The problem with those presuppositions is that denying them, and asserting the opposites doesn't necessarily result in contradiction. — Corvus

I don’t understand why that would be a problem.

This has been a very substantive discussion so far. I think the new approach we discussed in the previous thread gets the credit. — T Clark

That would be cool, but one way or the other, yes, good conversation.

But it makes a point about an inherent contradiction in physicalism.
— Wayfarer

It is, as you say, one of the main reasons to reject physicalism, at least as it's usually understood.
— J

I don't understand why this would be true. Maybe I misunderstood what Wayfarer meant when he wrote "are the mathematical laws themselves physical." — T Clark

And @Wayfarer can of course elucidate, but I took him to mean that a "law" isn't something made of physical items. You can adopt the thinnest ontology and still not find any numbers or laws among the sub-atomic particles. Or you can accept macro-items -- tables, groups, mereological items -- and still not find any laws. They're not "out there" in the way that the physical world is (or seems to be) out there. This is a challenge to physicalism about all non-physical items, but it's particularly stinging here because mathematical laws are supposed to be basic and explanatory. How does that square with a physicalist conception of what exists?

My elaboration of W's point was to compare a statement of a mathematical law produced by, say, an AI program, with the same statement produced by a mathematician. For physicalism to be true, you would have to say that there is no difference between the two instances; they're both just bits of writing, physical marks on paper. They both exist in exactly the same way. To me, that seems very unlikely -- the idea that explanation can really be reduced to an arrangement of ink on paper. (It's the same proposal that thoughts can be reduced to neuronal activity.)

And Wayfarer can of course elucidate, but I took him to mean that a "law" isn't something made of physical items. — J

Agreed, see the previous exchange between @Wayfarer and me below.

Physical systems instantiate regularities;
scientific laws articulate those regularities in mathematical form. The laws themselves are not physical objects but ideal structures, grasped through intellectual acts of abstraction and measurement.
To treat laws as physical is to confuse what is described with the means of description.
— Wayfarer

I misunderstood what you meant by “are the mathematical laws themselves physical.” Now that you’ve explained, I agree with you. — T Clark

This is a challenge to physicalism about all non-physical items, but it's particularly stinging here because mathematical laws are supposed to be basic and explanatory. How does that square with a physicalist conception of what exists? — J

Really this is one of the central points of E A Burtt's book, although he tends to imply it rather than state it in such bald terms. There's a hidden metaphysical assumption behind the modern idea that the Universe is solely physical.

A good follow up from Burtt is Husserl, Crisis of the European Sciences. That said, it's an extremely dense and detailed book - one of those books to know about if not necessarily read in full. (I outlaid for a copy but have never read the whole thing.) Husserl too sees the pivotal importance of Galileo's 'mathematicization of nature' in modern thought, at the cost of forgetting the subject to whom science is meaningful. The wiki article.

To overstate the case, in order to do physics you have to be a materialist. So...Yes, that does make it an absolute presupposition. — T Clark

I can't see why one would need to be a metaphysical materialist in order to do science. Scince can only deal with what is given by the senses―that is its methodology.

The question that jumps out at me is: are the mathematical laws themselves physical, and, if so, how? I don’t expect an answer to that, as there isn’t one, so far as I know. But it makes a point about an inherent contradiction in physicalism. — Wayfarer

I'm not arguing for physicalism but against the idea that it is inherently contradictory. It can be argued that what we think of as laws are simply the ways physical things behave on the macro level based on what is ultimately stochastic at the micro-physical level. That may not constitute a comprehensive or even satisfactory explanation, but it contains no logical contradiction.

The laws may not be timeless principles but evolved habits as Peirce thought.
.

I can't see why one would need to be a metaphysical materialist in order to do science. Scince can only deal with what is given by the senses―that is its methodology. — Janus

Interesting. I’m not sure I understand how you can have a materialist epistemology but a non-materialist ontology. Can you give me an example of how that might work?

The question that jumps out at me is: are the mathematical laws themselves physical, and, if so, how? I don’t expect an answer to that, as there isn’t one, so far as I know. But it makes a point about an inherent contradiction in physicalism. — Wayfarer

I'm not arguing for physicalism but against the idea that it is inherently contradictory. It can be argued that what we think of as laws are simply the ways physical things behave on the macro level based on what is ultimately stochastic at the micro-physical level. — Janus

I’m not sure this is important, but I’m not sure it’s not either. Burt’s formulation of the mathematical absolute presupposition is different from mine. I wrote "Scientific laws are mathematical in nature." He wrote (with some fiddling by me) "The real world in which man lives is a world of atoms, equipped with none but mathematical characteristics and moving according to laws fully statable in mathematical form."

I bolded what seems like an important difference. The characteristics of the phenomena which make up the world are mathematical. The question then becomes whether the mathematical characteristics of the phenomena are physical. I'm not as sure of that as I was when we were discussing the laws of nature, which are not physical.

Interesting. I’m not sure I understand how you can have a materialist epistemology but a non-materialist ontology. Can you give me an example of how that might work? — T Clark

Science can only deal with what our senses reveal...with what is measurable and quantifiable. There are other less 'hard' areas of enquiry such as psychology, anthropology, sociology, ethology that require thinking in terms of purpose and reasons rather than or as well as mechanical causal models. So I think it depends on what you mean by "epistemology".

A scientist doesn't even need to think of what is being investigated as physical. They can simply "shut up and calculate" or they could think everything is ultimately mind and still do science perfectly as adequately as they do thinking everything is physical.

Science can only deal with what our senses reveal...with what is measurable and quantifiable. There are other less 'hard' areas of enquiry such as psychology, anthropology, sociology, ethology that require thinking in terms of purpose and reasons rather than or as well as mechanical causal models. So I think it depends on what you mean by "epistemology". — Janus

For the purposes of this discussion, we’re talking physics—CERN, LIGO, dark matter, string theory, superconductivity.

A scientist doesn't even need to think of what is being investigated as physical. They can simply "shut up and calculate" or they could think everything is ultimately mind and still do science perfectly as adequately as they do thinking everything is physical. — Janus

Maybe. I’m not sure. I’ve always thought epistemology should be considered part of metaphysics. They’re too intimately connected to be separate.

Numbers are ideas, and ideas are not physical. Yet without math science couldn’t even get started.