Closure

The Power of a Name

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Fairy tales and other stories occasionally suggest the idea that a name gives some kind of power over the thing named, or at least that one’s problems concerning a thing may be solved by knowing its name, as in the story of Rumpelstiltskin. There is perhaps a similar suggestion in Revelation 2:7, “Whoever has ears, let them hear what the Spirit says to the churches. To the one who is victorious, I will give some of the hidden manna. I will also give that person a white stone with a new name written on it, known only to the one who receives it.” The secrecy of the new name may indicate (among other things) that others will have no power over that person.

There is more truth in this idea than one might assume without much thought. For example, anonymous authors do not want to be “doxxed” because knowing the name of the author really does give some power in relation to them which is not had without the knowledge of their name. Likewise, as a blogger, occasionally I want to cite something, but cannot remember the name of the author or article where the statement is made. Even if I remember the content fairly clearly, lacking the memory of the name makes finding the content far more difficult, while on the other name, knowing the name gives me the power of finding the content much more easily.

But let us look a bit more deeply into this. Hilary Lawson, whose position was somewhat discussed here, has a discussion along these lines in Part II of his book, Closure: A Story of Everything. Since he denies that language truly refers to the world at all, as I mentioned in the linked post on his position, it is important to him that language has other effects, and in particular has practical goals. He says in chapter 4:

In order to understand the mechanism of practical linguistic closure consider an example where a proficient speaker of English comes across a new word. Suppose that we are visiting a zoo with a friend. We stand outside a cage and our friend says: ‘An aasvogel.” …

It might appear at first from this example that nothing has been added by the realisation of linguistic closure. The sound ‘aasvogel’ still sounds the same, the image of the bird still looks the same. So what has changed? The sensory closures on either side may not have changed, but a new closure has been realised. A new closure which is in addition to the prior available closures and which enables intervention which was not possible previously. For example, we now have a means of picking out this particular bird in the zoo because the meaning that has been realised will have identified a something in virtue of which this bird is an aasvogel and which thus enables us to distinguish it from others. As a result there will be many consequences for how we might be able to intervene.

The important point here is simply that naming something, even before taking any additional steps, immediately gives one the ability to do various practical things that one could not previously do. In a passage by Helen Keller, previously quoted here, she says:

Since I had no power of thought, I did not compare one mental state with another. So I was not conscious of any change or process going on in my brain when my teacher began to instruct me. I merely felt keen delight in obtaining more easily what I wanted by means of the finger motions she taught me.

We may have similar experiences as adults learning a foreign language while living abroad. At first one has very little ability to interact with the foreign world, but suddenly everything is possible.

Or consider the situation of a hunter gatherer who may not know how to count. It may be obvious to them that a bigger pile of fruit is better than a smaller one, but if two piles look similar, they may have no way to know which is better. But once they decide to give “one fruit and another” a name like “two,” and “two and one” a name like “three,” and so on, suddenly they obtain a great advantage that they previously did not possess. It is now possible to count piles and to discover that one pile has sixty-four while another has sixty-three. And it turns out that by treating the “sixty-four” as bigger than the other pile, although it does not look bigger, they end up better off.

In this sense one could look at the scientific enterprise of looking for mathematical laws of nature as one long process of looking for better names. We can see that some things are faster and some things are slower, but the vague names “fast” and “slow” cannot accomplish much. Once we can name different speeds more precisely, we can put them all in order and accomplish much more, just as the hunter gatherer can accomplish more after learning to count. And this extends to the full power of technology: the men who landed on the moon, did so ultimately due to the power of names.

If you take Lawson’s view, that language does not refer to the world at all, all of this is basically casting magic spells. In fact, he spells this out himself, in so many words, in chapter 3:

All material is in this sense magical. It enables intervention that cannot be understood. Ancient magicians were those who had access to closures that others did not know, in the same way that the Pharaohs had access to closures not available to their subjects. This gave them a supernatural character. It is now that thought that their magic has been explained, as the knowledge of herbs, metals or the weather. No such thing has taken place. More powerful closures have been realised, more powerful magic that can subsume the feeble closures of those magicians. We have simply lost sight of its magical character. Anthropology has many accounts of tribes who on being observed by a Western scientist believe that the observer has access to some very powerful magic. Magic that produces sound and images from boxes, and makes travel swift. We are inclined to smile patronisingly believing that we merely have knowledge — the technology behind radio and television, and motor vehicles — and not magic. The closures behind the technology do indeed provide us with knowledge and understanding and enable us to handle activity, but they do not explain how the closures enable intervention. How the closures are successful remains incomprehensible and in this sense is our magic.

I don’t think we should dismiss this point of view entirely, but I do think it is more mistaken than otherwise, basically because of the original mistake of thinking that language cannot refer to the world. But the point that names are extremely powerful is correct and important, to the point where even the analogy of technology as “magic that works” does make a certain amount of sense.

Words, Meaning, and Formal Copies

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There is quick way to respond to the implicit questions at the end of the last post. I noted in an earlier discussion of form that form is not only copied into the mind; it is also copied into language itself. Any time you describe something in words, you are to some degree copying its form into your description.

