Being and Unity II

Content warning: very obscure.

This post follows up on an earlier post on this topic, as well on what was recently said about real distinction. In the latter post, we applied the distinction between the way a thing is and the way it is known in order to better understand distinction itself. We can obtain a better understanding of unity in a similar way.

As was said in the earlier post on unity, to say that something is “one” does not add anything real to the being of the thing, but it adds the denial of the division between distinct things. The single apple is not “an apple and an orange,” which are divided insofar as they are distinct from one another.

But being distinct from divided things is itself a certain way of being distinct, and consequently all that was said about distinction in general will apply to this way of being distinct as well. In particular, since being distinct means not being something, which is a way that things are understood rather than a way that they are (considered precisely as a way of being), the same thing applies to unity. To say that something is one does not add something to the way that it is, but it adds something to the way that it is understood. This way of being understood is founded, we argued, on existing relationships.

We should avoid two errors here, both of which would be expressions of the Kantian error:

First, the argument here does not mean that a thing is not truly one thing, just as the earlier discussion does not imply that it is false that a chair is not a desk. On the contrary, a chair is in fact not a desk, and a chair is in fact one chair. But when we say or think, “a chair is not a desk,” or “a chair is one chair,” we are saying these things in some way of saying, and thinking them in some way of thinking, and these ways of saying and thinking are not ways of being as such. This in no way implies that the statements themselves are false, just as “the apple seems to be red,” does not imply that the apple is not red. Arguing that the fact of a specific way of understanding implies that the thing is falsely understood would be the position described by Ayn Rand as asserting, “man is blind, because he has eyes—deaf, because he has ears—deluded, because he has a mind—and the things he perceives do not exist, because he perceives them.”

Second, the argument does not imply that the way things really are is unknown and inaccessible to us. One might suppose that this follows, since distinction cannot exist apart from someone’s way of understanding, and at the same time no one can understand without making distinctions. Consequently, someone might argue, there must be some “way things really are in themselves,” which does not include distinction or unity, but which cannot be understood. But this is just a different way of falling into the first error above. There is indeed a way things are, and it is generally not inaccessible to us. In fact, as I pointed out earlier, it would be a contradiction to assert the existence of anything entirely unknowable to us.

Our discussion, being in human language and human thought, naturally uses the proper modes of language and thought. And just as in Mary’s room, where her former knowledge of color is a way of knowing and not a way of sensing, so our discussion advances by ways of discussion, not by ways of being as such. This does not prevent the way things are from being an object of discussion, just as color can be an object of knowledge.

Having avoided these errors, someone might say that nothing of consequence follows from this account. But this would be a mistake. It follows from the present account that when we ask questions like, “How many things are here?”, we are not asking a question purely about how things are, but to some extent about how we should understand them. And even when there is a single way that things are, there is usually not only one way to understand them correctly, but many ways.

Consider some particular question of this kind: “How many things are in this room?” People might answer this question in various ways. John Nerst, in a previous discussion on this blog, seemed to suggest that the answer should be found by counting fundamental particles. Alexander Pruss would give a more complicated answer, since he suggests that large objects like humans and animals should be counted as wholes (while also wishing to deny the existence of parts, which would actually eliminate the notion of a whole), while in other cases he might agree to counting particles. Thus a human being and an armchair might be counted, more or less, as 1 + 10^28 things, namely counting the human being as one thing and the chair as a number of particles.

But if we understand that the question is not, and cannot be, purely about how things are, but is also a question about how things should be understood, then both of the above responses seem unreasonable: they are both relatively bad ways of understanding the things in the room, even if they both have some truth as well. And on the other hand, it is easy to see that “it depends on how you count,” is part of the answer. There is not one true answer to the question, but many true answers that touch on different aspects of the reality in the room.

From the discussion with John Nerst, consider this comment:

My central contention is that the rules that define the universe runs by themselves, and must therefore be self-contained, i.e not need any interpretation or operationalization from outside the system. As I think I said in one of the parts of “Erisology of Self and Will” that the universe must be an automaton, or controlled by an automaton, etc. Formal rules at the bottom.

