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Disputed term/author/ism | Author |
Entry |
Reference |
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Description Levels | Genz | II 47
Description/level/Genz: systems in which everything really depends on everything do not allow for a delimitation of levels. The laws apply on all levels, the system is "self-similar".
>Levels (order).Self-similarity/laws/system/Genz: if you know a little bit about self-similar systems, you know the whole thing. The big is created by enlarging the small. >Self-similarity. II 304
Level/natural law/legislative level/description/Genz: different levels of description can be delimited, on which laws apply that use terms that do not require the deeper levels to be used for their definition.
For example, the physician can draw conclusions about a disease of the liver from the blood count without knowledge of chemistry. >Laws, >Laws of nature, >Inferences, >Conclusions, >Symptoms. II 304
Level/natural laws/legislative level/description/Genz: levels are possible because not everything depends on everything.
Levels/Genz: why they can be delimited at all can only be answered anthropically: if there are no laws, we could not have formed ourselves.Cf. >Anthropic Principle, >Explanations. |
Gz I H. Genz Gedankenexperimente Weinheim 1999 Gz II Henning Genz Wie die Naturgesetze Wirklichkeit schaffen. Über Physik und Realität München 2002 |

Invariants | Thiel | I 301
Def Scale Invariance/Thiel: Shape equality of all distances. Because of the scale invariance, the size statements of the geometry are always only those about proportions. But these have to be defined first with a form-theoretical approach. Especially the equality of size.
(FregeVs: first equality, then number).Since we could explain geometric shape equality only after the determination of excellent shapes in protogeometry, the fitting equality does not provide the size equality (congruence) required in shape-theoretical geometry. This can be defined differently, e.g. for distances by the possibility of connecting both by a sequence of symmetrical triangles. >Self-similarity, >Congruence, |
T I Chr. Thiel Philosophie und Mathematik Darmstadt 1995 |

Reality | Deutsch | I 105
Criterion for reality: something that can hit back exists. But also Dr. Johnson did not directly hit the stone. He just hit some nerves, and so on.
Cf. >Reality/Hacking.I 107
Def Reality/Deutsch: if a quantity is complex and autonomous according to the simplest explanation, then it is real.
>Simplicity, >Complexity, >Explanation.I 111
Theory: the more fundamental a theory is, the more comprehensive are the observations that play a role in it. Physical reality is therefore self-similar in several ways.
>Theory, >Theory/Deutsch, >Self-similarity.After all, not everything that is real must be easy to identify. I 119
Simulation: A reality simulator indirectly conveys both internal and external experiences to the recipient, but it cannot be programmed to simulate a particular internal experience. Roulette example and tennis example: the framework conditions are defined here, the course of the game must be open, which means that the abstract laws themselves and not only their predictive power can be simulated in virtual reality.
>Laws, >Laws of nature, >Simulation, >Prediction.I 190
Life = simulation: both are embodiments of theories about the environment;
Something that only exists in the laws of classical physics does not exist in reality.Real hurricanes and butterflies obey the laws of quantum theory, not those of classical mechanics! I 225/26
Plato's apparent refutation that the methods of natural science could lead to mathematical truth: we cannot know anything about perfect circles because we only have access to imperfect circles.
DeutschVsPlato: then we can also only build inaccurate tool machines, because the first ones are built with inaccurate tools. So there would be no possibility of self-correction.Cf. >Ideas/Plato. |
Deutsch I D. Deutsch Fabric of Reality, Harmondsworth 1997 German Edition: Die Physik der Welterkenntnis München 2000 |

Similarity | Gleick | Gl 152
Self-similarity: symmetry in different scales exhibits self-similarity. It is dimensionless and applicable without a scale, e.g equations for fluid motion.
>Self-similarity. |
Gleick I James Gleick Chaos - Making a new Science. 1987 German Edition: Chaos - Die Ordnung des Universums: Vorstoß in die Grenzbereiche der modernen Physik München 1988 |

Similarity | Goodman | I 95
Similarity/Goodman: while we obviously have a similarity measure for sizes, we have none for similarity or dissimilarity of different shapes.
