# Dictionary of Arguments

Philosophical and Scientific Issues in Dispute

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Decidability Genz II 206
Compressibility/Decidability/Genz: there can be no computer program that decides if any amount of data is compressible. Stronger: there is no way to prove that it is not compressible.
Compressibility: can be proven but not refuted.
II 207
Example number pi: π can be generated by a finite program. There are numbers that cannot be calculated in principle:
Omega/Chaitin/Genz: this is what Chaitin calls a certain number of which not a single digit can be calculated. It is not accessible to any rule, it is outside mathematics.
>Gregory Chaitin.
II 218
Decidability/calculability/undecidable/non-calculable/Genz: non-calculable numbers are actually the same as non-decidable numbers. Incalculability/physics/quantum cosmology/Genz: apparent indecidability: the ... of the wave-function of the universe shows apparant indecidability. It deals with the possible geometry of three-dimensional spaces.
>Wave function.
Simplified: e. g. a circle (one dimensional): to calculate the wave function of the universe for the circle as an argument: the wave function can be represented as a sum of summands, where there is a series of handleless cups, one series of cups with a handle, one series of cups with two handles, etc., whereby the handles can be shaped differently in each case. These represent four-dimensional spaces (with time as 4th dimension).
Circle: here time is added as the 2nd dimension. Together they form the two dimensions of the cup surfaces.
II 219
3rd dimension: the 3rd dimension in which the surfaces are embedded, serves only as an illustration. It has no equivalent in reality. Problem: it is not possible to decide which cups are to be regarded as the same, which cups are to be regarded as different (cups with differently shaped handles have the same topology).
Question: undecidable: whether two cups have the same or different number of handles. (Of course, this is about four, not two dimensions.)
Indecidability/Genz: indecidability occurs here only if a computer is to perform the calculation: to describe a cup, it is covered with a certain number of equal triangles.
Problem: there cannot be a computer program that decides for any number of covering flat triangles whether two (four-dimensional) cups have the same number of handles.
II 220
Theorem: the theorem is rather tame: it now excludes that a program makes a decision for any number of flat triangles, but not for a given number - e. g. one million - flat triangles. This is simply a matter of increasing accuracy. That would be an example of an unpredictable number.
Wave function of the Universe/Genz: it could be shown that there are calculable representations of it, so that its incalculability (similar to that of > NOPE) suggested by the regulation of the figure does not actually exist.
Definition NOPE/Genz: the smallest number that can only be determined by more than thirteen words minus the smallest number that can only be determined by more than thirteen words
N.B.: the rule is impracticable, but we still know that NOPE = 0!
II 223
Problem/Genz: there cannot be a program that decides in finite time if any program ever stops. "Stopping problem"/"Non-stopping theorem"/Genz: the "stopping problem" is not a logical but a physical problem. It is impossible to perform infinitely many logical steps in finite time.
Time travel/time reversal/time/decision problem/Genz: if time travel were possible, the stopping problem would only be valid to a limited extent.
>Time, >Time reversal, >Time arrow, >Symmetries.
II 224
Stopping problem/Platonism/Genz: in a platonic world where there are only logical steps instead of time, the non-stopping theorem would also be valid. The point here is the admissibility of evidence rather than its feasibility. >Proofs, >Provability.

Gz I
H. Genz
Gedankenexperimente Weinheim 1999

Gz II
Henning Genz
Wie die Naturgesetze Wirklichkeit schaffen. Über Physik und Realität München 2002

