Words, Meaning, and Formal Copies

January 28, 2019January 28, 2019 entirelyuseless Logic, Metaphysics, Science, Uncategorized Aristotelianism, Aristotle, Brain, Causes, Closure, Essence, Form, Hilary Lawson, Intelligence, Matter, Meaning, Words

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.

And Fire by Fire

January 26, 2019 entirelyuseless Metaphysics, Uncategorized Aristotle, Brain, Color, Details, Embodiment, Epistemology, Form, Image, Knowledge, Mind, Paradoxes, Rational Soul, Self-Reference, Understanding

Superstitious Nonsense asks about the last post:

So the answer here is that -some- of the form is present in the mind, but always an insufficient amount or accuracy that the knowledge will not be “physical”? You seem to be implying the part of the form that involves us in the self-reference paradox is precisely the part of the form that gives objects their separate, “physical” character. Is this fair? Certainly, knowing progressively more about an object does not imply the mental copy is becoming closer and closer to having a discrete physicality.

I’m not sure this is the best way to think about it. The self-reference paradox arises because we are trying to copy ourselves into ourselves, and thus we are adding something into ourselves, making the copy incomplete. The problem is not that there is some particular “part of the form” that we cannot copy, but that it is in principle impossible to copy it perfectly. This is different from saying that there is some specific “part” that cannot be copied.

Consider what happens when we make “non-physical” copies of something without involving a mind. Consider the image of a gold coin. There are certain relationships common to the image and to a gold coin in the physical world. So you could say we have a physical gold coin, and a non-physical one.

But wait. If the image of the coin is on paper, isn’t that a physical object? Or if the image is on your computer screen, isn’t your screen a physical object? And the image is just the colors on the screen, which are apparently just as “physical” (or non-physical) as the color of the actual coin. So why we would say that “this is not a physical coin?”

Again, as in the last post, the obvious answer is that the image is not made out of gold, while the physical coin is. But why not? Is it that the image is not accurate enough? If we made it more accurate, would it be made out of gold, or become closer to being made out of gold? Obviously not. This is like noting that a mental copy does not become closer and closer to being a physical one.

In a sense it is true that the reason the image of the coin is not physical is that it is not accurate enough. But that is because it cannot be accurate enough: the fact that it is an image positively excludes the copying of certain relationships. Some aspects can be copied, but others cannot be copied at all, as long as it is an image. On the other hand, you can look at this from the opposite direction: if you did copy those aspects, the image would no longer be an image, but a physical coin.

As a similar example, consider the copying of a colored scene into black and white. We can copy some aspects of the scene by using various shades of gray, but we cannot copy every aspect of the scene. There are simply not enough differences in a black and white image to reflect every aspect of a colored scene. The black and white image, as you make it more accurate, does not become closer to being colored, but this is simply because there are aspects of the colored scene that you never copy. If you do insist on copying those aspects, you will indeed make the black and white image into a colored image, and thus it will no longer be black and white.

The situation becomes significantly more complicated when we talk about a mind. In one way, there is an important similarity. When we say that the copy in the mind is “not physical,” that simply means that it is a copy in the mind, just as when we say that the image of the coin is not physical, it means that it is an image, made out of the stuff that images are made of. But just as the image is physical anyway, in another sense, so it is perfectly possible that the mind is physical in a similar sense. However, this is where things begin to become confusing.

Elsewhere, I discussed Aristotle’s argument that the mind is immaterial. Considering the cases above, we could put his argument in this way: the human brain is a limited physical object. So as long as the brain remains a brain, there are simply not enough potential differences in it to model all possible differences in the world, just as you cannot completely model a colored scene using black and white. But anything at all can be understood. Therefore we cannot be understanding by using the brain.

I have claimed myself that anything that can be, can be understood. But this needs to be understood generically, rather than as claiming that it is possible to understand reality in every detail simultaneously. The self-reference paradox shows that it is impossible in principle for a knower that copies forms into itself to understand itself in every aspect at once. But even apart from this, it is very obvious that we as human beings cannot understand every aspect of reality at once. This does not even need to be argued: you cannot even keep everything in mind at once, let alone understand every detail of everything. This directly suggests a problem with Aristotle’s argument: if being able to know all things suggests that the mind is immaterial, the obvious fact that we cannot know all things suggests that it is not.

Nonetheless, let us see what happens if we advance the argument on Aristotle’s behalf. Admittedly, we cannot understand everything at once. But in the case of the colored scene, there are aspects that cannot be copied at all into the black and white copy. And in the case of the physical coin, there are aspects that cannot be copied at all into the image. So if we are copying things into the brain, doesn’t that mean that there should be aspects of reality that cannot be copied at all into the mind? But this is false, since it would not only mean that we can’t understand everything, but it would also mean that there would be things that we cannot think about at all, and if it is so, then it is not so, because in that case we are right now talking about things that we supposedly cannot talk about.

Copying into the mind is certainly different from copying into a black and white scene or copying into a picture, and this does get at one of the differences. But the difference here is that the method of copying in the case of the mind is flexible, while the method of copying in the case of the pictures is rigid. In other words, we have a pre-defined method of copying in the case of the pictures that, from the beginning, only allows certain aspects to be copied. In the case of the mind, we determine the method differently from case to case, depending on our particular situation and the thing being copied. The result is that there is no particular aspect of things that cannot be copied, but you cannot copy every aspect at once.

In answer to the original question, then, the reason that the “mental copy” always remains mental is that you never violate the constraints of the mind, just as a black and white copy never violates the constraints of being black and white. But if you did violate the constraints of the black and white copy by copying every aspect of the scene, the image would become colored. And similarly, if you did violate the constraints of the mind in order to copy every aspect of reality, your mind would cease to be, and it would instead become the thing itself. But there is no particular aspect of “physicality” that you fail to copy: rather, you just ensure that one way or another you do not violate the constraints of the mind that you have.

Unfortunately, the explanation here for why the mind can copy any particular aspect of reality, although not every aspect at once, is rather vague. Perhaps a clearer explanation is possible? In fact, someone could use the vagueness to argue for Aristotle’s position and against mine. Perhaps my account is vague because it is wrong, and there is actually no way for a physical object to receive copied forms in this way.

Earth By Earth

January 24, 2019January 24, 2019 entirelyuseless Metaphysics, Uncategorized Distinction, Empedocles, Epistemology, Essence, Form, Formal Cause, Knowledge, Matt, Perfection, Prime Matter, Relation, Unity

In an earlier post I quoted 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.

I argued in that post that the mind does have something in common with what is known, and that this common thing is the form of the thing known. However, I took for granted that Empedocles is mistaken in assuming that the thing itself must be in common in order to be known.

I did not directly say why he is mistaken. If form makes a thing what it is, and the form of a thing known is in the mind, why does the mind not become that thing? If the form of earth is in your mind, then why is your mind not literally earth?

