This seems to be your fundamental error:
"This seems very confused, and unrealistic. A molecular state of affairs would also contain atomic states of affairs. So atomic states of affairs would have dual existence."
Then you are aren't understanding, because it does not entail this at all. Oxygen molecules exist, and so do each of the oxygen atoms that comprise the molecule. This is not "dual existence" - it is simply a consistent mereological account.

If you want to try to understand Armstrong's ontology, you have to let go of your current ontological commitments and accept his account. Consider it a stipulation that everything that exists is a state of affairs. Every object of experience (e.g. your computer, your chair, yourself) is a state of affairs. Each is composed of smaller parts, but each part is also a state of affairs. It's states of affairs all the way down, but stopping at the atomic states of affairs. Once you understand it, you could perhaps try to find something incoherent - but you'll never understand it if you just dismiss the basics because it doesn't fit your preconceived model of reality.

Then you are aren't understanding, because it does not entail this at all. Oxygen molecules exist, and so do each of the oxygen atoms that comprise the molecule. This is not "dual existence" - it is simply a consistent mereological account. — Relativist

This is inconsistent with the account you gave. According to that account, what exists, as "objects" are states of affairs. And accordingly, if the same oxygen atom is involved in an atomic state of affairs, and also a molecular state of affairs at the same time, it has a dual existence, existing in two distinct objects at the same time. Therefore an oxygen atom has multiple existences, existing in many states of affairs (objects) at the same time.

Once you understand it, you could perhaps try to find something incoherent - but you'll never understand it if you just dismiss the basics because it doesn't fit your preconceived model of reality. — Relativist

As I said, I dismiss it because it's quite clearly contradictory, just like saying that "2" refers to two distinct objects, and one object (the number 2) at the same time.

You seem to be reading meaning into the word "object" that I didn't intend. I was just referring to existents - anything that can be said to exist. An oxygen atom can be said to exist. An oxygen molecule (consisting of two bound oxygen atoms) can be said to exist. This does not entail "dual existence." It is mereological.

Do you want to try and understand it, or are you hell bent on finding some reason to dismiss it? I don't mind spending time explaining it to you, but not if you're going to be combative. David Armstrong was a well-respected Australian metaphysician, not a crackpot whose framework is a house of cards that falls with a faint breath.

Well, Armstrong’s major thesis was ‘A Materialist Theory of Mind’ (and as it happens he was professor of the department where I was an undergrad in philosophy). He certainly was no crackpot, but his philosophy stands or falls with materialism, and I don’t think his style of materialism is defensible, knowing what we now know from physics. I mean, there are far too many unanswered questions about the nature of matter itself; his philosophy seems to assume a pretty simplistic kind of atomism, within which the reality of fundamental units of matter is simply a given. But even a casual acquaintance with current philosophy of science calls that into question.

Armstrong's philosophy is broadly naturalistic. In Sketch for a Systematic Metaphysics, Armstrong states that his philosophical system rests upon "the assumption that all that exists is the space time world, the physical world as we say". He justifies this by saying that the physical world "seems obviously to exist" while other things "seem much more hypothetical". From this fundamental assumption flows a rejection of abstract objects including Platonic forms.

Whereas, there are very many mathematical physicists who are indeed Platonist of some variety, with some of them adopting such views because of the discoveries associated with quantum mechanics in the 1920’s. Typical of those is Werner Heisenberg, whose Physics and Philosophy argues for a broadly Platonist interpretive framework for modern physics.

I think the decisive argument against Armstrong’s type of naturalism, is the transcendental nature of mathematics itself. As is declared in the SEP article, Platonism in the Philosophy of Mathematics:

Mathematical platonism has considerable philosophical significance. If the view is true, it will put great pressure on the physicalist idea that reality is exhausted by the physical. For platonism entails that reality extends far beyond the physical world and includes objects which aren’t part of the causal and spatiotemporal order studied by the physical sciences. Mathematical platonism, if true, will also put great pressure on many naturalistic theories of knowledge. For there is little doubt that we possess mathematical knowledge. The truth of mathematical platonism would therefore establish that we have knowledge of abstract (and thus causally inefficacious) objects. This would be an important discovery, which many naturalistic theories of knowledge would struggle to accommodate.

Consequently, there have been elaborate arguments developed about ‘the indispensability of mathematics’ [e.g. here) which attempt to reconcile this rather inconvenient truth with the naturalism that indeed depends on mathematics for its basic methodology. The fact that such an argument has to be made in the first place speaks volumes in my opinion.

ll, Armstrong’s major thesis was ‘A Materialist Theory of Mind.He certainly was no crackpot, but his philosophy stands or falls with materialism, and I don’t think his style of materialism is defensible, knowing what we now know from physics. — Wayfarer

His materialist theory of mind was only a component of his comprehensive metaphysics. Indeed it "stands or falls" with materialism - his comprehensive metaphysics aims to show that materialist metaphysics is coherent.

