Paul Almond

Nature of Form

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We add one final claim to the list in the last post:

(8) Form is a network of relationships apt to make something one.

I will approach this in the manner of a disputed question, first raising a number of objections, then giving my explanation and replies to the objections.

Objection 1. According to this definition, form consists of many relations. But form makes a thing one. Thus form should not be in itself many, such as many relationships are, since many things are composed of units.

Objection 2. The definition begs the question by saying “apt to make something one.” Form is supposed to make things one, but if we want to say something about the nature of form, we should explain exactly how and why it does this.

Objection 3. A “network of relationships” might be some kind of form, but it seems to be an accidental form, not a substantial form, while the definition of form should be general enough to include both.

Objection 4. A thing can have the relations it has because of its particular nature. Therefore its nature cannot be defined by its relationships, since this would be circular. Thus form cannot be a network of relationships.

Objection 5. The definition is implicitly reductionist, and therefore opposed to thesis (4). For a composite thing, whether animal or artifact or anything else, will have many relations among its parts which define it, but it can be looked at and considered in many ways, while what appears to be most real must be its most basic parts, such as atoms or quarks or whatever.

Objection 6. Form seems to be unknown to us in a way in which the content of this definition is not, and therefore they must be somehow distinct. For example, whatever might be said about the definitions of blue proposed in the last post, it is clear that something is lacking there. There is something about the nature of blue that is quite unknown to us. So it seems unlikely that blue can be defined in the way proposed, and similarly unlikely that form can be defined as a network of relationships.

Objection 7. Christians, at least, must reject this definition, along with thesis (3), since the essence of God cannot be naturally known by human beings. Therefore God has a hidden essence, and since it is entirely simple, it cannot be a network of relationships.

Objection 8. This definition implies that the human soul is like a harmony, with all the consequences suggested by Simmias in the Phaedo, namely that the soul is mortal. So again Christians, at least, must reject this definition.

Objection 9. Composite things are made of both form and matter, so a relationship to matter should be included in the definition of form.

Objection 10. The network of relationships seems to be a construct of the mind more than a real thing. So one should reject this definition together with rejecting thesis (4), since what a thing really is, is something more basic that causes these relationships.

Objection 11. The definition might be true of material things, but if there are any immaterial things, it will not apply to them. Instead, they might well exist in themselves, without relation to other things, or at least not being defined by such relations. Likewise thesis (3) should probably be denied in relation to such things.

But let us go on to the explanation of this definition. If we consider the question, “what is form?”, one might immediately see a problem. Form is supposed to provide us the answer to the question about what a thing is, so if we ask what form is, we would seem to need a form of form. And even if this is possible, it is a process that cannot possibly go on forever, and therefore we will reach a point where we cannot find a form of form, and therefore we will not be able to answer the question. This is a complex issue which I will set aside for now, simply remarking for now that the question “what is this” needs to be answered in different ways for different things, including for form itself.

At the same time, however, the arguments of the previous post imply that form is accessible to us, and that we can know it both specifically and in general. Essences are not hidden from us, and it is form that both gives a thing the essence it has and that makes us understand. And since it is the very thing that is present in our mind when we understand the thing, it should be just as accessible to us as the contents of our own mind. In other words, we can say what a form is by answering the question, “What does my mind have in common with this thing when I understand it?” And thus we can answer the general question about form by noticing what our minds have in common with things they understand in general.

This answer is implicit in the discussion of thesis (7) in the last post. We noted in the case of “blue” that what both the senses and the mind have in common with things is a certain relation or network of relationships, namely those that correspond to the relations possessed by things apt to be seen by the sight as blue. And this will always be the case whenever we understand anything, since our understanding will always produce a sort of “model” of the thing understood. This is necessary since the understanding does not become an actual copy of the thing; such a becoming would in fact exclude understanding. If your mind literally became a tree when it attempted to understand it, you would understand nothing, since trees do not understand.

