Reductionist vs Anti-Reductionist Dichotomy

I started this post with a promise to return to issues raised by this earlier one. I haven’t really done so, or at least not as I intended, basically because it simply turned out that there was still too much to discuss, some but not all of which I discussed in the last two posts. I am still not ready to return to those original issues. However, the purpose of this post is to keep the promise to explain the relevance of my rejection of both reductionism and anti-reductionism to my account of form. To some extent this has already been done, but a clearer account is possible.

Before going through this kind of consideration, I expect almost everyone to accept implicitly or explicitly an account which maintains one or the other side of this false dichotomy. And consequently, I expect almost everyone to find my account of form objectionable.

Reductionists in general will simply deny the existence of form: there is nothing that makes a thing one, because nothing is actually one. We might respond that if you are reducing things to something else, say to quarks, there still must be something that makes a quark one. The reductionist is likely to respond that a quark is one of itself, and does not need anything else to make it one. And indeed, you might satisfy the general definition of form in such a way, but at that point you are probably discussing words rather than the world: the question of form comes up in the first place because we wonder about the unity of things composed of parts. Thus, at any rate, the most a reductionist will concede is, “Sure, in theory you can use that definition.” But they will add, “But it is a badly formed concept that will mostly lead people away from the truth.” The error here is analogous to that of Parmenides.

Anti-reductionists will admit the existence of form, but they will reject this account, or any other account which one actually explains in detail, because their position implicitly or explicitly requires the existence of hidden essences. The basic idea is that form should make a thing so absolutely one that you cannot break it down into several things even when you are explaining it. It is very obvious that this makes explanation impossible, since any account contains many words referring to many aspects of a thing. I mentioned Bertrand Russell’s remark that science does not explain the “intrinsic character” of matter. Note that this is precisely because every account, insofar as it is an account, is formal, and form is a network of relationships. It simply is not an “intrinsic character” at all, insofar as this is something distinct from such a network. Anti-reductionism posits form as such an intrinsic character, and as such, it requires the existence of a hidden essence that cannot be known in principle. The error here is basically that of Kant.

There is something in common to the two errors, which one might put like this: Nature is in the business of counting things. There must be one final, true answer to the question, “How many things are here?” which is not only true, but excludes all other answers as false. This cannot be the case, however, for the reasons explained in the post just linked. To number things at all, whether as many or as one, is to apply a particular mode of understanding, not to present their mode of being as such.

I expect both reductionists and anti-reductionists to criticize my account at first as one which belongs to the opposite side of this dichotomy. And if they are made aware that it does not, I expect them to criticize it as anti-realist. It is not, or at any rate not in a standard sense: I reject this kind of anti-realism. If it is anti-realist, it is anti-realist in a much more reasonable way, namely about “not being something,” or about distinction. If one thing is not another, that “not another” may be a true attribution, but it is not something “out there” in the world. While the position of Parmenides overall is mistaken, he was not mistaken about the particular point that non-being is not being.

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Replies to Objections on Form

This post replies to the objections raised in the last post.

Reply 1. I do not define form as “many relations”, in part for this very reason. Rather, I say that it is a network, and thus is one thing tied together, so to speak.

Nonetheless, the objection seems to wish to find something absolutely one which is in no way many and which causes unity in other things which are in some way lacking in unity. This does not fit with the idea of giving an account, which necessarily involves many words and thus reference to many aspects of a thing. And thus it also does not fit with the idea of form as that which makes a thing what it is, because it is evident that when we ask what a thing is, we are typically asking about things that have many aspects, as a human being has many senses and many body parts and so on.

In other words, form makes a thing one, but it also makes it what it is, which means that it also makes a thing many in various ways. And so form is one in some way, and thus called a “network,” but it also contains various relations that account for the many aspects of the thing.

Someone might extend this objection by saying that if a form contains many relations, there will need to be a form of form, uniting these relations. But there is a difference between many material parts, which might need a form in order to be one, and relations, which bind things together of themselves. To be related to something, in this sense, is somewhat like being attached to it in some way, while a number of physical bodies are not attached to each other simply in virtue of being a number of bodies. It is true that this implies a certain amount of complexity in form, but this is simply the result of the fact that there is a certain amount of complexity in what things actually are.

