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...

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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.

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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...

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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.

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