A whole may never be greater than the sum of its parts

This item concerns the belief/assertion -- widespread and erroneous -- that "A whole may be greater than the sum of its parts;" that is, it concerns the notion(s) of 'emergence' and/or 'supervenience.' The context specifically concerns the assertion that 'consciousness' and 'self-conscioisness' (and ultimately 'mind' itself) is an emergent 'property' (or 'substance') of brains.


I wish it to be clear that I scoff at the very notion and assertion that 'consciousness' (and 'mind' itself) is an emergent 'property' (or 'substance') of brains. I scoff at the very concept of 'emergence.' And I double up in laughter, metaphorically at any rate, when proponents of 'emergence' take umbrage at my scoffing and dust off their dignity (and education!) as the refutation of that scoffing. How dare I, a mere no one with no MA, much less a PhD, scoff at the risible notions that highly-educated philosophers take seriously! Is it not, Gentle Reader, just too much to be endured?


This will be, I hope, a continuation of an aborted discussion from William Vallicella's "Maverick Philosopher" blog. So, I need to supply the discussion to this point.


In his OP, William Vallicella said this:

We [Mr Vallicella and his friend, Peter Lupu] agreed that consciousness exists, that it cannot be intelligibly viewed as an illusion. We also agreed that it cannot be reduced to the physical. Thus we agreed that it can neither be eliminated nor identified with the physical. We also seemed to agree that identifications collapse into eliminations. And of course we also agreed that consciousness as we normally experience it is tied to a physical substratum. Our main disagreement concerned the nature of the tie. Peter thinks of consciousness as necessarily tied to its physical substratum so that a particular synchronic and diachronic unity of consciousness cannot exist apart from a living brain/body. If I understood Peter, his view is that consciousness and self-consciousness are emergent from matter but not reducible to it. So his position could be called nonreductive physicalism. The most interesting way to develop this would be in terms of the view that consciousness is not an emergent property but an emergent substance. Thus a person's consciousness would be a genuine individual unity with irreducible causal powers, but one which somehow emerges from its material base while remaining necessarily tied to it for its continuing existence. By contrast, I take seriously the possibility of a particular unity of consciousness existing apart from a material substratum. This possibility could be cashed out it dualist terms or in idealist terms. Either way, the necessary ontological dependence of mind on matter is denied.

Deogolwulf said this:

For what it is worth, I second Mr Bortignon’s recommendation of J.R. Lucas, who is an excellent but much-neglected philosopher. Deriving from Lucas and ultimately Gödel, a sketch of an argument ad absurdum against mechanism or computationalism can be given as follows:

I.The human mind is fallible and contains inconsistencies.
II.The human mind is a formal system like that of a machine.
Therefore,
III.The human mind is an inconsistent formal system.
IV.An inconsistent formal system is thoroughly inconsistent, that is to say, any proposition that can be stated in that system can be proven using its rules.
Therefore,
V.The human mind is thoroughly inconsistent, that is to say, any proposition that can be stated by it can be proven using its rules.
Therefore,
VI.The human mind can prove itself to be a consistent formal system.
And,
VII.Propositions (I)-(VI), and propositions in contradiction to them, can be proven by the human mind.
And,
VIII. The contradiction of (VII) can be proven thereby.
And,
IX. The contradiction of (VIII) can be proven thereby.
Ad infinitum.
Therefore,
X. The human mind, being thoroughly inconsistent, cannot recognise its own mistakes or recognise the truth of anything.

Since every reasonable man rejects (X) but accepts (I) and (IV), given an understanding of the world of humanity along with the validity of Gödel’s theorem, he must reject (II), given that the reasoning is valid.

[Deogolwulf's blog is here, by the way]
Now, Deogolwulf's comment isn't directly tied in to the subject of this post; but, it does supply some important context, and it's a very good argument in its own right. I wish my readers (all one of you) to not miss it.

