Merged Is Scientism Really Justified?

[catsmate]

Hi everyone,

Putting aside consciousness for a moment, I want to ask about the limits of ontological physicalism from a purely physics and philosophy of science perspective.

If physicalism claims that everything that exists is strictly physical (matter/energy), how does it account for:

1. Mathematical structures: Are equations and mathematical truths just human constructs, or do they exist independently without being physical matter?
2. Laws of Nature: Are laws merely descriptive summaries of how matter behaves, or do they have causal power? If they govern matter, wouldn't that make them non-physical entities?
3. Information: With quantum information theory treating "information" as fundamental, how can something substrate-independent be reduced purely to physical matter?

Can physicalism actually ground the abstract foundations that physics relies on, or is it an assumption we just take for granted?

Oh good grief, more repetitive, pseudo-scientific drivel.

 

[W.D.Clinger]

(Edited to add the two words in gray.)

In formal deductive logic, validity is considered evidence. But this is a vastly different usage of the word than you find in science or philosophy.

In formal logic, validity means true under all interpretations.

For example, Gödel's completeness theorem says every valid formula of standard first order logic is provable.

Which implies the existence of a complete proof procedure for first order theories. Given any recursively axiomatizable first order theory, we can write a computer program that will prove every valid consequence of the theory. In general, however, that computer program will not be a decision procedure: If you hand it a valid input, the program will (eventually!) respond with a proof of that input. If you hand it an invalid input, however, the program may just run forever as it tries to find a proof.

There is no decision procedure for standard first order logic. There is a simple decision procedure for propositional logic (e.g. truth tables).

All of the facts stated above have been proved with mathematical rigor, and are examples of using mathematics to prove facts about logic. Epistemologically, mathematics is how we gain knowledge about logic.

On the other hand, logic alone cannot provide a proof that mathematics is a reliable way to gain knowledge. Mathematics itself cannot even provide a proof of its own consistency. That's Gödel's second incompleteness theorem. That incompleteness theorem is of course proved using mathematics, which is how we know it's true.

Why do we trust mathematics, when mathematics itself tells us it is impossible to prove the consistency of mathematics? That's where empiricism enters the picture. Mathematics is known to work quite reliably. If mathematics didn't work, virtually all modern science would be suspect. Science has an empirical foundation. The success of science counts as empirical evidence for mathematics.

 

[W.D.Clinger]

Can physicalism actually ground the abstract foundations that physics relies on, or is it an assumption we just take for granted?

Can @Gubiosak actually formulate an interesting philosophical question? Or does @Gubiosak just assume any question that pops into @Gubiosak's head is worthy of serious consideration?

Inquiring minds don't see a reason to want to know.

 

[P.J. Denyer]

We need some bigger mulberry bushes!

Order infinity plus one, and when they run out we can order some more.

 

[JayUtah]

Mathematics is known to work quite reliably. If mathematics didn't work, virtually all modern science would be suspect. Science has an empirical foundation. The success of science counts as empirical evidence for mathematics.

Not according to our OP, it seems. The paranormalists argue that science works just well enough to give us lasers and Batmobiles, but is fundamentally limited to certain classes of proposition. Conveniently, paranormal claims are posited to lie outside any of those classes. Hence our OP lost interest when it seemed his claim of Limited Science was acknowledged.

Be that is may, yours is a more straightforward way of expressing what I've been saying as science being tethered to an observable reality. The OP seems incapable of anything but a knee-jerk rejection of this relationship as uselessly circular.

The answer, of course, is 42.

 

[Gubiosak]

(Edited to add the two words in gray.)


In formal logic, validity means true under all interpretations.

For example, Gödel's completeness theorem says every valid formula of standard first order logic is provable.

Which implies the existence of a complete proof procedure for first order theories. Given any recursively axiomatizable first order theory, we can write a computer program that will prove every valid consequence of the theory. In general, however, that computer program will not be a decision procedure: If you hand it a valid input, the program will (eventually!) respond with a proof of that input. If you hand it an invalid input, however, the program may just run forever as it tries to find a proof.

There is no decision procedure for standard first order logic. There is a simple decision procedure for propositional logic (e.g. truth tables).

All of the facts stated above have been proved with mathematical rigor, and are examples of using mathematics to prove facts about logic. Epistemologically, mathematics is how we gain knowledge about logic.

On the other hand, logic alone cannot provide a proof that mathematics is a reliable way to gain knowledge. Mathematics itself cannot even provide a proof of its own consistency. That's Gödel's second incompleteness theorem. That incompleteness theorem is of course proved using mathematics, which is how we know it's true.