---III 15f
Self-similarity/representation/Goodman: an object is similar to itself to the highest degree, but rarely represents itself. Similarity is, unlike representation, reflexive. A painting of the castle of Marlborough Constable is more similar to any other picture, than to the castle and yet it represents the castle and not another picture, not even the most faithful copy.
>Representation, cf. >Forgery.III 42ff
The proposed measure for realism exists in the likelihood of confusion between representation with the represented. This is an important advance over the image theory. If the likelihood of confusion = 1, then we have no more representation, then we have identity. Even with a trompe l'oeuil the probability rarely rises above zero, because seeing a picture as a picture excludes to mistake it for something else. (> Forgery). III 43f
E.g. a copy that is painted in negative colors: the second picture provides exactly the same level of information. The information income is not a measure for realism. Realism is relative.
>Information, >Realism.--- IV 150
We often know what an image represents, without knowing (or without us worrying about) whether it is similar to his subject. E.g. we do not know whether images of the Crucifixion are similar to the actual happening. Nonetheless, we can, of course, say what these images represent. IV 151
Every thing has a lot of views. Therefore the assertion that an image looks like its subject means not that a particular relationship between the two is specified.
>Aspects.IV 152
X-ray or cloud chamber photographs also have no resemblance to the visible aspects of their subjects.
>Picture, >Image, >Mapping.IV 163
Even if an image has a clearly recognizable resemblance to its subject, we are not always able to perceive this similarity, if we do not know what we should look for.
Knowing how to look at a picture is necessary to recognize the ways in which it resembles its subject. To reject similarity as a basis for pictorial representation does not mean that everything can be a picture of everything else.Wrong: that comparative similarity is a preceding constant that acts as a measure for realism. |
G IV N. Goodman Catherine Z. Elgin Reconceptions in Philosophy and Other Arts and Sciences, Indianapolis 1988 German Edition: Revisionen Frankfurt 1989 Goodman I N. Goodman Ways of Worldmaking, Indianapolis/Cambridge 1978 German Edition: Weisen der Welterzeugung Frankfurt 1984 Goodman II N. Goodman Fact, Fiction and Forecast, New York 1982 German Edition: Tatsache Fiktion Voraussage Frankfurt 1988 Goodman III N. Goodman Languages of Art. An Approach to a Theory of Symbols, Indianapolis 1976 German Edition: Sprachen der Kunst Frankfurt 1997 |

Disputed term/author/ism | Author Vs Author |
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Reference |
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Principia Mathematica | Gödel Vs Principia Mathematica | Russell I XIV
Circular Error Principle/VsPrincipia Mathematica^{(1)}/PM/Russell/Gödel: thus seems to apply only to constructivist assumptions: when a term is understood as a symbol, together with a rule to translate sentences containing the symbol into sentences not containing it.
Classes/concepts/Gödel: can also be understood as real objects, namely as "multiplicities of things" and concepts as properties or relations of things that exist independently of our definitions and constructions!This is just as legitimate as the assumption of physical bodies. They are also necessary for mathematics, as they are for physics. Concept/Terminology/Gödel: I will use "concept" from now on exclusively in this objective sense. A formal difference between these two conceptions of concepts would be: that of two different definitions of the form α(x) = φ(x) it can be assumed that they define two different concepts α in the constructivist sense. (Nominalistic: since two such definitions give different translations for propositions containing α.) For concepts (terms) this is by no means the case, because the same thing can be described in different ways. For example, "Two is the term under which all pairs fall and nothing else. There is certainly more than one term in the constructivist sense that satisfies this condition, but there could be a common "form" or "nature" of all pairs. All/Carnap: the proposal to understand "all" as a necessity would not help if "provability" were introduced in a constructivist manner (..+...). Def Intensionality Axiom/Russell/Gödel: different terms belong to different definitions. This axiom holds for terms in the circular error principle: constructivist sense. Concepts/Russell/Gödel: (unequal terms!) should exist objectively. (So not constructed). (Realistic point of view). When only talking about concepts, the question gets a completely different meaning: then there seems to be no objection to talking about all of them, nor to describing some of them with reference to all of them. Properties/GödelVsRussell: one could surely speak of the totality of all properties (or all of a certain type) without this leading to an "absurdity"! ((s) > Example "All properties of a great commander". Gödel: this simply makes it impossible to construe their meaning (i.e. as an assertion about sense perception or any other non-conceptual entities), which is not an objection to someone taking the realistic point of view. Part/whole/Mereology/GödelVsRussell: neither is it contradictory that a part should be identical (not just the same) with the whole, as can be seen in the case of structures in the abstract sense. Example: the structure of the series of integers contains itself as a special part. I XVI/XVII
Even within the realm of constructivist logic there are certain approximations to this self-reflectivity (self-reflexivity/today: self-similarity) of impredicative qualities, namely e.g. propositions, which as parts of their meaning do not contain themselves, but their own formal provability.
