123, available from [mh10026(a)cam.ac.uk]. 18 March 4:00 PM 6th floor 6.54 Language: Hungarian T i h a m e r M a r g i t a y Department of Philosophy and History of Science Technical University of Budapest Quine, megismeres es kognitiv szabadsag (Quine, cognition and cognitive freedom) Ket alapveto tapasztalatot minden ismeretelmeletnek szem elott kell tartania. Egyreszt, az emberek meglehetosen kulonbozo, inkompatibilis nezeteket vallanak - azaz tekintenek tudasnak -, masreszt, ugy tunik, megsem lehet barmit gondolni a vilagrol, azaz nem fordul elo minden logikailag lehetseges nezet. Ezt a ket szempontot osszekapcsolhatjuk, ha az ismeretelmelet alapkerdeseit - mi a tudas, es hogyan dontheto el egy hitrol, hogy tudas-e? - a szabadsag segitsegevel fogalmazzuk meg. Mennyiben all szabadsagunkban azt tekinteni tudasnak, amit akarunk, illetve azt tudni, amit akarunk? Nyilvan mar csak az elozoek alapjan is feltetelezhetjuk, hogy bizonyos kenyszerek, illetve feltetelek korlatozzak e szabadsagunkat. Ebben az osszefuggesben az ismeretelmeleti elemzes feladata e korlatok, feltetelek felderitese, es a kognitiv szabadsag hatarainak felterkepezese. Milyen korlatok akadalyozhatjak meg, hogy a legvadabb kepzelgeseinket tudasnak tekintsuk, es milyen szabadsag all az alkoto fantazia rendelkezesere? Az eloadasban a quinei meghatarozatlansagi tezisek (aluldeterminaltsag, holizmus) altal biztositott kognitiv szabadsagot vizsgalom. 25 March 4:00 PM 6th floor 6.54 Language: Hungarian G a b o r F o r r a i Department of Philosophy University of Miskolc Ideak es korpuszkulak: Locke tudomanyfilozofiaja (Ideas and Copuscules: Locke's philosophy of science) A klasszikus arisztoteleszi felfogasban a tudomany szuksegszeru igazsagokrol tokeletesen bizonyos ismereteket nyujt. A modern, durvan hume-ianus felfogasban, a tudomany kontingens igazsagok fallibilis ismereteben all. Az eloadas azt kivanja bemutatni, hogy Locke milyen szerepet jatszott a modern nezet kialakulasaban. Diohejban a kovetkezot. Ismeretelmeleti fomuve azzal a rendkivul pesszimista konkluzioval zarul, hogy a termeszetrol nem lehetseges tudomany, s e pesszimista konkluziotol a tudomanyos ismeret fogalmanak modern atertelmezese reven lehetett legkonnyebben megszabadulni. Az eloadas kozpontjaban az a kerdes all, hogy mikent jut Locke erre a pesszimista konkluziora. Ennek kifejtesehez azonban nemcsak Locke-rol kell majd beszelnem, hanem a skolasztikus es a descartes-i tudomanyfelfogasrol, valamint a korpuszkularis-mechanista termeszetkeprol is. ____________________________ The 60-minute lecture is followed by a 5-minute break. Then we held a 30-60-minute discussion. The participants may comment the talks and initiate discussion on the Internet. The comments should be written in the language of the presentation. The organizer of the seminar: Laszlo E. Szabo -- Laszlo E. Szabo Department of Theoretical Physics Department of History and Philosophy of Science Eotvos University, Budapest H-1518 Budapest, Pf. 32, Hungary Phone/Fax: (36-1)372-2924 Home: (36-1) 200-7318 Mobil/SMS: (36) 20-366-1172 http://hps.elte.hu/~leszabo