If I had believed that the criticisms you offered had truly understood what was being proposed, I might be inclined to so believe. But, no. — Wayfarer

Ok. I'll bow to the true Scotsman. Those who disagree with you have not truly understood.

Those who disagree with you have not truly understood. — Banno

I haven't said that, either. I will deal with any cogent disagreements, but not those which betray a failure to grasp the point at issue. (If you would like to take this up again in the thread in which it started, please do. It is still active.)

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

In formal logic, there is a difference between the domain of discourse - the a's, b's and c's that make up the content being discussed - and the logical connectives - the ^'s, ∃'s and =.

In physics, the content, the a's, b's and c's, are all of them physical. The connectives, including the mathematics, are not physical.

No presumption is made that 4+4=8 is physical.

He'd then be like someone who insists on moving the bishop along a column instead of a diagonal. Yes, he can do that, but it's not what we set out to do. — Banno

I like this metaphor.

A good explanation. It's a bit like setting up the domain of discourse to only include the physical, and sticking to that rule. What we ought keep in mind is that setting up the domain of discourse is making a choice as to what we include and exclude. — Banno

Agreed. Beyond that, just because you and I might agree that absolute presuppositions are not true or false, most people probably think they are. If that happens, their understanding of how the world works could be rigid and biased.

Corvus
...Collingwood is not saying these presuppositions are true, but that they underpin the method that was, historically, adopted. Further, if we instead of treating them as metaphysical truths treat them as methodological prescriptions, their truth is irrelevant. — Banno

This discussion has been great for me. There’s a bunch of things that have been bubbling around on the back burner that got brought out in the open. That has been really helpful.

Cheers. And likewise. Good thread.

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

In formal logic, there is a difference between the domain of discourse - the a's, b's and c's that make up the content being discussed - and the logical connectives - the ^'s, ∃'s and =.

In physics, the content, the a's, b's and c's, are all of them physical. The connectives, including the mathematics, are not physical.

No presumption is made that 4+4=8 is physical. — Banno

Not in formal logic. But surely the many fervent disagreements sorrounding the ontological status of numbers and scientific laws indicate that there is an issue there, beyond the strictures of formal logic. Specifically, the question of, if everything is indeed reducible to the physical, what of the nature of the mathematical reasoning that underpins physics? Why did Eugene Wigner's essay on The Unreasonable Effectiveness of Mathematics in the Natural Sciences become such a celebrated essay in modern philosophy of physics?

But surely the many fervent disagreements sorrounding the ontological status of numbers and scientific laws indicate that there is an issue there, beyond the strictures of formal logic. Specifically, the question of, if everything is indeed reducible to the physical, what of the nature of the mathematical reasoning that underpins physics? — Wayfarer

It simply depends on what you call a "thing". It's pretty clear that thinking one can apply F=ma to 7+1=8 and find the mass of = is a category mistake.

These are different games. As if you had complained that a checkmate beats a royal flush.

That some folk make such errors does not imply they have a point.

The point is, it's a glaring contradiction:

[1] We live in an ordered universe that can be understood by humans.
[2] The universe consists entirely of physical substances - matter and energy.
[3] These substances behave in accordance with scientific principles, laws.
[4] Scientific laws are mathematical in nature.

If reality is wholly physical, why is it necessarily and lawfully answerable to non-physical mathematical reasoning, and why does that reasoning carry binding normative force?

From Collingwood's perspective, there is an absolute presupposition:

That reality is mathematically intelligible in a binding, law-governed way.

But physics cannot justify that presupposition. Formal logic cannot adjudicate it. Calling it a “different game” does not remove its necessity.

The point is, it's a glaring contradiction:

[1] We live in an ordered universe that can be understood by humans.
[2] The universe consists entirely of physical substances - matter and energy.
[3] These substances behave in accordance with scientific principles, laws.
[4] Scientific laws are mathematical in nature.

If reality is wholly physical, why is it necessarily and lawfully answerable to non-physical mathematical reasoning, and why does that reasoning carry binding normative force? — Wayfarer

There is only a contradiction because you don’t accept the possibility that mental processes can be understood in terms of physical, chemical, biological, and neurological processes. You and I agree that reductionist physicalist explanations for many phenomena are limiting and misleading. You just take it significantly further than I do.

