Reduction and Elimination in Philosophy and the Sciences
Reduction and Elimination in Philosophy and the Sciences
Reduction and Elimination in Philosophy and the Sciences
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386<br />
On <strong>the</strong> Characterization of Objects by <strong>the</strong> Language of Science — Paul We<strong>in</strong>gartner<br />
description can be obta<strong>in</strong>ed <strong>and</strong> used for <strong>the</strong> <strong>in</strong>dividuation<br />
of quantum mechanical objects. S<strong>in</strong>ce trans-world-identity<br />
of objects implies reidentifiablity of one unique object <strong>in</strong><br />
different worlds, it follows that trans-world-identity of quantum<br />
mechanical objects is not possible. There may be<br />
however a k<strong>in</strong>d of weak analogy of trans-world-identity if<br />
<strong>the</strong> follow<strong>in</strong>g restrictions <strong>and</strong> deviations with respect to a<br />
Kripke style semantics are made:<br />
(1) Possible worlds are replaced by measur<strong>in</strong>g<br />
processes.<br />
(2) "There is a world W' (different from <strong>the</strong> actual<br />
world W) <strong>in</strong> which <strong>the</strong> proposition A' about system<br />
S' is true" is replaced by: "There is a measur<strong>in</strong>g<br />
process M' (different from <strong>the</strong> actual (or<br />
earlier) measur<strong>in</strong>g process M) with <strong>the</strong> result<br />
that proposition A' about system S' is true."<br />
(3) The accessibility relation R(S, S') is satisfied,<br />
when A(S, M) = A'(S', M').<br />
(4) There is a non-zero probability for reach<strong>in</strong>g result<br />
A' about S' by measur<strong>in</strong>g process M' from<br />
<strong>the</strong> earlier result A about S by measur<strong>in</strong>g process<br />
M.<br />
(5) If (4) is satisfied, <strong>the</strong>re is a non-zero probability<br />
for a weak temporal identity of <strong>the</strong> system (object)<br />
S.<br />
4. Are <strong>the</strong> Pr<strong>in</strong>ciples about <strong>the</strong> Objects of<br />
Reference of Ch. 2 valid when applied to<br />
SR <strong>and</strong> GR?<br />
4.1 Value-Completeness<br />
Special Relativity (SR): Value-completeness or valuedef<strong>in</strong>iteness<br />
of properties of an object (reference system,<br />
cf. 2.4) is not satisfied for an observer at every po<strong>in</strong>t of<br />
time. But <strong>in</strong> this case (we have just <strong>in</strong>ertial movement <strong>and</strong><br />
no acceleration or gravitation <strong>and</strong> M<strong>in</strong>kowski space-time)<br />
<strong>the</strong> observer may always wait until <strong>the</strong> object appears <strong>in</strong><br />
his past light cone.<br />
General Relativity (GR): As soon as acceleration or gravitation<br />
is taken <strong>in</strong>to account, <strong>the</strong>re are always some doma<strong>in</strong>s<br />
<strong>in</strong> space-time with objects that will never appear <strong>in</strong><br />
<strong>the</strong> past light cone of <strong>the</strong> observer. This is so even if <strong>the</strong><br />
observer moves on a geodesic, i.e. free from forces. It is<br />
pla<strong>in</strong> <strong>the</strong>n that <strong>the</strong> description of such objects cannot be<br />
value-complete.<br />
4.2 Permanence<br />
SR <strong>and</strong> GR: The essential properties of <strong>the</strong> object of reference<br />
(as <strong>the</strong> bearer) are no more permanent, although<br />
with one exception: charge. The o<strong>the</strong>r properties like<br />
mass, length <strong>and</strong> geometrical shape change <strong>in</strong> case of fast<br />
<strong>in</strong>ertial motion <strong>in</strong> accordance with <strong>the</strong> Lorentz-<br />
Transformation; this holds also <strong>in</strong> local <strong>in</strong>ertial reference<br />
systems of Rimanean space-time (GR).<br />
which could not serve anymore as <strong>in</strong>dividuat<strong>in</strong>g) was proposed by Thomas<br />
Aqu<strong>in</strong>as (Ver), 19, as one, though not <strong>the</strong> only possibility, s<strong>in</strong>ce it is not sufficient<br />
<strong>in</strong> all cases (like children who die immediately after birth).<br />
4.3 Uniqueness<br />
Accord<strong>in</strong>g to 2.6, uniqueness of objects of Classical Mechanics<br />
can be satisfied by special values of <strong>the</strong> accidental<br />
properties position (p), momentum (q) <strong>and</strong> po<strong>in</strong>t of time (t).<br />
But <strong>in</strong> 3.3 it was shown that uniqueness is no more satisfied<br />
on <strong>the</strong> microlevel (<strong>in</strong> QM). Concern<strong>in</strong>g SR, uniqueness<br />
w.r.t. p, q, t holds only partially; namely it holds only for<br />
objects appear<strong>in</strong>g <strong>in</strong> <strong>the</strong> past <strong>and</strong> future light cone of <strong>the</strong><br />
observer (dynamical laws presupposed). With respect to<br />
GR, uniqueness is dependent on <strong>the</strong> space-time curvature.<br />
4.4 Reidentifiability<br />
With respect to both, SR <strong>and</strong> GR, <strong>the</strong> object of reference is<br />
not <strong>in</strong> general reidentifiable through time; this is so because<br />
essential properties of <strong>the</strong> object like geometrical<br />
shape <strong>and</strong> mass may change depend<strong>in</strong>g on movement.<br />
Therefore reidentifiability holds only approximately <strong>in</strong> local<br />
reference frames of space-time.<br />
4.5 Time <strong>and</strong> Simultaneity<br />
With respect to both, SR <strong>and</strong> GR, <strong>the</strong>re is nei<strong>the</strong>r a universal<br />
time, nor universal simultaneity. Each different observer<br />
(each different laboratory or reference system) has<br />
its own time <strong>and</strong> simultaneity. Therefore <strong>the</strong> object of reference<br />
is not <strong>the</strong> same for all observers.<br />
Literature<br />
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Kant, I. (1787, KRV) Kritik der re<strong>in</strong>en Vernunft. Riga.<br />
Mittelstaedt, P. (1986, SRM) Sprache und Realität <strong>in</strong> der modernen<br />
Physik. Mannheim, Bibliographisches Institut.<br />
Mittelstaedt, P./We<strong>in</strong>gartner, P. (2005, LNt) Laws of Nature.<br />
Spr<strong>in</strong>ger, Heidelberg-Berl<strong>in</strong>.<br />
Russell, B. (1919, IMP) Introduction to Ma<strong>the</strong>matical <strong>Philosophy</strong>.<br />
London, Allen <strong>and</strong> Unw<strong>in</strong>.<br />
Russell, B. (1925, ABC) The ABC of Relativity. London, Kegan<br />
Paul.<br />
Russell, B. (1927, AMt) The Analysis of Matter. London, Kegan<br />
Paul.<br />
Thomas Aqu<strong>in</strong>as (Ver) De Veritate. Engl. Transl.: The Disputed<br />
Questions on Truth. Henry Regnery Company, Chicago 1952<br />
We<strong>in</strong>gartner, P. (1996, UWT) "Under What Transformations are<br />
Laws Invariant?" <strong>in</strong>: We<strong>in</strong>gartner, P./Schurz, G. (eds.) Law <strong>and</strong><br />
Prediction <strong>in</strong> <strong>the</strong> Light of Chaos Research. Spr<strong>in</strong>ger, Heidelberg-<br />
Berl<strong>in</strong>, p. 47-88.