We will naturally be inclined to say that the form in your mind is apart from its proper matter, and that you need both form and matter to make a thing. And there is nothing wrong with this answer, as far as it goes, but it seems insufficient. Suppose you have a gold coin: what is its matter? The gold coin is presumably made out of atoms of gold, and since these atoms are not in your head, you do not see gold by gold. The problem is that atoms of gold also have some form, since this is just to say there is an answer when we ask, “What is this?”, and this will be true of anything whatever that you call matter. And there is nothing to prevent you from knowing that thing as well. There is nothing to prevent you from knowing the nature of gold atoms. And thus it seems that the matter will be present, and thus there should be actual gold in your mind.

Perhaps an Aristotelian will suggest that it is prime matter that is missing. But this answer will not work, because humans have this sort of matter in common with other things. And in any case, nothing is meant by “matter” in this sense except the ability to have the form. And since the knower can have the form, they have the ability to have the form, and thus matter. So nothing is missing, and the thing known should be literally in the knower.

Thus it appears that we have a reductio. Either my account of knowledge is mistaken, or earth should actually by known by earth, which it obviously is not.

The conclusion is only apparent, however. We can resolve it by going back to what I said about form in that post and the following one. Form is a network of relationships apt to make something one. But being one not only includes internal unity, but also separation from other things. For example, suppose we now have three gold coins, instead of one: each coin is one coin, and this depends on its parts being together, rather than in a loose heap of gold dust. But the fact that the coins are three depends on their separation from one another, and thus also the fact that each coin is “one” depends on that separation.

In other words, the form of a thing includes not only internal relationships, but also external relationships. This implies that to know the nature of a thing, one must know its external relationships. And to know a thing perfectly would require knowing both its internal and external relationships perfectly.

Now one of the things to which it is related is the very one who knows it. Thus, if the knower is to know the thing perfectly, they must perfectly understand the relationships between themselves and the thing. But this is not possible, for reasons explained in the post on self-reference. The person who attempts to know something perfectly is in the situation of someone attempting to draw a picture of themselves drawing a picture: to make a perfect copy of the gold coin, it is necessary to copy its context, which includes the knower. But this cannot be done; therefore perfect knowledge of the coin is impossible.

A different way to state the same analysis: “perfect copy” is a contradiction in terms, because such perfection would imply identity with the original, and thus not being a copy at all. In other words, perfect knowledge of a thing is impossible because perfect knowledge would imply, as in the argument of Empedocles, that one’s knowledge would literally be the thing known, and thus not knowledge at all.

Place, Time, and Universals

January 22, 2019 entirelyuseless Metaphysics, Uncategorized Essence, Existence, Form, Kantian Error, Matter, Nominalism, Numbers, Place, Plato, Realism, Reality, Relation, Senses, Space, Time, Together, Unity, Universals

Consider the following three statements:

1. The chair and keyboard that I am currently using are both here in this room.

2. The chair and keyboard that I am currently using both exist in January 2019.

3. The chair and keyboard that I am currently using both came in the color black.

All three claims, considered as everyday statements, happen to be true. They also have a common subject, and something common about the predicate, namely the “in.” We have “in this room,” “in January,” and “in the color black.” Now someone might object that this is a mere artifact of my awkward phrasing: obviously, I deliberately chose these formulations with this idea in mind. So this seems to be a mere verbal similarity, and a meaningless one at that.

The objection seems pretty reasonable, but I will argue that it is mistaken. The verbal similarity is not accidental, despite the fact that I did indeed choose the formulations deliberately with this idea in mind. As I intend to argue, there is indeed something common to the three cases, namely that they represent various ways of existing together.

The three statements are true in their ordinary everyday sense. But consider the following three questions:

1. Are the chair and keyboard really in the same room, or is this commonality a mere appearance?

2. Do the chair and keyboard really exist in the same month, or is this commonality a mere appearance?

3. Did the chair and keyboard really come in the same color, or is this commonality a mere appearance?

These questions are like other questions which ask whether something is “really” the case. There is no such thing as being “really” on the right apart from the ordinary understanding of being on the right, and there is no such thing as being really in the same room apart from the ordinary everyday understanding of being in the same room. The same thing applies to the third question about color.

The dispute between realism and nominalism about universals starts in the following way, roughly speaking:

Nominalist: We say that two things are black. But obviously, there are two things here, and no third thing, and the two are not the same thing. So the two do not really have anything in common. Therefore “two things are black” is nothing but a way of speaking.

Platonic Realist: Obviously, the two things really are black. But what is really the case is not just a way of speaking. So the two really do have something in common. Therefore there are three things here: the two ordinary things, and the color black.

Since the Platonic Realist here goes more against common speech in asserting the existence of “three things” where normally one would say there are “two things,” the nominalist has the apparent advantage at this point, and this leads to more qualified forms of realism. In reality, however, one should have stopped the whole argument at this point. The two positions above form a Kantian dichotomy, and as in all such cases, both positions affirm something true, and both positions affirm something false. In this particular case, the nominalist acts as the Kantian, noting that universality is a mode of knowing, and therefore concludes that it is a mere appearance. The Platonic Realist acts as the anti-Kantian, noting that we can know that several things are in fact black, and concluding that universality is a mode of being as such.

But while universality is a way of knowing, existing together is a way of being, and is responsible for the way of knowing. In a similar way, seeing both my chair and keyboard at the same time is a way of seeing things, but this way of seeing is possible because they are here together in the room. Likewise, I can know that both are black, but this knowledge is only possible because they exist together “in” the color black. What does this mean, exactly? Since we are discussing sensible qualities, things are both in the room and black by having certain relationships with my senses. They exist together in those relationships with my senses.

There is no big difference when I ask about ideas. If we ask what two dogs have in common in virtue of both being dogs, what they have in common is a similar relationship to my understanding. They exist together in that relationship with my understanding.

It might be objected that this is circular. Even if what is in common is a relationship, there is still something in common, and that seems to remain unexplained. Two red objects have a certain relationship of “appearing red” to my eyes, but then do we have two things, or three? The two red things, or the two red things and the relationship of “appearing red”? Or is it four things: two red things, and their two relationships of appearing red? So which is it?

Again, there is no difference between these questions and asking whether a table is really on the left or really on the right. It is both, relative to different things, and likewise all three of these methods of counting are valid, depending on what you want to count. As I have said elsewhere, there are no hidden essences, no “true” count, no “how many things are really there?”

“Existing together,” however, is a reality, and is not merely a mode of knowing. This provides another way to analyze the problem with the nominalist / Platonic realist opposition. Both arguments falsely assume that existing together is either logically derivative or non-existent. As I said in the post on existential relativity, it is impossible to deduce the conclusion that many things exist from a list of premises each affirming that a single thing exists, if only because “many things” does not occur as a term in that list. The nominalist position cannot explain the evident fact that both things are black. Likewise, even if there are three things, the two objects and “black,” this would not explain why the two objects are black. The two objects are not the third, since there are three. So there must be yet another object, perhaps called “participation”, which connects the two objects and blackness. And since they both have participation, there must be yet another object, participation in general, in which both objects are also participating. Obviously none of this is helping: the problem was the assumption from the start that togetherness (whether in place, time, or color) could be something logically derivative.