Perhaps I should take a moment to point out that I'd have expressed premise #1 as "I.The human mind is fallible and [generates] inconsistencies." Though, at the same time, in the context of asserting premise #2 (and intermediate conclusion #3), Deogolwulf's wording and mine are identical in meaning.


Peter Lupu replied:

Deogolwulf,
Your proof assumes classical logic in which the consequence relation is *explosive*: i.e., from P and ~P any proposition Q (expressible within the formal system) follows. This feature of classical logic (and intuitionistic logic as well) seems to be counterintuitive because there may be systems that while contain a contradiction are, nonetheless, not trivial (i.e., everything follows within such a system). Paraconsistent logics are designed to formulate a consequence relation that is not explosive, thus allow for a system to contain a contradiction without rendering it trivial.

I think that the specific formulation of the view that consciousness does not exists in terms of illusion is vulnerable to the argument Bill outlined in his previous post. The concept of illusion presupposes consciousness; therefore, to say that consciousness is an illusion presupposes that consciousness exists and, hence, such an argument presupposes that which it explicitly denies. I think somewhat more complicated arguments along these lines may be proposed against other versions of the nada-consciousness view.

I said this:

Do not all assertions of 'emergence' or 'supervenience' depend upon and simply restate the assertion that "The whole may be greater than the sum of the parts?"

And, is not that assertion exactly to assert that "1 + 1 may = 4 (or some other non-2 sum) in some circumstances?"


A whole may never be greater that the sum of its parts. When we mistakenly believe that we have identified a whole greater than the sum of its parts, it will always be the case that we have missed something or misidentified something.

Peter Lupu replied:

Ilion,
While some conflate emergence and supervenience, I would rather find a way of distinguishing them, although that feat may not be easy.

I do not think that "the whole is greater than the parts" issue captures the issue of the emergence of consciousness. I am unsure what you mean by saying that the view that consciousness is emergent is analogous to that 1+1 may sometimes not equal 2? While the later is provably contradictory, I have not yet seen a similar proof that the former also leads to a contradiction.

Consciousness, the way I view it, emerges as a property or, going along with Bill's suggestion, as a substance under certain conditions which involve among other things a specific biological mechanism. Once it emerges, however, it features characteristics that are not reducible to the underlying physical conditions which gave rise to it. I think that emergence might be required in order to explain other phenomena as well.

Why do I hold (hope) that the emergence route is the most promising? Well, what are the alternatives? I reject reductive or eliminative materialism for some of the reasons Bill already articulated. I cannot see how Cartesian dualism solves the interaction problem. The interaction problem for me is much deeper and pervasive than merely to account for cases such as for instance how a conscious desire makes my arm go up. Actions, complicated activities (to be distinguished from mere isolated actions), long term planned and deliberately executed chunks of activities, behavior, and even routine and repeated behavior, among others, appear to be produced by antecedent causes that seamlessly integrate and combine conscious and as well as physical elements. We need an account of consciousness that can work seamlessly with underlying physical component, yet no be completely reducible to it. Emergence, I believe, is the only option that holds the promise to deliver this result.

I replied:

Peter Lupu: "I do not think that "the whole is greater than the parts" issue captures the issue of the emergence of consciousness."

But of course it does, no matter what one is asserting 'emerges.'

"Emergentists" claim that "as feature or property 'X' does not exist in any constituent part of this whole under consideration, yet does exist in the whole, it is the case that 'X' "emerges" from the whole." How is this not just a long-winded way of asserting that "the whole is greater than the sum of its parts," and perhaps of disguising just what one is asserting?

Consider one of the premier exemplars of 'emergence:' the wetness of water. No individual water molecule is wet, yet, supposedly, out of a mass of them "wetness" emerges. But the truth is that "wetness" is not a property of water, whether of individual molecules or en masse: "wetness" is a human perception of water in quantity (I suppose that the correct term is 'qualia').