Reply 2. “Apt to make something one” is included in the definition in order to point to the relationships and networks of relationships that we are concerned with. For example, one could discuss the idea of a mereological sum, for example the tree outside my window together with my cell phone, and talk about a certain network of relationships intrinsic to that “sum.” This network would have little share in the idea of form, precisely because it is not apt to make anything one thing in any ordinary sense. However, I say “little share” here rather than “no share”, because this is probably a question of degree and kind. As I said here, “one thing” is said in many ways and with many degrees, and thus also form exists in many ways and with many degrees. In particular, there is no reason to suppose that “one” has one true sense compared to which the other senses would be more false than true.

Reply 3. A network of relationships could be an accidental form. Thus the form that makes a blue thing blue would normally be an accidental form. But there will be a similar network of relationships that make a thing a substance. If something is related to other things as “that in which other things are present,” and is not related to other things as “that which is present in something else,” then it will exist as substance, and precisely because it is related to things in these ways. So the definition is in fact general in comparison to both substance and accident.

Reply 4. This objection could be understood as asserting that everything relative depends on something prior which is absolute. Taken in this sense, the objection is simply mistaken. The existence of more than one thing proves conclusively that relationship as such does not need to depend on anything absolute.

Another way to understand the objection would be as asserting that whatever we may say about the thing in relation to other things, all of this must result from what the thing is in itself, apart from all of this. Therefore the essence of the thing is prior to anything at all that we say about it. And in this way, there is a truth here and an error here, namely the Kantian truth and the Kantian error. Certainly the thing is the cause of our knowledge, and not simply identical with our knowledge. Nonetheless, we possess knowledge, not ignorance, of the thing, and we have this knowledge by participation in the network of relationships that defines the thing.

Reply 5. The objection gratuitously asserts that our definition is reductionist, and this can equally well be gratuitously denied. In fact, this account includes the rejection of both reductionist and anti-reductionist positions. Insofar as people suppose that these positions are the only possible positions, if they see that my account implies the rejection of their particular side of the argument, they will naturally suppose that my account implies the acceptance of the other side. This is why the 10th objection claims the opposite: namely that my account is mistaken because it seems to be anti-reductionist.

Reply 6. I agree, in fact, that we are mostly ignorant of the nature of “blue,” and likewise of the natures of most other things. But we are equally ignorant of the network of relationships that these things share in. Thus in an earlier post about Mary’s Room, I noted that we do not even come close to knowing everything that can be known about color. Something similar would be true about pretty much everything that we can commonly name. We have some knowledge of what blue is, but it is a very imperfect knowledge, and similarly we have some knowledge of what a human being is, but it is a very imperfect knowledge. This is one reason why I qualified the claim that the essences of things are not hidden: in another way, virtually all essences are hidden from us, because they are typically too complex for us to understand exhaustively.

An additional problem, also mentioned in the case of “blue,” is that the experience of blue is not the understanding of blue, and these would remain distinct even if the understanding of blue were perfect. But again, it would be an instance of the Kantian error to suppose that it follows that one would not understand the nature of blue even if one understood it (thus we make the absurdity evident.)

Reply 7. God is not an exception to the claim about hidden essences, nor to this account of form, and these claims are not necessarily inconsistent with Christian theology.

The simplicity of God should not be understood as necessarily being opposed to being a network of relationships. In particular, the Trinity is thought to be the same as the essence of God, and what is the Trinity except a network of relations?

Nor does the impossibility of knowing the essence of God imply that God’s essence is hidden in the relevant sense. Rather, it is enough to say that it is inaccessible for “practical” reasons, so to speak. For example, consider St. Thomas’s argument that no one knows all that God can do:

The created intellect, in seeing the divine essence, does not see in it all that God does or can do. For it is manifest that things are seen in God as they are in Him. But all other things are in God as effects are in the power of their cause. Therefore all things are seen in God as an effect is seen in its cause. Now it is clear that the more perfectly a cause is seen, the more of its effects can be seen in it. For whoever has a lofty understanding, as soon as one demonstrative principle is put before him can gather the knowledge of many conclusions; but this is beyond one of a weaker intellect, for he needs things to be explained to him separately. And so an intellect can know all the effects of a cause and the reasons for those effects in the cause itself, if it comprehends the cause wholly. Now no created intellect can comprehend God wholly, as shown above (Article 7). Therefore no created intellect in seeing God can know all that God does or can do, for this would be to comprehend His power; but of what God does or can do any intellect can know the more, the more perfectly it sees God.

