It seems to me that "determinism" is not a rigorously defined concept. It obviously involves
the order-structure of time T(what determines "before" and "after") as well as the possibility of capturing the instantaneous state of the universe at a given time t in T by an element in a certain phase-space Q.
Our notion of "determinism" will greatly depend on the order-structure of T as well as Q (for instance, its cardinality: is an infinite amount of information required to specify the state of the universe).
The popular concept of "determinism" corresponds to finite computational determinism. T is given the order structure of the natural numbers N and Q is finite. Then the state q(t) of the universe at time t can be computed via a recursive function F from the states q(t') at previous times for t' < t (more commonly the immediately preceeding state state is enough ?).
But suppose that F were not recursive but belonged to some other order of the arithmetical hierarchy (let us say Sigma^1) ? Could we still speak of "determinism" ? What if F were beyond the arithmetical hierarchy ?
What is the best way of extending our notion of "computability" to the case in which T has a dense linear order and/or in which Q has infinite cardinality ? How do we express the "determinism" paradigm of differential equations in a rigorous way ? What if the coeficients of analytic solutions are not computable ?
By "predetermination" I mean the idea that the entire evolution of the universe through time already "exists". Suppose that the law of evolution of the universe F were undefinable in first-order logic but that we had predeterminism. I call this "metaphysical predetermination".
What criteria or what experiment can we conceive of that could distinguish pure chance or free will
from metaphysical predetermination ?
I also note that for us conscious beings it seems arguable that finite computational determinism at least is false.
Clarence Lewis Protin An interesting question. Your definition of predetermination that the entire evolution of the universe already “exists“ is a bit like the view of Albert Einstein. He saw the entire past and future in the analogy of a movie film strip where the present is just one frame of the film which already exists.
There is a lot about the universe as a whole on the large scale which is predetermined as we could not conceive of the Earth Sun Moon and stars deviating from their path predicted by gravity.
There are things that are not predetermined. Imagine that there was an asteroid on target to destroy life on Earth. Imagine also that this was observed in time for a space mission to divert the asteroid so it crashed into the moon. The human decision to mount this space mission could not have been predetermined. This thought experiment refutes predetermination .
I think I understand why Albert Einstein took the view that all of space and time already exists. It is bound up with his ideas of special relativity in which absolute time is lost. We can now restore the concept of a universal reference time throughout the universe so that we have a well defined past present and future:
Preprint Space Rest Frame (March 2022)
Richard
You can’t control what other people are going to do to you, just how you are going to respond; certain things will happen to you and you can then use your free will to determine how you’re going to respond.
Example: there is somebody out there who is destined to be your life partner , but that you might not do the right things to meet them.
In Pirkei Avot 3:15, Rabbi Akiba said :Everything is foreseen, yet freedom of will is given.
Am in agreement with your statement Clarence Lewis Protin : By "predetermination" I mean the idea that the entire evolution of the universe through time already "exists``.
Approaching the question differently these two terms are quite different...
The determinism is the sum of conditions which will define the direction of evolution of a system (example physical body, features, and its contact with its surroundings). The predetermination is the ability of the humans to describe a situation which will be realized, subsequently... A very good example of this is the earthquake event... which is well determined by the phenomenon of crust and mantle... The earthquake's predetermination is deppend how we know this phenomenon which determines the earthquake happening...
Determinism is perfectly well defined: It means infinite precision. It is distinct from causality, that means that an ordering of the time variable implies an ordering of functions of that variable.
Regarding ``predetermination", as defined, it is distinct from ``determinism" and `` causality".
Feynman wrote: It always bothers me that according to the laws of physics as we understand them today, it takes a computing machine an infinite number of logical operations to figure out what goes on in no matter how tiny a region of space and no matter how tiny a region of time.
This is quoted in a Models of Massive Parallelism by Max Garzon.
Richard Lewis Yes, the mathematical treatment of space-time in relativistic cosmology is an important example of "predeterminism". However a four-dimensional (or higher dimensional) model cannot capture the phenomenon or experience of time, which suggests an interpretation as a three-dimensional submanifold "moving" within a four-dimensional one. In order to do this yet another spatialised time-coordinate must be introduce and so on in an infinite regress.
