Positivist perspective on predictability by Roger Schlafly

We can make predictions although the present is not known with 100% certainty. Plus the model is usually only approximate, e.g the noise is assumed to be Gaussian.The prediction is then not 100% certain, either. But it may be good enough. This is standard practice, e.g we assume linearity. That is why I feel that the theme of this contest is a bit weird. So there are assumptions and data uncertainties. If you do not even know the present with 100% certainty, then what is meant with "predictability"? This is somewhat confusing, as some answers are binary: does something happen, eg in a collision between elementary particles, or not? This looks like an exact answer.

Roger,

Another very readable and enjoyable essay. I'd thought I'd long understood logical positivism but your nuances and context were fascinating. I work hard on data driven analysis and not to have 'beliefs' but you've exposed that's not as founded in positivism as I'd assumed, as I apply that approach to poorly understood phenomena like the jet 'cusp' of an AGN (only room for a Mexican Hat potential not an old 'black hole'!

I also dive deep into QM and suggest a foundational error rendering it illogical (quntum spin wasn't required as Maxwell/Poincare already identified TWO inverse orthogonal momenta in OAM). Do those disqualify me? (not that I mind!)

And do we really know much at all 'for sure'? or do we fool ourselves picking some foundation? All good questions I too have raised.

But logic is another matter, and again I agree philosophy gets it wrong. Indeed I think I show it n badly misleads physics from foundations up, but I do hope you'll give me your view on that thesis I explore.

Great food for thought again Roger. Well done and thank you. A different slant but right on topic and right up there.

Very best

Peter

Roger thanks for your essay. It is nice to see someone holding to "correspondence to measurements" as a guideline to judge aspiring theories. I would like your input on my essay. The essay's theoretical projections correspond to "generally accepted" measurements for the visible universe and its important physical contents- Planck's length and time, H atoms, Stars, solar systems, galaxies, etc. However, it introduces a very different process for the creation and functioning of the visible universe. The essay introduces a different beginning, a different progression, the same current situation and a different ending than current theories. As such it is metaphysical to current physics. It also changes the fundamental "unit" from an unchanging particle to the smallest unit of changing (C*s) and describes how quantities of C*s become the smallest Stable Self Creating Unit (SSCU). The original SSCU then self replicates which creates quantities of copies that self organize to become the physical world that we currently measure. In that progression, the process creates its own mathematics, its own self creating algorithms and "maps" them to the physical results. It creates its own mathematics and embeds it within its forms and functioning. "Amazing". In this processing, as shown in the appendix of the essay, it determines the value in C*s between 0 and 1 SSCU and thus between the "real number quantities" of the processing.

In this Sucessful Self Creation case did it solve the " continuum hypothesis" of mathematics? Also, the theory describes what happens in Black Holes and how they fit into the creation of the physical world. Anyway I would appreciate your comments as a mathematician and as a Positivist. Thanks John Crowell

Very nice essay. You make a very persuasive case for logical positivism, and although I had not previously thought of myself as a logical positivist, I can see its attractions, and I can see that it is hard to argue against. As a mathematician, I agree with you that mathematics says nothing about truth - what mathematicians call truth is what logicians call tautology, and has nothing to say about the truth or otherwise of statements about the universe. In mathematics, everything depends on the assumptions you start with. In theoretical physics, the same is true. Which is why I find it so hard to understand why physicists (at least in my experience) absolutely refuse to discuss their assumptions. Perhaps you might be interested in my essay in which I attempt to discuss such assumptions.

Robert Wilson.

Dear Roger (if I may),

Thank you for an interesting essay (and for citing me therein!).

I guess we have several element of convergence. I like your quotation: "If these numbers could be found in nature, along with methods for extracting arbitrarily many digits, then we would have to revise what weknow about the feasibility of computation."

A few more comments: although I advocate the importance of operationalism which is a form of empiricism, I believe that defining an underlying ontology to theories could be extremely useful. Moreover, in my opinion, the criticisms against empirical positivism (e.g., against the method of induction) are sound and that position is not (at least fully tanable).

Anyways, I ranked you high. Best of luck for the contest,

Flavio

Dear Roger Schlafly,

I consider myself a "positivist" too in the sense of questioning the mandatory practice to deny natural reference points, in particular the border between past and future.

Careful reasoning requires to not puting fuzzy notions like today and presently between past and future. Just pragmatism and the insight that the map is not the territory suggest calculating as if there was no causality.

I am supporting your stance concerning causality as the fundamental of science.

Eckard Blumschein

I found your essay to be one of the hardest to rate. This is partly because it is an essay and thus too short to do justice to the topic. And thus, your essay was hard to rate because it is a breath of fresh air that I completely agree with, however, I do not support logical positivism. But I can agree with this:

"Logical positivism ... I believe that it should not have died, and that it is superior to the philosophies that replaced it."

I cannot support logical positivism because the logical positivists (of the past) often tended toward being quite "reductionist" and I also do not completely support the emphasis on logic, which is often not sufficiently defined.