St. Thomas argues that if anyone knew all that God can do, i.e. everything that can be God’s effect, he would not only know the essence of God, but know it perfectly. This actually supports our position precisely: if you have an exhaustive account of the network of relationships between God and the world, actual and potential, according to St. Thomas, this is to know the essence of God exhaustively.

Reply 8. I concede the objection, but simply note that the error is on the part of Christian theology, not on the part of this account.

In this case, someone might ask why I included this objection, along with the previous, where even if I consider the theology defensible, I do not consider it authoritative. The reason is that I included objections that I expected various readers to hold in one form or another, and these are two of them. But what is the use of addressing them if I simply reject the premise of the objection?

There is at least one benefit to this. There is an important lesson here. Religious doctrines are typically defined in such a way that they have few or no undue sensible implications, as I said for example about the Real Presence. But philosophy is more difficult, and shares in much of the same distance from the senses that such religious claims have. Consequently, even if you manage to avoid adopting religious doctrines that have false scientific implications (and many don’t manage to avoid even this), if you accept any religious doctrines at all, it will be much harder to avoid false philosophical implications.

In fact, the idea of an immortal soul probably has false scientific consequences as well as false philosophical consequences, at least taken as it is usually understood. Thus for example Sean Carroll argues that the mortality of the soul is a settled issue:

Adam claims that “simply is no controlled, experimental[ly] verifiable information” regarding life after death. By these standards, there is no controlled, experimentally verifiable information regarding whether the Moon is made of green cheese. Sure, we can take spectra of light reflecting from the Moon, and even send astronauts up there and bring samples back for analysis. But that’s only scratching the surface, as it were. What if the Moon is almost all green cheese, but is covered with a layer of dust a few meters thick? Can you really say that you know this isn’t true? Until you have actually examined every single cubic centimeter of the Moon’s interior, you don’t really have experimentally verifiable information, do you? So maybe agnosticism on the green-cheese issue is warranted. (Come up with all the information we actually do have about the Moon; I promise you I can fit it into the green-cheese hypothesis.)

Obviously this is completely crazy. Our conviction that green cheese makes up a negligible fraction of the Moon’s interior comes not from direct observation, but from the gross incompatibility of that idea with other things we think we know. Given what we do understand about rocks and planets and dairy products and the Solar System, it’s absurd to imagine that the Moon is made of green cheese. We know better.

We also know better for life after death, although people are much more reluctant to admit it. Admittedly, “direct” evidence one way or the other is hard to come by — all we have are a few legends and sketchy claims from unreliable witnesses with near-death experiences, plus a bucketload of wishful thinking. But surely it’s okay to take account of indirect evidence — namely, compatibility of the idea that some form of our individual soul survives death with other things we know about how the world works.

Claims that some form of consciousness persists after our bodies die and decay into their constituent atoms face one huge, insuperable obstacle: the laws of physics underlying everyday life are completely understood, and there’s no way within those laws to allow for the information stored in our brains to persist after we die. If you claim that some form of soul persists beyond death, what particles is that soul made of? What forces are holding it together? How does it interact with ordinary matter?

Everything we know about quantum field theory (QFT) says that there aren’t any sensible answers to these questions. Of course, everything we know about quantum field theory could be wrong. Also, the Moon could be made of green cheese.

Among advocates for life after death, nobody even tries to sit down and do the hard work of explaining how the basic physics of atoms and electrons would have to be altered in order for this to be true. If we tried, the fundamental absurdity of the task would quickly become evident.

Even if you don’t believe that human beings are “simply” collections of atoms evolving and interacting according to rules laid down in the Standard Model of particle physics, most people would grudgingly admit that atoms are part of who we are. If it’s really nothing but atoms and the known forces, there is clearly no way for the soul to survive death. Believing in life after death, to put it mildly, requires physics beyond the Standard Model. Most importantly, we need some way for that “new physics” to interact with the atoms that we do have.

Very roughly speaking, when most people think about an immaterial soul that persists after death, they have in mind some sort of blob of spirit energy that takes up residence near our brain, and drives around our body like a soccer mom driving an SUV. The questions are these: what form does that spirit energy take, and how does it interact with our ordinary atoms? Not only is new physics required, but dramatically new physics. Within QFT, there can’t be a new collection of “spirit particles” and “spirit forces” that interact with our regular atoms, because we would have detected them in existing experiments. Ockham’s razor is not on your side here, since you have to posit a completely new realm of reality obeying very different rules than the ones we know.