I mean, there are far too many unanswered questions about the nature of matter itself; his philosophy seems to assume a pretty simplistic kind of atomism,

Not really. It's consistent with atomism, but it's also consistent with quantum field theory.

there are very many mathematical physicists who are indeed Platonist of some variety, with some of them adopting such views because of the discoveries associated with quantum mechanics — Wayfarer

Since when did physicists become good at metaphysics? A Platonic interpretation of mathematics is a consequence of the way it's conceptualized - it's an intellectual convenience.

How does the platonic entity "6" become get involved in the building of a collection of 6 objects, from smaller collections? Physicalist account: Collections having the property 3 can be merged into a collection having property 6. The 3 (or 6) property is inherent in the states of affairs; the 6 property is necessitated by two collections with property 3.

Some platonist accounts treat equations (which are abstract objects) as causally efficacious. That seems problematic. Causal efficacy is more easily understood by physicalist account.

there have been elaborate arguments developed about ‘the indispensability of mathematic — Wayfarer

Mathematics is essential to understanding much of the world (i.e. physics), but that doesn't change under physicalism. Physicalism just implies that the things that exist stand in relation to one another in ways that are describable mathematically. It seems more parsimonious than to think equations exist apart from the physical things they describe. Which brings up another of set of Armstrong's contributions: his theory of universals and his theory of natural law.

BTW, I'm not claiming Armstrong's metaphysics is necessarily true. I'm just claiming it's coherent and sufficiently complete in its accounts.

How does the platonic entity "6" become get involved in the building of a collection of 6 objects, — Relativist

The problem here, as I see it, is treating a number - 6, in this case - as ‘an entity’ in the same sense that an object is an entity. However, a number is not an entity in the sense that the objects are; its reality is purely intellectual or noetic. But it can be said to be an object in a metaphorical sense, i.e. an 'intelligible object'.

But I think it’s a widespread mistake to mis-conceptualise the notion of the ‘domain of numbers’ as a literal ethereal domain or place, or of numbers as existing in the sense that phenomena exist. This mistake arises because the modern attitude is almost exclusively, but unconsciously, oriented towards the objective domain. Instead, number (and the like) has to be understood in terms of them being the organising principles of the mind. So to count and to abstract requires the ability to grasp numerical, syntactical and logical relationships; that is the only domain in which numbers ‘exist’. And I use the quotations deliberately, because numbers don’t exist in any sense other than as operations of thought, or relations of ideas. Yet at the same time the ability to grasp those ideas is fundamental to science itself.

Nowadays it is widely assumed that evolutionary science and neurobiology have an in-principle grasp of how the brain might do this; indeed a naturalistic account must provide such an account. But I argue that there's a very deep problem of recursion in any naturalistic account, as we must already be able to count and to reason in order to even begin to develop such an account. That is the sense in which number (and the like) transcends a strictly empiricist account; as the grasp of number is required to organise and make sense of experience, so in that sense must always precede the empiricist explanation (which is essentially a Kantian argument).

Some platonist accounts treat equations (which are abstract objects) as causally efficacious. — Relativist

I think it's more the case that so-called natural or scientific laws again belong to a different order, to that of the phenomena which they explain. I mean, for example, if you look at the Laws of Motion, they are clearly efficacious within the very wide range in which they apply. So science can use those laws to explain all manner of phenomena. But I don't think science actually explains the laws themselves; however many people seem to think it does. That is the subject of Wittgenstein's aphorism, 'the whole modern conception of the world is founded on the illusion that the so-called laws of nature are explanations of nature' (TLP 6.371).

So again, the platonist attitude is that such laws pertain to a different level or mode than the domain of phenomena; that being the 'formal realm', although that is not an expression that is in wide circulation. They don't exist - in a sense, they 'subsist' or underlie and inform the phenomenal domain, although the sense in which they are real is difficult to express in the current lexicon of philosophy.

The problem here, as I see it, is treating a number - 6, in this case - as ‘an entity’ in the same sense that an object is an entity. — Wayfarer

That's not done in Armstrong's metaphysics. Remember that what exists is a state of affairs. 6 doesn't exist distinct from a state of affairs that has the property "6" .

But it can be said to be an object in a metaphorical sense, i.e. an 'intelligible object'.

