Positivist perspective on predictability by Roger Schlafly

Roger Schlafly

Essay Abstract

Mathematicians rely on rigorous proofs to know what is true. By analogy, there are positivist scientists who similarly confine their work to what can be empirically established. Under such views, physicists need not hope to predict everything, just as mathematicians do not hope to decide everything.

Author Bio

Roger Schlafly has a BSE from Princeton U, and a PhD in Mathematics from U California Berkeley, under I. Singer. He blogs at DarkBuzz.com.

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Satyavarapu Gupta

Respected Professor Roger Schlafly,

Amazing essay and wonderful conclusion words.............Positivism is a legitimate philosophical view. Mathematics has a long tradition of sticking to what can be formally proved from axioms. Physics would be enriched by popularizing a similar view, so that we can more easily distinguish established knowledge from speculation.

I am not trying to persuade anyone to stop speculating about the interior of black holes, but to understand that positivists can reasonably argue that such heorizing has no known scientific value..............................

I request you see the axioms of Dynamic Universe model where there are no Blackholes. See "A properly deciding, Computing and Predicting new theory's Philosophy"

Best Regards

=snp.gupta

Roger Schlafly

Thanks. I don't have any quarrel with black holes. That is, I am convinced that large stars can collapse to the point where gravity prevents light from escaping.

Martin Staveren

That is why I am a Bayesian, which I think is positivism. This means however that hypotheses for which there are no relevant data have nothing to do with physics. This attitude clearly conflicts with many worldviews, such as religions. Furthermore, many mathematicians do not care about usefullness; beauty should be enough. This attitude certainly The succes of the Standard Model (symmetry breaking etc) has attracted many mathematically inclined people. The idea that we can understand the Universe by pure thinking is 2500 years old, and apparently irresistable.

Peter Morgan

You invited us on DarkBuzz to comment on this, Roger, so, ...

Your statement that "The nature of positivism is to emphasize what can be known for sure, and to avoid speculation about other matters" seems to disregard the necessity to make predictions, which I take in mathematical terms to be interpolations or extrapolations from what is, so to speak, known for sure. Someone else could reasonably enough say that all such predictions are speculations.

For any given collection of experimental raw data (which different people might or might not accept as "known for sure"), we can imagine arbitrarily many possible ways to interpolate or extrapolate to what the experimental raw data would be if we performed a new, different experiment. A particular theory gives a particular scheme for constructing predictions, which we subsequently discover are more or less accurate and, hence, more or less useful. A particular theoretical system of interpolations and extrapolations gives a particular account of what the regularities are.

After a theory has been useful in a science lab for a while, engineers start wondering what they can build using the theory, then after a while we start to think of successful theories as rather more than speculations. Different people will think it's more or less speculative to extrapolate the theory to arbitrarily small scales or to arbitrarily great precision, say, but it's always reasonable to suppose that at least some extrapolations are reasonable, until it turns out that they are not.

I wonder whether you would agree with something like that discussion? I think I detect in your usual writings a mixture of realism and pragmatism as well as of positivism, which perhaps can be balanced rather than advocating only for positivism. FWIW, that's what I have tried to do above. Is it possible that you advocate positivism for a similar reason to mine: as a way to reign in my tendency to want a realist interpretation.

Your comments on QM are very brief, so I will pass over them except to say that I think you are a little too pessimistic insofar as QM is perhaps not a perfect scheme for constructing interpolations and extrapolations from insufficient experimental raw data, but with experience it can be made to work pretty well.

Having said all that, FWIW I agree with much of your essay. My own feeling is that I doubt positivism will find much favor with the voters here, but I could easily be wrong about that, so Good Luck.

[deleted]

Extrapolation: a car or aeroplane moves at speed V, so after a not too long time interval T it will have traversed a distance VT. Such predictions are commonly performed: model based Bayesian Estimation. Is this pragmatism or positivism?

The formulation "known for sure" is unfortunate, as usually data are not 100% certain, e.g. a distance or speed measurement.

Roger Schlafly

You make some good points. How can we make any predictions, as the future cannot be known for sure?

All predictions come with some sort of confidence level. I can predict that the Sun will rise tomorrow. Am I 100% sure? No, but I have a very high confidence. Maybe I am 99.999999% sure. It has always risen in the past, and there is good reason to believe that will continue.

That is about as good as can be done in science.

Martin Staveren

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 Schlafly

That's right, there are uncertainties about the present, the past, and the future. This contest description said "They could discern what math corresponds to physical laws, and use those laws to predict anything that happens before it happens." I wonder if anyone really believed that everything was so predictable. You don't need modern math or physics to see that prediction is an imperfect process.

Eckard Blumschein

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

H.H.J. Luediger

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

Peter Jackson

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

John Crowell

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

Robert Wilson

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.

Flavio Del Santo

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

Roger Schlafly

Thanks. I liked your comments about determinism.

Jason Steinmetz

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.

Roger Schlafly

Thanks for your good remarks.

I actually do not agree that Godel refuted Russell's Principia, Hilbert's program, or the logicist program. Math today can be seen as working out the theorems of ZF set theory. It is true that we cannot prove self-consistency from within the system, but that is just a minor detail in the larger program of axiomatizing mathematics. These programs succeeded in axiomatizing math, and Godel's work contributed towards that goal.

Roger Schlafly

Not sure what you mean by logic being "not sufficiently defined". If there is one field of study where everything is carefully defined, it is logic.

Yes, a lot of people believe that computers will someday wake up and become sentient. But do they believe the computers will be all-knowing? I doubt it.

I agree that the continuum beckoned a solution, as soon as transfinite numbers were discovered. It was a solution to find that it is independent of ZFC set theory. Maybe not a very satisfactory solution, but we cannot expect things to work out as we might like.

Jason Steinmetz

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.

Roger Schlafly

There is a big field called Mathematics, and it has been using logic for centuries. While you can find some disagreements in some areas, there has been a consensus on the major issues for 100 years or so. So yes, I do think that logic is well defined.