This is isn’t convincing to you I guess but I suppose I rule out fundamental vagueness because vagueness implies complexity and fundamental complexity is a contradiction in terms. If you keep zooming in on a fuzzy picture you must, at some point, come down to sharply delineated pixels.

Among other things, the argument of the present post shows why this cannot be right. “Sharply delineated pixels” includes the distinction of one pixel from another, and therefore includes something which is a way of understanding as such, not a way of being as such. In other words, while intending to find what is really there, apart from any interpretation, Nerst is directly including a human interpretation in his account. And in fact it is perfectly obvious that anything else is impossible, since any account of reality given by us will be a human account and will thus include a human way of understanding. Things are a certain way: but that way cannot be said or thought except by using ways of speaking or thinking.


Truth and Expectation

Suppose I see a man approaching from a long way off. “That man is pretty tall,” I say to a companion. The man approaches, and we meet him. Now I can see how tall he is. Suppose my companion asks, “Were you right that the man is pretty tall, or were you mistaken?”

“Pretty tall,” of course, is itself “pretty vague,” and there surely is not some specific height in inches that would be needed in order for me to say that I was right. What then determines my answer? Again, I might just respond, “It’s hard to say.” But in some situations I would say, “yes, I was definitely right,” or “no, I was definitely wrong.” What are those situations?

Psychologically, I am likely to determine the answer by how I feel about what I know about the man’s height now, compared to what I knew in advance. If I am surprised at how short he is, I am likely to say that I was wrong. And if I am not surprised at all by his height, or if I am surprised at how tall he is, then I am likely to say that I was right. So my original pretty vague statement ends up being made somewhat more precise by being placed in relationship with my expectations. Saying that he is pretty tall implies that I have certain expectations about his height, and if those expectations are verified, then I will say that I was right, and if those expectations are falsified, at least in a certain direction, then I will say that I was wrong.

This might suggest a theory like logical positivism. The meaning of a statement seems to be defined by the expectations that it implies. But it seems easy to find a decisive refutation of this idea. “There are stars outside my past and future light cones,” for example, is undeniably meaningful, and we know what it means, but it does not seem to imply any particular expectations about what is going to happen to me.

But perhaps we should simply somewhat relax the claim about the relationship between meaning and expectations, rather than entirely retracting it. Consider the original example. Obviously, when I say, “that man is pretty tall,” the statement is a statement about the man. It is not a statement about what is going to happen to me. So it is incorrect to say that the meaning of the statement is the same as my expectations. Nonetheless, the meaning in the example receives something, at the least some of its precision, from my expectations. Different people will be surprised by different heights in such a case, and it will be appropriate to say that they disagree somewhat about the meaning of “pretty tall.” But not because they had some logical definition in their minds which disagreed with the definition in someone’s else’s mind. Instead, the difference of meaning is based on the different expectations themselves.

But does a statement always receive some precision in its meaning from expectation, or are there cases where nothing at all is received from one’s expectations? Consider the general claim that “X is true.” This in fact implies some expectations: I do not expect “someone omniscient will tell me that X is false.” I do not expect that “someone who finds out the truth about X will tell me that X is false.” I do not expect that “I will discover the truth about X and it will turn out that it was false.” Note that these expectations are implied even in cases like the claim about the stars and my future light cone. Now the hopeful logical positivist might jump in at this point and say, “Great. So why can’t we go back to the idea that meaning is entirely defined by expectations?” But returning to that theory would be cheating, so to speak, because these expectations include the abstract idea of X being true, so this must be somehow meaningful apart from these particular expectations.

These expectations do, however, give the vaguest possible framework in which to make a claim at all. And people do, sometimes, make claims with little expectation of anything besides these things, and even with little or no additional understanding of what they are talking about. For example, in the cases that Robin Hanson describes as “babbling,” the person understands little of the implications of what he is saying except the idea that “someone who understood this topic would say something like this.” Thus it seems reasonable to say that expectations do always contribute something to making meaning more precise, even if they do not wholly constitute one’s meaning. And this consequence seems pretty natural if it is true that expectation is itself one of the most fundamental activities of a mind.

