Polytropy

The original purpose of this article is to record a passage in The Idea of History of R.G. Collingwood (1889–1943). I bought and read this book in 2001. I was looking back at it recently, because I was reading Herodotus, and I wanted to see again what Collingwood had to say about him and other ancient historians.

The passage that I want to talk about reminded me of some psychological experiments whose conclusions can be overblown. Writing before those experiments, Collingwood shows that the similar conclusions can be drawn, in more useful form, without the pretence of a scientific experiment.

Collingwood praises the best Greek and Roman historians for seeing history as the working out, not of the divine, but of the human will. His examples are Herodotus, Thucydides, Polybius, Livy, and Tacitus. He continues as follows (emphasis on the key passage being mine):

Greco-Roman humanism, however, had a special weakness of its own because of its inadequate moral or psychological insight. It was based on the idea of man as essentially a rational animal, by which I mean the doctrine that every individual human being is an animal capable of reason. So far as any given man develops that capacity and becomes actually, and not potentially, reasonable, he makes a success of his life; according to the Hellenic idea, he becomes a force in political life and a maker of history; according to the Hellenistic-Roman idea, he becomes capable of living wisely, sheltered behind his own rationality, in a wild and wicked world. Now the idea that every agent is wholly and directly responsible for everything that he does is a naïve idea which takes no account of certain important regions in moral experience. On the one hand, there is no getting away from the fact that men’s characters are formed by their actions and experiences; the man himself undergoes change as his activities develop. On the other hand, there is the fact that to a very great extent people do not know what they are doing until they have done it, if then. The extent to which people act with a clear idea of their ends, knowing what effects they are aiming at, is easily exaggerated. Most human action is tentative, experimental, directed not by a knowledge of what it will lead to but rather by a desire to know what will come of it. Looking back over our actions, or over any stretch of past history, we see that something has taken shape as the actions went on which certainly was not present to our minds, or to the mind of any one, when the actions which brought it into existence began. The ethical thought of the Greco-Roman world attributed far too much to the deliberate plan or policy of the agent, far too little to the force of a blind activity embarking on a course of action without forseeing its end and being led to that end only through the necessary development of that course itself.

It seems to me Collingwood is right, even obviously so. Considering broad features of my own life, I note that I did not attend St John’s College to help me develop courses at a conventional university; however, in fact I have in recent years been developing such courses, inpired by my experience at St John’s. I did not attend graduate school for the sake of becoming a university teacher at all; but this is what I have become. I studied mathematics because, if I didn’t, I would always regret not knowing the subject as it is pursued today. Otherwise, I never had a grand plan, although hindsight may be able to detect what looks like a plan.

If I am hungry or otherwise irritated, I am liable to continue a contentious argument over matters that seem important at the time, but really are not.

Is there an experiment or study that would tend to confirm, or possibly disprove, my own conclusions about my own behavior?

Apparently there are experiments, performed by Benjamin Libet and then others, showing that our decisions can be made before we are conscious of them. These experiments involve inconsequential decisions, such as pushing a button that is connected to nothing but a recording device. Such experiments do not justify extrapolation of their results to grander matters. If we do extrapolate, it is on some other basis.

Newton was able to show that an inverse-square law of gravitation explained the motion of bodies both on earth and in the heavens above. Did he thus prove that the earth and the heavens are all part of one world, operating by one set of laws? It was the very fact that Newton could conceive of such a world that allowed him to find some of the laws by which it operates.

It is not clear whether Galileo actually dropped balls from the Tower of Pisa, to show that they would fall at the same rate, regardless of their weight. Apparently he did have a thought experiment, establishing the same result. Indeed, if the heavier ball fell faster, then tying the balls together would make an object that fell faster than either ball separately. Once such an argument is made, is there really any need to test it physically? We can test it on Earth; but would we get the same results on the Moon? Apparently it has been shown that we do. But is this enough to tell us that we would get the same results on Mars or anywhere else? It is rather some kind of principle of universality that tells us this.