Peter Lupu: "I am unsure what you mean by saying that the view that consciousness is emergent is analogous to that 1+1 may sometimes not equal 2? While the later is provably contradictory, I have not yet seen a similar proof that the former also leads to a contradiction."

I mean precisely that "a whole" cannot ever be "greater than the sum of its parts." I mean that the belief/assertion that "A whole may be greater than the sum of its parts" expresses a logical impossiblity, and is thus always a false assertion. I mean that everytime a person imagines he has identified "a whole" which is "greater than the sum of its parts," it is the case that he has overlooked something or misidentified something.

In short, I mean that the concept of "emergence" is nothing but irrational woo-woo; it's Magick (the spelling is to distinguish such a manner of thinking from the 'magic' of fairy-tales and fantasy novels). It is, amusingly, an example of the sort of thinking in which some 'atheists' like to accuse that Christians necessarily engage.


Peter Lupu: "... analogous to that 1+1 may sometimes not equal 2? While the later is provably contradictory, ..."

Does not that proof depend upon the very thing you appear to be disparaging in your response to Deolgolwulf -- classical logic and intuition? (I wonder, does "This feature of classical logic (and intuitionistic logic as well) seems to be counterintuitive because ..." strike you as a bit odd?)


Peter Lupu: "While the later is provably contradictory, I have not yet seen a similar proof that the former also leads to a contradiction."

Should we believe to be true anything which has not been proven false? (And who is setting the criterion of 'proof?' What makes that fellow over there the authority over what I, or you, should believe?)

Where have we ever seen a whole which is greater than the sum of its parts? Many people believe this and assert this, but where have we ever seen such a thing?

=========
Does not all our (individually and collectively) knowledge rest upon that which we know intuitionally, which is to say, non-rationally -- which is to say, that which we know to be true *simply* because we know it to be true? Yes, it does.

Now, of course, one realizes that we may be mistaken about some belief being known intuitionally. Nevertheless -- since intuitional knowledge is the basis of *all* our knowledge -- the burden of proof lies with the one who seeks to deny an intuition.

That "the whole may not be greater than the sum of its parts" *appears* to be self-evidently true (i.e. it appears to be something we know intuitionally). That is what "emergentists" are up against; until they show that this is not really true then no rational man should take 'emergence' seriously.

Peter Lupu replied:

Ilion,
1) You maintain the following two theses:

(a) The emergence-thesis is identical to the thesis that “the whole is greater than its parts”;
(b) The thesis that the whole is greater than its parts is logically impossible, always false, etc:

“I mean precisely that "a whole" cannot ever be "greater than the sum of its parts." I mean that the belief/assertion that "A whole may be greater than the sum of its parts" expresses a logical impossiblity, and is thus always a false assertion. I mean that everytime a person imagines he has identified "a whole" which is "greater than the sum of its parts," it is the case that he has overlooked something or misidentified something.”

Therefore,
(c) The emergence-thesis is “logically impossible”, “always false”, and every time a person entertains the emergence thesis, they “overlooked something or misidentified something.”

2) I do not know what you mean by “greater” in the thesis “the whole is greater than its parts”. So perhaps you will be kind enough to explicate the meaning of this term in the whole/part thesis. It seems to me that there are obvious examples where a whole can be coherently, legitimately, and by necessity be said to be greater (in a reasonable interpretation of this relationship) than the parts. e.g.,
(i) Consider my house. Suppose I dismantle my house brick by brick, 2 x 4 by 2 x 4, every nail, screw, etc., and place all of these parts in one big pile exactly where my house used to be. Now, surely my house has properties that the pile does not: e.g., while the house protects me from rain, sun, wind and so forth, the pile does nothing of the sort. So there is a clear sense in which my house is greater than merely the totality of its parts.

