By Günther Ludwig
ISBN-10: 3540308326
ISBN-13: 9783540308324
Written within the culture of G. Ludwig’s groundbreaking works, this publication goals to elucidate and formulate extra exactly the primary principles of actual theories. via introducing a easy descriptive language of easy shape, during which it's attainable to formulate recorded proof, ambiguities of actual theories are shunned up to attainable. during this process the sector of physics that are meant to be defined via a conception depends on simple thoughts merely, i.e. ideas that may be defined with no theory.
In this context the authors introduce a brand new inspiration of idealization and evaluation the method of gaining knowledge of new recommendations. they suspect that, whilst the theories are formulated inside of an axiomatic foundation, ideas are available to many tricky difficulties corresponding to the translation of actual theories, the family among theories in addition to the advent of actual concepts.
The ebook addresses either physicists and philosophers of technology and may inspire the reader to give a contribution to the certainty of the lasting center of actual wisdom in regards to the actual constructions of the world.
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Extra resources for A new foundation of physical theories
Sample text
The recording rules are in fact the relations of denotation described in Sect. 1. These relations of denotation are construed as the composition of the relations of designation and of reference between the ‘linguistic level’ and the - reality level - via the “conceptual level”! ) denoted by A formulated in the basic language Bl . Here, it should be distinguished between recorded facts: (i) stated (the factual truth is stated) and (ii) not stated or not knowing that they were stated. Example A We have a finite collection of sentences such as ‘the object a1 has the property marked spot and the object a2 has the property marked spot and between a1 , a2 and the real number α ∈ J1 there is the distance relation δ(a1 , a2 , α)’.
In Bl some properties are characterized as basic properties. Let p1 , p2 , p3 be the basic properties in Bl , and let p1 , p2 , p3 be the corresponding relations added by (i) to M T . We then define the relation p0 = p1 ∨ p2 ∨ p3 . The first axiom is the collectivizing axiom Collx p0 (x). 1) The relation ∃y(p0 (x) ⇔ x ∈ y) and, briefly, p0 (x) ⇔ x ∈ y are equivalent. The set y is then uniquely determined by p0 (x); we write y = {x | p0 (x)}. Instead of p1 (x) ∨ p2 (x) ∨ p3 (x) we can write x ∈ y. The second axiom is {x | p0 (x)} is a finite set.
En , one obtains new sets. Such a process, applicable in a finite number of steps, is called an echelon construction and the set thus obtained is called an echelon. The sets E1 , . . , En are the base sets of the echelon construction. We denote an echelon by S(E1 , . . , En ), where the letter S denotes the echelon construction scheme, whereby one obtained the echelon. If E1 , . . , En are n different sets, then S(E1 , . . , En ) is also an echelon of scheme S, but on the base sets E1 , .
A new foundation of physical theories by Günther Ludwig
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