Set theory is a good treatment.

Hey,
This thread is about correct formulation of sense-datum statements... Don't forget about it.

See section 9 in Empiricism and the Philosophy of Mind. Sellars says '(X looks red to S) = There is a class of red sense-data which belong to X, and are sensed by S'.

This is roughly Davidson's view of radical interpretation (divorced from his anomalous monism). — Pierre-Normand

You remind me of radical interpretation. Great!

The assumption is that causes and effects occur in space and time. Descartes defines minds as not being located in space and time. According to Descartes' definition of mind, minds can't be causes or effects. Interactions imply causation. So, Descartes' definition is wrong. In order to explain mind-body interaction, minds must be located in space and time. If minds are located in space and time, then Descartes' definition of mind is false, and dualism is false, too.

Descartes' solution is also false. Pineal glands themselves are extended in space and time. Minds that are not extended in space and time cannot be moderated by pineal glands that are extended in space and time.

'Spatio-temporal' means space and time where we are.
Bodies are spatio-temporal because they are extended in space-time points.
According to Cartesian dualism, minds are not extended in space-time points.

Mind-body identity theory is a better choice than dualism is. According to identity theory, mind and body occupy the same space-time point. In this view, the problem of mind-body interaction is automatically solved. They are both located in space and time.

It's because they are located in entirely different areas. Bodies are located in space and time. Minds are not there. They never met each other. It's the result of dualistic scenarios. Fortunately, they can meet each other. Dualism is false.

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

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

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

I think that it is an empirical fact.

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.

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.

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 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.

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

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.

'Evidence' is a tricky expression because it's ambiguous. When 'all ravens are black' is equivalent to 'everything that is not black is not a raven', it is about logical forms. 'Green apples' has nothing to do with the logical forms of 'all ravens are black' and 'everything that is not black is not a raven'. So, the paradox is a mixture of two different issues.

The logical form of 'there are green apples' goes as follows:
(3) There exists some x such that x is green, and x is an apple.
Do you think that (3) is relevant to (1*) and (2*) in terms of formalization?

'A green apple' is not related to the equivalence of (1) and (2). The logical form of (1) can be as follows:
(1*) For every x, if x is a raven, then x is black.
Do you see that 'a green apple' is irrelevant to (1*)?
The logical form of (2) would be:
(2*) For every x, if x is not black, then x is not a raven.
Do you see that 'a green apple' is not related to (2*)?
You should be able to distinguish the talk about formalization from the talk about matters of fact.

I said that 'evidence' is a tricky expression. Evidence is not related to formalization. Equivalence is about formalization. Evidence is about matters of fact. The paradox suggested above is a mixture of two different kinds of issues. '(1) and (2) are logically equivalent' - It's about formalization. 'Evidence of (2) supports evidence of (1)' - It's about matters of fact.

Formally, (1) and (2) are the one same proposition. 'Evidence' is a tricky expression. Evidence is irrelevant to formal equivalence.
In natural language, a green apple is relevant to (2), but it isn't relevant to (1). Formally accurate language guarantees the equivalence of (1) and (2). Natural language merely shows that they are two different strings of symbols.

Not all evidence of (2) is evidence of (1). (1) and (2) are formally equivalent. 'Evidence' is a matter of fact.
A green apple is evidence in support of (2) in terms of matters of fact. It is not evidence in support of (1) in terms of matters of fact.

"To be is to be the value of a variable." - W. V. O. Quine

If they can't be reduced, then how are they physical? — Marchesk

Reductive physicalism is type identity physicalism. Non-reductive physicalism is token identity physicalism. According to reductive physicalism, the type of mental phenomena is reduced to the type of physical phenomena. Non-reductive physicalism says that some tokens of mental properties are matched with some tokens of physical properties.

Many things are logically conceivable. Merely logically conceivable things can't refute anything. P-zombies are logically conceivable. Do P-zombies refute physicalism? I don't think so.

What makes you think so?

So, what's your objection to my argument?

It's like infinite regress of evidence.

Every human being is conscious.

Diablo 1
Diablo 2

I mean, by definition, P-zombies are non-conscious beings that are observed as conscious. The concept of P-zombies is itself contradictory. That's what I wanted to say.

A P-zombie might be observed in a possible world...

Here's an argument:
Everything that can be observed as conscious is conscious. Every P-zombie can be observed as conscious. Therefore, every P-zombie is conscious.

Everything conscious can be observed as conscious. Every P-zombie can be observed as conscious. So, what do you think?

Some statements are expressed in second-order logic even though they can be expressed in first-order logic. For example, 'A supervenes on B' can be enough translated into first-order logic, but Stanford Encyclopedia 'supervenience' entry states its formula by second-order logic. This means all first-order statements can be symbolized as second-order statements as all propositional calculuses can be expressed as predicate calculuses.

How about this:

(5) (∃X)(∃x)((Xx & (∀y)(Xy → x = y)) & Fx & (∀y)(Fy → x = y))

(4) The king of France is bald.

I think that (4) can be expressed as (3) in first-order logic. Is it possible that (4) is expressed in second-order logic?

Let's say 'The F is G' instead.

(3) (∃x)(Fx & (∀y)(Fy → x = y) & Gx)

I think that (3) completely express 'The F is G' in first-order logic. The question would be: What is the equivalent form to (3) in second-order logic?