There are certainly different ways to think about this, but this is in fact a common way of thinking about the soul in relation to the body. For example, consider this discussion by James Chastek:

Objection: Conservation laws require that outcomes be already determined. By your own admission, life has to be able to “alter what would happen by physical causes alone” and therefore violates conservation laws.

Response: Again, laws and initial conditions do not suffice to explain the actual world. Life only “alters” physical causes under the counterfactual supposition that physical causes could act alone, i.e. in a way that could suffice to explain outcomes in the actual world.

Objection: It is meaningless to describe life acting on physical laws and conditions when we can’t detect this. Life-actions are vacuous entities about which we can say nothing at all. What’s their Hamiltonian?

Response: Physical laws and conditions as physical are instrumental or partial accounts of the actual world. The interactive mechanisms and measurement devices appropriate to establishing the existence of physical causes are not appropriate tools for describing all causes of the actual world.

Chastek is deliberately ignoring the question that he poses himself. But we know his opinion of the matter from previous discussions. What physics would calculate would be one thing; what the human being will do, according to Chastek, is something different.

This almost certainly does imply a violation of the laws of physics in the sense of the discussion in Chastek’s post, as well as in the sense that concerns Sean Carroll. In fact, it probably would imply a violation of conservation of energy, very possibly to such a degree that it would be possible in principle to exploit the violation to create a perpetual motion machine, somewhat along the lines of this short story by Scott Alexander. And these violations would detectable in principle, and very likely in practice as well, at least at some point.

Nonetheless, one might think about it differently, without suggesting these things, but still suppose that people have immortal souls. And one might be forgiven for being skeptical of Sean Carroll’s arguments, given that his metaphysics is wrong. Perhaps there is some implicit dependence of his argument on this mistaken metaphysics. The problem with this response is that even the correct metaphysics has the same implications, even without considering Carroll’s arguments from physics.

It is easy to see that there still loopholes for someone who wishes to maintain the immortality of the soul. But such loopholes also indicate an additional problem with the idea. In particular, the idea that the soul is subsistent implies that it is a substantial part of a human being: that a human is a whole made of soul and body much as the body is a whole made of various parts such as legs and arms. If this were the case, the soul might not be material in a quantitative sense, but it would be “matter” in the sense that we have argued that form is not matter. In this case, it would be reasonable to suppose that an additional substantial form would be necessary to unify soul and body, themselves two substantial parts.

Reply 9. There in fact is an implicit reference to matter in the definition. “Apt to make something one” refers to what is made, but it also refers to what it is made out of, if there is anything out of which it is made. The form of a chair makes the chair one chair, but it also makes the stuff of the chair into one chair.

There is more to say about matter, but my intention for now was to clarify the concept of form.

Reply 10. The network of relationships is most certainly not a construct of the mind, if one places this in opposition to “real thing.” You cannot trace back relationships to causes that do not include any relationships, if only because “cause” is in itself relative.

I have argued against reductionism in many places, and do not need to repeat those arguments here, but in particular I would note that the objection implies that “mind” is a construct of the mind, and this implies circular causality, which is impossible.

Reply 11. The objection is not really argued, and this is mainly because there cannot be a real argument for it. There is however a rough intuition supporting it, which is that applying this idea of form to immaterial things seems unfair to reality, as though we were trying to say that the limits of reality are set by the limits of the human mind. Once again, however, this is simply a case of the usual Kantian error, mixed together with choosing something that would be especially unknown to us. An immaterial thing could not exist without having some relationship with everything else. As we have suggested elsewhere, “there is an immaterial thing,” cannot even be assigned a meaning without the implied claim that I stand in some relation with it, and that it stands in some relation to me. But evidently I know very little about it. This does not mean that we need some new definition of what it is to be something; it simply means I do not know much of what that thing is, just as I do not know much of anything about it at all.

 

Nature of Form

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.

Form and Reality II

This is a followup to this earlier post, but will use a number of other threads to get a fuller understanding of the matter. Rather than presenting this in the form of a single essay, I will present it as a number of distinct theses, many of which have already been argued or suggested in various forms elsewhere on the blog.

(1) Everything that exists or can exist has or could have some relationship with the mind: relationship is in fact intrinsic to the nature of existence.

This was argued here, with related remarks in several recent posts. In a sense the claim is not only true but obviously so. You are the one who says or can say “this exists,” and you could not say or understand it unless the thing had or could have some relationship with your mind.