Nonetheless, the precision that can be contributed in this way will never be an infinite precision, because one’s expectations themselves cannot be defined with infinite precision. So whether or not I am surprised by the man’s height in the original example, may depend in borderline cases on what exactly happens during the time between my original assessment and the arrival of the man. “I will be surprised” or “I will not be surprised” are in themselves contingent facts which could depend on many factors, not only on the man’s height. Likewise, whether or not my state actually constitutes surprise will itself be something that has borderline cases.

Idealized Idealization

On another occasion, I discussed the Aristotelian idea that the act of the mind does not use an organ. In an essay entitled Immaterial Aspects of Thought, James Ross claims that he can establish the truth of this position definitively. He summarizes the argument:

Some thinking (judgment) is determinate in a way no physical process can be. Consequently, such thinking cannot be (wholly) a physical process. If all thinking, all judgment, is determinate in that way, no physical process can be (the whole of) any judgment at all. Furthermore, “functions” among physical states cannot be determinate enough to be such judgments, either. Hence some judgments can be neither wholly physical processes nor wholly functions among physical processes.

Certain thinking, in a single case, is of a definite abstract form (e.g. N x N = N²), and not indeterminate among incompossible forms (see I below). No physical process can be that definite in its form in a single case. Adding cases even to infinity, unless they are all the possible cases, will not exclude incompossible forms. But supplying all possible cases of any pure function is impossible. So, no physical process can exclude incompossible functions from being equally well (or badly) satisfied (see II below). Thus, no physical process can be a case of such thinking. The same holds for functions among physical states (see IV below).

In essence, the argument is that squaring a number and similar things are infinitely precise processes, and no physical process is infinitely precise. Therefore squaring a number and similar things are not physical processes.

The problem is unfortunately with the major premise here. Squaring a number, and similar things, in the way that we in fact do them, are not infinitely precise processes.

Ross argues that they must be:

Can judgments really be of such definite “pure” forms? They have to be; otherwise, they will fail to have the features we attribute to them and upon which the truth of certain judgments about validity, inconsistency, and truth depend; for instance, they have to exclude incompossible forms or they would lack the very features we take to be definitive of their sorts: e.g., conjunction, disjunction, syllogistic, modus ponens, etc. The single case of thinking has to be of an abstract “form” (a “pure” function) that is not indeterminate among incompossible ones. For instance, if I square a number–not just happen in the course of adding to write down a sum that is a square, but if I actually square the number–I think in the form “N x N = N².”

The same point again. I can reason in the form, modus ponens (“If p then q“; “p“; “therefore, q”). Reasoning by modus ponens requires that no incompossible forms also be “realized” (in the same sense) by what I have done. Reasoning in that form is thinking in a way that is truth-preserving for all cases that realize the form. What is done cannot, therefore, be indeterminate among structures, some of which are not truth preserving. That is why valid reasoning cannot be only an approximation of the form, but must be of the form. Otherwise, it will as much fail to be truth-preserving for all relevant cases as it succeeds; and thus the whole point of validity will be lost. Thus, we already know that the evasion, “We do not really conjoin, add, or do modus ponens but only simulate them,” cannot be correct. Still, I shall consider it fully below.

“It will as much fail to be truth-preserving for all relevant cases as it succeeds” is an exaggeration here. If you perform an operation which approximates modus ponens, then that operation will be approximately truth preserving. It will not be equally truth preserving and not truth preserving.

I have noted many times in the past, as for example here, here, here, and especially here, that following the rules of syllogism does not in practice infallibly guarantee that your conclusions are true, even if your premises are in some way true, because of the vagueness of human thought and language. In essence, Ross is making a contrary argument: we know, he is claiming, that our arguments infallibly succeed; therefore our thoughts cannot be vague. But it is empirically false that our arguments infallibly succeed, so the argument is mistaken right from its starting point.

