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By Günther Ludwig
Written within the culture of G. Ludwig’s groundbreaking works, this publication goals to explain and formulate extra exactly the primary rules of actual theories. by way of introducing a uncomplicated descriptive language of easy shape, within which it truly is attainable to formulate recorded proof, ambiguities of actual theories are refrained from up to attainable. during this process the sphere of physics that are supposed to be defined through a concept depends upon simple innovations merely, i.e. suggestions that may be defined and not using a theory.
In this context the authors introduce a brand new suggestion of idealization and overview the method of studying new innovations. they think that, while the theories are formulated inside of an axiomatic foundation, recommendations are available to many tough difficulties corresponding to the translation of actual theories, the kinfolk among theories in addition to the creation of actual concepts.
The e-book addresses either physicists and philosophers of technological know-how and may motivate the reader to give a contribution to the knowledge of the lasting center of actual wisdom concerning the actual constructions of the world.
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3 and especially Chap. 4) are added: (f) Let A be a relation in M T , and let M T be the theory obtained by adjoining A to the axioms of M T . If B is a theorem in M T , then “A ⇒ B” is a theorem in M T . (Proof: see C 14 of [6, Chap. I, Sect. 3]). (g) Let A(x) and B be relations in M T (x is not a constant of M T ), let T be a term such that A(T ) is a theorem in M T , and let M T be the theory obtained by adjoining A(x) to the axioms of M T (x is thus a constant of M T ). If B is a theorem in M T , then B is a theorem in M T .
An , α1 , . . , αn )’. We have in Sect. 1 used the real number α as the symbol of a possible result of measurement with the help of a pre-theory. Now it is necessary to say a little bit more about the description of measurements by pre-theories. In general, we can have more than one kind of measurement. Therefore, there can be more than one real number in r(a1 , . . , α1 , . ). The choice of pre-theories establishes from which physical reality the various α are measurements. For instance, for a gas in a container we can measure the pressure and the volume.
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 , . . , En . , for any x ∈ Ei one has fi (x) ∈ Ei , where fi (x) is deﬁned for any x ∈ Ei . From the mappings fi , one can then very easily build by canonical extension mappings of E1 , . . , En onto E1 , . . , En . This is carried out step by step: 1. By deﬁning a mapping g of P(E) onto P(E ) starting from a mapping f of E onto E such that, for a subset e ⊂ E, g(e) is deﬁned as the subset of all f (x) such that x ∈ e.
A new foundation of physical theories by Günther Ludwig