Download Structure and Approximation in Physical Theories by A. Hartkämper, H.-J. Schmidt (auth.), A. Hartkämper, H.-J. PDF

By A. Hartkämper, H.-J. Schmidt (auth.), A. Hartkämper, H.-J. Schmidt (eds.)

The current quantity comprises 14 contributions awarded at a colloquium on "Structure and Approximation in actual Theories" held at Osnabruck in June 1980. The articles are awarded within the revised shape written after the colloquium and for this reason additionally take account of the result of the dialogue on the colloquium. it's a extraordinary characteristic that the matter of approximation in actual theories has just recently discovered a few recognition within the philosophy of technological know-how, even supposing the operating physicist is con­ stantly faced with these questions. No attention-grabbing conception of actual technology precisely matches its experimental info; nearly each relation among diverse theories is an approximate one. There­ fore an enough reconstruction of actual theories needs to take into consideration and conceptualize the instant of approximation. nearly all of the articles during this booklet is headquartered round this topic. There are no less than complex, 'structuralistic' ways to the formalization of actual theories during which the element of approximation has been included: the technique as a result of P. Suppes, J. Sneed, W. Stegmuller ("S-approach") and the procedure of G. Lud­ wig and his co-workers ("L-approach"). The articles during this e-book correspondingly fall into 3 sessions: presentation, elaboration and critique of the L-approach [Hartkamper/Schmidt, Ludwig, Neumann, Werner, Schmidt, Mayr, Kamiah, Majer, Grafe] or of the S-approach [Moulines, Balzer, Cooke], and articles touching on either methods or fascinated about similar concerns [Scheibe, Pfarr, Castrigiano]. in fact, this can be just a tough category and every article needs to be appraised in its personal right.

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NEUMANN Since in the quantum case to be discussed later (4a) has some surprising consequences one might consider less idealized causality postulates. An obvious weakening taking into account the imprecision of probability measurements would be the replacement of (4a) by i - i < E (413) o 0 for a finite but sufficiently small Eo > O. Let us also consider i - i < E(d(cr,cr'» (4y) o where E is a function E: 1R + 1R+ and d(cr,cr') + + 2 {-(x _x,)2 + (x-x') }. inf o 0 xEcr,xEcr' For an experimental test with a certain fixed imprecision set Uo postulates (4a), (413) and (4y) with appropriately chosen E and E(d) should be physically equivalent with respect to Uo .

Clearly, (MGM n MG-1 M)MEU resp. (MGMGM)MEU are Cauchy-nets in P(XXX), thus converging towards Y resp. Z (cf. T1). We have to prove y·c ~ and Z c G. S~ppose first (x,yl E Y. r all M E U, hence (x,y) E G and, -1 - analogously, (x,y) E G = G • Because G is an ordering, this implies (x,y) E ~. Now consider the case (x,y) E Z. - If Gx n --1 G y * ¢, --1 sets Gx and G -1 we are done, thus let us assume that the closed A yare disjoint. Since X is normal, MGMx and ~ MG My must be disjoint for some M E U.

Scheibe: Theorien, Strukturarten und mengentheoretische Pradikate. Preprint 1976. E. Scheibe: On the Structure of Physical Theories. In: The Logic and Epistomology of Scientific Change. Acta Phil. Fenn. XXX (1978), Issues 2-4. 205-224. E. Scheibe: Invariance and covariance. To appear in: Festschrift for Mario Bunge. : J. Agassi and R. Cohen. N. Bourbaki: Theory of Sets. Hermann, Paris 1974 (2 nd printing) . J. Sneed: The Logical Structure of Mathematical Physics. Reidel, Dordrecht, 1971. G. Ludwig: Axiomatische Basis einer physikalischen Theorie und theoretische Begriffe.

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