There is also a strawmanning of the opposing position here insofar as Ross describes those who disagree with him as saying that “we do not really conjoin, add, or do modus ponens but only simulate them.” This assumes that unless you are doing these things perfectly, rather than approximating them, then you are not doing them at all. But this does not follow. Consider a triangle drawn on a blackboard. Consider which of the following statements is true:

  1. There is a triangle drawn on the blackboard.
  2. There is no triangle drawn on the blackboard.

Obviously, the first statement is true, and the second false. But in Ross’s way of thinking, we would have to say, “What is on the blackboard is only approximately triangular, not exactly triangular. Therefore there is no triangle on the blackboard.” This of course is wrong, and his description of the opposing position is wrong in the same way.

Naturally, if we take “triangle” as shorthand for “exact rather than approximate triangle” then (2) will be true. And in a similar way, if take “really conjoin” and so on as shorthand for “really conjoin exactly and not approximately,” then those who disagree will indeed say that we do not do those things. But this is not a problem unless you are assuming from the beginning that our thoughts are infinitely precise, and Ross is attempting to establish that this must be the case, rather than claiming to take it as given. (That is, the summary takes it as given, but Ross attempts throughout the article to establish it.)

One could attempt to defend Ross’s position as follows: we must have infinitely precise thoughts, because we can understand the words “infinitely precise thoughts.” Or in the case of modus ponens, we must have an infinitely precise understanding of it, because we can distinguish between “modus ponens, precisely,” and “approximations of modus ponens“. But the error here is similar to the error of saying that one must have infinite certainty about some things, because otherwise one will not have infinite certainty about the fact that one does not have infinite certainty, as though this were a contradiction. It is no contradiction for all of your thoughts to be fallible, including this one, and it is no contradiction for all of your thoughts to be vague, including your thoughts about precision and approximation.

The title of this post in fact refers to this error, which is probably the fundamental problem in Ross’s argument. Triangles in the real world are not perfectly triangular, but we have an idealized concept of a triangle. In precisely the same way, the process of idealization in the real world is not an infinitely precise process, but we have an idealized concept of idealization. Concluding that our acts of idealization must actually be ideal in themselves, simply because we have an idealized concept of idealization, would be a case of confusing the way of knowing with the way of being. It is a particularly confusing case simply because the way of knowing in this case is also materially the being which is known. But this material identity does not make the mode of knowing into the mode of being.

We should consider also Ross’s minor premise, that a physical process cannot be determinate in the way required:

Whatever the discriminable features of a physical process may be, there will always be a pair of incompatible predicates, each as empirically adequate as the other, to name a function the exhibited data or process “satisfies.” That condition holds for any finite actual “outputs,” no matter how many. That is a feature of physical process itself, of change. There is nothing about a physical process, or any repetitions of it, to block it from being a case of incompossible forms (“functions”), if it could be a case of any pure form at all. That is because the differentiating point, the point where the behavioral outputs diverge to manifest different functions, can lie beyond the actual, even if the actual should be infinite; e.g., it could lie in what the thing would have done, had things been otherwise in certain ways. For instance, if the function is x(*)y = (x + y, if y < 10^40 years, = x + y +1, otherwise), the differentiating output would lie beyond the conjectured life of the universe.

Just as rectangular doors can approximate Euclidean rectangularity, so physical change can simulate pure functions but cannot realize them. For instance, there are no physical features by which an adding machine, whether it is an old mechanical “gear” machine or a hand calculator or a full computer, can exclude its satisfying a function incompatible with addition, say quaddition (cf. Kripke’s definition of the function to show the indeterminacy of the single case: quus, symbolized by the plus sign in a circle, “is defined by: x quus y = x + y, if x, y < 57, =5 otherwise”) modified so that the differentiating outputs (not what constitutes the difference, but what manifests it) lie beyond the lifetime of the machine. The consequence is that a physical process is really indeterminate among incompatible abstract functions.

Extending the list of outputs will not select among incompatible functions whose differentiating “point” lies beyond the lifetime (or performance time) of the machine. That, of course, is not the basis for the indeterminacy; it is just a grue-like illustration. Adding is not a sequence of outputs; it is summing; whereas if the process were quadding, all its outputs would be quadditions, whether or not they differed in quantity from additions (before a differentiating point shows up to make the outputs diverge from sums).

For any outputs to be sums, the machine has to add. But the indeterminacy among incompossible functions is to be found in each single case, and therefore in every case. Thus, the machine never adds.