This applies at many levels. For example, not only does it apply to meaning and understanding, in some way it applies even to our language on the level of syntax. For example, Word2vec is famously capable of producing analogies which somewhat reflect analogies between the things signified, even though the meanings of the words are absent from its analysis. We should not stress this too much, however, since this takes a very small subset of relationships, even a small subset of relationships found in language, and shows how they will have a structural similarity to their causes. In a sense this does mean that the forms of things are present in linguistic syntax, but it is a very attenuated sense. In contrast, the forms of things are fully present in our understanding to the precise degree that we understand them. The qualification is important: we don’t understand anything perfectly, and consequently no form should be expected to be found perfectly in our understanding.

Others have suggested similar ideas about the natures of things. For example, Sean Collins says:

But for now I will set that aside and come to what I should like to propose as the heart of my thesis. I mentioned a moment ago that Scholastic thought has always acknowledged a dependence of the qualitative on the quantitative. There are many things, nevertheless, which we may recognize without really grasping their full implications. This brings me to what my son Liam wanted to say about form. He proposed, seemingly rather starkly, that there is no such thing as form in material things. But I believe what he meant is that there is cannot be a form in the manner frequently assumed; and I think he is absolutely right. What do I mean by “the manner frequently assumed”? What I mean is that we can cheerfully assert that quality, and therefore also substance, depends on quantity, but yet not see what this really means. What it means – what science proves over and over again – is not just that quality and substance depend on form externally as it were, but that they depend on it much more internally, which is to say structurally. In other words, in material things, form turns out not only to be compatible with an internal structure and heterogeneity, but to depend on it profoundly. I want to say in effect that in material things, to a surprisingly large extent, form IS structure. And so a conception of form which unifies things to the exclusion of a structure is a false conception.

You will perhaps recognize that this solves some problems, but raises others. The biggest problem that it solves is that very Scholastic principle that I have been referring to, which is that quality and substance, the more formal principles, depend on quantity. Now we can start to affirm that we know a little better what that really means. What it means is not just that things have to “be the right size,” but rather that quality and substance depend on quantity internally, because it is quantity that makes structure possible; and structure is, if you will, the intermediary between matter and whatever more abstract kind of form we may have yet to consider. And what I want to insist on again is that this structure is not a negligible thing; in fact it is so important that scientists spend a very large portion of their time examining it. Without it we could know, did know, only the first rudiments of how material things are made. And so this is why the metric part of scientific investigation acquires such a prominent aspect; it isn’t because that is all that the scientists are interested in or that they arbitrarily restrict themselves to it; on the contrary, it is because that is the very condition upon which an understanding of material forms hinges. In various places, Aristotle notes that there is a real difference between a mere dialectical or logical investigation of physical reality, and a truly physical one. The latter, as Aristotle understands it, depends on a sufficient accounting of the material aspects of things so that we can begin to see how forms are truly materialized. Now we can see perhaps a little better how this materialization of forms really happens. It happens especially through the understanding of quantitative structure.

Sean Collins is speaking about material things in particular, and structure as quantitative. My account is similar but more general: if there are any immaterial things, or things without quantity, it applies to them as well. Thus I speak of a network of relationships, of which “quantitative structure” would be more like a particular example.

Paul Almond gives a similar account:

Reality can only be meaningfully described in terms of relationships between things and internal properties of things. That being the case, why do we take the approach of reducing everything to relationships only, so that the “things” being connected by the relationships have no internal properties and all that exists is the structure of relationships itself? The idea of reducing everything to relationships only has been proposed by Tegmark. Suppose reality were viewed as a structure of relationships between things that had internal properties. Those internal properties could themselves only be described in terms of relationships between things. This means that we would have a structure of relationships between “things” and, inside each such “thing” there would also be a structure of relationships between some more basic entities. We would have no reason for declaring a boundary between the relationships outside the “thing” and the relationships inside the “thing”. Instead, we could just take the “edge of a thing” away and say that whatever relationships existed within a thing were just part of the external structure of relationships. The end result of this is that the “things” connected by these relationships have no internal properties at all. All that is left is a structure of relationships between points that have no internal properties. All that remains is the structure itself.