There are also sentences that refer to a totality of sentences to which they themselves belong: Example: "Each sentence of a (given) language contains at least one relational word".This makes it necessary to look for other solutions to the paradoxes, according to which the fallacy does not consist in the assumption of certain self-reflectivities of the basic terms, but in other assumptions about them! The solution may have been found for the time being in simple type theory. Of course, all this refers only to concepts. Classes: one should think that they are also not created by their definitions, but only described! Then the circular error principle does not apply again. Zermelo splits classes into "levels", so that only sets of lower levels can be elements of sets of higher levels. Reducibility Axiom/Russell/Gödel: (later dropped) is now taken by the class axiom (Zermelo's "axiom of choice"): that for each level, for any propositional function φ(x) the set of those x of this level exists for which φ(x) is true. This seems to be implied by the concept of classes as multiplicities. I XVIII
Extensionality/Classes: Russell: two reasons against the extensional view of classes: 1. the existence of the zero class, which cannot be well a collection, 2. the single classes, which should be identical with their only elements.
GödelVsRussell: this could only prove that the zero classes and the single classes (as distinguished from their only element) are fictions to simplify the calculation, and do not prove that all classes are fictions!Russell: tries to get by as far as possible without assuming the objective existence of classes. According to this, classes are only a facon de parler. Gödel: but also "idealistic" propositions that contain universals could lead to the same paradoxes. Russell: creates rules of translation according to which sentences containing class names or the term "class" are translated into sentences not containing them. Class Name/Russell: eliminate by translation rules. Classes/Principia Mathematica/Russell/Gödel: the Principia Mathematica can do without classes, but only if you assume the existence of a concept whenever you want to construct a class. First, some of them, the basic predicates and relations like "red", "colder" must be apparently considered real objects. The higher terms then appear as something constructed (i.e. something that does not belong to the "inventory of the world"). I XIX
Ramsey: said that one can form propositions of infinite length and considers the difference finite/infinite as not so decisive.
Gödel: Like physics, logic and mathematics are based on real content and cannot be "explained away".Existence/Ontology/Gödel: it does not behave as if the universe of things is divided into orders and one is forbidden to speak of all orders, but on the contrary: it is possible to speak of all existing things. But classes and concepts are not among them. But when they are introduced as a facon de parler, it turns out that the extension of symbolism opens the possibility of introducing them in a more comprehensive way, and so on, to infinity. To maintain this scheme, however, one must presuppose arithmetics (or something equivalent), which only proves that not even this limited logic can be built on nothing. I XX
Constructivist posture/constructivism/Russell/Gödel: was abandoned in the first edition, since the reducibility axiom for higher types makes it necessary that basic predicates of arbitrarily high type exist.
From constructivism remains only1. Classes as facon de parler 2. The definition of ~, v, etc. as valid for propositions containing quantifiers, 3. The stepwise construction of functions of orders higher than 1 (of course superfluous because of the R-Axiom) 4. the interpretation of definitions as mere typographical abbreviations (all incomplete symbols, not those that name an object described by the definition!). Reducibility Axiom/GödelVsRussell: this last point is an illusion, because of the reducibility axiom there are always real objects in the form of basic predicates or combinations of such according to each defined symbol. Constructivist posture/constructivism/Principia Mathematica/Gödel: is taken again in the second edition and the reducibility axiom is dropped. It is determined that all basic predicates belong to the lowest type. Variables/Russell/Gödel: their purpose is to enable the assertions of more complicated truth functions of atomistic propositions. (i.e. that the higher types are only a facon de parler.). The basis of the theory should therefore consist of truth functions of atomistic propositions. This is not a problem if the number of individuals and basic predicates is finite. Ramsey: Problem of the inability to form infinite propositions is a "mere secondary matter". I XXI
Finite/infinite/Gödel: with this circumvention of the problem by disregarding the difference between finite and infinite a simpler and at the same time more far-reaching interpretation of set theory exists:
Then Russell's Apercu that propositions about classes can be interpreted as propositions about their elements becomes literally true, provided n is the number of (finite) individuals in the world and provided we neglect the zero class. (..) + I XXITheory of integers: the second edition claims that it can be achieved. Problem: that in the definition "those cardinals belonging to each class that contains 0 and contains x + 1 if it contains x" the phrase "each class" must refer to a given order. I XXII
Thus whole numbers of different orders are obtained, and complete induction can be applied to whole numbers of order n only for properties of n!
