Is and Ought

In Book III of his Treatise of Human Nature, David Hume argues that reason and morality are completely independent:

Reason is the discovery of truth or falsehood. Truth or falsehood consists in an agreement or disagreement either with the real relations of ideas, or with real existence and matter of fact. So anything that isn’t capable of this agreement or disagreement isn’t capable of being true or false, and can never be an object of our reason. Now, our passions, volitions, and actions are basic facts and realities; they are complete in themselves and aren’t in any way about other passions, volitions, and actions; so they aren’t capable of either of those sorts of agreement or disagreement; so they can’t be sorted into ‘true’ and ‘false’, and can’t be either in conflict with reason or in accord with it.

It is true that an action is not true or false, nor can it be the conclusion of an argument. And in that sense there is some separation between action and reason, as Hume says here. Nonetheless, Hume intends to imply something more, namely that reason cannot tell us what we should do. If reason can tell us what we should do, then doing something else instead is an action in conflict with reason, even though it is not a false statement.

Later, Hume clarifies his position:

I can’t forbear adding an observation that may be found of some importance. In every system of morality I have met with I have noticed that the author proceeds for some time reasoning in the ordinary way to establish the existence of a God, or making points about human affairs, and then he suddenly surprises me by moving from propositions with the usual copula ‘is’ (or ‘is not’) to ones that are connected by ‘ought’ (or ‘ought not’). This seems like a very small change, but it is highly important. For as this ‘ought’ (or ‘ought not’) expresses some new relation or affirmation, it needs to be pointed out and explained; and a reason should be given for how this new relation can be—inconceivably!—a deduction from others that are entirely different from it. Authors don’t ordinarily take the trouble to do this, so I recommend it to you; and I’m convinced that paying attention to this one small matter will subvert all the vulgar systems of morality and let us see that the distinction between vice and virtue is not based merely on the relations of objects, and is not perceived by reason.

Hume suggests that it is “inconceivable” that a statement involving the word “ought” would derive from statements without that word. This can be taken as a mere point of logic: the conclusion of a syllogism will not contain a term which is not contained in the premises. But if we understand it in this way, his point is true but rather unimportant, at least in relation to his argument about morality. For the same thing is true of all terms. In the statement, “Trees have leaves and branches,” the word “trees” cannot possibly be logically derived from statements that do not mention trees. It does not follow that statements about trees are somehow cut off from all the rest of reality. It does not even follow that people cannot explain what they mean by a “tree.” Someone can explain this by referring to various fairly common experiences that people have.

So as a logical point, this proves nothing in particular about morality, although it is a partial explanation for the difficulty of philosophy. I pointed out in the discussion of Spinoza’s Ethics that the fact that philosophy wishes to speak about reality in general implies that it must use a practically unlimited number of terms, and consequently that it cannot be built up as a formal system like geometry.

In his Nicomachean Ethics, Aristotle discusses ethics as a kind of art which aims at an end:

Every art and every inquiry, and similarly every action and pursuit, is thought to aim at some good; and for this reason the good has rightly been declared to be that at which all things aim. But a certain difference is found among ends; some are activities, others are products apart from the activities that produce them. Where there are ends apart from the actions, it is the nature of the products to be better than the activities. Now, as there are many actions, arts, and sciences, their ends also are many; the end of the medical art is health, that of shipbuilding a vessel, that of strategy victory, that of economics wealth. But where such arts fall under a single capacity- as bridle-making and the other arts concerned with the equipment of horses fall under the art of riding, and this and every military action under strategy, in the same way other arts fall under yet others- in all of these the ends of the master arts are to be preferred to all the subordinate ends; for it is for the sake of the former that the latter are pursued. It makes no difference whether the activities themselves are the ends of the actions, or something else apart from the activities, as in the case of the sciences just mentioned.

If, then, there is some end of the things we do, which we desire for its own sake (everything else being desired for the sake of this), and if we do not choose everything for the sake of something else (for at that rate the process would go on to infinity, so that our desire would be empty and vain), clearly this must be the good and the chief good. Will not the knowledge of it, then, have a great influence on life? Shall we not, like archers who have a mark to aim at, be more likely to hit upon what is right? If so, we must try, in outline at least, to determine what it is, and of which of the sciences or capacities it is the object. It would seem to belong to the most authoritative art and that which is most truly the master art. And politics appears to be of this nature; for it is this that ordains which of the sciences should be studied in a state, and which each class of citizens should learn and up to what point they should learn them; and we see even the most highly esteemed of capacities to fall under this, e.g. strategy, economics, rhetoric; now, since politics uses the rest of the sciences, and since, again, it legislates as to what we are to do and what we are to abstain from, the end of this science must include those of the others, so that this end must be the good for man. For even if the end is the same for a single man and for a state, that of the state seems at all events something greater and more complete whether to attain or to preserve; though it is worth while to attain the end merely for one man, it is finer and more godlike to attain it for a nation or for city-states. These, then, are the ends at which our inquiry aims, since it is political science, in one sense of that term.

