By Günther Ludwig
Written within the culture of G. Ludwig’s groundbreaking works, this publication goals to elucidate and formulate extra exactly the basic rules of actual theories. by way of introducing a easy descriptive language of easy shape, during which it truly is attainable to formulate recorded proof, ambiguities of actual theories are refrained from up to attainable. during this technique the sector of physics that are meant to be defined through a concept relies on simple ideas in simple terms, i.e. suggestions that may be defined with out a theory.
In this context the authors introduce a brand new notion of idealization and evaluate the method of gaining knowledge of new thoughts. they suspect that, while the theories are formulated inside an axiomatic foundation, options are available to many tough difficulties reminiscent of the translation of actual theories, the family members among theories in addition to the advent of actual concepts.
The booklet addresses either physicists and philosophers of technology and will motivate the reader to give a contribution to the certainty of the lasting middle of actual wisdom in regards to the genuine constructions of the world.
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Extra resources for A new foundation of physical theories
By these pre-theories it is established which objects are described by real numbers α. For instance, if we use Newton’s theory of space–time as a pre-theory, we can construct the description of time by one real number t as describing a timepoint, and a triplet of real numbers (x1 , x2 , x3 ) as standing for a spot in space. The real numbers t, x1 , x2 , x3 can only be determined by ﬁxing a space–time reference system. Thus real numbers in (r) only make sense if one says from which pre-theory, and in which way these real numbers appear in (r).
E. if S(y) is functional in y), according to Sect. 3, then “S(y) ⇔ (y = τy (S))” is also true. ” But the set Ex (r) “exists” only if Collx R is a theorem in M T . In no case, for all R(x), is the relation Collx R a theorem in M T . ” Wouldn’t it be easy to conceive of Collx R as an axiom for all R(x)? All those who have dealt with problems of an “intuitive” set theory know that such a general condition contains problems. For this reason we will proceed in a more careful way. , Collx R becomes a theorem in M T .
Is less easy to grasp in its intuitive content. , that the process of selection τ chooses “in the same manner” the identical properties R and S. For a detailed description of the consequences of this axiom we refer to  I, Sect. 5. Two theorems will be given, without proof, since they will often be used later and they will also have an importance from the physical point of view in Chap. 3. Let us begin with a deﬁnition: If the relation (∀y)(∀x)((R(y) and R(x)) ⇒ (x = y)) is a theorem in M T (it is often said that there exists at most one x such that R), then R(x) is said to be “single-valued in x” in M T .