(Postscript: the reader might notice that in the linked post on “in,” I said that a thing is considered to be in something as form in matter. This seems odd in the context of this post, since we are talking about being “in a color,” and a color would not normally be thought of as material, but as formal. But this simply corresponds with the fact that it would be more usual to say that the color black is in the chair, rather than the chair in the black. This is because it is actually more correct: the color black is formal with respect to the chair, not material. But when we ask, “what things can come in the color black,” we do think of black as though it were a kind of formless matter that could take various determinate forms.)

Fair and Unfair Logic

January 14, 2019January 14, 2019 entirelyuseless Logic, Metaphysics, Politics, Uncategorized Alexander Pruss, Conventions, Epikeia, Fairness, God, Justice, Law, Parmenides, St. Thomas, Vagueness

St. Thomas discusses cases in which one should not follow the law:

As stated above (Article 4), every law is directed to the common weal of men, and derives the force and nature of law accordingly. Hence the jurist says [Pandect. Justin. lib. i, ff., tit. 3, De Leg. et Senat.]: “By no reason of law, or favor of equity, is it allowable for us to interpret harshly, and render burdensome, those useful measures which have been enacted for the welfare of man.” Now it happens often that the observance of some point of law conduces to the common weal in the majority of instances, and yet, in some cases, is very hurtful. Since then the lawgiver cannot have in view every single case, he shapes the law according to what happens most frequently, by directing his attention to the common good. Wherefore if a case arise wherein the observance of that law would be hurtful to the general welfare, it should not be observed. For instance, suppose that in a besieged city it be an established law that the gates of the city are to be kept closed, this is good for public welfare as a general rule: but, it were to happen that the enemy are in pursuit of certain citizens, who are defenders of the city, it would be a great loss to the city, if the gates were not opened to them: and so in that case the gates ought to be opened, contrary to the letter of the law, in order to maintain the common weal, which the lawgiver had in view.

He calls the attitude that leads one to set aside the law in such cases “epikeia,” or “equity,” which in this context means something like fairness or moderation:

As stated above (I-II:96:6), when we were treating of laws, since human actions, with which laws are concerned, are composed of contingent singulars and are innumerable in their diversity, it was not possible to lay down rules of law that would apply to every single case. Legislators in framing laws attend to what commonly happens: although if the law be applied to certain cases it will frustrate the equality of justice and be injurious to the common good, which the law has in view. Thus the law requires deposits to be restored, because in the majority of cases this is just. Yet it happens sometimes to be injurious—for instance, if a madman were to put his sword in deposit, and demand its delivery while in a state of madness, or if a man were to seek the return of his deposit in order to fight against his country. On these and like cases it is bad to follow the law, and it is good to set aside the letter of the law and to follow the dictates of justice and the common good. This is the object of “epikeia” which we call equity. Therefore it is evident that “epikeia” is a virtue.

“Fairness” is probably a good translation here, since someone who rigidly demands the application of the law in such a situation would often be called unfair in relation to the people involved.

Someone might object that much of the benefit of having a law directly depends on following it consistently, without making exceptions based on minute analysis of particular situations, as we saw in the last post. This is correct as far as it goes, but St. Thomas is not talking about analyzing each situation in detail and making an exception whenever there appears to be a benefit, but rather talking about situations which are extremely different from the situations considered by the law. Thus he says in the reply to the second objection:

He who follows the intention of the lawgiver, does not interpret the law simply; but in a case in which it is evident, by reason of the manifest harm, that the lawgiver intended otherwise. For if it be a matter of doubt, he must either act according to the letter of the law, or consult those in power.

To the degree that “laws of logic” can be analogously interpreted as rules for sensible thought and speech, telling one to behave in some ways and not in others, similar principles will apply. Thus, for example, an atheist confronted with the argument of Alexander Pruss for the existence of God based on the indeterminacy of language might not only be inclined to call it sophistical, but to add that it is an unfair way to argue. And indeed it is, precisely in the sense that it applies the rule “either say that A is B or say that A is not B” to situations for which it was not intended, namely situations where B is simply too vague to say. The rule is intended to make people think and speak sensibly, but Pruss is abusing the rule with the opposite result: that he does not speak and think sensibly.

Someone might agree that this is reasonable insofar as we are considering these laws as rules of behavior, but another issue comes up. Human laws are really intended to exclude some kinds of behavior that are really possible. And likewise, rules of logic are really intended to exclude some kinds of behavior that are really possible, e.g. making arguments like:

A: You always say I am wrong.

B: I said you were right about X.

A: See, you just said I was wrong again. You always say I am wrong!

I know from experience that this behavior is possible, and it does violate the laws of logic considered as rules of behavior. But someone might add that the laws of logic are also based on the nature of reality itself, and for this very reason we said that they are not conventions, but could not have been otherwise. So it seems to follow that it should be possible to expound the laws of logic in a form in which they are truly exceptionless, by expressing reality as it truly is.

There is some truth here, but there is also a problem analogous to a similar objection about human law. Consider the third objection and reply in the above article from St. Thomas:

Objection 3. Further, every wise man knows how to explain his intention by words. But those who framed the laws should be reckoned wise: for Wisdom says (Proverbs 8:15): “By Me kings reign, and lawgivers decree just things.” Therefore we should not judge of the intention of the lawgiver otherwise than by the words of the law.

…

Reply to Objection 3. No man is so wise as to be able to take account of every single case; wherefore he is not able sufficiently to express in words all those things that are suitable for the end he has in view. And even if a lawgiver were able to take all the cases into consideration, he ought not to mention them all, in order to avoid confusion: but should frame the law according to that which is of most common occurrence.

The objection here is similar. If there are cases where it wouldn’t be good to apply the law, the lawgiver ought to have enumerated those cases. St. Thomas replies that in reality you will not foresee every case, and that even if you could, enumerating them would simply cause confusion.

A similar thing applies if we consider the laws of logic. You can say, “If you say that A is B in an infinitely precise sense, and that B is C in an infinitely precise sense, you should also say that A is C,” and your claim might be exceptionless. The problem is that your claim has no cases: no one ever says anything in an infinitely precise sense.

And on the other hand, if you try to make your claim include some actual cases, you will not be able to avoid the possibility of exceptions, just as the human lawgiver does not foresee all cases. And as in the case of human law, if you attempt to enumerate all cases, you will simply cause confusion. Thus, for example, someone might say that the problem in the case of Queen Elizabeth is that we simply don’t have a precise enough definition for “old,” and they might then attempt to give a precise definition. But this would have several results:

1. First, the new word “old” would not have the same meaning as the original word, because the very fact that the original word is vague is part of what the word is. It is not accidental; it is not meant to have a precise cut-off.