(ii) Consider objects a, b, c, d. Suppose S is a set such that S = {a, b, c, d}. Now, S has properties that none of its members has: e.g., while S has the property of having object a as a member, none of the objects a, b, c, d, has this property. Moreover, suppose S is an ordered set S = . Then S has the property of having object a as its first member. But neither any of its members has the property of having object a as the first member nor does the mere collection of these objects.

(iii) Consider any population: e.g., the population of US citizens. The mean income of this population is say $X. None of the elements of this population has the property of having the mean income of $X. In fact, it is quite possible that no US citizen earns $X. So the whole has a property that none of its members has.

(iv) A painting can be beautiful, but its parts may not be. In fact it could be that only this particular configuration of parts yields the beauty this painting has. So none of the parts nor a pile of the parts has the property of being beautiful.
Etc.,

3) Therefore, unless you explain in what sense you deny the logical possibility that the whole is greater than its parts, your thesis (b) is trivially false. As for thesis (a), we cannot evaluate it unless we know more what is meant by thesis (a).

4) As for the wetness example. If wetness is not a property of any molecule of water or a mass of water but rather it is, in your words “… a human perception of water in quantity (I suppose that the correct term is 'qualia')” then it is not an example of emergence or of the whole/parts case and we need not worry about it.

5) You say: “In short, I mean that the concept of "emergence" is nothing but irrational woo-woo; it's Magick (the spelling is to distinguish such a manner of thinking from the 'magic' of fairy-tales and fantasy novels). It is, amusingly, an example of the sort of thinking in which some 'atheists' like to accuse that Christians necessarily engage.”

I understand that you hold the view that emergence is nothing but “woo-woo” “Magick” etc., very intensely and with a firm conviction. But, could you be kind enough and *prove* these claims or *demonstrate them by some arguments* rather than just announce them so that all of us including myself can benefit from the certainty you seem to have regarding these views?

6) Regarding the venerable matter of 1 + 1 = 2?
“Does not that proof depend upon the very thing you appear to be disparaging in your response to Deolgolwulf -- classical logic and intuition? (I wonder, does "This feature of classical logic (and intuitionistic logic as well) seems to be counterintuitive because ..." strike you as a bit odd?)”
I am having trouble understanding what you are trying to say here, so let me simply clarify my previous comments on the subject. One of Deolgolwulf’s premises is this:
IV.An inconsistent formal system is thoroughly inconsistent, that is to say, any proposition that can be stated in that system can be proven using its rules.
The idea that an inconsistent formal system; i.e., one in which (P & ~P) is provable, entails every proposition Q (no matter what Q is) depends upon a certain interpretation of the consequence relation; namely, that it is explosive. Now, I do not “disparage” classical, intuitionistic logics nor even the consequence relation being explosive. I merely point out an obvious fact, one which no one so far as I know denies: the fact that an inconsistent system (in the above sense) entails every proposition whatsoever and therefore becomes trivially useless is simply counterintuitive. This fact that I have just stated has absolutely nothing to do with the proof of the proposition that 1 +1 = 2 in classical or intuitionistic or any logic nor does such a proof depend upon a consequence relation being explosive or not being explosive. If mathematics is consistent, then the proof of this proposition is simple and requires very few premises. So going back to Deolgolwulf’s premise (IV) one could legitimately deny this premise on the grounds that it presupposes an explosive consequence relation that is counterintuitive but essential to his argument. That is all I have said. On the other hand, I have no clue what you were trying to say.

7) You say:
(i) “Should we believe to be true anything which has not been proven false? (And who is setting the criterion of 'proof?' What makes that fellow over there the authority over what I, or you, should believe?)”
and also
(ii) “That "the whole may not be greater than the sum of its parts" *appears* to be self-evidently true (i.e. it appears to be something we know intuitionally). That is what "emergentists" are up against; until they show that this is not really true then no rational man should take 'emergence' seriously.”
So in (i) you appear to be saying that proof should not be a necessary condition of belief (and also that we lack agreement as to which proofs are to be accepted) and in (ii) you are saying that (and I paraphrase) until the proponents of emergentism prove that it is not identical to the whole/parts thesis or that if it is, the later is coherent, “no rational man should take 'emergence' seriously.”i.e., proof is a necessary condition of belief. Which one you hold?

