ELFT HÍRADÓ

["Laszlo E. Szabo" <leszabo AT hps.elte.hu>]

Department of HISTORY AND PHILOSOPHY OF SCIENCE
Eötvös University, Budapest
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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
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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


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The organizer of the seminar: László E. Szabó
<http://hps.elte.hu/~leszabo><mailto:leszabo AT 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