Perhaps this seems a bit unfair to reality, as though the limits of reality were being set by the limits of the thinker. What if there were a limited being that could only think of some things, but other things could exist that it could not think about? It is easy to see that in this situation the limited being does not have the concept of “everything,” and so can neither affirm nor deny (1). It is not that it would affirm it but be mistaken. It would simply never think of it.

Someone could insist: I myself am limited. It might be that there are better thinkers in the world that can think about things I could never conceive of. But again, if you have concept of “everything,” then you just thought of those things: they are the things that those thinkers would think about. So you just thought about them too, and brought them into relationship with yourself.

Thus, anyone who actually has the idea of “everything,” and thinks about the matter clearly, will agree with (1).

(2) Nothing can be true which could not in principle (in some sense of “in principle”) in some way be said to be true.

Thesis (1) can be taken as saying that anything that can be, can also be understood, at least in some way; and thesis (2) can be taken as saying that anything that can be understood, can also be said, at least in some way.

Since language is conventional, this does not need much of an argument. If I think that something exists, and I don’t have a name for it, I can make up a name. If I think that one thing is another thing, but don’t have words for these things, I can make up words for them. Even if I am not quite sure what I am thinking, I can say, “I have a thought in my mind but don’t quite have the words for it,” and in some way I have already put it into words.

One particular objection to the thesis might be made from self-reference paradoxes. The player in the Liar Game cannot correctly say whether the third statement is true or false, even though it is in fact true or false. But note two things: first, he cannot do this while he is playing, but once the game is over, he can explicitly and correctly say whether it was true or false. Second, even while playing, he can say, “the third statement has a truth value,” and in this way he speaks of its truth in a generic way. This is in part why I added the hedges to (2), “at least in some way”, and “in principle.”

(3) Things do not have hidden essences. That is, they may have essences, but those essences can be explained in words.

This follows in a straightforward way from (1) and (2). The essence of a thing is just “what it is,” or perhaps, “what it most truly is.” The question “what is this thing?” is formed with words, and it is evident that anyone who answers the question, will answer the question by using words.

Now someone might object that the essence of a thing might be hidden because perhaps in some cases the question does not have an answer. But then it would not be true that it has an essence but is hidden: rather, it would be false that it has an essence. Similarly, if the question “where is this thing,” does not have any answer, it does not mean the thing is in a hidden place, but that the thing is not in a place at all.

Another objection might be that an essence might be hidden because the answer to the question exists, but cannot be known. A discussion of this would depend on what is meant by “can be known” and “cannot be known” in this context. That is, if the objector is merely saying that we do not know such things infallibly, including the answer to the question, “what is this?”, then I agree, but would add that (3) does not speak to this point one way or another. But if it is meant that “cannot be known” means that there is something there, the “thing in itself,” which in no way can be known or expressed in words, this would be the Kantian error. This is indeed contrary to (3), and implicitly to (1) or (2) or both, but it is also false.

People might also think that the essence cannot be known because they notice that the question “what is this?” can have many legitimate answers, and suppose that one of these, and only one, must be really and truly true, but think that we have no way to find out which one it is. While there are certainly cases where an apparent answer to the question is not a true answer, the main response here is that if both answers are true, both answers are true: there does not need to be a deeper but hidden level where one is true and the other false. There may however be a deeper level which speaks to other matters and possibly explains both answers. Thus I said in the post linked above that the discussion was not limited to “how many,” but would apply in some way to every question about the being of things.

(4) Reductionism, as it is commonly understood, is false.

I have argued this in various places, but more recently and in particular here and here. It is not just one-sided to say for example that the universe and everything in it is just a multitude of particles. It is false, because it takes one of several truths, and says that one is “really” true and that the other is “really” false.

(5) Anti-reductionism, as it is commonly understood, is false.

This follows from the same arguments. Anti-reductionism, as for example the sort advocated by Alexander Pruss, takes the opposite side of the above argument, saying that certain things are “really” one and in no way many. And this is also false.

(6) Form makes a thing to be what it is, and makes it to be one thing.

This is largely a question of definition. It is what is meant by form in this context.

Someone might object that perhaps there is nothing that makes a thing what it is, or there is nothing that makes it one thing. But if it is what it is of itself, or if it is one of itself, then by this definition it is its own form, and we do not necessarily have an issue with that.

Again, someone might say that the definition conflates two potentially distinct things. Perhaps one thing makes a thing what it is, and another thing makes it one thing. But this is not possible because of the convertibility of being and unity: to be a thing at all, is to be one thing.