If we understand ethics in this way, this explains what is meant by saying that something “ought” to be done, because we know what is meant when we say, for example, “If you want to attach those boards with a nail, you ought to use a hammer.” This implies that a hammer is useful, or perhaps even necessary, in relation to the goal in question. In fact, “ought” is sometimes replaced with “must,” which is a word directly expressing necessity.

Of course, “you must use a hammer” does not imply that there is a physical necessity that you use a hammer, so that you cannot avoid using one. The necessity is a hypothetical one: given that you are going to obtain the end, you must use a hammer. If you do not use a hammer, you will not obtain the end.

This explains, in a certain way, why Hume has difficulty with the point. A repeated concern in his work is that he cannot see a way to understand the idea of necessity. He says for example that he has a hard time understanding any “necessary connection” between cause and effect:

Having thus explained how we reason beyond our immediate impressions, and conclude that such and such causes must have such and such effects, we must now retrace our steps and pick up again the question that first occurred to us, and that we dropped along the way (near the end of section 2). The question is: What is our idea of necessity, when we say that two objects are necessarily connected? As I have often said already, if we claim to have such an idea we must find some impression that gives rise to it, because we have no idea that isn’t derived from an impression. So I ask myself: In what objects is necessity commonly supposed to lie? And finding that it is always ascribed to causes and effects, I turn my attention to two objects that are supposed to be related as cause and effect, and examine them in all the situations in which they can occur. I see at once that they are contiguous in time and place, and that the one we call ‘cause’ precedes the one we call ‘effect’. In no instance can I go any further: I can’t find any third relation between these objects.

He does go on to say that there is something else, but in turns out to be something like the vividness with which the mind expects the effect, or in other words, a property of the mind, not of the causes and effects. Similar concerns lead him to deny the possibility of probable knowledge about the future, and here to effectively deny the possibility of the knowledge of morals. If moral knowledge consists in knowing that something must be done, even for the sake of an end, then according to Hume, it is not possible to know this. If we cannot even know that the sun will rise tomorrow, we also cannot know that we need to use a hammer in order to attach two boards.

Aristotle’s account of ethics is, I think, the correct account. But people find it troubling, mostly because they suspect that it has unlikely or unpleasant implications. If saying that you “ought” to do something only means that you must do it in order to obtain a certain end, what if you do not care about that end? There will no longer be a need to do that thing. Likewise, if you do want certain ends, then perhaps you ought to do certain things which we really think you ought not do. For example, if you want to inherit money, perhaps you ought to murder your elderly relatives. But this consequence is absurd: of course you ought not to murder your relatives.

In order to be sure e.g. that you ought not to murder your relatives, regardless of what ends you have in mind, people prefer something like Immanuel Kant’s categorical imperatives. I will not discuss Kant’s moral philosophy in detail at the moment, nor am I necessarily asserting that the usual understanding of his philosophy is correct. But the usual idea is that the rule is absolute: “you must not kill” is not relative to an end, but stands in itself.

This seems to me to be a mistake, and one where Hume’s criticism would be valid. There is obviously no physical necessity that you abstain from killing. It is quite possible to kill people, and it is sometimes done. So if you say that you “must” not kill, and you do not refer to hypothetical necessity, to what do you refer? There does not seem to be anything left here. And this is probably the motivation behind error theory. The obvious interpretation of the theory is that it is saying, “I do not believe in right and wrong.” In reality, however, it seems to be based on the mistaken assumption that right and wrong refer to something like categorical imperatives, and then it proceeds to rightly deny the existence of these things. For no one except an actual follower of Hume would deny the existence of hypothetical necessity, namely that if you want to obtain certain ends, you must use certain means. In this sense, error theory is mistaken, but it is mistaken much in the way that Richard Dawkins is mistaken to suppose that theists intend to speak of something complex when they speak of God.

The objection to Aristotelian ethics, then, is that it is too flexible, and may ultimately imply that people may do whatever they want. I would respond to this by making two claims, although I will not establish their truth in this post.

First, the truth about ethics is in fact more flexible than people suppose. If you take extremely complex situations, the moral truth about those situations will be complicated, not simple.

Second, the truth about ethics is less flexible than people tend to suppose would follow from an Aristotelian account. It does not follow in any meaningful way, for example, that it is sometimes fine to murder your relatives in order to obtain an inheritance.