Determinism Genz II 250
Time/Newton/mechanics/Genz: in Newtonian mechanics, not only the earlier point of time determines the later point of time, but also vice versa the later determines the earlier one. >Isaac Newton.
Deterministic/Genz: we must distinguish between forward deterministic laws and forward and backward deterministic laws.
>Laws, >Natural laws.
II 251
Question: are there also purely backwards deterministic laws? Definition Time/Genz: as long as we do not know anything else, we can simply define time as the direction in which deterministic laws of nature apply. This is necessarily identical to the direction in which the order cannot increase.
>Time, >Space, >Time reversal, >Time arrow, >Order, >Symmetries, cf. >Chirality.
II 252
Deterministic/time/forward/backwards/quantum mechanics/Genz: the deterministic laws of quantum mechanics are deterministic in both temporal directions.
II 253
N.B.: but it does not say whether they are the same in both time directions! The fact that they are not the same was first shown directly by an experiment in 1998.
CPT-Theorem/Genz: the CPT-Theorem says together with the "CP violation" that backwards deterministic laws of quantum mechanics must differ from forward deterministic laws.
Experiment 1998: a K-Meson (neutral) can develop into its anti-particle. This can also be done in the opposite direction, but the process must then proceed more quickly (asymmetry).
II 254
N.B.: then we can decide from the laws of nature alone, whether we have a real process that takes place in time, or whether a backwards running film is shown by a physical process. Not time-reversal-invariant: for example, the transformation of a K-Meson into its anti-particle is not time-reversal-invariant.
Experiment: has of course not been observed directly, but by observations on numerous particles in the same state.
Asymmetry/Genz: asymmetry only applies to the duration of the process, not to it itself.
>Asymmetry.

Gz I
H. Genz
Gedankenexperimente Weinheim 1999

Gz II
Henning Genz
Wie die Naturgesetze Wirklichkeit schaffen. Über Physik und Realität München 2002

Evolution Vollmer I 51
Evolutionary Epistemology/Vollmer: in the evolution of science, there are no "mutations" because there is no "offspring" in scientific theories. Evolutionary epistemology is only useful insofar as subjective knowledge structures are inherited.
>Success, >Pragmatism, >Proofs, >Provability.
I 75
The evolutionary epistemology does not have the concept of truth of pragmatism - it is not proven by success. Success/Vollmer: only proves that the hypothesis was not entirely wrong.
>Hypotheses.
I 217
VsEvolution theory/VsDarwinismus. Circular. VollmerVsVs: it is wrong that "Fitness" can be defined without recourse to "surviving". >Survival, >Fitness.
I 260
Fitness is not determined by the survival of the individual, but by reproductive success, more food, more habitat, more partners, more offspring, etc.
I 264
Entropy/Evolution/life/Vollmer: contrary to popular belief it is not always a measure of disorder. >Entropy.
Under special conditions (low total energy and existence of lasting interactions or inclusion by external forces) the increase in entropy even includes an increase of order and structure - thus the second law does not contradict the origin of living things.
>Life, >Energy, >Order.
I 279
Adaptation/selection/VsEvolutionary Epistemology is no falsification - the original eye is not falsyfied by the eye of the eagle - proper mapping does not matter - transferring the selection theory on cognitive skills can only succeed if there is objective truth and if knowledge is more useful than error (Simmel, 1895) - VollmerVsVs: this is not an argument VsEvolution - no matter who is adapting to whom - Co-adaption.
I 298
Evolution/success/Vollmer: the accuracy of knowledge cannot be inferred from evolutionary success - otherwise naturalistic fallacy - confusion of facts with norms. >Naturalistic fallacy, >Norms, >Facts.
---
II 190
Evolution/time direction/Vollmer: due to cosmic expansion there are no two moments of evolution identical - (> time arrow).

Vollmer I
G. Vollmer
Was können wir wissen? Bd. I Die Natur der Erkenntnis. Beiträge zur Evolutionären Erkenntnistheorie Stuttgart 1988

Vollmer II
G. Vollmer
Was können wir wissen? Bd II Die Erkenntnis der Natur. Beiträge zur modernen Naturphilosophie Stuttgart 1988