(...) The question of the theory of integers based on ramified type theory is still unsolved. I XXIII
Theory of Order/Gödel: is more fruitful if it is considered from a mathematical point of view, not a philosophical one, i.e. independent of the question of whether impredicative definitions are permissible.
(...) impredicative totalities are assumed by a function of order α and ω .Set/Class/Principia Mathematica ^{(1)}/Russell/Type Theory/Gödel: the existence of a well-ordered set of the order type ω is sufficient for the theory of real numbers.Def Continuum Hypothesis/Gödel: (generalized): no cardinal number exists between the power of any arbitrary set and the power of the set of its subsets. Type Theory/VsType Theory/GödelVsRussell: mixed types (individuals together with predications about individuals etc.) obviously do not contradict the circular error principle at all! I XXIV
Russell based his theory on quite different reasons, similar to those Frege had already adopted for the theory of simpler types for functions.
Propositional functions/statement function/Russell/Gödel: always have something ambiguous because of the variables. (Frege: something unsaturated).Propositional function/p.f./Russell/Gödel: is so to speak a fragment of a proposition. It is only possible to combine them if they "fit together" i.e. are of a suitable type. GödelVsRussell: Concepts (terms) as real objects: then the theory of simple types is not plausible, because what one would expect (like "transitivity" or the number two) to be a concept would then seem to be something that stands behind all its different "realizations" on the different levels and therefore does not exist according to type theory. I XXV
Paradoxes in the intensional form/Gödel: here type theory brings a new idea: namely to blame the paradoxes not on the axiom that every propositional function defines a concept or a class, but on the assumption that every concept results in a meaningful proposition if it is claimed for any object as an argument.
The objection that any concept can be extended to all arguments by defining another one that gives a false proposition whenever the original one was meaningless can easily be invalidated by pointing out that the concept "meaningfully applicable" does not always have to be meaningfully applicable itself.1. Whitehead, A.N. and Russel, B. (1910). Principia Mathematica. Cambridge: Cambridge University Press. |
Göd II Kurt Gödel Collected Works: Volume II: Publications 1938-1974 Oxford 1990 |

Steady State Theory | Verschiedene Vs Steady State Theory | Kanitscheider I 359
Steady State Theory/SST/Bondi/Kanitscheider: Thesis: Priority of cosmology over local physics. Bondi's Thesis: the unclear complexity of the phenomenon world is only one property of the mesocosm. I 360
VsSST: incompatible with our empiricism: a static universe has long been in thermodynamic equilibrium. All development would already have reached its final state. It would no longer be possible to determine the direction of the time flow.
Of the two types of motion allowed by Perfect Cosmological Principle, expansion and contraction, contraction is already eliminated because the necessary excess of radiation in relation to matter is lacking.For expansion, however, the steady state theory now needs the assumption of constant additional generation of matter. But this overrides the important principle of hydrodynamic continuity! I 361
However, at the current values for density and recession constant (distance movement of galaxies from each other), the origin of matter would only be one H atom per litre every 5x10 exp 11 years.
Conservation of Matter/BondiVsVs: he even believes he can save the conservation of matter. He says that in a certain, observable area, seen globally, the observable amount of matter does not change, i.e. that in a constant eigenvolume matter is preserved, in contrast to the relativistic models, where the conservation applies rather to the coordinate volume. The Def Eigenvolume is the part of space that is fixed by a fixed distance from the observer, while the Def coordinate volume is given by the constancy of the com mobile coordinates. I 362
Steady State Theory/SST: here there is always the same amount of matter within the range of a certain telescope, while here the relativity theory assumes a dilution, i.e. the matter remains the same in the expanding volume.