Clarence Lewis Protin Once you start talking about the experience of time that is a completely different discussion involving an understanding of consciousness:
Preprint The Conscious Brain
When it comes to what time actually is, I tend to think in terms of light waves in the medium of space. We could define 1 second as the time it takes for light to travel 300,000 km.
So given the concept of universal time we can think about the future as not predetermined but dependent on chance events which get more and more random the smaller the scale.
Richard
In short:
1) metaphysical predetermination, more general and distinct from computational determinism, would seem to be a scientifically undecidable question.
2) computational determinism is scientifically undecidable at the current state of our scientific knowledge.
Friends, greetings. I have been enjoying the discussion here. If any of you find it useful to take a look at the following related discussions and give your feedbacks, I appreciate that. THESE HAVE A DIFFERENT VIEWPOINT, BUT MAY BE USEFUL.
Please do not feel disturbed by this. These are just a few suggestions.
1. Gravitational Coalescence Paradox (GCP). Introduction to Gravitational Coalescence Cosmology (GCC).
https://www.researchgate.net/post/Gravitational_Coalescence_Paradox_GCP_Introduction_to_Gravitational_Coalescence_Cosmology_GCC
2. Minimal Metaphysical Physicalism (MMP) vs. Panpsychisms and Monisms: Beyond Mind-Body Dualism
https://www.researchgate.net/post/Minimal_Metaphysical_Physicalism_MMP_vs_Panpsychisms_and_Monisms_Beyond_Mind-Body_Dualism
3. Source of Major Flaws in Cosmological Theories: Mathematics-to-Physics Application Discrepency
https://www.researchgate.net/post/Source_of_Major_Flaws_in_Cosmological_Theories_Mathematics-to-Physics_Application_Discrepency
4. Complexity in Science, Philosophy, and Consciousness: Differences and Importance
https://www.researchgate.net/post/Complexity_in_Science_Philosophy_and_Consciousness_Differences_and_Importance
5. Do Electromagnetic Quanta and Gravitational Quanta (Gravitons) Gravitate from Within? Do they Exist, or Are They Mere Mathematical Equations?
https://www.researchgate.net/post/Do_Electromagnetic_Quanta_and_Gravitational_Quanta_Gravitons_Gravitate_from_Within_Do_they_Exist_or_Are_They_Mere_Mathematical_Equations
6. A GAME-CHANGER CAUSALITY FOR PHYSICS: Beyond the Two Millennia
https://www.researchgate.net/post/A_GAME-CHANGER_CAUSALITY_FOR_PHYSICS_Beyond_the_Two_Millennia
7. New Grounded Physical-Ontological Categories behind Physics
https://www.researchgate.net/post/New_Grounded_Physical-Ontological_Categories_behind_Physics
8. The Ontology behind Physics: Critique of Traditional Categories
https://www.researchgate.net/post/The_Ontology_behind_Physics_Critique_of_Traditional_Categories
9. How Does Physics Know? The Epistemology Presupposed by Physics and Other Sciences
https://www.researchgate.net/post/How_Does_Physics_Know_The_Epistemology_Presupposed_by_Physics_and_Other_Sciences
10. Causality and Statistics: Levels of Effect and of Explanation
https://www.researchgate.net/post/Causality_and_Statistics_Levels_of_Effect_and_of_Explanation
11. The Fallacies of Space, Time, and Spacetime in Physics
https://www.researchgate.net/post/The_Fallacies_of_Space_Time_and_Spacetime_in_Physics
Another important concept is that of definability in formal logic. Since formulas are countable there must be an uncountable number of real numbers r which cannot be described as r = iota x. \phi(x), r is the real number such that condition \phi(x) is satisfied, where \phi(x) is some first-order (or higher-order) formula with free variable x. Let U be the set of all these undefinable reals. There is no way to distinguish between the elements of U. U of course is itself definable (in the metalanguage). U could not have a minimal element or infimum for such would be definable and thus not a part of U.
It would be interesting to postulate that some particle trajectories are indefinable. Thus explain the wave-function as a kind of analogue of U. The wave function is definable/deterministic but the particular trajectories it incorporates are indefinable and indestinguishable.
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