2. Someone might attempt to remedy the above flaw by enumerating various circumstances, rather than giving a precise cut-off. “If you are less then 10 years old and you say that someone is ‘old,’ it signifies someone who is at least 15.” “If you are in your 30s and you say that someone is ‘old’, it signifies that they are at least 67.” And so on. But attempting to fix the first problem, you have simply compounded it. The new word still does not have the same meaning as the original word, because the original word was meant to be flexible; even your new rules have too much rigidity.

You could attempt to remedy the above problems by listing all the situations where people in fact use the word “old,” but that is not a definition: it is just an indefinitely long list. What St. Thomas said about human law, that it “ought not to mention them all,” is equally true about this situation. The point of defining “old” is to provide an explanation which is both general and flexible. Someone might argue that we should provide a list of all possible circumstances and what should be done in those circumstances, in order to avoid the flexibility of “epikeia,” but such an attempt would be absurd, and harmful to a good life. And it is equally absurd when we attempt to apply the same process to logic or to definitions, and harmful to sensible thought and speech.

What about reality itself? Isn’t it an exceptionless reality that a thing is what it is? Indeed. But this is neither a rule of behavior nor of speech. Nor is it a rule making something be some way; reality does not need something else to make sure that it turns out to be reality rather than something else. There is simply nothing else to be. Parmenides was right at least to this degree.

C.S. Lewis on Punishment

January 6, 2019January 6, 2019 entirelyuseless Ethics, Politics, Uncategorized Authority, Bryan Caplan, C.S. Lewis, Common Good, Community, Deserving, Evil, Good, Justice, Kavka's Toxin, Kelsey Piper, Law, Natural Laws, Punishment, Retribution, St. Thomas, Thomas Hobbes, Utilitarianism

C.S. Lewis discusses a certain theory of punishment:

In England we have lately had a controversy about Capital Punishment. … My subject is not Capital Punishment in particular, but that theory of punishment in general which the controversy showed to be almost universal among my fellow-countrymen. It may be called the Humanitarian theory. Those who hold it think that it is mild and merciful. In this I believe that they are seriously mistaken. I believe that the “Humanity” which it claims is a dangerous illusion and disguises the possibility of cruelty and injustice without end. I urge a return to the traditional or Retributive theory not solely, not even primarily, in the interests of society, but in the interests of the criminal.

According to the Humanitarian theory, to punish a man because he deserves it, and as much as he deserves, is mere revenge, and, therefore, barbarous and immoral. It is maintained that the only legitimate motives for punishing are the desire to deter others by example or to mend the criminal. When this theory is combined, as frequently happens, with the belief that all crime is more or less pathological, the idea of mending tails off into that of healing or curing and punishment becomes therapeutic. Thus it appears at first sight that we have passed from the harsh and self-righteous notion of giving the wicked their deserts to the charitable and enlightened one of tending the psychologically sick. What could be more amiable? One little point which is taken for granted in this theory needs, however, to be made explicit. The things done to the criminal, even if they are called cures, will be just as compulsory as they were in the old days when we called them punishments. If a tendency to steal can be cured by psychotherapy, the thief will no doubt be forced to undergo treatment. Otherwise, society cannot continue.

My contention is that this doctrine, merciful though it appears, really means that each one of us, from the moment he breaks the law, is deprived of the rights of a human being.

The reason is this. The Humanitarian theory removes from Punishment the concept of Desert. But the concept of Desert is the only connecting link between punishment and justice. It is only as deserved or undeserved that a sentence can be just or unjust. I do not here contend that the question “Is it deserved?” is the only one we can reasonably ask about a punishment. We may very properly ask whether it is likely to deter others and to reform the criminal. But neither of these two last questions is a question about justice. There is no sense in talking about a “just deterrent” or a “just cure”. We demand of a deterrent not whether it is just but whether it will deter. We demand of a cure not whether it is just but whether it succeeds. Thus when we cease to consider what the criminal deserves and consider only what will cure him or deter others, we have tacitly removed him from the sphere of justice altogether; instead of a person, a subject of rights, we now have a mere object, a patient, a “case”.

Later in the essay, he gives some examples of how the Humanitarian theory will make things worse, as in the following case:

The immediate starting point of this article was a letter I read in one of our Leftist weeklies. The author was pleading that a certain sin, now treated by our laws as a crime, should henceforward be treated as a disease. And he complained that under the present system the offender, after a term in gaol, was simply let out to return to his original environment where he would probably relapse. What he complained of was not the shutting up but the letting out. On his remedial view of punishment the offender should, of course, be detained until he was cured. And of course the official straighteners are the only people who can say when that is. The first result of the Humanitarian theory is, therefore, to substitute for a definite sentence (reflecting to some extent the community’s moral judgment on the degree of ill-desert involved) an indefinite sentence terminable only by the word of those experts–and they are not experts in moral theology nor even in the Law of Nature–who inflict it. Which of us, if he stood in the dock, would not prefer to be tried by the old system?

This post will make three points:

(1) The “Humanitarian” theory is basically correct about the purpose of punishment.

(2) C.S. Lewis is right that there are good reasons to talk about justice and about what someone deserves or does not deserve. Such considerations are, as he supposes, essential to a system of justice. Lewis is also right to suppose that many supporters of the Humanitarian theory, despite being factually correct about the purpose of punishment, are mistaken in opposing such talk as cruel and immoral.

(3) Once the Humanitarian theory is corrected in such a way as to incorporate the notion of “just deserts”, Lewis’s objections fail.

Consider the first point, the purpose of punishment. There was already some discussion of this in a previous post. In a sense, everyone already knows that Humanitarians are right about the basic purpose of punishment, including C.S. Lewis. Lewis points out the obvious fact himself: whatever you call them and however you explain them, punishments for crime are compulsory in a society because “otherwise, society cannot continue.” But why cannot society continue without punishment? What supposedly would happen if you did not have any punishments? What would actually happen if a government credibly declared that it would never again punish anything?

What would actually happen, of course, is that this amount to a declaration that the government was dissolving itself, and someone else would take over and establish new crimes and new punishments, either at that same level of generality as the original government, or at more local levels (e.g. perhaps each town would become a city-state.) In any case each of the new governments would still have punishments, so you would not have succeeded in abolishing punishment.

What happens in the imaginary situation where you do succeed, where no one else takes over? This presumably would be a Hobbesian “state of nature,” which is not a society at all. In other words, the situation simply does not count as a society at all, unless certain rules are followed pretty consistently. And those rules will not be followed consistently without punishments. So it is easy to see why punishment exists: to make sure that those rules are followed, generally speaking. Since rules are meant to make some things happen and prevent other things, punishment is simply to make sure that the rules actually function as rules. But this is exactly what the Humanitarian theory says is the purpose of punishment: to make others less likely to break the rules, and to make the one who has already broken the rules less likely to break them in the future.

