Reduction, Elimination, and Material Composition

Yesterday I wrote,  "And yet if particular a reduces to particular b, then a is nothing other than b, and is therefore identical to b." This was part of an argument that reduction collapses into elimination.  A reader objects: "I am not sure that this is an accurate definition of reduction." 

He gives an argument having to do with material composition.  I'll put the argument in my own way, so as to strengthen it and make it even more of a challenge for me.

1. Whether or not minds are physically reducible, physical reductionism is surely true of some things, statues for example.  A statue is reducible to the matter that composes it, a hunk of bronze, say.  No one is a statue-hunk dualist.  It is not as if there are two things in the same place, the statue and the hunk of bronze.  Nor is anyone an eliminativist when it comes to statues.There are such things, but what they are is just hunks of matter. We avoid both dualism and eliminativism by adopting reductionism.

2. But surely the matter of the statue might have been configured or worked in some other way to make a different statue or a non-statue.  Before the sculptor went to work on it, the hunk of bronze was just a hunk, and after it became a statue it could have reverted  back to being a mere hunk if it were melted down.

Therefore

3. The statue and the hunk differ property-wise:  the hunk, but not the statue, has the property of existing at times at which the statue does not exist.  And at every time at which both hunk and statue exist, the hunk, but not the statue, has the modal property of being possibly such as to be a non-statue. 

Therefore

4. By the indiscernibility of Identicals, statue and hunk are not identical.

Therefore

5. The statue is reducible to its constituent matter but not identical to it. (By 1, 4)

Therefore

6.  It is not the case that if particular a reduces to particular b, then a is identical to b.

This is an impressive argument, but I don't see that it shows that one can have reduction without identity of the reduced to the reducer.  I take the argument as further evidence of the incoherence of the notion of the reduction of one particular to another.  The first premise, though plausible, is not obviously true. What's more, it seems inconsistent with the second premise.  I have argued many times before that in cases like these, statue and lump, fist and hand, brick house and bricks, the thing and its matter differ property-wise and so cannot be identical.  They are both temporally and modally discernible.  If fist and hand cannot be numerically identical, then they must be numerically distinct.  When I take my hand and make a fist of it, the hand does not cease to exist, but something new comes into existence, a fist.  Hand and fist, as long as both exist, are two numerically different things occupying exactly the same spatiotemporal position.  Admittedly, that sounds strange.  Nevertheless, I claim here is just as much reason to be a hand-fist dualist as there is to be a fist-to-hand reductionist.

One could also be an eliminativist.  Amazingly, Peter van Inwagen -- no slouch of a philosopher; you don't get a chair if you slouch -- is an eliminativist about artifacts such as the house built by the Wise Pig.  See here. 

Perhaps I can drive the reductionist onto the horns of a dilemma.  Either fist and hand are identical or they are not.  They cannot  be identical because they differ property-wise.  If two things are not numerically identical, however, then they are numerically different.  But if fist and hand are numerically different, then the fist does not reduce to the hand.

So I persist in my view that reduction is an incoherent notion.  There is no viable via media between dualism and eliminativism.  

Comments

[David Brightly]

Bill, let me see if I have understood you. You are saying

(a) If we accept your reader's argument then we conclude that some particular (the statue, the fist) can be reduced to a non-identical particular (the lump, the hand). But this is incoherent.

(b) To rescue reductionism we must reject the argument and you do so by denying premise 1. This leads to a dualism of statue/hunk and fist/hand where two numerically distinct things occupy the one spatio-temporal location.

(c) Options (a) and (b) are equally reasonable/unreasonable.

I, as you will have guessed, reject (3). Now, we have been here before several times I know, but please bear with me. I think the crux of this is reference. Let me take the second part of (3) first. Let's imagine the hunk/statue before us on a table. If we are to accept (3.2) then we must accept the following sentence:

This (pointing with the right hand to the statue) does not have the modal property of being possibly such as to be a non-statue.

I think this is plainly false.

Turning to (3.1), If we are to accept (3.1) we must accept the following:

This (pointing with the right hand to the hunk) has the property of existing at times at which that (pointing with the left hand to the statue) does not exist.

I think this is plainly contradictory. Upshot: The statue and the hunk are indiscernible and identical.

Where do I think we are inclined to go wrong in all this? I suspect our mistake is to associate a type with the referring terms ('the hunk', 'the statue') rather than with the individual referred to. This mistake is easily made when the referring terms involve common nouns. The mistake is less easily made if we use proper names as referring terms, but since we tend to associate proper names with descriptions, and in this case the descriptions will involve common nouns, the mistake can still occur. I hope I've shown that if we use demonstratives the chance of making the mistake is nil.