Almond gives this as an account of reality as such, while we give it as an account of form. This is not entirely the same, and consequently Almond’s account could be taken as denying the existence of matter, much like Alexander Pruss. This will be discussed more in my response to objection 9, but my account is not intended to reject the existence of matter. Nonetheless, matter does not contribute to the intelligibility of a thing, and it is therefore true in a sense that form is “most of” reality.

This kind of account is sometimes taken to imply that our understanding is entirely and permanently superficial. For example, Bertrand Russell says in The Analysis of Matter (page 10):

Physics, in itself, is exceedingly abstract, and reveals only certain mathematical characteristics of the material with which it deals. It does not tell us anything as to the intrinsic character of this material.

While mathematical physics as such does have specific limitations, both by reason of the mathematical approach and by the deliberate limitation of subject implied in “physics,” there is a more general problem here. Any account whatsoever of a thing will explain that thing in relationship to everything else, without giving an account of the “intrinsic character of this material.” But this is not because we are necessarily failing to account for something. It is because this is what it is to give an account at all, and because the network of relationships really is the what it is to be of the thing. There is no hidden essence, and the appearance that there must be some other nature, more fundamental, but which cannot be found by us, derives from a temptation towards the Kantian error. The thing does indeed exist in itself, and its mode of existence is not our mode of understanding, but this does not necessarily mean we do not understand it. On the contrary, this distinction is absolutely necessary for understanding at all.

The replies to the objections will be in another post, and as is usual with a disputed question, will clarify various aspects of this position.

An Existential Theory of Relativity

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Paul Almond suggests a kind of theory of relativity applied to existence (section 3.1):

It makes sense to view reality in terms of an observer-centred world, because the only things of which you have direct knowledge are your basic perceptions – both inner and outer – at any instant. Anything else that you know – including your knowledge of the past or future – can only be inferred from these perceptions.

We are not trying to establish some silly idea here that things, including other people, only exist when you observe them, that they only start existing when you start observing them, and that they cease existing when you stop observing them. Rather, it means that anything that exists can only be coherently described as existing somewhere in your observer-centred world. There can still be lots of things that you do not know about. You do not know everything about your observer-centred world, and you can meaningfully talk about the possibility or probability that some particular thing exists. In saying this, you are talking about what may be “out there” somewhere in your observer-centred world. You are talking about the form that your observer-centred world may take, and there is nothing to prevent you from considering different forms that it may take. It would, therefore, be a straw man argument to suggest that we are saying that things only exist when observed by a conscious observer.

As an example, suppose you wonder if, right now, there is an alien spaceship in orbit around Proxima Centauri, a nearby star. What we have said does not make it invalid at all for you to speculate about such a thing, or even to try to put a probability on it if you are so inclined. The point is that any speculation you make, or any probability calculations you try to perform, are about what your observer-centred world might be like.

This view is reasonable because to say that anything exists in a way that cannot be understood in observer-centred world terms is incoherent. If you say something exists you are saying it fits into your “world view”. It must relate to all the other things that you think exist or that you might in principle say exist if you knew enough. Something might exist beyond the horizon in your observer-centred world – in the part that you do not know about – but if something is supposed to exist outside your observer-centred world completely, where would it be? (Here we mean “where” in a more general “ontological” sense.)

As an analogy, this is somewhat similar to the way that relativity deals with velocities. Special relativity says that the concept of “absolute velocity” is incoherent, and that the concept of “velocity” only makes sense in some frame of reference. Likewise, we are saying here that the concept of “existence” only makes sense in the same kind of way. None of this means that consciousness must exist. It is simply saying that it is meaningless to talk about reality in non-observer-centred world terms. It is still legitimate to ask for an explanation of your own existence. It simply means that such an explanation must lie “out there” in your observer-centred world.