How about as an "abstraction?" That fits the bill. The only possible point of contention is how we consider abstractions. If we treat them as mental objects, produced by the way of abstraction, that's consistent with physicalism. When we start treating them as existing apart from minds, that's platonism.

But I argue that there's a very deep problem of recursion in any naturalistic account, as we must already be able to count and to reason in order to even begin to develop such an account. That is the sense in which number (and the like) transcends a strictly empiricist account;

I don't see the problem. The only "transcendence" I see is that universals exist, and relations between universals exist. This seems transcendent, but doesn't really entail true transcendent existence. We could explore this further.

I don't think science actually explains the laws themselves;

Agreed, and that's where metaphysics comes in. A lot of anti-physicalist analysis just counters the Humean tradition. The modern tradition (exemplified by Armstrong, Tooley, and Sosa) isn't subject to those problems.

So again, the platonist attitude is that such laws pertain to a different level or mode than the domain of phenomena; that being the 'formal realm', although that is not an expression that is in wide circulation. They don't exist - in a sense, they 'subsist' or underlie and inform the phenomenal domain, although the sense in which they are real is difficult to express in the current lexicon of philosophy.

The attitude you express seems consistent with physicalism. We kind of pretend "4" and equations exist, but they don't ACTUALLY exist apart from the states of affairs in which they are instantiated.

You seem to be reading meaning into the word "object" that I didn't intend. I was just referring to existents - anything that can be said to exist. An oxygen atom can be said to exist. An oxygen molecule (consisting of two bound oxygen atoms) can be said to exist. This does not entail "dual existence." It is mereological. — Relativist

My argument is that Armstrong's, as described by you, is an incoherent form of mereology. Instead of producing an acceptable explanation of the relations between part and whole, it provides a description which does nothing to resolve the contradiction involved with saying that a whole exists and its parts exist, simultaneously. To give existence to the individual parts requires dividing the whole, and this annihilates the unity which makes it a whole.

An oxygen molecule does not consist of two distinct oxygen atoms, because of the way that the atoms are bonded with electron sharing. The atoms within a molecule are not distinct, that's what a molecule is. So either there is two separate oxygen atoms, or there is an oxygen molecule, but there is not both at the same time. The description of an oxygen molecule is not the same as the description of two independent oxygen atoms, so the existence of an oxygen molecule is not the same as the existence of two oxygen atoms.

If we treat them as mental objects, produced by the way of abstraction, that's consistent with physicalism. When we start treating them as existing apart from minds, that's platonism. — Relativist

The way I express it is that the natural numbers (and the like) are the same for anyone who can count - hence, they exist apart from minds - but they can only be grasped by intelligence that is capable of counting. So they're real, but intelligible - hence, 'intelligible objects'. That is why Armstrong has to reject real abstractions - because if they're real, then his philosophy fails. I'm arguing they are real, and that it does fail, because it fails to account for them.

As Jacques Maritain explains:

What the empiricist speaks of and describes as sense-knowledge is not exactly sense-knowledge, but sense-knowledge plus unconsciously introduced intellective ingredients -- sense-knowledge in which he has made room for reason without recognizing it.

So much of modern thinking is like this. It doesn't even understand itself! It is what physicalism is doing - it draws on the relationships of ideas, which are not themselves physical, to even establish what is 'physical'! And then it says - tah dah! - physical. What we're actually doing is still incorporating the traditionalist understanding of the Platonic intelligible forms, without realising, and then denying, that this is what is happening.

That is why strictly physicalist philosophies of mind, like Dennett's, must deny that there actually is any mind. The very existence of mind defeats their philosophy. (Which is why Dennett's critics called his first book 'Consciousness Ignored'.)

I don't see the problem. — Relativist

Right!

We kind of pretend "4" and equations exist, but they don't ACTUALLY exist apart from the states of affairs in which they are instantiated. — Relativist

The laws of motion, Pythagoras' theorem, and so on, are discovered. They're not simply mental conventions or projections, they enable us to know things that we otherwise wouldn't be able to. And we can be wrong about them, or fail to understand them (as I mostly do.) In which case, we're failing to understand something real.

"To give existence to the individual parts requires dividing the whole, and this annihilates the unity which makes it a whole."
Incoherent. Existence isn't "given". Consideration of parts doesn't entail dividing it. The universe exists. Does that preclude YOU existing? The universe has parts, and you are one of them.

I see that you don't actually want to understand, so we're done.

The way I express it is that the natural numbers (and the like) are the same for anyone who can count - hence, they exist apart from minds  — Wayfarer

What exists apart from minds are the properties "1", "2", "3",... but that doesn't imply they exist detached from the states of affairs that have these properties. 7 marbles exist, 7 forks exist, and we can abstract out the property "7" from each of these states of affairs. There's a logical relation between the abstracted properties of "7" and "4", but that doesn't entail the existence of numbers except as mental entities.