Humean World Bigelow I 243
Humean World/slippery slope argument/Jackson/Bigelow/Pargetter: (Jackson 1977a) pro Humean World: (slippery slope) For example, a world in which laws of the 1st level are not only not necessary, but also have exceptions. >Laws, >Laws of nature, >Causality, >Determinism.
For example, suppose it is pure coincidence whether an F is a G or not. Any non-G would be a contingent thing that would not have existed. If it exists, it does not affect any F.
Then there is a world where it is also coincidental whether an F is a G, but where there is one F less, which is a non-G.
>Possible worlds, >Random.
From this world we can deduce the existence of another world that still has one less F, which is a non-G. etc. In the end, this proves that there is a world where every F has a 0.5 chance to be a G and yet all F's are G's!
This is completely consistent with a theory of probability theory.
From this we conclude that it is quite possible that there is a Humean World for every possible world.
Humean World/Bigelow/Pargetter: is easy to define when we are dealing with laws in the form of simple sentences (describing regularities).
>Regularities.
It is more difficult with more complex shapes. (See below Chapter 6).
Accessibility/Bigelow/Pargetter: the Humean World obliges us to an accessibility relation that does not supervene on properties of the 1st level and relations.
>Accessibility, >Supervenience.
I 245
Counterfactual conditionals: those that are valid for laws in the actual world fail in the Humean World. >Counterfactual conditional.
Therefore, the accessibility of the Humean world would differ from the actual world in its accessibility without differing from its properties of the 1st level.
>Actual world.
Accessibility/Bigelow/Pargetter: nevertheless, there are strong reasons to believe in a supervenience of the accessibility relation on the contents of the world. This leads us to assume that the contents of the 1st level do not exhaust all the contents of the world.
>Modal properties.
Combinatorial theories: they must therefore adopt universals of higher level and therefore also the property theory of world properties.
>Universals.
I 279
Causal World/Bigelow/Pargetter: be a world in which some things cause some others. How many such worlds may there be? Some authors: all worlds are causal worlds. From reflections on individuality.
Individual/some authors/Bigelow/Pargetter: according to some theories, they are just "bundles of properties".
>Individuals.
Question, what holds them together? Thesis: properties are held together causally.
Causal world/some authors/Bigelow/Pargetter: say that every possible world is causal because no possible world is timeless.
>Time, >Timeless, >Impossible world.
Time/Bigelow/Pargetter: we believe in the causal theory of the time arrow and in the asymmetry of past and future, but not in a causal theory of time itself.
>Time arrow, >Past, >Future, >Present.
Therefore, we do not think that all possible worlds are causal. We believe that there are Humean Worlds and Heimson Worlds. What we need now is a Humean world.
Humean World/Bigelow/Pargetter: it does not matter whether it is accessible or not. Only their existence counts. We need to show their logical possibility. (i.e. the possibility of a world like ours in terms of regularities of the 1st level, but without causes and without laws).
I 280
Modality: the difference between the actual world and a Humean world cannot be merely modal. Modal differences must be based on differences in the content of the possible world. They cannot be identical in terms of their content and can still be modally different. There must be something present in the causal world, and absent in the non-causal. >Content.
Def Humean World/Bigelow/Pargetter: it therefore cannot be defined by the absence of causality. We define it as a world that corresponds to ours on the 1st level of properties and relations. But they differ in relation to relations between properties and relations of relations.
>Properties, >Relations.
They differ in terms of higher-level universals. Some of these will not supervene on those of the 1st level.
Def Cause/Bigelow/Pargetter: is a relation of the 2nd level between events. (Relation between properties). It does not supervene on intrinsic properties of the 1st Level of events.
>Events, >Supervenience.
The relations of the 2nd level apply contingently if we allow Humean Worlds.
>Contingency.
I.e. effect and cause could also occur, with the same properties of the 1st level, if they are not in the relevant relations of the 2nd level. These are external.
>Levels/order, >Description levels.
Events: can have the same properties of the 1st level and yet still differ in properties of the 2nd level. Therefore, the Humean world can be similar to the actual one.
I 281
If they occur in the same possible world, on the other hand, they will be the same on both levels. (Because we treat them as universals). >Degrees/Graduals.
Degree/Level/Order/Terminology/Bigelow/Pargetter: therefore, one match on the 1st level implies a match of 2nd degree (sic) for all event pairs in the same world.
>Quantities/Bigelow.
Degree/Properties: (see above I 53) Properties 2nd degree: the commonality of properties. For example, green includes all shades of green.
Causation: but because of their local character (see above) it may be that the pairs of events are causally different! This means that causation is a relation of the 2nd level which does not supervene, neither on properties of the 1st Level, nor on the 2nd degree and relations.
N.b.: causation connects not only universals, but structures that involve both. Universals of higher level and individual items.
Causal relation/Bigelow/Pargetter: must therefore be of a higher level itself. Question: Which properties and relations do they constitute? For this, we look at another difference between the Humean world and the actual world.
Definition Berkeley World/Bigelow/Pargetter: one in which causation is an act of will (of God). Berkeley, for example, thought that the distant planets could not possibly exert a force on the sun. So it was God who caused the sun to be moved away a little from its place.
Hume: removed the act of will from the Berkeley World and so his world became a world without causation.
Humean World/Bigelow/Pargetter: is first and foremost a world without powers.
>Forces.