Why do we trust mathematics, when mathematics itself tells us it is impossible to prove the consistency of mathematics? That's where empiricism enters the picture. Mathematics is known to work quite reliably. If mathematics didn't work, virtually all modern science would be suspect. Science has an empirical foundation. The success of science counts as empirical evidence for mathematics.

W.D. Clinger’s argument is technically sophisticated, but it presents an important epistemological limitation: it confounds the instrumental effectiveness of mathematics with a foundation of its validity.

 

[JayUtah]

W.D. Clinger’s argument is technically sophisticated, but it presents an important epistemological limitation: it confounds the instrumental effectiveness of mathematics with a foundation of its validity.

What if your notion of foundational validity is unimportant?

 

[Gubiosak]

(Edited to add the two words in gray.)


In formal logic, validity means true under all interpretations.

For example, Gödel's completeness theorem says every valid formula of standard first order logic is provable.

Which implies the existence of a complete proof procedure for first order theories. Given any recursively axiomatizable first order theory, we can write a computer program that will prove every valid consequence of the theory. In general, however, that computer program will not be a decision procedure: If you hand it a valid input, the program will (eventually!) respond with a proof of that input. If you hand it an invalid input, however, the program may just run forever as it tries to find a proof.

There is no decision procedure for standard first order logic. There is a simple decision procedure for propositional logic (e.g. truth tables).

All of the facts stated above have been proved with mathematical rigor, and are examples of using mathematics to prove facts about logic. Epistemologically, mathematics is how we gain knowledge about logic.

On the other hand, logic alone cannot provide a proof that mathematics is a reliable way to gain knowledge. Mathematics itself cannot even provide a proof of its own consistency. That's Gödel's second incompleteness theorem. That incompleteness theorem is of course proved using mathematics, which is how we know it's true.

Why do we trust mathematics, when mathematics itself tells us it is impossible to prove the consistency of mathematics? That's where empiricism enters the picture. Mathematics is known to work quite reliably. If mathematics didn't work, virtually all modern science would be suspect. Science has an empirical foundation. The success of science counts as empirical evidence for mathematics.

Clinger, argues that we trust mathematics because it has demonstrated extraordinary success within empirical science. However, this argument does not provide an independent justification for mathematics, because modern science itself relies on mathematical and logical structures to formulate hypotheses, construct models, interpret data, and evaluate predictions.
The problem is not simply a logical circularity in the formal sense, but an epistemological circularity: the method used to confirm the reliability of mathematics already presupposes the mathematical and logical tools whose reliability is being evaluated.
The empirical success of science demonstrates that certain mathematical structures are extremely effective for representing aspects of the physical world, but it does not, by itself, demonstrate that mathematical axioms are true, that mathematical objects exist, or that mathematics possesses necessary validity independent of experience.
Therefore, Clinger’s argument may justify a pragmatic trust in mathematics — that is, the belief that mathematics is an extraordinarily effective tool — but it does not provide an ultimate epistemological

 

[Gubiosak]

Not according to our OP, it seems. The paranormalists argue that science works just well enough to give us lasers and Batmobiles, but is fundamentally limited to certain classes of proposition. Conveniently, paranormal claims are posited to lie outside any of those classes. Hence our OP lost interest when it seemed his claim of Limited Science was acknowledged.

Be that is may, yours is a more straightforward way of expressing what I've been saying as science being tethered to an observable reality. The OP seems incapable of anything but a knee-jerk rejection of this relationship as uselessly circular.

The answer, of course, is 42.

JayUtah appears to misunderstand the objection. The issue is not whether mathematics works, nor whether science is successfully connected to observable reality. No one disputes that mathematical methods are extraordinarily effective in modern science.

The epistemological question is different: does the empirical success of science provide an independent justification for the validity of mathematics itself?

Clinger’s argument shows that mathematics is indispensable for successful scientific practice. However, the success of science cannot serve as a completely independent confirmation of mathematics, because the very processes by which science establishes success — measurement, data analysis, statistical inference, theoretical modeling, and prediction — already rely on mathematical and logical structures.

This does not make scientific reasoning useless or "circular" in a trivial sense. It means that the justification is holistic or mutually supportive rather than foundational. Science and mathematics form an interconnected epistemic framework, but the success of one cannot be used as a non-circular proof of the ultimate validity of the other.

The analogy with paranormal claims is also beside the point. Rejecting the claim that empirical success provides an ultimate foundation for mathematics does not imply rejecting empirical science or accepting claims outside scientific investigation. It only distinguishes two different statements:

1. Mathematics is an extremely reliable and effective tool within science.
2. The empirical success of science proves the ultimate epistemic validity of mathematics.