Thus C.S. Lewis himself is implicitly recognizing that the Humanitarians are basically right about the purpose of punishment, in acknowledging that punishment is necessary for the very existence of society.

Let’s go on to the second point, the idea of just deserts. C.S. Lewis is right that many proponents of Humanitarian view either believe that the idea is absurd, or that if there is such a thing as deserving something, no one can deserve something bad, or that if people can deserve things, this is not really a relevant consideration for a justice system. For example, it appears that Kelsey Piper blogging at The Unit of Caring believes something along these lines; here she has a pretty reasonable post responding to some criticisms analogous to those of C.S. Lewis to the theory.

I will approach this by saying a few things about what a law is in general. St. Thomas defines law: “It is nothing else than an ordinance of reason for the common good, made by him who has care of the community, and promulgated.” But let’s drop the careful formulation and the conditions, as necessary as they may be. St. Thomas’s definition is simply a more detailed account of what everyone knows: a law is a rule that people invent for the benefit of a community.

Is there such a thing as an unjust law? In St. Thomas’s account, in a sense yes, and in a sense no. “For the common good” means that the law is beneficial. In that sense, if the law is “unjust,” it is harmful, and thus it is not for the common good. And in that sense it does not satisfy the definition of a law, and so is not a law at all. But obviously ordinary people will call it a law anyway, and in that way it is an unjust law, because it is unsuited to the purpose of a law.

Now here’s the thing. An apparent rule is not really a rule at all unless it tends to make something happen. In the case that we are talking about, namely human law, that generally means that laws require penalties for being broken in order to be laws at all. It is true that in a society with an extremely strong respect for law, it might occasionally be possible to make a law without establishing any specific penalty, and still have that law followed. The community would still need to leave itself the option of establishing a penalty; otherwise it would just be advice rather than a law.

This causes a slight problem. The purpose of a law is to make sure that certain things are done and others avoided, and the reason for penalties is to back up this purpose. But when someone breaks the law, the law has already failed. The very thing the law was meant to prevent has already happened. And what now? Should the person be punished? Why? To prevent the law from being broken? It has already been broken. So we cannot prevent it from being broken. And the thing is, punishment is something bad. So to inflict the punishment now, after the crime has already been committed, seems like just stacking one bad thing on top of another.

At this point the “Retributive” theory of justice will chime in. “We should still inflict the punishment because it is just, and the criminal deserves it.”

This is the appeal of the Humanitarian’s condemnation of the retributive theory. The Retributive theory, the Humanitarian will say, is just asserting that something bad, namely the punishment, in this situation, is something good, by bringing in the idea of “justice.” But this is a contradiction: something bad is bad by definition, and cannot be good.

The reader is perhaps beginning to understand the placement of the previous post. A law is established, with a penalty for being broken, in order to make certain things happen. This is like intending to drink the toxin. But if someone breaks the law, what is the point of inflicting the punishment? And the next morning, what is the point of drinking the toxin in the afternoon, when the money is already received or not? There is a difference of course, because in this case the dilemma only comes up because the law has been broken. We could make the cases more analogous, however, by stipulating in the case of Kavka’s toxin that the rich billionaire offers this deal: “The million will be found in your account, with a probability of 99.99%, if and only if you intend to drink the toxin only if the million is not found in your account (which will happen only in the unlucky 0.01% of cases), and you do not need to drink or intend to drink in the situation where the million is found in your account.” In this situation, the person might well reason thus:

If the morning comes and the million is not in my account, why on earth would I drink the toxin? This deal is super unfair.

Nonetheless, as in the original deal, there is one and only one way to get the million: namely, by planning to drink the toxin in that situation, and by planning not to reconsider, no matter what. As in the case of law, the probability factor that I added means that it is possible not to get the million, although you probably will. But the person who formed this intention will go through with it and drink the toxin, unless they reconsider; and they had the definite intention of not reconsidering.

The situations are now more analogous, but there is still an additional difference, one that makes it even easier to decide to follow the law than to drink the toxin. The only reason to commit to drinking the toxin was to get the million, which, in our current situation, has already failed. But in the case of the law, one purpose was to prevent the criminal from performing a certain action, and that purpose has already failed. But it also has the purpose of preventing them from doing it in the future, and preventing others from doing it. So there additional motivations for carrying out the law.

We can leave the additional difference to the side for now, however. The point would be essentially valid even if you made a law to prevent one particular act, and that act ended up being done. The retributionist would say, “Ok, so applying the punishment at this point will not prevent the thing it was meant to prevent. But it is just, and the criminal deserves it, and we should still inflict it.” And they are right: the whole idea of establishing the the rule included the idea that the punishment would actually be carried out, in this situation. There was a rule against reconsidering the rule, just as the fellow in the situation with the toxin planned not to reconsider their plan.

What is meant when it is said that a punishment is “just,” and that the criminal “deserves it,” then is simply that it is what is required by the rules we have established, and that those rules are reasonable ones.

Someone will object here. It seems that this cannot be true, because some punishments are wicked and unjust even though there were rules establishing them. And it seems that this is because people simply do not deserve those things: so there must be such a thing as “what they deserve,” in itself and independent of any rules. But this is where we must return to the point made above about just and unjust laws. One hears, for example, of cases in which people were sentenced to death for petty theft. We can agree that this is unjust in itself: but this is precisely because the rule, “someone who steals food should be killed,” is not a reasonable rule which will benefit the community. You might have something good in mind for it, namely to prevent stealing, but if you carry out the penalty on even one occasion, you have done more harm than all the stealing put together. The Humanitarians are right that the thing inflicted in a punishment is bad, and remains bad. It does not become something good in that situation. And this is precisely why it needs some real proportion to the crime.

We can analyze the situation in two ways, from the point of view of the State, considered as though a kind of person, and from the point of the view of the person who carries out the law. The State makes a kind of promise to inflict a punishment for some crimes, in such a way as to minimize the total harm of both the crimes and their punishment. Additionally, to some extent it promises not to reconsider this in situation where a crime is actually committed. “To some extent” here is of course essential: such rules are not and should not be absolutely rigid. If the crime is actually committed, the State is in a situation like our person who finds himself without the million and having committed to drink the toxin in that situation: the normal result of the situation will be that the State inflicts the punishment, and the person drinks the toxin, without any additional consideration of motivations or reasons.

From the point of view of the individual, he carries out the sentence “because it is just,” i.e. because it is required by reasonable rules which we have established for the good of the community. And that, i.e. carrying out reasonable laws, is a good thing, even though the material content includes something bad. The moral object of the executioner is the fulfillment of justice, not the killing of a person.