1.Jackson, F. (1977a) A causal theory of counterfactuals. Australasian Journal of Philosphy 55, pp.3-21

Big I
J. Bigelow, R. Pargetter
Science and Necessity Cambridge 1990

Quantum Mechanics Barrow I 233
Quantum mechanics/QM/Atom/Uniformity/Equality/Barrow: the quantization of energy is the reason why hydrogen atoms are identical. >Energy, >Symmetries.
I 235
Measurement Problem/QM/Barrow: it is about whether the quantum theory describes everything that happens in nature, including the measurement process, or not. >Measurement problem.
I 237
EPR/Barrow: Paradox: we cannot predict which the two photons will move clockwise in the decay - but if we were to go to the other end of the universe, we would know instantly because of quantum mechanics that the other photon rotates in the other direction, without having measured it. - I.e. the unmeasured momentum must match reality. - It must be real, because it is predictable. Knowledge without measurement, i.e. independent of observation.
>Observation, >Observation independence.
Paradox: the second photon must know the direction of the other.
Proof: Alain Aspect experiment, 1982.
I 240
Barrow: in fact, no information is transmitted - VsEPR: simultaneity is a concept that depends on the observer. - E.g. three observers could be in motion relative to each other and to the experiment - one would see that the measurements of the spins are conducted simultaneously, while the others would first observe one or the other.
I 238f
John Bell/QM/Non-Locality/Barrow: (1960s): John Bell showed that every theory that describes EPR phenomena needs to have a non-local description if a simple arithmetic condition is satisfied. >Non-locality.
Bell Test/Uncertainty: Uncertainty is not about the coarseness of the observer - this would be a local explanation.
Bell: Each correct view of nature must be non-local.
I 242
Copenhagen Interpretation/Bohr: In the traditional sense, no deeper reality can be discovered, but only a description of it. - It is useless to say that the measurement somehow changed a deeper reality.
I 245
While the wave function is deterministic, linear, continuous and local, and does not know any determinate time direction, the measuring process is almost random, non-linear, discontinuous, non-local and non-reversible. >Wave function, >Measurements, >Time arrow, >Time, >Time reversal.
SchrödingerVsBohr: Schrödinger's cat: is in a mixture of dead and alive, as long as we do not look.
I 247
Wheeler: Problem: all astronomical measurements are made with radiation. - So according to Bohr's Copenhagen interpretation, they would only be made alive by measuring.
I 253ff
Copenhagen Interpretation/Many-Worlds Interpretation/MWI/Aspect/Experiment/Barrow: the assumption of non-locality was experimentally confirmed by Aspect. >Many-Worlds Theory, >Copenhagen Interpretation.
Barrow: The Copenhagen and the many-worlds interpretation appear to be completely incompatible, but there is the unanimous opinion that they are experimentally indistinguishable.