This seems right, more or less, but it could be explained more clearly. In the first place Almond is referring to the fact that we see the world as though it existed around us a center, a concept that we have discussed on various past occasions. But in particular he is insisting that in order to say that anything exists at all, we have to place it in some relation to ourselves. In a way this is obvious, because we are the ones who are saying that it exists. If we say that the past or the future do not exist, for example, we are saying this because they do not exist together with us in time. On the other hand, if we speak of “past existence” or “future existence,” we are placing things in a temporal relationship with ourselves. Likewise, if someone asserts the existence of a multiverse, it might not be necessary to say that every part of it has a spatial relationship with the one asserting this, but there must be various relationships. Perhaps the parts of the multiverse have broken off from an earlier universe, or at any rate they all have a common cause. Similarly, if someone asserts the existence of immaterial beings such as angels, they might not have a spatial relationship with the speaker, but they would have to have some relation in order to exist, such as the power to affect the world or be affected by it, and so on. Almond is speaking of this sort of thing when he says, “but if something is supposed to exist outside your observer-centred world completely, where would it be?”

Almond is particularly concerned to establish that he is not asserting the necessary existence of observers, or that a thing cannot exist without being observed. This is mostly a distraction. It is true that this does not follow from his account, but it would be better to explain the theory in a more general way which makes this point clear. A similar mistake is sometimes made regarding special relativity or quantum mechanics. Einstein holds that velocity is necessarily relative to a reference frame, so some interpret this to mean that it is necessarily relative to a conscious observer, and a similar mistake can be made regarding quantum mechanics. But a reference frame is not necessarily conscious. So one body can have a velocity relative to another body, even without anyone observing this.

In a similar way, a reasonable generalization of Almond’s point would be to say that the existence of a thing is relative to a reference frame, which may or may not include an observer. As we are observers in fact, we observe things existing relative to our own reference frame, just as we observe the velocity of objects relative to our own reference frame. But just as one body can have a velocity relative to another, regardless of observers, so one thing can exist relative to another, regardless of observers.

It may be that the theory of special relativity is not merely an illustration here, but rather an instance of the fact that existence is relative to a reference frame. Consider two objects moving apart at 10 miles per hour. According to Einstein, neither one is moving absolutely speaking, but each is moving relative to the other. A typical philosophical objection would go like this: “Wait. One or both of them must be really moving. Because the distance between them is growing. The situation is changing. That doesn’t make sense unless one of them is changing in itself, absolutely, and before considering any relationships.”

But consider this. Currently there are both a calculator and a pen on my desk. Why are both of them there, rather than just one of them? It is easy to see that this fact is intrinsically relative, and cannot in any way be made into something absolute. They are both there because the calculator is with the pen, and because the pen is with the calculator. These cannot be absolute facts about the pen and the calculator – they are relationships to the other.

Now someone will respond: the fact that the calculator is there is an absolute fact. And the fact that the pen is there is an absolute fact. So even if the togetherness is a relationship, it is one that follows logically from the absolute facts. In a similar way, we will want to say that the 10 miles per hour relative motion should follow logically from absolute facts.

But this response just pushes the problem back one step. It only follows logically if the absolute facts about the pen and the calculator exist together. And this existence together is intrinsically relative: the pen is on the desk when the calculator is on the desk. And some thought about this will reveal that the relativity cannot possibly be removed, precisely because the relativity follows from the existence of more than one thing. “More than one thing exists” does not logically follow from any number of statements about individual things, because “more than one thing” is a missing term in those statements.

This is related to the error of Parmenides. Likewise, there is a clue here to the mystery of parts and wholes, but for now I will leave that point to the reader’s consideration.

Going back to the point about special relativity, insofar as “existence together” is intrinsically relative, it would make sense that “existing together spatially” would be an instance of such relative existence, and consequently that “moving apart spatially” would be a particular way of two bodies existing relative to each other. In this sense, the theory of special relativity does not seem to be merely an illustration, but an actual case of what we are talking about.