This implies that Aristotle’s objection that a mind using an organ would not be able to know all things could equally be made against the possibility of describing all things in words. There simply are not enough combinations of words to relate them to all possible combinations of things; thus, just as a black and white image cannot imitate every aspect of a colored scene, so words cannot possibly describe every aspect of reality.

Two things are evident from this comparison:

First, the objection fails overall. There is nothing that cannot be described in words because words are flexible. If we don’t have a word for something, then we can make up a name. Similarly, the meaning of a single word depends on context.  The word “this” can refer to pretty much anything, depending on the context in which it is used. Likewise meaning can be affected by the particular situation of the person using the word, or by broader cultural contexts, and so on.

Second, there is some truth in the objection. It is indeed impossible to describe every aspect of reality at the same time and in complete detail, and the objection gives a very good reason for this: there are simply not enough linguistic combinations to represent all possible combinations of things. The fact that language is not prime matter does mean that language cannot express every detail of reality at once: the determination that is already there does exclude this possibility. But the flexibility of language prevents there from being any particular aspect of things that cannot be described.

My claim about the mind is the same. There is nothing that cannot be understood by the mind, despite the fact that the mind uses the brain, because the relationship between the brain, mind, and world is a flexible one. Just as the word “this” can refer to pretty much anything, so also the corresponding thought. But on the other hand, the limitations of the brain do mean that a perfectly detailed knowledge of everything is excluded.

Our Interlocutor Insists

In a sense, the above account is sufficient to respond to the objection. There does not seem to be a reason to hold Aristotle’s account of the immateriality of the mind, unless there is also a reason to hold that language cannot be used to describe some things, and this does not seem like a reasonable position. Nonetheless, this response will give rise to a new and more detailed objection.

A black and white scene, it will be said, really and truly copies some aspects of a colored scene, and fails to copy others. Thus right angles in the black and white scene may be identical to right angles in the colored scene. The angles are really copied, and the angles are not. But language seems different: since it is conventional, it does not really copy anything. We just pretend, as it were, that we are copying the thing. “Let the word ‘cat’ stand for a cat,” we say, but there is nothing catlike about the word in reality. The form of the cat is not really copied into the word, or so it will be argued. And since we are not really copying anything, this is why language has the flexibility to be able to describe all things. The meaning of thoughts, however, is presumably not conventional. So it seems that we need to copy things in a real way into the mind, the way we copy aspects of a colored scene into a black and white image. And thus, meaning in the mind should not be flexible in this way, and a particular material medium (such as the brain) would still impede knowing all things, the way the black and white image excludes color.

Formal Copies

The above objection is similar to Hilary Lawson’s argument that words cannot really refer to things. In the post linked above on form and reality, we quoted his argument that cause and effect do not have anything in common. I will reproduce that argument here; for the purpose of the following discussion it might be useful to the reader to refer to the remainder of that post.

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.

Lawson’s basic argument is that any particular effect could result from any of an infinite number of different causes, and the cause and effect might be entirely different: the effect might be ringing of a bell, but the cause was not bell-like at all, and did not have a ringing sound. So the effect, he says, tells you nothing at all about the cause. In a similar way, he claims, our thoughts cause our words, but our words and our thoughts have nothing in common, and thus our words tell us nothing about our thoughts; and in that sense they do not refer to anything, not even to our thoughts. Likewise, he says, the world causes our thoughts, but since the cause and effect have nothing in common, our thoughts tell us nothing about the world, and do not even refer to it.

As I responded at the time, this account is mistaken from the very first step. Cause and effect always have something in common, namely the cause-effect relationship, although they each have different ends of that relationship. They will also have other things in common depending on the particular nature of the cause and effect in question. Similarly, the causes that are supposedly utterly diverse, in Lawson’s account, have something in common themselves: every situation that rings the bell has “aptness to ring the bell” in common. And when the bell is rung, it “refers” to these situations by the implication that we are in a situation that has aptness to ring the bell, rather than in one of the other situations.

It is not accidental here that “refer” and “relate” are taken from forms of the same verb. Lawson’s claim that words do not “refer” to things is basically the same as the claim that they are not really related to things. And the real problem is that he is looking at matter (in this case the bell) without considering form (in this case the bell’s relationship with the world.)

In a similar way, to say that the word “cat” is not catlike is to look at the sound or at the text as matter, without considering its form, namely the relationship it has with the surrounding context which causes that word to be used. But that relationship is real; the fact that the word is conventional does not prevent it from being true that human experience of cats is the cause of thoughts of cats, and that thoughts of cats are concretely the cause of the usage of the word “cat,” even if they could in some other situation have caused some other word to be used.

I argued in the post on the nature of form (following the one with the discussion of Lawson) that form is a network of relationships apt to make something one. Insofar as an effect really receives form from a cause in the above way, words really receive meaning from the context that gives rise to their use. And in this way, it is not true that form in language is unlike form in a black and white scene, such that one could say that form in the scene is “real” and form in language is not. Both are real.

Thus the objection fails. Nonetheless, it is true that it is easier to see why it is possible to describe anything in words, than it is to see why anything can be known. And this happens simply because “anything is describable in words” precisely because “anything can be known.” So the fact that anything can be known is the more remote cause, and thus harder to know.

 

Form and Reality II

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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

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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 statements, Gödel’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.