The point is, it's a glaring contradiction: — Wayfarer

Formally, there is a difference between the domain and the formation rules, and how each is used. The language is about the items in the domain, the rules for that language are not the subject of that language.

When a physicist looks for explanations in terms of physical substances, they don't presume that those explanations have mass.

You and I agree that physicalism, at the extreme, is erroneous - that maths does not have mass. We agree that this shows science to be incomplete. You try to explain this by supposing that there must be some other substance, some spirit, to go along with the physical. That brings in all the problems of dualism.

My response is less forthright - I am just pointing out that maths is something we do, rather than some sort of substance. Mathematics is a practice, a framework of reasoning, not a thing with substance.

No doubt this is another example of not truly understanding you.

(Can I point out how much I appreciate your putting up with my crap? Thanks for the replies. )

There is only a contradiction because you don’t accept the possibility that mental processes can be understood in terms of physical, chemical, biological, and neurological processes. You and I agree that reductionist physicalist explanations for many phenomena are limiting and misleading. You just take it significantly further than I do. — T Clark

Yep - sort of.

A coin (remember coins? It's how we used to do money) is just a bit of alloy, but it takes on a special role in some of our games. There is a physical description and a financial description, and perhaps never the twain.

No doubt this is another example of not truly understanding you. — Banno

No, I think we're operating in different registers. What you're saying is quite true about domains of discourse. But I'm extending that to a further argument about epistemology and about the inherent contradictions of physicalism.

There is only a contradiction because you don’t accept the possibility that mental processes can be understood in terms of physical, chemical, biological, and neurological processes. — T Clark

I’m not denying that acts of reasoning are reliably correlated with physical, biological, and neurological processes. I’m denying that logical relations themselves—validity, necessity, entailment—can be reduced to physical causation. Actually it's very much the kind of point that Collingwood is pressing in his Essay on Metaphysics. And, for that matter, to attempt to reduce normative argument to physical causation would require invoking the very normativity that the argument seeks to explain! Whenever you engage in reasoned inference - because of x, then y - you are appealing only to the relations of ideas, not to anything physical as such.

No, I think we're operating in different registers. What you're saying is quite true about domains of discourse. But I'm extending that to a further argument about epistemology and about the inherent contradictions of physicalism. — Wayfarer

Epistemology just is a domain of discourse.

You couldn't complete the formalising of your argument, and I think that's because there is a mismatch between your four presumptions and your conclusion. They are in different domains.

Re-arranged:

I’m denying that logical relations themselves—validity, necessity, entailment—can be reduced to physical causation. — Wayfarer

That's not unlike someone complaining about being given a fifty dollar note cut in half instead of twenty five dollars. I don't think Clarky disagrees - I certainly don't. I agree.

But I don't think we need ghosts to explain the difference.


(indeed, I don't think physics can be reduced to physical causation... but that's another topic...)

There is only a contradiction because you don’t accept the possibility that mental processes can be understood in terms of physical, chemical, biological, and neurological processes.
— T Clark

I’m not denying that acts of reasoning are reliably correlated with physical, biological, and neurological processes. I’m denying that logical relations themselves—validity, necessity, entailment—can be reduced to physical causation. — Wayfarer

I didn’t mean what I said as criticism and I don’t discuss my relationship with my children in neurological terms. The message I get from Collingwood is that you choose your metaphysical and epistemological tools based on the specific work you’re trying to complete. I can be a physicalist when I want to do cognitive science and an idealist when I want to go out to lunch with my kids.

Another gem from Collingwood (p46)

it is a special characteristic af modern European civilization that metaphysics is habitually frowned upan and the existence of absolute presuppositions denied. This habit is neurotic. It is an attempt to overcome a superstitious dread by denying that there is any cause for it. If this neurosis ever achieves its astensible object, the eradication of metaphysics from the Eurapean mind, the eradication af science and civilization will be accomplished at the same time. If a sufficient number of Europeans want to destroy science and thus accomplish the suicide of civilization, nothing I can do will stop them; but at present, in England, they have not the power to prevent me from warning those who neither share nor suspect their design.