B I
John D. Barrow
Warum die Welt mathematisch ist Frankfurt/M. 1996

B II
John D. Barrow
The World Within the World, Oxford/New York 1988
German Edition:
Die Natur der Natur: Wissen an den Grenzen von Raum und Zeit Heidelberg 1993

B III
John D. Barrow
Impossibility. The Limits of Science and the Science of Limits, Oxford/New York 1998
German Edition:
Die Entdeckung des Unmöglichen. Forschung an den Grenzen des Wissens Heidelberg 2001

Time Lewis V 32
Time/Arrow of time/Past/Future/Lewis: future: depends counterfactually (not only causally) on the present. >Causal dependence/Lewis, >Counterfactual dependence/Lewis.
Asymmetry: former things do not depend on later ones - we find no counterfactual conditional that explains what would have been different in the past if the presence was different - such a counterfactual conditional would be unclear at most.
V 33
Asymmetry: we can use all assumptions about the past, but not about the future - assumptions about the past are not counter factually dependent - therefore they can serve as auxiliary hypotheses.
V 35
Time/Asymmetry/Counterfactual conditional/Lewis: Asymmetry: comes about like this: wA>wC assumes that C is later, if C is earlier, the counterfactual conditionals are only true if C is true - the counterfactual conditional tells us, like the way, how things are earlier, not depending on how things are later.
V 36
Time Arrow/Epistemic/Asymmetry/Lewis: the asymmetry (that we know more about the past than about the future) is gradual, no difference in kinds.
V 37f
Time/Asymmetry/Past/Future/Lewis: 1) the epistemic contrast (that we know more about the past) is gradual. - 2) (irrelevant) - 3) Even determinism would allow an asymmetry. - 4) past, present and future are equally unchangeable. - That t is later, is irrelevant.
V 38
5) in a sense we can change the future by our present actions, however. - Asymmetry: branch in the future: are the alternatives under counterfactual assumptions. - Past: here the fact remains the same, even in counterfactual assumptions.
V 57
Time/Laws of Nature /LoN/Asymmetry/Lewis: if there is an asymmetry (between past and future). - Then it is a property of time, not of the laws. - It makes a difference between possible worlds. >Possible world/Lewis.
V 66
Asymmetry/Time/Lewis: my argument for it is empirical. - Too many traces would have to be hidden later on. ---
V 94
Time/Asymmetry/Past/Future/Possible world/Lewis: the asymmetry is contingent. - i.e. the properties which justify the distinction between past and future opportunities. They may be different from possible worlds to other possible worlds. >Asymmetry, >Past, >Present, >Future, >Time traveller/Lewis, >Timelessness/Lewis.

Lewis I
David K. Lewis
Die Identität von Körper und Geist Frankfurt 1989

Lewis I (a)
David K. Lewis
An Argument for the Identity Theory, in: Journal of Philosophy 63 (1966)
In
Die Identität von Körper und Geist, Frankfurt/M. 1989

Lewis I (b)
David K. Lewis
Psychophysical and Theoretical Identifications, in: Australasian Journal of Philosophy 50 (1972)
In
Die Identität von Körper und Geist, Frankfurt/M. 1989

Lewis I (c)
David K. Lewis
Mad Pain and Martian Pain, Readings in Philosophy of Psychology, Vol. 1, Ned Block (ed.) Harvard University Press, 1980
In
Die Identität von Körper und Geist, Frankfurt/M. 1989

Lewis II
David K. Lewis
"Languages and Language", in: K. Gunderson (Ed.), Minnesota Studies in the Philosophy of Science, Vol. VII, Language, Mind, and Knowledge, Minneapolis 1975, pp. 3-35
In
Handlung, Kommunikation, Bedeutung, Georg Meggle Frankfurt/M. 1979

Lewis IV
David K. Lewis
Philosophical Papers Bd I New York Oxford 1983

Lewis V
David K. Lewis
Philosophical Papers Bd II New York Oxford 1986

Lewis VI
David K. Lewis
Convention. A Philosophical Study, Cambridge/MA 1969
German Edition:
Konventionen Berlin 1975

LewisCl
Clarence Irving Lewis
Collected Papers of Clarence Irving Lewis Stanford 1970

LewisCl I
Clarence Irving Lewis
Mind and the World Order: Outline of a Theory of Knowledge (Dover Books on Western Philosophy) 1991

