[FOM] On foundations of special relativistic kinematics
Istvan Nemeti
inemeti at axelero.hu
Sat Jan 31 15:46:08 EST 2004
Dear friends and colleagues,
We have recently posted some items that may be of interest to FOM
readers. They are on our web-page
http://www.math-inst.hu/pub/algebraic-logic/Contents.html .
These are completely within the spirit of Harvey Friedman's postings
Foundational Thinking and Foundations of Special Relativistic
Kinematics. (Harvey's norm that in such a foundation one should use
experience gained in FOM is satisfied by a school of thought deriving
directly from Alfred Tarski.)
On our web-page we suggest looking at:
[1] Andreka-Madarasz-Nemeti: Logical axiomatizations of space-time.
Samples
from the literature
[2] Madarasz-Nemeti-Toke: Generalizing the logic-approach to space-time
towards general relativity: first steps
[3] Madarasz: Logic and relativity (in the light of definability theory)
[4] Andreka-Madarasz-Nemeti: Introduction to logical analysis of
relativity
theories.
We find that Harvey's postings of Jan 20 01:17:00, Jan 21 17:50:00, and
Jan 24 05:14:58 explain the main motivation and philosophy we were
following in elaborating [1]-[4] so beautifully that we find these three
postings provide an ideally perfect introduction for our own work. (This
is so much true that we already quote these postings from [1].)
At the end of posting #208, Harvey formulated the following future
goals:
- Autonomous axiomatization (of SRK),
- Observational foundations,
- Logical relationships between observational and theoretical
foundations.
Using this terminology, the above papers [1]-[4] do the following.
(I) Elaborate autonomous axiomatizations for the observational
foundation of SRK and its generalizations. Our aims are the same as
listed in Harvey's essays. E.g. one of our aims is mathematical
simplicity, transperency, elegance and elimination of any kind of tacit
assumptions. Another aim is doing reverse mathematics for the subject.
Further aim is "to be able to explain the theory to the next man coming
to you on the street".
(II) Study the logical relationships between the observational and the
theoretical foundations. This is done in [3, Chapter 4] and in [4,
Chapter 6]. For the latter we use and refine the definability theory of
(many-sorted) FOL. ([3, Chap.4.3], [4, Chap.6.3])
(III) The logical statuses of famous principles of science like
Galileo's principle of relativity SPR are studied by the methods of
logic e.g. in [3, 2.8.3 (pp.84-90)]. Some of these principles come up in
the present FOM discussion e.g. by Tim Y. Chow. (Besides SPR, several
debates of long history present ideal testing-ground for logic in
relativity. An example is the "No FTL" prediction. This, too, receives a
careful logical analysis and clear-cut logic based answer. Cf. e.g.
[1].)
Hajnal Andreka and Istvan Nemeti
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