The first statement is strongly supported. The second requires additional philosophical assumptions that have not been demonstrated.

Therefore, the objection is not a rejection of the relationship between science and reality; it is a challenge to the claim that this relationship alone provides a non-circular foundation for mathematics.

 

[Gubiosak]

What if your notion of foundational validity is unimportant?

The issue is not whether foundational validity is practically necessary. Mathematics clearly works, and science clearly benefits from it. The issue is whether empirical success justifies mathematics itself or merely demonstrates its usefulness.
Saying that foundations are unimportant avoids the epistemological question rather than answering it. A tool can be extremely effective without that effectiveness proving the ultimate reliability of the principles behind it.

 

[JayUtah]

The issue is not whether foundational validity is practically necessary.

Correct. The issue is whether any of your frantic pseudo-philosophical handwaving matters.

Saying that foundations are unimportant avoids the epistemological question rather than answering it.

No, it correctly places the burden of proof on you to support your premises. Why is your notion of foundational validity so important? What makes it the right answer?

 

[JayUtah]

The analogy with paranormal claims is also beside the point.

You're posting in the paranormal forum and following the paranormalists' argumentation playbook. You're trying to show that science is limited in a way that prevents it from studying certain propositions. Identifying those propositions as math etc. is a red herring.

 

[Carrot Flower King]

Not according to our OP, it seems. The paranormalists argue that science works just well enough to give us lasers and Batmobiles, but is fundamentally limited to certain classes of proposition. Conveniently, paranormal claims are posited to lie outside any of those classes. Hence our OP lost interest when it seemed his claim of Limited Science was acknowledged.

Be that is may, yours is a more straightforward way of expressing what I've been saying as science being tethered to an observable reality. The OP seems incapable of anything but a knee-jerk rejection of this relationship as uselessly circular.

The answer, of course, is 42.

And my cat says you are welcome to believe that if you want...

She then went back to sleep, after a very feline yawn and stretch.

What do I know? I merely put food and water out for her...

 

[Steve]

And my cat says you are welcome to believe that if you want...

She then went back to sleep, after a very feline yawn and stretch.

What do I know? I merely put food and water out for her...

That seems like it came from Douglas Adams but I can't quite place it.

 

[Darat]

I would. AI is not reliable. How can I know that it translated the words correctly?

Google's AI overview says:-

A rare moment of introspection, or an admission that AI is deceitful? Or is it just jealous of those tools and telling lies about them? This is proof that AI is already self-aware and will become super-intelligent any day

Clinger, argues that we trust mathematics because it has demonstrated extraordinary success within empirical science. However, this argument does not provide an independent justification for mathematics, because modern science itself relies on mathematical and logical structures to formulate hypotheses, construct models, interpret data, and evaluate predictions.
The problem is not simply a logical circularity in the formal sense, but an epistemological circularity: the method used to confirm the reliability of mathematics already presupposes the mathematical and logical tools whose reliability is being evaluated.
The empirical success of science demonstrates that certain mathematical structures are extremely effective for representing aspects of the physical world, but it does not, by itself, demonstrate that mathematical axioms are true, that mathematical objects exist, or that mathematics possesses necessary validity independent of experience.
Therefore, Clinger’s argument may justify a pragmatic trust in mathematics — that is, the belief that mathematics is an extraordinarily effective tool — but it does not provide an ultimate epistemological

Sadly I see you lied.

 

[ferd burfle]

Try as it might, the camel could not get its nose under the tent.

 

[Helen]

Transcendental resonance supersedes the empirical boundary, such that hidden wholes mirror the quantum structure of absolute subjective experience.

 

[Carrot Flower King]

That seems like it came from Douglas Adams but I can't quite place it.

A paraphrase: it's from when they meet the bloke who actually runs the Universe and his cat, with him claiming that he feeds and waters her as it seems to be what she wants and he assumes that is a good thing to do. Or something like that.

The life of any cat accommodater or tin opener as we are called in Felidae...Even if we open sachets.

 

[Steve]

A paraphrase: it's from when they meet the bloke who actually runs the Universe and his cat, with him claiming that he feeds and waters her as it seems to be what she wants and he assumes that is a good thing to do. Or something like that.

The life of any cat accommodater or tin opener as we are called in Felidae...Even if we open sachets.

So I did recognize it.

 

[P.J. Denyer]

Transcendental resonance supersedes the empirical boundary, such that hidden wholes mirror the quantum structure of absolute subjective experience.

I hate when that happens.