Time Vollmer II 51
Time/time direction/time reversal/Vollmer: the designation of a time direction is empirical and is made always only secondarily by additional assumptions. - E.g. initial conditions in the mechanics and thermodynamics - rediance conditions in electrodynamics. >Initial conditions.
II 234
Time/logical form/Vollmer: temporal relationships can be expressed by real functions t(e1, e2) that are defined on event pairs. >Events.
Asymmetry: is then a formal property of this function to change the sign at reversal. - This has nothing to do with reversibility of physical processes, also not with designation of one direction.
>Asymmetry, >Symmetries.
Time Reversal: Time Reversal is only a formal operation of changing the sign.
>Equations, >Time reversal, cf. >Time travel, >Past, >Present,
>Future.
II 325
Invariant: a formula is invariant that does not change under time reversal. >Invariants.
Time reversal invariance: So is a property of formulas or functions. - E.g. Newtonian equation of motion.
>Formulas.
On the other hand:
The question of whether natural processes are reversible, relates to the real world.
Problem: a T-invariant equation can describe both reversible and non-reversible processes. - If, then it does not yet contain complete information.
II 236
Definition Time Arrow/time direction/Vollmer: so we will call the fact that there are chains of events, whose part events never happen in reverse order. Time direction is not a characteristic of the time, but of processes.
>Processes.
That there are different classes of irreversible processes, there are different arrows of time: the expansion of the universe, the electrodynamic of spherical waves - that a process is irreversible, one cannot see that in looking at it. - It can also never be proven. - Causality/cause/effect/VollmerVsReichenbach: cannot define the arrow of time. - Reversed: these are not to defined without time arrow.
>Causality, >Cause, >Effect.
II 238
Irreversibility/Physics/time reversal/time arrow/Vollmer: We expect that the fundamental equations, equations of motion, laws of force, field equations are T-invariant, that is, that they change with time reversal.
II 252
Entropy/universe/Boltzmann/Vollmer: for him, the universe as a whole is in a thermodynamic equilibrium, so in the entropy maximum.
II 253
VollmerVsBoltzmann: the observations state the contrary. If we advance into more distant parts of the universe, we can always find low entropy. >Entropy.
If there were a region of space with decreasing entropy (increasing order), there would also be irreversible processes, but some time arrows would be reversed.

Vollmer I
G. Vollmer
Was können wir wissen? Bd. I Die Natur der Erkenntnis. Beiträge zur Evolutionären Erkenntnistheorie Stuttgart 1988

Vollmer II
G. Vollmer
Was können wir wissen? Bd II Die Erkenntnis der Natur. Beiträge zur modernen Naturphilosophie Stuttgart 1988

Time Travel Vollmer II 238
Time reversal-invariance/T-invariance/irreversibility/Vollmer: E.g. equations that contain a (first or higher) derivative with respect to time. - E.g. equation for motion with friction - E.g. movement under radiation damping. - E.g. Fourier equation for heat conduction. - But these are not yet the basic equations - E.g. friction consists of many shocks. >Equations, >Formulas, >Natural laws, >Entropy.
II 243f
Time reversal-invariance/T-invariance/time asymmetry/asymmetry/time/time direction/Vollmer: single injury in nature: the decay of neutral kaons (K02 mesons) due to the weak interaction. - N.B.: the asymmetry occurs here also in the fundamental equation. - That is, it is the dynamic law that distinguishes between past and future and so distinguishes a time direction. - (As the only in nature).
II 245
Time reversal/Physics/Vollmer: can only mean a reversal of all the processes - E.g. electrodynamics: here, too, the currents and the magnetic fields must be reversed. - Then their equations are also T-invariant. >Processes, >Invariance, >Symmetries, >Asymmetry.
II 254
Time reversal/film/backwards/Vollmer: if we were in a movie and it would run backwards, we would not notice because all time arrows would be reversed.

Vollmer I
G. Vollmer
Was können wir wissen? Bd. I Die Natur der Erkenntnis. Beiträge zur Evolutionären Erkenntnistheorie Stuttgart 1988

Vollmer II
G. Vollmer
Was können wir wissen? Bd II Die Erkenntnis der Natur. Beiträge zur modernen Naturphilosophie Stuttgart 1988