 

Making Arguments vs. Manipulating Symbols

There is still another problem with Spinoza’s manner of argumentation. Spinoza is trying to get geometrical certainty about metaphysics by a logical arrangement of his claims. But this cannot work even in principle. If you take the rules of logic and the forms of the syllogisms, and fit sentences into them using their mere verbal patterns, without thinking about what you are saying, what it means and in what sense it is true or untrue, then you are manipulating symbols, not actually making arguments, and it may well mean that your conclusion is false, whether or not each of your premises is true in some way.

Alexander Pruss, in a recent blog post, argues for the existence of God from certain facts about language:

This argument is valid:

  1. All semantic truths are knowable to members of the community of language users.
  2. There are semantic truths that are not knowable to human language users.
  3. Therefore, there is at least one non-human language user.

There is some reason to accept (1) in light of the conventionality of language. Premise (2) is going to be quite controversial. I justify it by means of a standard argument for epistemicism. Consider Queen Elizabeth II. There are 88 statements of the form:

  • Elizabeth was not old at age n but she was old at age n+1

where n ranges from 1 to 88. It’s a straightforward matter of classical logic to show that if all 88 statements are false, then:

  1. Elizabeth was old at age 1 or Elizabeth is not old at age 89.

But (4) is clearly false: Her Majesty is old now at age 89, and she surely wasn’t old at age one. So, at least one of the 88 statements is false. This means that there is a sharp transition from being not old to being old. But it is clear that no matter what we find out about our behavior, biology and other relevant things, we can’t know exactly where that transition lies. It seems very plausible that the relevant unknowable fact about the transition is a semantic fact. Hence, (2) is true.

The most plausible candidate for the non-human language user who is capable of knowing such semantic facts is God. God could institute the fundamental semantic facts of human language and thereby know them.

(“So, at least one of the 88 statements is false” should be “So, at least one of the 88 statements is true.”) I would consider this to be more a case of manipulating symbols than of making a serious argument.

An atheist is likely to say about this argument, “Wait a minute. Maybe it’s not obvious to me what is wrong with your argument. But there’s just no way you can prove the existence of God from simple facts about how words are used. So there must be something wrong with the argument.”

I agree with the hypothetical atheist that reasonable intuitions would say that you cannot prove the existence of God in such a way, and that this is a reason for doubting the argument even if you cannot formally point out what is wrong with it.

But in fact I think there are two basic problems with it. In the first place, Pruss seems to be failing to consider the actual meaning of his premises. He says, “There is some reason to accept (1) in light of the conventionality of language.” What does this mean? A semantic fact is a fact about the meaning of words or sentences. Pruss is arguing that all facts about the meanings of words or sentences should be knowable to members of the community of language users, and that we should accept this because language is conventional. In other words, human beings make up the meanings of words and sentences. So they can know these meanings; whatever they cannot know about the meaning is not a part of the meaning, since they have not invented it.

But later Pruss says:

This means that there is a sharp transition from being not old to being old. But it is clear that no matter what we find out about our behavior, biology and other relevant things, we can’t know exactly where that transition lies. It seems very plausible that the relevant unknowable fact about the transition is a semantic fact. Hence, (2) is true.

But if this is right, it undercuts the justification for believing the first premise. For the only reason we had to believe that all of the semantic facts are knowable to the community of language users, was a reason to believe that they were knowable to human beings. If they are not knowable to human beings, we no longer have a reason to believe that they are knowable to anyone, or at any rate not a reason that Pruss has given.

This illustrates my point about the necessity of considering the meaning of what you are saying. The argument for the first premise is in fact an argument that human beings can know all of the semantic facts; thus if they cannot, we no longer have a good reason to accept the first premise. We cannot simply say, “This argument is logically valid, we’ve given a reason for the first and a reason for the second, that gives us reason to accept the conclusion.” We need to think about what those reasons are and how they fit together.

The second problem with this argument is that the “standard argument for epistemicism” is just wrong. And likewise, the argument consists of precisely nothing but manipulating words, without thinking about the meaning behind them. It is a “a straightforward matter of classical logic” in the sense that we can fit these words into the logical forms, but this does not mean that this process is telling us anything about reality.

To see this, consider this new word that we can construct by convention, namely “zold.” A person who is between 80 and 90 years old is said to be zold; a person who is between 1 and 10 years old is said not to be zold.

Now consider the 88 statements of the form, “Elizabeth was not zold at age n but she was zold at age n+1.” It’s a straightforward matter of classical logic to show that if all 88 statements are false, then either Elizabeth was zold at age 1, or she was not zold at age 89. But this is clearly false according to the conventions already defined. So at least one of the statements must be true, and there is a sharp transition from being not zold to being zold. It is obvious that no matter what we find out about human beings, that will not tell us where the transition is; the transition must be a semantic fact, a fact about the meaning of the word “zold.”