We have perhaps already pointed the way to the last point, namely that with the incorporation of the idea of justice, C.S. Lewis’s criticisms fail. Lewis argues that if the purpose of punishment is medicinal, then it is in principle unlimited: but this is not true even of medicine. No one would take medicine which would cause more harm than the disease, nor would it be acceptable to compel someone else to take such medicine.

More importantly, Lewis’s criticism play off the problems that are caused by believing that one needs to consider at every point, “will the consequences of this particular punishment or action be good or not?” This is not necessary because this is not the way law works, despite the fact that the general purpose is the one supposed. Law only works because to some extent it promises not to reconsider, like our fellow in the case of Kavka’s toxin. Just as you are wrong to focus on whether “drinking the toxin right now will harm me and not benefit me”, so the State would be wrong to focus too much on the particular consequences of carrying out the law right now, as opposed to the general consequences of the general law.

Thus for example Lewis supposes rulers considering the matter in an entirely utilitarian way:

But that is not the worst. If the justification of exemplary punishment is not to be based on desert but solely on its efficacy as a deterrent, it is not absolutely necessary that the man we punish should even have committed the crime. The deterrent effect demands that the public should draw the moral, “If we do such an act we shall suffer like that man.” The punishment of a man actually guilty whom the public think innocent will not have the desired effect; the punishment of a man actually innocent will, provided the public think him guilty. But every modern State has powers which make it easy to fake a trial. When a victim is urgently needed for exemplary purposes and a guilty victim cannot be found, all the purposes of deterrence will be equally served by the punishment (call it “cure” if you prefer) of an innocent victim, provided that the public can be cheated into thinking him guilty. It is no use to ask me why I assume that our rulers will be so wicked.

As said, this is not the way law works. The question will be about which laws are reasonable and beneficial in general, not about whether such and such particular actions are beneficial in particular cases. Consider a proposed law formulated with such an idea in mind:

When the ruling officials believe that it is urgently necessary to deter people from committing a crime, and no one can be found who has actually committed it, the rulers are authorized to deceive the public into believing that an innocent man has committed the crime, and to punish that innocent man.

It should not be necessary to make a long argument that as a general rule, this does not serve the good of a community, regardless of might happen in particular cases. In this way it is quite right to say that this is unjust in itself. This does not, however, establish that “what someone deserves” has any concrete content which is not established by law.

As a sort of footnote to this post, we might note that “deserts” are sometimes extended to natural consequences in much the way “law” is extended to laws of nature, mathematics, or logic. For example, Bryan Caplan distinguishes “deserving” and “undeserving” poor:

I propose to use the same standard to identify the “deserving” and “undeserving” poor. The deserving poor are those who can’t take – and couldn’t have taken – reasonable steps to avoid poverty. The undeserving poor are those who can take – or could have taken – reasonable steps to avoid poverty. Reasonable steps like: Work full-time, even if the best job you can get isn’t fun; spend your money on food and shelter before you get cigarettes or cable t.v.; use contraception if you can’t afford a child. A simple test of “reasonableness”: If you wouldn’t accept an excuse from a friend, you shouldn’t accept it from anyone.

This is rather different from the sense discussed in this post, but you could view it as an extension of it. It is a rule (of mathematics, really) that “if you spend all of your money you will not have any left,” and we probably do not need to spend much effort trying to change this situation, considered in general, even if we might want to change it for an individual.

Kavka’s Toxin

January 5, 2019January 6, 2019 entirelyuseless Ethics, Uncategorized Belief, Decision Theory, Decisions, Future, Gregory Kavka, Kavka's Toxin, Prediction

Gregory Kavka discusses a thought experiment:

You are feeling extremely lucky. You have just been approached by an eccentric billionaire who has offered you the following deal. He places before you a vial of toxin that, if you drink it, will make you painfully ill for a day, but will not threaten your life or have any lasting effects. (Your spouse, a crack biochemist, confirms the properties of the toxin.) The billionaire will pay you one million dollars tomorrow morning if, at midnight tonight, you intend to drink the toxin tomorrow afternoon. He emphasizes that you need not drink the toxin to receive the money; in fact, the money will already be in your bank account hours before the time for drinking it arrives, if you succeed. (This is confirmed by your daughter, a lawyer, after she examines the legal and financial documents that the billionaire has signed.) All you have to do is sign the agreement and then intend at midnight tonight to drink the stuff tomorrow afternoon. You are perfectly free to change your mind after receiving the money and not drink the toxin. (The presence or absence of the intention is to be determined by the latest ‘mind-reading’ brain scanner and computing device designed by the great Doctor X. As a cognitive scientist, materialist, and former student of Doctor X, you have no doubt that the machine will correctly detect the presence or absence of the relevant intention.)

Confronted with this offer, you gleefully sign the contract, thinking ‘what an easy way to become a millionaire’. Not long afterwards, however, you begin to worry. You had been thinking that you could avoid drinking the toxin and just pocket the million. But you realize that if you are thinking in those terms when midnight rolls around, you will not be intending to drink the toxin tomorrow. So maybe you will actually have to drink the stuff to collect the money. It will not be pleasant, but it is sure worth a day of suffering to become a millionaire.

However, as occurs to you immediately, it cannot really be necessary to drink the toxin to pocket the money. That money will either be or not be in your bank account by 10 a.m. tomorrow, you will know then whether it is there or not, and your drinking or not drinking the toxin hours later cannot affect the completed financial transaction. So instead of planning to drink the toxin, you decide to intend today to drink it and then change your mind after midnight. But if that is your plan, then it is obvious that you do not intend to drink the toxin. (At most you intend to intend to drink it.) For having such an intention is incompatible with planning to change your mind tomorrow morning.

The discussion goes on from here for some time, but the resolution of the puzzle is easier than Kavka realizes. There is only a problem because it is implicitly assumed that the belief that you will or will not drink the toxin is something different from the intention to drink it. But in the case of voluntary actions, these are one and the same. The reason you cannot intend to drink the toxin without thinking that you will end up drinking it is simply that the intention to drink the toxin is the belief that you will end up drinking it. If the brain scanner works correctly, it registers that you intend to drink the toxin if you in fact think you will end up drinking it, and it registers that you do not intend this if you in fact think you will not drink it.

Is there a problem on the practical level? That is, is it possible for someone to get the million, or is it impossible because everyone in such a situation would expect that they would reconsider tomorrow morning, and therefore they will not believe that they will end up drinking it?

Possibly, and for some people. It is entirely possible in some situations that beliefs about what you will in fact do, apparently simply based on facts, entirely prevent certain decisions and intentions. Thus if someone has tried dozens of times in the past to give up smoking, and consistently failed, it will become more and more difficult to intend to give up smoking, and may very well become impossible.

However, Kavka gives a theoretical argument that this should be impossible in the case of his thought experiment:

Thus, we can explain your difficulty in earning a fortune: you cannot intend to act as you have no reason to act, at least when you have substantial reason not to act. And you have (or will have when the time comes) no reason to drink the toxin, and a very good reason not to, for it will make you quite sick for a day.

