I have long been in agreement with this argument.

Descartes was aware of the problem: If mind and body are entirely incommensurate, how can mind make the body do things? His solution was the quite unsatisfactory notion that "god did it".

Dualism fails.

If dualism is true, then mind is not spatio-temporal, and body is spatio-temporal. — quine

Why can't the mind be spatio-temporal? Of course you mean the human mind, but why can't the human mind be a physical representation of this mind-stuff? Wouldn't this still be dualism, but with the division between physical and mental moved over slightly?

but why can't the human mind be a physical representation of this mind-stuff? — tom

Such a thought is called 'epiphenomenalism'. Epiphenomenalism is a kind of dualism. Many philosophers reject epiphenomenalism.

Such a thought is called 'epiphenomenalism'. Epiphenomenalism is a kind of dualism. Many philosophers reject epiphenomenalism. — quine

It can't be epiphenomenalism, because the mind in this case is exactly the causal physical structure. It's almost indistinguishable from physicalism, but admits that certain purely abstract entities - e.g. the non-computable numbers exist.

So, it's similar to the distinction between computable and non-computable numbers. Physical reality can only instantiate computable numbers. The suggestion would be that physical reality can only instantiate computable-minds, which appears to be the case.

I'm sure this view must exist and have a name? Maybe it is just physicalism and I've not been paying attention?

According to physicalism, mind is located in spatio-temporal realms. Dualists deny this view. My argument is against dualistic thoughts.

I have long been in agreement with this argument.

Descartes was aware of the problem: If mind and body are entirely incommensurate, how can mind make the body do things? His solution was the quite unsatisfactory notion that "god did it".

Dualism fails. — Banno

I don't think it fair to say that dualism fails because it hasn't explained how the mind and the body interact. There are a lot of things that physics hasn't explained (which is why we don't have a theory of everything) but it doesn't then follow that it's fair to say that physicalism fails for this reason.

That would be an argument from ignorance.

I don't think it fair to say that dualism fails because it hasn't explained how the mind and the body interact. There are a lot of things that physics hasn't explained (which is why we don't have a theory of everything) but it doesn't then follow that it's fair to say that physicalism fails for this reason.

That would be an argument from ignorance. — Michael

The problem is not that dualism fails to explain so-and-so, but that dualism defines mind and body not to interact one another.

The problem is not that dualism fails to explain so-and-so, but that dualism defines mind and body not to interact one another. — quine

No, it defines them to be different with the mind not being a spatial thing. Your second premise isn't part of the dualist's definition(s).

My argument against physicalism (and possibly some of variants of dualism, such as emergent dualism:

1. If physicalism is true, then physical matter produces the mind and consciousness.

2. It is not the case that physical matter produces the mind and consciousness.

Therefore:

3. Physicalism is false.

The problem is not that dualism fails to explain so-and-so, but that dualism defines mind and body not to interact one another. — quine

Dualism specifically defines that the mind and body do interact with each other.

1. If physicalism is true, then physical matter produces the mind and consciousness.

2. It is not the case that physical matter produces the mind and consciousness.

Therefore:

3. Physicalism is false. — Chany

How about this:

1. If physicalism is true, then physical matter produces the mind and consciousness.

2. It is the case that physical matter produces the mind and consciousness.

Therefore:

3. Physicalism is true

Descartes defines mind as non-spatio-temporal entity. He defines body as spatio-temporal one. According to these definitions, mind and body cannot interact. It seems that pineal gland is irrelevant to mind-body interaction.

I'm not endorsing the argument that I presented. It is a bad argument. However, it is bad in the same way that the OP argument is bad. They carry the same amount of weight. Pretty much, both are arguments from ignorance: the negating premise in the modena tollens is simply asserted because the creator of the argument does not hold it to be true.

Dualist response:

Clearly, the immaterial substance of the mind and the material substance of the body do interact, as we can clearly see observe them doing so.

According to these definitions, mind and body cannot interact. — quine

Only if you define spatial and non-spatial things as being unable to causally influence one another, but the dualist doesn't define them this way.

Mind-body interaction is evidence of which dualism is false.
(1) Mind and body obviously interact one another.
(2) If mind and body obviously interact one another, then dualism is false.
Therefore, (3) dualism is false.

(1) If dualism is true, then mind is not spatio-temporal, and body is spatio-temporal.
(2) If mind is not spatio-temporal, and body is spatio-temporal, then mind and body cannot interact. — quine

Just so you know where I'm coming from, I'm a physicalist who thinks that the idea of nonphysical existents is incoherent.

However, I'm wondering whether your first and/or second premises aren't straw men.

Does a dualist have to believe that nonphysical existents are not spatio-temporal?

And does a dualist have to believe that nonphysical existents that are not spatio-temporal can not interact with spatio-temporal things?

I don't think either one of those are clear. Although that's of course because there's not a uniformly agreed-upon, clear characterization of just what nonphysical existents would amount to. Usually people just give examples of things they consider to be nonphysical, or they just describe them functionally. It's rare to run into someone who tries to explain just what their "nature" would be ontologically a la "what sort of 'stuff' they are."

Does a dualist have to believe that nonphysical existents are not spatio-temporal? — Terrapin Station

According to Cartesian dualism, the mind is a non-spatial thing, so we can grant quine the first premise.

The problem is that Descartes claimed that the mind and the body can nonetheless causally influence one another, and so the Cartesian dualist would reject quine's claim that that non-spatial things are defined as not being able to causally influence the body (and would also reject the claim that as a matter of fact non-spatial things are not able to causally influence the body).

Descartes says that the essence of mind is thinking. He claims that the essential feature of body is extension. It implies that Descartes thinks that mind is beyond space and time. Anything beyond space and time cannot interact with something in space and time.

Anything beyond space and time cannot interact with something in space and time. — quine

Is that true by definition or is it just an empirical fact?

I think that it is an empirical fact.

I think that it is an empirical fact. — quine

Then it was wrong to claim that "dualism defines [my emphasis] mind and body not to interact one another".

Descartes says that the essence of mind is thinking. He claims that the essential feature of body is extension. It implies that Descartes thinks that mind is beyond space and time. Anything beyond space and time cannot interact with something in space and time. — quine

This is the entire crux of the problem. The dualist clearly believes that the immaterial, non-spatial mind can interact with the material, spatial body. They reject the notion that this interaction is prima facie wrong until proven otherwise. The dualist thinks the mind is obviously not material, and holds their position to be more likely than a physicalist notion of the mind.

Cartesian dualists are wrong because they wrongly define mind and body.

According to Cartesian dualism, the mind is a non-spatial thing, so we can grant quine the first premise. — Michael

But why does a dualist have to be a Cartesian dualist?

But why does a dualist have to be a Cartesian dualist? — Terrapin Station

He doesn't. But @quine explicitly said in the opening post "I am going to offer an argument against Cartesian dualism".

There are various dualisms. The target of my argument above is Cartesian dualism.

How? Please assert how you falsified and/or demonstrated how the substance dualist is false.

My argument against Cartesian dualism is formally valid. The conclusion is derived from premises.

Yes, it's modus tollens.

However, I was talking about the premise:

If mind is not spatio-temporal, and body is spatio-temporal, then mind and body cannot interact. — quine

Why should we accept it as true?