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Pázmány P. sétány
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Budapest, Hungary
Phone/Fax: (36-1) 372 2924
Location?
The web site of the seminar:
http://hps.elte.hu/seminar |
Philosophy
of Science Seminar
Room 6.54 (6th
floor) Monday 4:00 PM
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Program
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September
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30 September
4:00 PM
6th floor 6.54 
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| Giora Hon |
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Department of Philosophy
University of Haifa
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Revised! (26/09/02)
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Gödel, Einstein, Mach: Casting Constraints on All-embracing Concepts
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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-á-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 60-minute lecture is followed by a 10-minute break. Then
we hold a 30-60-minute discussion. The language of the presentation is indicated
in the following way:
English
English, except if all participants speak Hungarian
Hungarian
The participants
may comment on the talks and are encouraged to initiate discussion through the
Internet. The comments should be written in the language of the presentation.
The organizer of the seminar: László E. Szabó
(email: leszabo@hps.elte.hu) |
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