Again, it may well be that this reasoning would cause an individual to fail to obtain the million. But it is not necessary for this to happen. For the person does have a reason to intend to drink the toxin in the first place: namely, in order to obtain the million. And tomorrow morning their decision, i.e. their belief that they will drink the toxin, will be an efficient cause of them actually drinking the toxin, unless they reconsider. Thus if a person expects to reconsider, they may well fail to obtain the million. But someone wanting to obtain the million will also therefore plan not to reconsider. And tomorrow morning their belief that they will not reconsider will be an efficient cause of them not reconsidering, unless they reconsider their plan not to reconsider. And so on.

Thus, someone can only obtain the million if they plan to drink the toxin, they plan not to reconsider this plan, and so on. And someone with this plan can obtain the million. And maybe they will end up drinking the toxin and maybe they won’t; but the evening before, they believe that they factually will drink it. If they don’t, they fail to obtain the million. And they may well in fact drink it, simply by carrying out the original plan: going about their day without thinking about it, and simply drinking that afternoon, without any additional consideration of reasons to drink or not drink.

There is also a way to obtain the million and avoid drinking, but it cannot happen on purpose. This can happen only in one way: namely, by being lucky. You plan on every level not to reconsider, and expect this to happen, but luckily you end up being mistaken, and you do reconsider, despite expecting not to. In this case you both obtain the million, and avoid the drink.

Laws of Logic

January 3, 2019January 3, 2019 entirelyuseless Logic, Metaphysics, Uncategorized Carin Robinson, Facts, Games, Law, Rules

In the last post, we quoted Carin Robinson’s claim:

For instance, where we use the laws of logic, let us remember that there are no known/knowable facts about logic. These laws are therefore, to the best of our knowledge, conventions not dissimilar to the rules of a game.

Law

I intend to discuss Robinson’s claim in a bit more detail shortly, but first consider the meaning of a law in its plainest sense. In the USA there is a law that you must pay your taxes for the previous year by mid April. What does this law do? Presumably the purpose of the law is to get people to pay their taxes by that time. Without the law, they would likely not pay by then, and if there were no rule that you have to pay taxes at all, people presumably would not pay taxes. So the law is meant to make something happen, namely the payment of taxes by a certain date, something that otherwise might not happen.

Rules of a game

What about the rules of a game? Consider the game of hide and seek. Wikipedia describes it in some detail:

Hide-and-seek, or hide-and-go-seek, is a popular children’s game in which any number of players (ideally at least three) conceal themselves in a set environment, to be found by one or more seekers. The game is played by one player chosen (designated as being “it”) closing their eyes and counting to a predetermined number while the other players hide. For example, count to 100 in units of 5 or count to 20, one two three and keep counting up till it reaches twenty. After reaching this number, the player who is “it” calls “Ready or not, here I come!” and then attempts to locate all concealed players.

This is partly a factual description, but it is also attempting to give the rules. It seems to be a rule that the players who are hiding have some amount of time to hide, and it would seem to be a violation of the rules if the seeker simply starts the game by announcing, “I see everyone here, so I’ve found everyone,” without there being any time to hide.

What do these rules do? Are they like the law?

Yes and no, in different respects. You can certainly imagine a player breaking the rules in the above manner. So the rules, like the law, are meant to make something happen, namely the players act in a certain manner, and they are meant to exclude what might happen without the rule, just like the law.

There is a difference, however. If a player did the above, they would not be playing the game at all. It is possible to go about your life and not pay any taxes; but it is not possible to play hide-and-seek without there being a space or time for people to hide. In this sense, the law excludes some possibilities for life, but the rule of the game does not exclude some possibilities for that game; it simply describes what the game is. It does exclude possibilities that would be rules for other games. So it excludes some possibilities; but not possibilities for the game of hide and seek.

Facts

Why does Robinson say that there are no “facts” about logic? The English word “fact” is taken from the Latin factum, which means “done” or “made.” This is not accidental to the claim here. There is nothing making things follow the rules of logic, and for this reason Robinson asserts that there are no facts, i.e. nothing made to be the case in the realm of logic. Precisely for this reason, you don’t have to go out and look at the “facts”, i.e. things that are made to be the case in the world, to determine whether or not a statement of logic or mathematics is correct or not.

Laws of Logic

Robinson argues that since the laws of logic don’t make anything be the case in the world, they must be conventional, like “rules of a game”. But in our discussion of the rules of a game, we saw that such rules do exclude certain types of possibility, while they constitute the game itself, and therefore do not exclude any possibilities for the game. How would this work if the rules of logic were rules of a game? What sorts of possibility are excluded by the rules, and what game is constituted by the rules?

As we said, it is possible to break the rules of a game, although when you do, you often stop playing the game by definition. It it similarly possible to break the laws of logic?

If we take the game to be a certain sort of speaking, yes, it is. It is possible for someone to say the words, “Blue things are not blue.” It is possible for someone to say the words, “All cats are mammals. Alvin is a cat. Therefore Alvin is not a mammal.” Someone doing this, however, is not playing the particular game in question. What is that game? I suggest we call it “speaking sensibly about reality.” Someone who breaks the laws of logic, by that very fact, fails to speak sensibly about reality, just as someone who breaks the rules of hide-and-seek fails to play the game.

The rules of hide-and-seek are conventional, in the sense that you could have other rules. But if you did have other rules, you would be playing a different game. In the same way, if you had rules other than the laws of logic for your speaking game, you would be doing something entirely different. You would not be doing what we are normally trying to do when we speak, namely speaking sensibly about reality.

Up to this point, we have actually succeeded in making a certain sort of sense out of Robinson’s claim. But does it follow, as supposed, that logic tells us nothing about reality? We pointed out in the previous post that this is not true. But why is it not, if the laws of logic are conventions about how to speak?

Do the rules of hide-and-seek tell us something about the game of hide-and-seek? Clearly they do, despite the fact that they are conventional. They tell us most of what there is to know about the game. They tell us what the game is, in fact. Likewise, the laws of logic tell us how to speak sensibly about reality. Do they also tell us about reality itself, or just about how to speak about it?

They do, in the way that considering the effect reveals the cause. Reality is what it is, and therefore certain ways of speaking are sensible and others are not. So to tell someone how to speak sensibly is to tell them something about reality. However, there is another difference between the laws of logic and the rules of a game. The rules of a game are conventional in the sense that we could have different rules and different games. And similarly, if we didn’t want to follow the “conventions” of logic, we could speak nonsensically instead of trying to speak sensibly about reality. But there is not some possible alternate reality which could be spoken of sensibly by using different “conventions.” In this sense, you can call the laws of logic rules of a game, if you wish. But they are the rules of the game of understanding, and there is only such game, not only in practice but in principle, and the rules could not have been otherwise.