You wrote: "The XX century can be seen as an era when limits to human knowledge were discovered. Goedel showed that not all truths could be proved. "

I will never disparage Gödel's beautiful proof, but I also do not unequivocally support the conclusion that he proved a (conclusive) limit. Something I hinted at in my essay is, what does a contradiction actually mean? Can we really take a contradiction to be an absolute falsehood? (Note, I do not go as far as Graham Priest and his paraconsistent ilk and call contradictions true.)

I think Gödel's proof can only be interpreted within the context of the Principia Mathematica and (David) Hilbert's program, which his proof was a direct response to. In the same way that Gödel's proof is taken to be a refutation of Hilbert's program, the Principia Mathematica is often considered to be the end of what could be called the logicist program, which Gödel also helped refute.

You wrote: "Did previous scientists really believe that someday a computer could be programmed to determine all mathematical truths and predict all physical phenomena? I doubt it. That would require a belief in an extreme form of determinism, and a depressing view of humanity."

Yeah, I actually think they did and they still do. Some people (appear) to actually think that computers might wake up and become sentient... When science became something to believe in it became Scientism; an intellectually bankrupt dogma.

I apologize for rambling; I will close with this:

You wrote: "Continuum hypothesis not meaningful"

Of course it is meaningful. Once you have Transfinite Set Theory (Hilbert's paradise), this question immediately emerges and beckons a solution. I would argue that the entire theory of the Transfinte is not meaningful. Solomon Feferman, which I have the utmost respect for, also argued that the Continuum hypothesis was not meaningful. However, I think his excellent book In the Light of Logic made my point better than it made his.

I wish you well in the contest.

Dear author, commenters,

the term prediction is first used in English (approx. 1600) in the sense of foretelling and prophecy. It thus involves historical time, namely the future. Enlightenment spoke of causality or causation, which changed the meaning of prediction from temporal to sequential. Note that neither Hume nor Kant granted causality natural or physical existence or capacity, though for different reasons. This was the reason why under the positivists (e.g. Russell, Schlick, Carnap) causality fell from grace, it was considered unprovable and thus mere metaphysical baggage. The substitute term was explanation (sometimes function) because the explanation was believed to be positively tractable and verifiable. Today we know better...

In my mind, the only tenable of these definitions is Kant's a priori causation, i.e. in the sense of making observable in the first place. In this sense it is very precise (e.g. Newton's laws) - albeit limited to HUMAN EXPERIENCE, that is, the Kantian phenomena, to which neither the quantum nor intergalactic space belong.

Heinz

I tend to find that Logic is a term that everyone immediately understands but, despite that or maybe because of that, everyone is not always working with precisely the same definition. For example, are the LEM and LNC incontrovertible logical laws? Is logic fundamentally based on the syllogism? And since I do consider what I called the logicist program to have been refuted, the logical conclusion is that mathematics consists of what is logical (true by means of logic), illogical (false by means of logic) and nonlogical (inapplicable, or the application of logic is... illogical). Not surprisingly, this a violation of the LEM!

I definitely agree with the unequivocal importance of definition, but we certainly run into a myriad of problems when we try to define the undefinable... That might be going a bit too far.

Dear Roger Schlafly,

Logical/Empirical Positivism is a term notoriously resisting clear definition. I agree that it has a number of interesting and even desirable facets, but overall, I think, that it has led (and under the cover of analytical philosophy still leads) science into a dead end.

Three criticalities:

POSITIVISM: The term implies analysis, affirmation and verification, which it inherited from the linguistic turn (e.g. Frege, Wittgenstein). But already the late Wittgenstein denied language to be positively=affirmatively tractable and Quine's confirmation holism kissed the idea of scientific Positivism goodbye. Only Lego-worlds are affirmatively tractable.

LOGICAL: Today there are more than a dozen of most varied logics in use. Which one is the right one? Moreover, all of them suffer from what is called the foundational or grounding problem of logic. The idea that logic represents something in the world goes into the face of philosophical tradition since Kant, who located it in the mind. This is why the '3-uns' of the contest theme are mere logical pastime and have no effect whatsoever in physics or elsewhere.

EMPIRICAL: Positivism, by discriminating metaphysical ideas like causation, elevated instrument readings, photon counter knacks, etc. to the level of empirical evidence. Ever since scientists verify theories by instrument readings (data). And don't absurdities attributed to data like entanglement, Big Bang and multiverses confirm Kant, i.e. that logical constructions have no existence in the world?

Overall, positivism (unfortunately) isn't dead but has survived in analytical philosophy, which emphasizes analyticity and hence logic, with the consequence that science has adopted the processuality of logic and hence become temporal itself. This - timelessness vs. time - in my opinion, is the key difference between classical and modern science and surfaces in the difference between law and model.

Heinz

OK, I think I got the message...

...just ohne thing: Cantor's LOGICAL paradise is alive and kicking. So, which ideology has been rejected?

Dear Roger Schlafly,

Did you overlook my argument that there is no extended state "present" between past and future? FT introduced redundancy.

Are you aware of what I yesterday wrote on Klingman'n page concerning Einstein's SR?

Perhaps, missing practical relevance is a good indication of inapproriateness. Not just therefore I disagree with Luediger's claim that "Cantor's LOGICAL paradise is alive and kicking."

Best, Eckard