[Bill Vallicella]

David,

One problem concerns what Quine calls the inscrutability of reference. If I point in the direction of the statue it is not clear whether I am pointing at the statue or at its matter, the hunk of bronze. To have a definite reference I must bring in a noun such as 'hunk' or 'statue.'

You seem to think that your use of 'this' somehow harpoons a bare particular x which is at the core of both hunk and statue. You seem to think that when the hunk became a statue, the x took on statue properties in addition to its hunk properties. So there is exactly one thing x which goes from being a non-statue to a statue to a non-statue.

Is this how you are thinking?

[Leo Carton Mollica]

Mr. Brightly:

"Turning to (3.1), If we are to accept (3.1) we must accept the following:

[3.1'] This (pointing with the right hand to the hunk) has the property of existing at times at which that (pointing with the left hand to the statue) does not exist.

I think this is plainly contradictory. Upshot: The statue and the hunk are indiscernible and identical."

But isn't this more plausibly taken as a deficency in our pragmatic abilities than a feature of our semantics? We cannot, only using demonstrative pronouns a gesture of our index finger, practically distinguish between co-occupants of space for the simple reasons that a.) demonstrative pronouns (as opposed to demonstrative adjectives or determiners) cannot express distinctions between sortals and b.) all an index finger can point to is some one region of space. The demonstrative point is merely linguistic, and the digital point is to do only with the limitations of physical gesturing, so neither would seem to have any profound semantic ramifications.

A point in favour of my view might be that we can easily make (3.1') intelligible by replacing the demonstrative pronouns with demonstrative adjectives or determiners:

3.1'' This hunk (pointing with the right hand to the hunk) existed prior to that statue (pointing with the left hand to the statue) existing.

Am I making sense?

[David Brightly]

Hi Bill,

I think that pointing picks out, by default, untyped individuals, which I think of as maximally connected (in the topological sense) aggregations of matter that can be sensed by eye or touch. To pick out a proper part of an individual I need a noun phrase such as 'head' or 'left foot'. To refer to the material of a whole or part I need a further qualifier such as 'the bronze of' 'the stuff of', though sometimes this can be inferred from what's predicated of 'this', as in 'This was mined in Etruria', for example. Your second paragraph captures my thinking exactly.

[Bill Vallicella]

David,

Since I am a little weak on topology, please supply a definition of 'maximally connected.'

>>I think that pointing picks out, by default, untyped individuals, which I think of as maximally connected (in the topological sense) aggregations of matter that can be sensed by eye or touch.<<

By an untyped individual you presumably mean an individual taken in abstraction from its properties and relations, the individual as the support or substratum of those properrties and relations. I don't see how pointing could pick out an untyped individual. I see a white coffee cup and I point in its direction. The pointing doesn't uniquely pick out anything, as it seems to me. I could be pointing at the cup, or the spatial position the cup occupies, or the surface of the cup, or its color, or its contents (coffee), or . . . . Furthermore, whatever I am pointig at is a typed individual, is it not? I cannot literally see or touch an untyped individual or bare particular.

I believe what I am saying is consistent with and complements what Leo is saying above.

[David Brightly]

Hi Leo,

I think I understand what you are trying to convey, something like

Before it was moulded into a statue this piece of material was a shapeless lump,

but I'm afraid I can't make much sense of 'co-occupants of space'. As far as I can see, no two distinct macroscopic material objects can occupy the same space. And words like 'lump' and 'statue' refer to such objects.

[David Brightly]

Hello Bill,

Let's say a body of material is 'connected' if any two points in the material can be joined by a line running wholly in the body. Maximally connected then means that the body includes as much connected material as possible. So a solid ball is (maximally) connected, two solid balls are not connected, and one hemisphere of a solid ball is connected but not maximally connected. I think our visual and tactile senses can identify such maximally connected bodies without us knowing what they are, ie, being able to assign a type to them. Of course, they will be of some kind. Could you not pick up the coffee cup blindfold and sense that it is a maximally connected body without knowing what it is? I'm trying to home in on what we must mean by material individual or object.

[Leo Carton Mollica]

Mr. Brightly,

That doesn't quite capture my intended sense: the salient feature of (3.1'') is that it attributes different and inconsistent properties to the hunk and to the statue, which difference is not captured by your reformulation.

As for your second point, why can't two individuals occupy the same space? By my lights, we could only affirm that if we denied either a.) that a statue and the marble whereof it is composed occupy the same space, b.) that the hunk existed at a time when the statue did not exist, or c.) that the hunk and the statue are individuals. All seem like fairly heavy prices to pay for denying that two distinct individuals can occupy the same space.

