By Günther Ludwig

Written within the culture of G. Ludwig’s groundbreaking works, this ebook goals to explain and formulate extra exactly the basic rules of actual theories. via introducing a simple descriptive language of straightforward shape, within which it really is attainable to formulate recorded proof, ambiguities of actual theories are kept away from up to attainable. during this technique the sector of physics that are supposed to be defined by means of a conception depends upon simple ideas merely, i.e. strategies that may be defined with no theory.

In this context the authors introduce a brand new proposal of idealization and overview the method of learning new thoughts. they suspect that, whilst the theories are formulated inside an axiomatic foundation, options are available to many tough difficulties equivalent to the translation of actual theories, the relatives among theories in addition to the creation of actual concepts.

The booklet addresses either physicists and philosophers of technological know-how and may motivate the reader to give a contribution to the certainty of the lasting center of actual wisdom in regards to the genuine constructions of the world.

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A relation R can be characterized by a subset of an echelon or as an element of an echelon. In the same way, functions, applications, etc. can be characterized by an element of an echelon. In particular the relations of representation Rµ (see Chap. 3) can thus be described by a subset rµ of an echelon Sµ on the terms of representation as base sets or as elements rµ ∈ P(Sµ ). One can also naturally consider for all Rµ the element (r1 , r2 , . ) = s of P(S1 ) × P(S2 ) × · · ·; and if, conversely, s ∈ P(S1 ) × P(S2 ) × · · ·, then s = (r1 , r2 , .

I, Sect. 3]): (A and (B or C)) ⇔ ((A and B) or (A and C)), (A or (B and C)) ⇔ ((A or B) and (A or C)), (not (A and B)) ⇔ ((not A) or (not B)), (C) (not (A or B)) ⇔ ((not A) and (not B)), (not (not A)) ⇔ A. If we “formally” regard the sign ⇔ as a sign of equality, and if we put the sign “∧” instead of “and” and the sign “∨” instead of “or,” then the logical theorems written above enter formally into the rules of calculation for a complemented distributive lattice. The fact that (A ⇒ B) ⇔ [(A or B) ⇒ B] is a theorem can formally be interpreted so that the sign ⇒ is the order determined by the lattice operations ∧, ∨, so that also conversely the sign ⇔ becomes formally a sign of equality.

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 [6] 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 .