(7) Form is what is in common between the mind and the thing it understands, and is the reason the mind understands at all.

This is very distinctly not a question of definition. This needs to be proved from (6), along with what we know about understanding.

It is not so strange to think that you would need to have something in common with a thing in order to understand it. Thus Aristotle presents the words of Empedocles:

For ’tis by Earth we see Earth, by Water Water,

By Ether Ether divine, by Fire destructive Fire,

By Love Love, and Hate by cruel Hate.

On the other hand, there is also obviously something wrong with this. I don’t need to be a tree in order to see or think about a tree, and it is not terribly obvious that there is even anything in common between us. In fact, one of Hilary Lawson’s arguments for his anti-realist position is that there frequently seems to be nothing in common between causes and effects, and that therefore there may be (or certainly will be) nothing in common between our minds and reality, and thus we cannot ultimately know anything. Thus he says in Chapter 2 of his book on closure:

For a system of closure to provide a means of intervention in openness and thus to function as a closure machine, it requires a means of converting the flux of openness into an array of particularities. This initial layer of closure will be identified as ‘preliminary closure’. As with closure generally, preliminary closure consists in the realisation of particularity as a consequence of holding that which is different as the same. This is achieved through the realisation of material in response to openness. The most minimal example of a system of closure consists of a single preliminary closure. Such a system requires two discrete states, or at least states that can be held as if they were discrete. It is not difficult to provide mechanical examples of such systems which allow for a single preliminary closure. A mousetrap for example, can be regarded as having two discrete states: it is either set, it is ready, or it has sprung, it has gone off. Many different causes may have led to it being in one state or another: it may have been sprung by a mouse, but it could also have been knocked by someone or something, or someone could have deliberately set it off. In the context of the mechanism all of these variations are of no consequence, it is either set or it has sprung. The diversity of the immediate environment is thereby reduced to single state and its absence: it is either set or it is not set. Any mechanical arrangement that enables a system to alternate between two or more discrete states is thereby capable of providing the basis for preliminary closure. For example, a bell or a gate could function as the basis for preliminary closure. The bell can either ring or not ring, the gate can be closed or not closed. The bell may ring as the result of the wind, or a person or animal shaking it, but the cause of the response is in the context of system of no consequence. The bell either rings or it doesn’t. Similarly, the gate may be in one state or another because it has been deliberately moved, or because something or someone has dislodged it accidentally, but these variations are not relevant in the context of the state of system, which in this case is the position of the gate. In either case the cause of the bell ringing or the gate closing is infinitely varied, but in the context of the system the variety of inputs is not accessible to the system and thus of no consequence.

A useful way to think about Lawson is that he is in some way a disciple of Heraclitus. Thus closure is “holding that which is different as the same,” but in reality nothing is ever the same because everything is in flux. In the context of this passage, the mousetrap is either set or sprung, and so it divides the world into two states, the “set” state and the “sprung” state. But the universes with the set mousetrap have nothing in common with one another besides the set mousetrap, and the universes with the sprung mousetrap have nothing in common with one another besides the sprung mousetrap.

We can see how this could lead to the conclusion that knowledge is impossible. Sight divides parts of the world up with various colors. Leaves are green, the sky is blue, the keyboard I am using is black. But if I look at two different green things, or two different blue things, they may have nothing in common besides the fact that they affected my sight in a similar way. The sky and a blue couch are blue for very different reasons. We discussed this particular point elsewhere, but the general concern would be that we have no reason to think there is anything in common between our mind and the world, and some reason to think there must be something in common in order for us to understand anything.

Fortunately, the solution can be found right in the examples which supposedly suggest that there is nothing in common between the mind and the world. Consider the mousetrap. Do the universes with the set mousetrap have something in common? Yes, they have the set mousetrap in common. But Lawson does not deny this. His concern is that they have nothing else in common. But they do have something else in common: they have the same relationship to the mousetrap, different from the relationship that the universes with the sprung mousetrap have to their mousetrap. What about the mousetrap itself? Do those universes have something in common with the mousetrap? If we consider the relationship between the mousetrap and the universe as a kind of single thing with two ends, then they do, although they share in it from different ends, just as a father and son have a relationship in common (in this particular sense.) The same things will be true in the case of sensible qualities. “Blue” may divide up surface reflectance properties in a somewhat arbitrary way, but it does divide them into things that have something in common, namely their relationship with the sense of sight.