There is some truth here, and some error here. If we think about a physical process in the particular way that Ross is considering it, it will be true that it will always be able to be interpreted in more than one way. This is why, for example, in my recent discussion with John Nerst, John needed to say that the fundamental cause of things had to be “rules” rather than e.g. fundamental particles. The movement of particles, in itself, could be interpreted in various ways. “Rules,” on the other hand, are presumed to be something which already has a particular interpretation, e.g. adding as opposed to quadding.

On the other hand, there is also an error here. The prima facie sign of this error is the statement that an adding machine “never adds.” Just as according to common sense we can draw triangles on blackboards, so according to common sense the calculator on my desk can certainly add. This is connected with the problem with the entire argument. Since “the calculator can add” is true in some way, there is no particular reason that “we can add” cannot be true in precisely the same way. Ross wishes to argue that we can add in a way that the calculator cannot because, in essence, we do it infallibly; but this is flatly false. We do not do it infallibly.

Considered metaphysically, the problem here is ignorance of the formal cause. If physical processes were entirely formless, they indeed would have no interpretation, just as a formless human (were that possible) would be a philosophical zombie. But in reality there are forms in both cases. In this sense, Ross’s argument comes close to saying “human thought is a form or formed, but physical processes are formless.” Since in fact neither is formless, there is no reason (at least established by this argument) why thought could not be the form of a physical process.


Those Who Walk Away from Omelas

In The Brothers Karamazov, after numerous examples of the torture of children and other horrors, Ivan Karamazov rejects theodicy with this argument:

“Besides, too high a price is asked for harmony; it’s beyond our means to pay so much to enter on it. And so I hasten to give back my entrance ticket, and if I am an honest man I am bound to give it back as soon as possible. And that I am doing. It’s not God that I don’t accept, Alyosha, only I most respectfully return him the ticket.”

“That’s rebellion,” murmured Alyosha, looking down.

“Rebellion? I am sorry you call it that,” said Ivan earnestly. “One can hardly live in rebellion, and I want to live. Tell me yourself, I challenge your answer. Imagine that you are creating a fabric of human destiny with the object of making men happy in the end, giving them peace and rest at last, but that it was essential and inevitable to torture to death only one tiny creature — that baby beating its breast with its fist, for instance — and to found that edifice on its unavenged tears, would you consent to be the architect on those conditions? Tell me, and tell the truth.”

“No, I wouldn’t consent,” said Alyosha softly.

Ivan’s argument is that a decent human being would not be willing to bring good out of evil in the particular way that happens in the universe, and therefore much less should a good God be willing to do that.

I will leave aside the theological argument for the moment, although it is certainly worthy of discussion.

Ursula Le Guin wrote a short story or thought experiment about this situation called The Ones Who Walk Away From Omelas. There is supposedly a perfectly happy society, but it all depends on the torture of a single child. Everybody knows about this, and at a certain age they are brought to see the child. Two very different responses to this are described:

The terms are strict and absolute; there may not even be a kind word spoken to the child.

Often the young people go home in tears, or in a tearless rage, when they have seen the child and faced this terrible paradox. They may brood over it for weeks or years. But as time goes on they begin to realize that even if the child could be released, it would not get much good of its freedom: a little vague pleasure of warmth and food, no doubt, but little more. It is too degraded and imbecile to know any real joy. It has been afraid too long ever to be free of fear. Its habits are too uncouth for it to respond to humane treatment. Indeed, after so long it would probably be wretched without walls about it to protect it, and darkness for its eyes, and its own excrement to sit in. Their tears at the bitter injustice dry when they begin to perceive the terrible justice of reality, and to accept it. Yet it is their tears and anger, the trying of their generosity and the acceptance of their helplessness, which are perhaps the true source of the splendor of their lives. Theirs is no vapid, irresponsible happiness. They know that they, like the child, are not free. They know compassion. It is the existence of the child, and their knowledge of its existence, that makes possible the nobility of their architecture, the poignancy of their music, the profundity of their science. It is because of the child that they are so gentle with children. They know that if the wretched one were not there snivelling in the dark, the other one, the flute-player, could make no joyful music as the young riders line up in their beauty for the race in the sunlight of the first morning of summer.