I am also a bit confused as to what you mean by calling an "untyped individual" a "maximally connected body": isn't "maximally connected body" a type just like "statue", "tiger", or "bubble"? If I tell you about the "maximally connected body" I am handling, then surely I have already identified it as a certain sort of thing (viz. a (maximally connected) body), have I not? Or am I missing something?

[Charles]

Dr Vallicella's argument seems to rely on this assumption:

1. A reduces to B implies A is identical to B.

But isn't that assumption the same as the conclusion, i.e. that reductionism collapses into eliminativism? Surely it is begging the question to assume that reduction implies identity.

If reduction implies identity, then reductionism collapses into eliminativism (rather trivially, it seems to me). However, it remains to be shown that reduction really does imply identity.

If reduction does not imply identity, then Dr Vallicella's dilemma fails: if fist and hand are numerically different, then the fist might still reduce to the hand.

Clearly the onus is on the reductionist to articulate a definition of reduction that does not imply identity. It is possible that nobody has managed to do this (I don't know) but you cannot argue against them by just assuming that reduction implies identity, can you?

[Bill Vallicella]

Charles,

I am making the assumption (1), but I don't agree that that is the same as the conclusion.

What would the reduction of a to b be if that did not entail the identity of a and b? If a bolt of lighnting reduces to an atmospheric electrical discharge, then the former is identical to the latter.

If fist and hand are numerically different, then there are two different particulars, in which case one cannot speak of the fist reducing to the hand.

You need to tell us what you mean by 'reduction' and give some examples.

[David Brightly]

Hi Leo,

Can I ask what are the different and inconsistent properties in question? Do you mean that lump and statue have different 'birthdays', as it were?

Bill and yourself see lump/statue and hand/fist as distinct individuals whereas I see them as single individuals under distinct (but not inconsistent) concepts. Does that capture our difference?

a.) that a statue and the marble whereof it is composed occupy the same space. I agree. They are identical.

b.) that the hunk existed at a time when the statue did not exist. I think this is a misleading way of putting things. I prefer my way: Before it was moulded into a statue this piece of material was a shapeless lump.

c.) that the hunk and the statue are individuals. I agree. They are same individual.

Regarding 'maximally connected body' and 'untyped individual', I'm struggling to elucidate the concept at the root of the 'type hierarchy' which I think must be 'Individual', or 'Thing', or 'Object'. I'm not sure this can be done in words. It is something our senses deliver to us, I suspect, whereas you get there by analysis of properties and the application of principles like Indiscernibility of Identicals. Is that fair, do you think?

[Leo Carton Mollica]

Mr. Brightly,

The inconsistent properties would be having existed at t and not having existed at t. Other candidates include possibly existing without this statue existing and not possibly existing without this statue existing.

It would seem, then, that we disagree on (b): the proposition I am trying to express therewith cannot be formulated as "Before it was moulded into a statue this piece of material was a shapeless lump," for the proposition I am trying to express consists in affirming inconsistent predicates of two individuals.

I'm not sure that I understand your concluding paragraph. Given its second sentence, perhaps we ought to pass over it in silence? I seem not to share some basic insight or idea of yours, and I fear that might make discussing the matter well-nigh impossible.

[Charles]

Dr Vallicella wrote: You need to tell us what you mean by 'reduction' and give some examples.

Just to be clear, I personally do not mean anything much by 'reduction'. I am not sure what it is that other people mean by it. You seem to think that other people are expressing something incoherent when they talk about reduction. That might be true but I am attempting to give them the benefit of the doubt: precisely because if 'reduction' means what you say it means then it is an incoherent concept, I think that maybe other people mean something else by 'reduction'.

What would the reduction of a to b be if that did not entail the identity of a and b?

How about material composition? I think this is roughly what non-philosophers think of when they think of reductionism: I am reducible to my constituent atoms in the sense that I am made out of atoms and nothing else. That is not the same thing as my being identical to my atoms: I am a particular arrangement of atoms, an arrangement whose constituents may change as long as the overall pattern remains.

Or there is explanatory reductionism, the claim that I am fully explicable by reference to physical laws governing the matter out of which I am composed. Again, this does not entail strict identity.

Or how about existential dependence? I would not exist if the matter out of which I am composed did not exist. I am not the same thing as that matter but I am reducible to it in the sense that if it did not exist then neither would I.

I have encountered all of the above senses of 'reduction' before, although admittedly mostly in the writings of non-philosophers.