Or consider the same thing with a picture. Does the picture have anything in common with the thing it represents? Since a picture is meant to actually look similar to the eye to the object pictured, it may have certain shapes in common, the straightness of certain lines, and so on. It may have some colors in common. This kind of literal commonness might have suggested to Empedocles that we should know “earth by earth,” but one difference is that a picture and the object look alike to the eye, but an idea is not something that the mind looks at, and which happens to look like a thing: rather the idea is what the mind uses in order to look at a thing at all.

Thus a better comparison would be between the the thing seen and the image in the eye or the activity of the visual cortex. It is easy enough to see by looking that the image in a person’s eye bears some resemblance to the thing seen, even the sort of resemblance that a picture has. In a vaguer way, something similar turns out to be true even in the visual cortex:

V1 has a very well-defined map of the spatial information in vision. For example, in humans, the upper bank of the calcarine sulcus responds strongly to the lower half of visual field (below the center), and the lower bank of the calcarine to the upper half of visual field. In concept, this retinotopic mapping is a transformation of the visual image from retina to V1. The correspondence between a given location in V1 and in the subjective visual field is very precise: even the blind spots are mapped into V1. In terms of evolution, this correspondence is very basic and found in most animals that possess a V1. In humans and animals with a fovea in the retina, a large portion of V1 is mapped to the small, central portion of visual field, a phenomenon known as cortical magnification. Perhaps for the purpose of accurate spatial encoding, neurons in V1 have the smallest receptive field size of any visual cortex microscopic regions.

However, as I said, this is in a much vaguer way. In particular, it is not so much an image which is in common, but certain spatial relationships. If we go back to the idea of the mousetrap, this is entirely unsurprising. Causes and effects will always have something in common, and always in this particular way, namely with a commonality of relationship, because causes and effects, as such, are defined by their relationship to each other.

How does all this bear on our thesis (7)? Consider the color blue, and the question, “what is it to be blue?” What is the essence of blue? We could answer this in at least two different ways:

  1. To be blue is to have certain reflectance properties.
  2. To be blue is to be the sort of thing that looks blue.

But in the way intended, these are one and the same thing. A thing looks blue if it has those properties, and it has those properties if it looks blue. Now someone might say that this is a direct refutation of our thesis, since the visual cortex presumably does not look blue or have those properties when you look at something blue. But this is like Lawson’s claim that the universe has nothing in common with the sprung mousetrap. It does have something in common, if you look at the relationship from the other end. The same thing happens when we consider the meaning of “certain reflectance properties,” and “the sort of thing that looks blue.” We are actually talking about the properties that make a thing look blue, so both definitions are relative to the sense of sight. And this means that sight has something relative in common with them, and the relation it has in common is the very one that defines the nature of blue. As this is what we mean by form (thesis 6), the form of blue must be present in the sense of sight in order to see something blue.

In fact, it followed directly from thesis (1) that the nature of blue would need to include something relative. And it followed from (2) and (3) that the very same nature would turn out to be present in our senses, thoughts, and words.

The same argument applies to the mind as to the senses. I will draw additional conclusions in a later post, and in particular, show the relevance of theses (4) and (5) to the rest.

Self Reference Paradox Summarized

Hilary Lawson is right to connect the issue of the completeness and consistency of truth with paradoxes of self-reference.

As a kind of summary, consider this story:

It was a dark and stormy night,
and all the Cub Scouts where huddled around their campfire.
One scout looked up to the Scout Master and said:
“Tell us a story.”
And the story went like this:

It was a dark and stormy night,
and all the Cub Scouts where huddled around their campfire.
One scout looked up to the Scout Master and said:
“Tell us a story.”
And the story went like this:

It was a dark and stormy night,
and all the Cub Scouts where huddled around their campfire.
One scout looked up to the Scout Master and said:
“Tell us a story.”
And the story went like this:

It was a dark and stormy night,
and all the Cub Scouts where huddled around their campfire.
One scout looked up to the Scout Master and said:
“Tell us a story.”
And the story went like this:
etc.

In this form, the story obviously exists, but in its implied form, the story cannot be told, because for the story to be “told” is for it to be completed, and it is impossible for it be completed, since it will not be complete until it contains itself, and this cannot happen.

Consider a similar example. You sit in a room at a desk, and decide to draw a picture of the room. You draw the walls. Then you draw yourself and your desk. But then you realize, “there is also a picture in the room. I need to draw the picture.” You draw the picture itself as a tiny image within the image of your desktop, and add tiny details: the walls of the room, your desk and yourself.