As perhaps explained elsewhere, my participation ended after that.

Edward said this in response to the above:

The nature of a house, at least from a materialist perspective) is purely material. How, then, can it not be reducible to its material parts? Let's say that we did take apart a house piece by piece and throw the pieces into a pile. We then call the collection of pieces a 'garbage pile.' Is the garbage pile greater than the sum of its parts, meaning every individual piece of the house? Since I am not a materialist, I would say that a house cannot be reduced to its material cause because a house also has a formal, efficient, and final cause as well. From the materialist perspective, though, it seems as if a house must always be merely the collection of the parts of a house, just arranged in a way that conforms to the definition of 'house.' This does not entail anything qualitatively different from the collection of the individual parts of the house, though. As long as you reject any immaterial cause, all of the properties that distinguish a house from a pile of house-parts must always be material, so matter + matter = matter. How can you ever get something that is essentially non-material from the material?

Joseph A responded and added:

Edward,
It's an emergent property, of course!

More seriously, I think I understand what you're saying. I suppose one reply would be that those distinctions you mentioned are at best useful fictions. On the other hand, how useful does a fiction have to be before you start considering that it might be real?

Peter Lupu replied:

Edward,
I wish to remind you that the question was whether the whole is *greater* than or is it identical to the *sum* of its parts. The example of the house parts then seems to be a counterexample to the *sum* claim. So is the example of a set, and ordered set, and so on.

Now, if someone wishes to change the thesis in some way and claim that the whole is identical to the parts relative to some other property, not merely with respect to a sum, then we can evaluate the new proposition accordingly. I have simply argued that a house has properties that a pile of its parts does not. Therefore, the house cannot be identical to or be merely the collection or sum of the parts. I don't think that there can be a dispute about this. Whether the properties which the house has and the house-pile lacks are themselves physical or are reducible to such and so forth was not part of my argument. That is a separate question that I did not address in discussing the whole/part issue.

You ask whether a garbage-pile is greater than the sum of its parts. I don't know: perhaps it is, perhaps it is not. But, either way it would not have a bearing upon my example. Why? Because I was giving the house example as a counterexample against the following general thesis:
(T) All wholes are identical to the sum of their parts.

In order to refute (T) all I need is one case in which a whole is not identical to the sum of its parts. I have proposed such an example. Whether the garbage-pile does or does not constitute another counterexample has no bearing upon whether the example I did give is a counterexample.

Edward replied:

Is there a difference between the whole being reducible to its parts and the whole being identical to its parts? I think there is, and that is what I was addressing in the above example.

In no way at all whatsoever being 'confused' or 'dogmatic' or 'anti-Socratic' or 'unreasonable' or behaving in an 'absurd[ly] superior' manner as, well, I am and do, William Vallicella "settled" the matter:

Edward,
If a house is reducible to the mereological sum of its parts, then the house is identical to the sum. But surely this is false: the house has properties that the sum does not have. For example, the house provides shelter, the sum does not. It's as simple as that. A house is a physical thing composed of physical things but it is not reducible to the latter. So there is a clear sense in which it is an emergent entity. That in a nutshell is Peter's point against the silly assertion that a whole is never greater than the sum of its parts.

There is nothing to debate here. It is just a matter of seeing a fairly obvious point. Whether mind is emergent from its material substratum is of course eminently debatable!

Isn't it so good to know, and such a relief, that we peons can just take the word of our betters?



Please note, Gentle Reader, that I have not (yet) written a response to Mr Lupu's last posting. I also want to try to work into this some of the comments made others. Of course, now -- even aside from the task of encompassing all the above in my comments -- I have to decide whether to further extend this already lengthy OP or to make my comments and critiques of the above in the combox.