Now do you believe in them? Are they not more credible? But there is one more thing to tell, and this is quite incredible.

At times one of the adolescent girls or boys who go to see the child does not go home to weep or rage, does not, in fact, go home at all. Sometimes also a man or woman much older falls silent for a day or two, and then leaves home. These people go out into the street, and walk down the street alone. They keep walking, and walk straight out of the city of Omelas, through the beautiful gates. They keep walking across the farmlands of Omelas. Each one goes alone, youth or girl man or woman. Night falls; the traveler must pass down village streets, between the houses with yellow-lit windows, and on out into the darkness of the fields. Each alone, they go west or north, towards the mountains. They go on. They leave Omelas, they walk ahead into the darkness, and they do not come back. The place they go towards is a place even less imaginable to most of us than the city of happiness. I cannot describe it at all. It is possible that it does not exist. But they seem to know where they are going, the ones who walk away from Omelas.

Some would argue that the ones who walk away are simply confused. In the real world we are constantly permitting evils for the sake of other goods, and as a whole the evils included here are much greater than the torture of a single child. So Omelas should actually be much better and much more acceptable than the real world.

This response however is mistaken, because the real issue is one about the moral object. It is not enough to say that the good outweighs the evil, because a case of doing evil for the sake of good remains a case of doing evil. This is a little more confusing in the story, where one could interpret the actions of those who stay to be merely negative: they are not the ones who brought the situation about or maintain it. But in Ivan’s example, the question is whether you are willing to torture a child for the sake of the universal harmony, and Ivan’s implication is that if there is to be a universal harmony, God must be willing to torture people, and in general to cause all the evils of the world, to bring it about.

In any case, whether people are right or wrong about what they do, it is certainly true that we are much more willing to permit evils in a vague and general way to bring about good, than we are to produce evils in a very direct way to bring about good.

Not All Things are Water

The basic point of the post on Thales was that material things are composed of one or more material elements. The ancient materialists were accustomed not only to maintain this position, but also to assert that it also followed that there was nothing but those elements. Thus Democritus is said to have said,

By convention, sweet; by convention, bitter; by convention, hot; by convention,
cold; by convention, color; but in reality, atoms and void.

One could say that this is an example of the attitude of “this or nothing.” If everything is made of atoms, then either a thing is atoms, or it is nothing.

The correct answer here is not to say “this or that,” but “this and that,” that is, that things made of atoms are in some way atoms, but they are also things made of them, and the things made of them are not merely atoms.


More on Knowing and Being

I promised some examples of the point made in the previous post. I will give just a few here, although the point could easily be extended to many more.

Parmenides argues that nothing can come to be, since “what is not” cannot be or become. He also claims that “it is the same thing that can be thought and that can be,” and apparently this is intended to cover not only what is, but also the way that it is. Consequently, his position seems to imply a perfect identity between thought and being, even if it is ultimately inconsistent, since he says that human beings are wrong about change and the like, and this implies a discrepancy between thought and being.

Alexander Pruss argues that all words are sharply defined, at least in the mind of God.  He makes the argument, “Words are part of the world, so if there is vagueness in words, there is vagueness in the world.” This is no different, of course, from arguing that since words are part of reality, and some words are universal, there are universal things. There are universal things, if we mean by that universal terms or concepts, and there are vague things, if we mean by that vague words or concepts. But there are no universal cats or dogs, nor are there vague cats or dogs, despite the words “cat” and “dog” being vague.

C.S. Lewis argues, “Either we can know nothing or thought has reasons only, and no causes.” As I argued in the linked post, reasons in fact are a kind of final cause relative to their consequences, and they do not exclude efficient causes. This case might be somewhat less evident than the two previous cases, but I would argue that the cause of Lewis’s error here is the fact that, as St. Thomas says, the human mind can understand many things at once only by understanding them as one. Consequently, we can understand that an efficient cause can be for the sake of an end, but if the efficient cause and the final cause are presented as simply two causes, without the order that they actually have, they are not intelligible in this way.