3+4=7 because any state of affairs with property "3" when combined with a state of affairs with property "4" will necessarily result in a state of affairs with property "7". This fact does not depend on 3, 4, and 7 existing independent of states of affairs. It just means properties can have relations to other properties, and these relations obtain irrespective of which states of affairs they are instantiated in.

That is why strictly physicalist philosophies of mind, like Dennett's, must deny that there actually is any mind. The very existence of mind defeats their philosophy. 

Physicalist theory of mind needn't deny the existence of mind. Certainly Armstrong didn't, nor do Jaegwon Kim and Michael Tye.

Reason is easy to reconcile with physicalism: computers can be programmed to reason. Physicalist theory of mind is not without problem (in particular: consciousness) but every theory of mind has problems.

The principle of parsimony applies to ontology: we should assume no more types of existent than necessary to account for that which we intuitively know exists, and which we infer exists. Alleged platonic entities are explainable as constituents of states of affairs, so there's no good reason to claim they actually exist independent of the states of affairs in which they are instantiated. We shouldn't be fooled by our intellectual powers of abstraction.

7 marbles exist, 7 forks exist, and we can abstract out the property "7" from each of these states of affairs. — Relativist

Which abstraction will be true in all possible worlds. Impressive, eh?

There's a logical relation between the abstracted properties of "7" and "4", but that doesn't entail the existence of numbers except as mental entities. — Relativist

I've just be re-reading Manjit Kumar's book Quantum, which I mentioned above, and I noted that when Bohr came up with the equation which describes the orbits of electrons, one of the factors is always an integer. Mathematical qualities seem deeply implicated in the structures of physics.

The constituents of pure mathematics have nothing to do with 'states of affairs', but by extrapolating on the basis of mathematics, physicists have been able to predict 'states of affairs' which otherwise could never have been known (such as Dirac's discovery of anti-matter which literally 'fell out of the equations').

And were you not able to count or to reason, then you wouldn't know if there were 7 or 4 of anything, nor that these were represented in any 'state of affairs'. Again, you're using, or rather, looking through the very faculty which you're purporting to explain, to create the explanation!

Physicalist theory of mind needn't deny the existence of mind. — Relativist

But they all say that the mind can only be understood in terms of neurobiology, which amounts to almost the same. Sure the 'eliminativists' are more apparently radical, but all materialism must deny the primacy of mind - that's what makes them materialist, after all!

computers can be programmed to reason. — Relativist

Computers are instruments of the human mind. They can indeed be programmed to emulate the processes of logic - that is fundamental to computation, after all - but they're artifacts.

Incoherent. Existence isn't "given". — Relativist

"Esixtence" is a word. It is assigned to things, we say that they exist. Therefore existence is given. Whenever we say that this or that exists, we give existence to that thing. My whole argument has been concerning the way we apprehend things. To say that existence is not given is what is incoherent.

We apprehend "2" as signifying one object, the number two, or we apprehend it as signifying two objects, but both at the same time is contradictory. We apprehend one family of swans as an object, or we apprehend seven individual swans as objects, but both at the same time is contradictory. To say that both, the one unity, and the multitude of individual parts, "exists" at the same time would require different definitions of "exists". Therefore the contradiction can only be avoided through equivocation.

Consideration of parts doesn't entail dividing it. — Relativist

Right, now you're starting to catch on. To consider a part as a part is to recognize the necessity of the whole. To consider the part as an independently existing object is to deny the whole of which the part is a part of, such that the part is not actually a part in this consideration. To call it a "part" is contradictory.
Therefore a part cannot be considered to be an independently existing object, It is dependent on the whole for its existence. It is given existence from the whole.

But they all say that the mind can only be understood in terms of neurobiology, which amounts to almost the same. Sure the 'eliminativists' are more apparently radical, but all materialism must deny the primacy of mind - that's what makes them materialist, after all! — Wayfarer

It would be overstatement to say the mind can only be understood in terms of X, for x=physicalism OR dualism (OR any other theory of mind). Some aspects of mind are easier to account for under physicalism, others are easier to account for under dualism. Being easier to account for doesn't make it true.

computers can be programmed to reason. — Relativist


Computers are instruments of the human mind. They can indeed be programmed to emulate the processes of logic - that is fundamental to computation, after all - but they're artifacts. — Wayfarer

Are you arguing intelligent design? My point is that the mental process can be accounted for under physicalism. The evolutionary development of a mind is another matter, but I don't see why that would be a problem. Traits that have a survival value are consistent with natural selection.