Of course, you then realize that your artwork can never be complete, in exactly the same way that the story above cannot be complete.

There is essentially the same problem in these situations as in all the situations we have described which involve self-reference: the paradox of the liar, the liar game, the impossibility of detailed future prediction, the list of all true statementsGödel’s theorem, and so on.

In two of the above posts, namely on future prediction and Gödel’s theorem, there are discussions of James Chastek’s attempts to use the issue of self-reference to prove that the human mind is not a “mechanism.” I noted in those places that such supposed proofs fail, and at this point it is easy to see that they will fail in general, if they depend on such reasoning. What is possible or impossible here has nothing to do with such things, and everything to do with self-reference. You cannot have a mirror and a camera so perfect that you can get an actually infinite series of images by taking a picture of the mirror with the camera, but there is nothing about such a situation that could not be captured by an image outside the situation, just as a man outside the room could draw everything in the room, including the picture and its details. This does not show that a man outside the room has a superior drawing ability compared with the man in the room. The ability of someone else to say whether the third statement in the liar game is true or false does not prove that the other person does not have a “merely human” mind (analogous to a mere mechanism), despite the fact that you yourself cannot say whether it is true or false.

There is a grain of truth in Chastek’s argument, however. It does follow that if someone says that reality as a whole is a formal system, and adds that we can know what that system is, their position would be absurd, since if we knew such a system we could indeed derive a specific arithmetical truth, namely one that we could state in detail, which would be unprovable from the system, namely from reality, but nonetheless proved to be true by us. And this is logically impossible, since we are a part of reality.

At this point one might be tempted to say, “At this point we have fully understood the situation. So all of these paradoxes and so on don’t prevent us from understanding reality perfectly, even if that was the original appearance.”

But this is similar to one of two things.

First, a man can stand outside the room and draw a picture of everything in it, including the picture, and say, “Behold. A picture of the room and everything in it.” Yes, as long as you are not in the room. But if the room is all of reality, you cannot get outside it, and so you cannot draw such a picture.

Second, the man in the room can draw the room, the desk and himself, and draw a smudge on the center of the picture of the desk, and say, “Behold. A smudged drawing of the room and everything in it, including the drawing.” But one only imagines a picture of the drawing underneath the smudge: there is actually no such drawing in the picture of the room, nor can there be.

In the same way, we can fully understand some local situation, from outside that situation, or we can have a smudged understanding of the whole situation, but there cannot be any detailed understanding of the whole situation underneath the smudge.

I noted that I disagreed with Lawson’s attempt to resolve the question of truth. I did not go into detail, and I will not, as the book is very long and an adequate discussion would be much longer than I am willing to attempt, at least at this time, but I will give some general remarks. He sees, correctly, that there are problems both with saying that “truth exists” and that “truth does not exist,” taken according to the usual concept of truth, but in the end his position amounts to saying that the denial of truth is truer than the affirmation of truth. This seems absurd, and it is, but not quite so much as appears, because he does recognize the incoherence and makes an attempt to get around it. The way of thinking is something like this: we need to avoid the concept of truth. But this means we also need to avoid the concept of asserting something, because if you assert something, you are saying that it is true. So he needs to say, “assertion does not exist,” but without asserting it. Consequently he comes up with the concept of “closure,” which is meant to replace the concept of asserting, and “asserts” things in the new sense. This sense is not intended to assert anything at all in the usual sense. In fact, he concludes that language does not refer to the world at all.

Apart from the evident absurdity, exacerbated by my own realist description of his position, we can see from the general account of self-reference why this is the wrong answer. The man in the room might start out wanting to draw a picture of the room and everything in it, and then come to realize that this project is impossible, at least for someone in his situation. But suppose he concludes: “After all, there is no such thing as a picture. I thought pictures were possible, but they are not. There are just marks on paper.” The conclusion is obviously wrong. The fact that pictures are things themselves does prevent pictures from being exhaustive pictures of themselves, but it does not prevent them from being pictures in general. And in the same way, the fact that we are part of reality prevents us from having an exhaustive understanding of reality, but it does not prevent us from understanding in general.

There is one last temptation in addition to the two ways discussed above of saying that there can be an exhaustive drawing of the room and the picture. The room itself and everything in it, is itself an exhaustive representation of itself and everything in it, someone might say. Apart from being an abuse of the word “representation,” I think this is delusional, but this a story for another time.