Obviously, in reality there is no such semantic fact. The convention that we used to define the word simply does not suffice to generate a sharp transition. The problem with the argument for the sharp transition is that the rules of logic presuppose perfectly well defined terms, and this term is not perfectly well defined.

And it is not difficult to see that the word “old” does not differ in a meaningful way from the word “zold.” In reality the two come to have meaning in very similar ways, and in a such a way that there cannot be a sharply defined transition, nor can classical logic force there to be such a sharp transition.

It is not enough to fit your sentences into a logical form. If you want the truth, the hard work of thinking about reality cannot be avoided.

Spinoza’s Geometrical Ethics

Benedict Spinoza, admiring the certainty of geometry, writes his Ethics Demonstrated in Geometrical Order in a manner imitating that of Euclid’s Elements.

Omitting his definitions and axioms for the moment, we can look at his proofs. Thus we have the first:

1: A substance is prior in nature to its states. This is evident from D3 and D5.

The two definitions are of “substance” and “mode,” which latter he equates with “state of a substance.” However, neither definition explains “prior in nature,” nor is this found in any of the other definitions and axioms.

Thus his argument does not follow. But we can grant that the claim is fairly reasonable in any case, and would follow according to many reasonable definitions of “prior in nature,” and according to reasonable axioms.

He proceeds to his second proof:

2: Two substances having different attributes have nothing in common with one another. This is also evident from D3. For each ·substance· must be in itself and be conceived through itself, which is to say that the concept of the one doesn’t involve the concept of the other.

D3 and D4 (which must be used here although he does not cite it explicitly in the proof) say:

D3: By ‘substance’ I understand: what is in itself and is conceived through itself, i.e. that whose concept doesn’t have to be formed out of the concept of something else. D4: By ‘attribute’ I understand: what the intellect perceives of a substance as constituting its essence.

Thus when he speaks of “substances having different attributes,” he means ones which are intellectually perceived as being different in their essence.

Once again, however, “have nothing in common” is not found in his definitions. However, it occurs once in his axioms, namely in A5:

A5: If two things have nothing in common, they can’t be understood through one another—that is, the concept of one doesn’t involve the concept of the other.

The axiom is pretty reasonable, at least taken in a certain way. If there is no idea common to the ideas of two things, the idea of one won’t be included in the idea of the other. But Spinoza is attempting to draw the conclusion that “if two substances have different attributes, i.e. are different in essence, then they have nothing in common.” But this does not seem to follow from a reasonable understanding of D3 and D4, nor from the definitions together with the axioms. “Dog” and “cat” might be substances, and the idea of dog does not include that of cat, nor cat the idea of dog, but they have “animal” in common. So his conclusion is not evident from the definition, nor does it follow logically from his definitions and axioms, nor does it seem to be true.

And this is only the second supposed proof out of 36 in part 1 of his book.

I would suggest that there are at least two problems with his whole project. First, Spinoza knows where he wants to get, and it is not somewhere good. Among other things, he is aiming for proposition 14:

14: God is the only substance that can exist or be conceived.

This is closely related to proposition 2, since if it is true that two different things can have nothing in common, then it is impossible for more than one thing to exist, since otherwise existence would be something in common to various things.

Proposition 14 is absolutely false taken in any reasonable way. Consequently, since Spinoza is absolutely determined to arrive at a false proposition, he will necessarily employ falsehoods or logical mistakes along the way.

There is a second problem with his project. Geometry speaks about a very limited portion of reality. For this reason it is possible to come to most of its conclusions using a limited variety of definitions and axioms. But ethics and metaphysics, the latter of which is the actual topic of his first book, are much wider in scope. Consequently, if you want to say much that is relevant about them, it is impossible in principle to proceed from a small number of axioms and definitions. A small number of axioms and definitions will necessarily include only a small number of terms, and speaking about ethics and metaphysics requires a large number of terms. For example, suppose I wanted to prove everything on this blog using the method of definitions and axioms. Since I have probably used thousands of terms, hundreds or thousands of definitions and axioms would be required. There would simply be no other way to get the desired conclusions. In a similar way, we saw even in the first few proofs that Spinoza has a similar problem; he wants to speak about a very broad subject, but he wants to start with just a few definitions and axioms.

And if you do employ hundreds of axioms, of course, there is very little chance that anyone is going to grant all of them. They will at least argue that some of them might be mistaken, and thus your proofs will lose the complete certainty that you were looking for from the geometrical method.