These are examples of speculative errors resulting from confusing the mind’s way of knowing with the way that things are. I asserted in the last post, however, that practical errors can also result from this confusion. There is a very fundamental way this can happen: by nature we know things only if they have some relation to ourselves. The corresponding practical error would be to suppose that those things are real and important only in relation to ourselves. Look around you, and it appears that the world is centered on you. If you take this appearance and attribute an absolute truth to it, you will conclude that everything else has its being and importance in relation to you. Consider that you exist, and that all of the past has past out of existence. It might seem that the past only existed to bring you about.

St. Therese says about humility, “To me it seems that humility is truth. I do not know whether I am humble, but I do know that I see the truth in all things.” This is related to the examples I gave above. Since we know things in relation to ourselves, there is the temptation to suppose that things exist in the very same way. This leads to a false idea about our place in reality. Humility consists, on the contrary, in the truth about our place in reality, as I noted here.

The Cave

Book VII of Plato’s Republic begins with this conversation between Socrates and Glaucon:

And now, I said, let me show in a figure how far our nature is enlightened or unenlightened: –Behold! human beings living in a underground den, which has a mouth open towards the light and reaching all along the den; here they have been from their childhood, and have their legs and necks chained so that they cannot move, and can only see before them, being prevented by the chains from turning round their heads. Above and behind them a fire is blazing at a distance, and between the fire and the prisoners there is a raised way; and you will see, if you look, a low wall built along the way, like the screen which marionette players have in front of them, over which they show the puppets.

I see.
And do you see, I said, men passing along the wall carrying all sorts of vessels, and statues and figures of animals made of wood and stone and various materials, which appear over the wall? Some of them are talking, others silent.

You have shown me a strange image, and they are strange prisoners.
Like ourselves, I replied; and they see only their own shadows, or the shadows of one another, which the fire throws on the opposite wall of the cave?

True, he said; how could they see anything but the shadows if they were never allowed to move their heads?

And of the objects which are being carried in like manner they would only see the shadows?

Yes, he said.
And if they were able to converse with one another, would they not suppose that they were naming what was actually before them?

Very true.
And suppose further that the prison had an echo which came from the other side, would they not be sure to fancy when one of the passers-by spoke that the voice which they heard came from the passing shadow?

No question, he replied.
To them, I said, the truth would be literally nothing but the shadows of the images.

That is certain.

The human situation with respect to truth is somewhat like Plato’s cave dwellers. I argued in the previous post that all human knowledge is imperfect and vague. A more precise argument to the same effect would be the following.

There are two basic ways that we can learn the meaning of words. In one way, by having the meaning of the word explained to us. This requires the knowledge of other words. In another way, by learning the contexts in which the word is used. This does not necessarily require the previous knowledge of other words. Thus for example we learn the meaning of the word “red” by seeing it used in reference to red things, without a necessity of explaining the idea of red using other words. Third, we might learn the meaning of some words by a combination of the above methods.

Defining a word by other words cannot lead to an absolutely precise meaning unless the other words that are used have an absolutely precise meaning, so such a definition cannot be a source of absolute precision. And unless one points to all possible cases in which a word might be used, which is a physical impossibility, experiencing the contexts in which a word is used will also never lead to an absolutely precise meaning. It is consequently unlikely that you can arrive at an absolutely precise meaning by any combination of these methods, and consequently unlikely that you can arrive at such absolute precision in any way.

Language and thought are very closely connected. There are perhaps not many real cases of feral children, but the experience we do have of such situations suggests that someone who does not learn a language is basically unable to think. This is perhaps not true absolutely, but it is surely true that such a child cannot think clearly. Clear thinking requires language. This at least suggests that perfectly clear thinking would require perfectly clear language. But this is impossible, by the above argument. Consequently perfectly clear thinking is impossible for human beings.

This argument does not refute itself. It it of course impossible to have a proof that there are no proofs. Likewise, if absolute subjective certainty is impossible, as I have suggested, then it is impossible to have such certainty about this very fact. There is no inconsistency here. Likewise, if all thoughts and all arguments are vague, then these very thoughts and this very argument is vague. There is no inconsistency here.