Tautologies Not Trivial

January 1, 2019January 1, 2019 entirelyuseless Logic, Mathematics, Metaphysics, Science, Uncategorized Carin Robinson, Causes, Charles Darwin, Daniil Kozhemiachenko, Desire, Good, Immanuel Kant, Impossibility, Knowledge, Mars Climate Orbiter, Natural Selection, Necessity, Self-Reference, Tautology, Timocrates, Trivial, Truth, Understanding

In mathematics and logic, one sometimes speaks of a “trivial truth” or “trivial theorem”, referring to a tautology. Thus for example in this Quora question, Daniil Kozhemiachenko gives this example:

The fact that all groups of order 2 are isomorphic to one another and commutative entails that there are no non-Abelian groups of order 2.

This statement is a tautology because “Abelian group” here just means one that is commutative: the statement is like the customary example of asserting that “all bachelors are unmarried.”

Some extend this usage of “trivial” to refer to all statements that are true in virtue of the meaning of the terms, sometimes called “analytic.” The effect of this is to say that all statements that are logically necessary are trivial truths. An example of this usage can be seen in this paper by Carin Robinson. Robinson says at the end of the summary:

Firstly, I do not ask us to abandon any of the linguistic practises discussed; merely to adopt the correct attitude towards them. For instance, where we use the laws of logic, let us remember that there are no known/knowable facts about logic. These laws are therefore, to the best of our knowledge, conventions not dissimilar to the rules of a game. And, secondly, once we pass sentence on knowing, a priori, anything but trivial truths we shall have at our disposal the sharpest of philosophical tools. A tool which can only proffer a better brand of empiricism.

While the word “trivial” does have a corresponding Latin form that means ordinary or commonplace, the English word seems to be taken mainly from the “trivium” of grammar, rhetoric, and logic. This would seem to make some sense of calling logical necessities “trivial,” in the sense that they pertain to logic. Still, even here something is missing, since Robinson wants to include the truths of mathematics as trivial, and classically these did not pertain to the aforesaid trivium.

Nonetheless, overall Robinson’s intention, and presumably that of others who speak this way, is to suggest that such things are trivial in the English sense of “unimportant.” That is, they may be important tools, but they are not important for understanding. This is clear at least in our example: Robinson calls them trivial because “there are no known/knowable facts about logic.” Logical necessities tell us nothing about reality, and therefore they provide us with no knowledge. They are true by the meaning of the words, and therefore they cannot be true by reason of facts about reality.

Things that are logically necessary are not trivial in this sense. They are important, both in a practical way and directly for understanding the world.

Consider the failure of the Mars Climate Orbiter:

On November 10, 1999, the Mars Climate Orbiter Mishap Investigation Board released a Phase I report, detailing the suspected issues encountered with the loss of the spacecraft. Previously, on September 8, 1999, Trajectory Correction Maneuver-4 was computed and then executed on September 15, 1999. It was intended to place the spacecraft at an optimal position for an orbital insertion maneuver that would bring the spacecraft around Mars at an altitude of 226 km (140 mi) on September 23, 1999. However, during the week between TCM-4 and the orbital insertion maneuver, the navigation team indicated the altitude may be much lower than intended at 150 to 170 km (93 to 106 mi). Twenty-four hours prior to orbital insertion, calculations placed the orbiter at an altitude of 110 kilometers; 80 kilometers is the minimum altitude that Mars Climate Orbiter was thought to be capable of surviving during this maneuver. Post-failure calculations showed that the spacecraft was on a trajectory that would have taken the orbiter within 57 kilometers of the surface, where the spacecraft likely skipped violently on the uppermost atmosphere and was either destroyed in the atmosphere or re-entered heliocentric space.^[1]

The primary cause of this discrepancy was that one piece of ground software supplied by Lockheed Martin produced results in a United States customary unit, contrary to its Software Interface Specification (SIS), while a second system, supplied by NASA, expected those results to be in SI units, in accordance with the SIS. Specifically, software that calculated the total impulse produced by thruster firings produced results in pound-force seconds. The trajectory calculation software then used these results – expected to be in newton seconds – to update the predicted position of the spacecraft.

It is presumably an analytic truth that the units defined in one way are unequal to the units defined in the other. But it was ignoring this analytic truth that was the primary cause of the space probe’s failure. So it is evident that analytic truths can be extremely important for practical purposes.

Such truths can also be important for understanding reality. In fact, they are typically more important for understanding than other truths. The argument against this is that if something is necessary in virtue of the meaning of the words, it cannot be telling us something about reality. But this argument is wrong for one simple reason: words and meaning themselves are both elements of reality, and so they do tell us something about reality, even when the truth is fully determinate given the meaning.

If one accepts the mistaken argument, in fact, sometimes one is led even further. Logically necessary truths cannot tell us anything important for understanding reality, since they are simply facts about the meaning of words. On the other hand, anything which is not logically necessary is in some sense accidental: it might have been otherwise. But accidental things that might have been otherwise cannot help us to understand reality in any deep way: it tells us nothing deep about reality to note that there is a tree outside my window at this moment, when this merely happens to be the case, and could easily have been otherwise. Therefore, since neither logically necessary things, nor logically contingent things, can help us to understand reality in any deep or important way, such understanding must be impossible.

It is fairly rare to make such an argument explicitly, but it is a common implication of many arguments that are actually made or suggested, or it at least influences the way people feel about arguments and understanding. For example, consider this comment on an earlier post. Timocrates suggests that (1) if you have a first cause, it would have to be a brute fact, since it doesn’t have any other cause, and (2) describing reality can’t tell us any reasons but is “simply another description of how things are.” The suggestion behind these objections is that the very idea of understanding is incoherent. As I said there in response, it is true that every true statement is in some sense “just a description of how things are,” but that was what a true statement was meant to be in any case. It surely was not meant to be a description of how things are not.

That “analytic” or “tautologous” statements can indeed provide a non-trivial understanding of reality can also easily be seen by example. Some examples from this blog:

Good and being. The convertibility of being and goodness is “analytic,” in the sense that carefully thinking about the meaning of desire and the good reveals that a universe where existence as such was bad, or even failed to be good, is logically impossible. In particular, it would require a universe where there is no tendency to exist, and this is impossible given that it is posited that something exists.

Natural selection. One of the most important elements of Darwin’s theory of evolution is the following logically necessary statement: the things that have survived are more likely to be the things that were more likely to survive, and less likely to be the things that were less likely to survive.

Limits of discursive knowledge. Knowledge that uses distinct thoughts and concepts is necessarily limited by issues relating to self-reference. It is clear that this is both logically necessary, and tells us important things about our understanding and its limits.

Knowledge and being. Kant rightly recognized a sense in which it is logically impossible to “know things as they are in themselves,” as explained in this post. But as I said elsewhere, the logically impossible assertion that knowledge demands an identity between the mode of knowing and the mode of being is the basis for virtually every sort of philosophical error. So a grasp on the opposite “tautology” is extremely useful for understanding.

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