At the SST, the new formation ensures that the total amount of all observable matter remains the same.Observer/SST: when investigating motion, each observer can perceive a preferred direction of motion apart from local deviations, whereby he determines the constant relationship between velocity and distance completely symmetrically within a small range. In relativistic cosmology this was the starting point for the Weyl principle. Def Weyl-Principle: Postulate: the particles of a substrate (galaxies) lie in spacetime on a bundle of geodesists that start from a point in the past (Big Bang) and never intersect except at this point. From this follows the existence of a family of hyperplanes (t = const) orthogonal to these geodesists and the only parameters possessing cosmic time. I 362/363
Bondi/SST/Steady State Theory: doubts now that in view of the scattering of the fog movement these hyperplanes exist secured.
Because of its stationary character, SST does not need Weyl's postulate and can define homogeneity without cosmic time.Thermodynamic imbalance/universe/SST: Explanation: a photon emanating from a star has a very long free path and reaches areas with strongly changed local motion. This shifts its frequency to red. However, the thermal energy it gives off on its way to the surrounding matter is only a very small part of that lost by its original star. Thus the universe represents a kind of cosmic sink for radiant energy. According to the Perfect Cosmological Principle, sources must exist that make up for the loss. Perfect Cosmological Principle: is logically compatible with three types of universes: 1. Static, without new creation of matter, 2. Expanding, with new development I 364
3. Collapsing, with destruction of matter
SST/Bondi: believes in the strict relationship between distance and speed R'(t)/R(t) = 1/T. This results in R as an exponential function and the metric of the SST takes the form of the line element of de Sitter. (see above). Already the self-similarity of the scale function shows the basic metric properties of this model. It is not possible for us to recognize at which point of the curve R = et/T we are. The universe has no beginning and no end. I 365
Age/Universe/SST: Advantage over relativistic theories where the inverse Hubble constant led to a too low age.
Metric/SST: while the de Sitter metric is unusable in Einstein's representation because it can only be reconciled with vanishing matter, this problem does not occur in the SST: here there is no necessary connection between physical geometry and matter content of space!According to the de Sitter structure, the world has an event horizon, i.e. every clock on a distant galaxy follows in such a way that there is a point in its history after which the emitted light can no longer reach a distant observer. If, however, a particle has formed within the range that can in principle be reached with ideal instruments, then it can never disappear from its field of view. I 367
Perfect Cosmological Principle: Problem: lies in the statistical character, which applies strictly on a cosmic scale, but not locally, whereby the local environment only ends beyond the galaxy clusters.
Steady State Theory/SST/Hoyle: starts from the classical field equations, but changes them so strongly that all Bondi and Gold results that they have drawn from the Perfect Cosmological Principle remain valid.Hoyle/SST: Thesis: In nature a class of preferred directions can obviously be observed in the large-scale movements, which makes a covariant treatment impossible! Only a preferred class of observers sees the universe in the same way. I 368
Weyl Principle/Postulate: defines a unique relationship of each event P to the origin O. It cannot be a strict law of nature, since it is constantly violated in the local area by its own movements!
Hoyle: (formula, tensors, + I 368). Through multiple differentiation symmetric tensor field, energy conservation does not apply, matter must constantly arise anew.Matter emergence/SST/Hoyle: there is an interpretation of matter origin caused by negative pressure in the universe. It should then be interpreted as work that this pressure does during expansion! VsSST: the synchronisation of expansion and origin is just as incomprehensible from theory as the fact that it is always matter and not antimatter that arises. (...+ formula, other choice of the coupling constant I 371/72). I 373
Negative Energy: it has been shown to cause the formation rate of particle pairs to "run away": infinite number in finite region.
VsSST/Empiricism: many data spoke against the SST: excess of distant and thus early radio sources, redshift of the quasars indicating a slowdown of expansion, background radiation. |
Kanitsch I B. Kanitscheider Kosmologie Stuttgart 1991 Kanitsch II B. Kanitscheider Im Innern der Natur Darmstadt 1996 |