You seem to be defending your metaphysical perspective. I was not challenging the (assumed) fact that it is coherent. I was challenging the notion that it's the only metaphysical framework that is coherent and presumably complete. I tried to do that by describing Armstrong's framework, and you simply rejected it based on your own ontological commitments. Believe whatever ontology you like, but if you are convinced your's is the only coherent one, or even that it's the best, then you're fooling yourself if you haven't seriously explored alternatives.

Are you arguing intelligent design? My point is that the mental process can be accounted for under physicalism. The evolutionary development of a mind is another matter, but I don't see why that would be a problem. Traits that have a survival value are consistent with natural selection. — Relativist

I'm not arguing for intelligent design if it amounts to any form of biblical literalism.

I am saying that the logic, mathematics, and the like, are of a different order to the physical and can't be derived from it. You can't get from knowledge of physics, to the underlying laws of logic or maths, and indeed you must already grasp logic and maths to some extent to even begin to understand physics. It is nowadays simply assumed that science provides, or will provide, an in-principle grasp of the nature of logic, reason and number, but I dispute that.

Describing rational thought in terms of survival value is the essence of 'biological reductionism'. Essentially what it says is that those very faculties which enable sapience - the distinguishing characteristic of the human - are on a continuum with claws or tentacles. But then on the other hand, whilst reducing every human trait to 'what works', it also removes any sense of there being a purpose for survival, other than propagation of the genome. It's sisyphean. So no, I'm not allied to intelligent design, but I'm equally dubious about the reigning neo-darwinian orthodoxy. Evolutionary biology is a biological theory, not a philosophy as such, but in our day it's a distinction that has been lost. (See It ain't Necessarily So, Antony Gottlieb.)

"You can't get from knowledge of physics, to the underlying laws of logic or maths, and indeed you must already grasp logic and maths to some extent to even begin to understand physics."
That's epistemology, and we can account for the epistemology with either ontology, and platonism entails reifying epistemological concepts.

"whilst reducing every human trait to 'what works', it also removes any sense of there being a purpose for survival, other than propagation of the genome"
It has the explanatory scope needed. Your rejection seems based on affirming the consequent. The facts are consistent with, but do not entail, a teleological goal.

platonism entails reifying epistemological concepts. — Relativist

But it doesn’t. That is what I’m trying (and obviously failing) to explain. The point I am trying to make is that number is real in a different way to objects of experience. But in modern philosophy, there are no ‘modes of existence’ - things are either said to exist or not. What I’m arguing - what mathematical platonism generally argues - is that number is real, but not phenomenal:

Gödel was a mathematical realist, a Platonist. He believed that what makes mathematics true is that it's descriptive—not of empirical reality, of course, but of an abstract reality. Mathematical intuition is something analogous to a kind of sense perception. In his essay "What Is Cantor's Continuum Hypothesis?", Gödel wrote that we're not seeing things that just happen to be true, we're seeing things that must be true. The world of abstract entities is a necessary world—that's why we can deduce our descriptions of it through pure reason.

Rebecca Goldstein, Godel and the Nature of Mathematical Truth.

What I’s saying is that because our culture has become so completely oriented to the objective domain, we’ve lost the ability to understand that dimension of reality. This is something that happened over the course of history, and now the way we think is a consequence of ‘history being wiitten by the victors’.

As for evolutionary biology and philosophy, this has been debated up hill and down dale on this an many other forums. Suffice to say that I have come to doubt the explanatory efficacy of biological evolution to account for those human traits which transcend biology - which, interestingly, is just the kind of argument that Alfred Russel Wallace used in his essay, Darwinism Applied to Man, when he announced his divergences from Darwin on this very point.

I tried to do that by describing Armstrong's framework, and you simply rejected it based on your own ontological commitments. — Relativist

Don't you remember? I rejected Armstrong's framework because it is contradictory. It allows that a single thing is also a plurality of things. That's contradictory, a thing is one and many at the same time. You may refer to this as an "ontological commitment" if you like, but don't you think that philosophers in general ought to adhere to the law of non-contradiction as an ontological commitment, if adhering to the law of non-contradiction is actually an ontological commitment? In any case, are suggesting that we ought to let the law of non-contradiction be violated?

Here's the quote again:

A state of affairs (a "thing") is not necessarily one thing... — Relativist

It is impossible that, a single thing, an entity, can be a multiplicity of things, or entities, by reason of contradiction. If we allow that the identified thing is a multiplicity of things, then the law of identity becomes useless and logic is futile. Therefore, as an ontological principle, we need to allow for an existential difference between a whole and its parts, to avoid this contradiction.