Department of HISTORY AND PHILOSOPHY OF SCIENCE Eötvös University, Budapest ------------------------------------------------------------------------ Pázmány P. sétány 1/A Budapest, Hungary Phone/Fax: (36-1) 372 2924 The web site of the seminar: http://hps.elte.hu/seminar Philosophy of Science Colloquium Room 6.54 (6th floor) Monday 4:00 PM _________________________________________ 30 September 4:00 PM 6th floor 6.54 (Language of presentation: English) G i o r a H o n <http://philo.haifa.ac.il/faculty_pages/hon.htm> Department of Philosophy University of Haifa Gödel, Einstein, Mach: Casting Constraints on All-embracing Concepts [Revised! (26/09/02)] Can a theory turn back, as it were, upon itself and vouch for its own features? That is, can the derived elements of a theory be the very primitive terms that provide the presuppositions of the theory? This form of an all-embracing feature assumes a totality in which there occurs quantification over that totality, quantification that is defined by this very totality. I argue that the Mach principle exhibits such features of all-embracing nature. To clarify the argument, I distinguish between on the one hand completeness and on the other wholeness and totality, as different all-embracing features: the former being epistemic while the latter - ontological. I propose an analogy between the Mach principle as a possible selection principle in general relativity and the vicious-circle principle in foundations of mathematics. I finally conclude with a consequence of this analogy vis-?-vis completeness and totality, viz., both should be constrained if they were to be valid concepts for a physical theory. The paper progresses chronologically. It focuses on the physical approach of Mach that formed the background for Einstein?s general theory of relativity. The solutions of the field equations in the form of cosmological models set the scene for the view of all-embracing concepts discussed in the paper. Specifically, the ideas encapsulated in what Einstein called the Mach principle, constitute the thread of this account. The principle is found however to falter, in view of the fact that there are several different types of solution of the field equations that contradict it. One such important cosmological model with ramifying consequences is the rotational mass solution of Gödel. The question arises then as to whether there is an analogy between incompleteness in foundations of mathematics and in physics? The analogy between the vicious-circle principle and the Mach principle demonstrates an affirmative answer which suggests in turn that completeness and totality must be curtailed ? that is, conditions and limits should be imposed on completeness and totality to render them valid for physical theories. 1. Introduction: all-embracing concepts ? completeness vs. wholeness and totality 2. Mach?s disposition: the overwhelming unity of the whole 3. Einstein?s choice: the total inertia of a mass is due to all the other masses 4. Gödel?s criticism: objective lapse of time should not be assumed 5. Conclusion: casting constraints ? the Mach and the vicious-circle principles ------------------------------------------------------------------------ The organizer of the seminar: László E. Szabó <http://hps.elte.hu/~leszabo><mailto:leszabo@hps.elte.hu>) L a s z l o E. S z a b o Theoretical Physics Research Group of the Hungarian Academy of Sciences Department of History and Philosophy of Science Eotvos University, Budapest H-1518 Budapest, Pf. 32, Hungary Phone/Fax: (36-1)372-2924 Mobil/SMS: (36) 20-366-1172 http://hps.elte.hu/~leszabo