To draw universal conclusions from particular experiments is to beg the question of whether universal conclusions are possible. By assuming that they are possible, we are able to make them, and I think we do not get into trouble by doing so, at least when the object of our study is the inanimate world. Even then, we might raise questions about the use of natural science in developing the weapons of war and of clearing forests: here is a kind of trouble that might possibly have some connection with our general views of science. But my particular concern at present is psychology. To draw a universal conclusion from a psychological experiment begs the question of whether there are universal properties of humanity.

Perhaps the decisions that we have already made in our lives were bound to be made as they were. And yet at every moment we are faced with a new decision: what shall we do now? Usually the decision is easy. In the hard cases though, what help can a psychological experiment be? It is no use to be told, You will not be making the decision anyway, it is your Unconscious that is in control.

Collingwood mentions psychology here and there throughout his œuvre, as for example in the Essay on Philosophical Method. In one chapter of this, he shows that the assertions of philosophy are categorical, unlike those of exact or empirical science, which are hypothetical. Psychology is used as an example of empirical science, as opposed to the philosophical sciences of logic and moral philosophy.

I suppose it is clear enough that exact science is hypothetical. All of the conclusions of Euclid are based on the hypothesis that a straightedge and compass are available, along with a set square to establish the equality of all right angles, and the parallel postulate. It may well be that Euclid himself asserted these hypotheses categorically, as simply being true of the world we live in. But we need not take the hypotheses this way in order to be able to understand Euclid’s mathematics and add to it.

As for empirical science, the observations on which it is based may be stated categorically; but science is more than observation. Again, if we decide that a Galilean ball-dropping experiment would work on the Mars as on the Earth and the Moon, this decision is not the direct result of any observation; it is rather based on the hypothesis that such a universal conclusion can be drawn from an experiment performed at one particular place and time. This is not however Collingwood’s example, which is:

The statement in a medical or botanical text-book that all cases of tuberculosis or all rosaceae have these and these characteristics, turns out to mean that the standard case has them; but it does not follow that the standard case exists; it may be a mere ens rationis; and since that would not disturb the truth of the original statement, it follows that the original statement was in intention hypothetical.

By contrast, the intention of a philosophical statement is categorical, no matter how tentatively the statement may in fact be made. The argument is based on Anselm’s Ontological Proof: to think of a perfect being at all is to think of it as existing. Collingwood adapts the argument to logic, as contrasted with psychology, in a passage that I quote below. First I summarize it, according to my understanding.

A normative account of thinking would be an exact science, like mathematics. A descriptive account of thinking would be an empirical science, and indeed a part of psychology. But logic is both normative and descriptive at once, because a part of its object of study is the work that itself creates. Logic consists of thinking about thinking. Logic aims to engage in correct thinking about thinking. So does psychology; but logic is interested in correct thinking as such. So by its very existence, logic asserts that correct thinking is not merely hypothetical, but is actually possible.

Here is Collingwood:

Logic is concerned with thought as its subject-matter. It has a double character. On the one hand it is descriptive, and aims at giving an account of how we actually think; on the other it is normative, and aims at giving an account of the ideal of thought, the way in which we ought to think. If logic were merely descriptive, it would be a psychology of thinking; like all psychology, it would abstract from the distinction of thoughts into true and false, valid and invalid, and would consider them merely as events happening in the mind. In that case its purpose would be to provide a kind of anatomy or physiology of the understanding, and its aims, structure, and methods would conform on the whole to the pattern of empirical science. Throughout its long history logic has never taken up this position. It has no doubt ignored the distinction between true and false judgement, but it has done this only in pursuance of its conception of itself as the theory of inference; the distinction between valid and invalid reasoning it has never ignored.

But neither is logic merely normative. A purely normative science would expound a norm or ideal of what its subject-matter ought to be, but would commit itself to no assertion that this ideal was anywhere realized. If logic were a science of this kind, it would resemble the exact sciences; it would in fact either be, or be closely related to, mathematics. The reason why it can never conform to that pattern is that whereas in geometry, for example, the subject-matter is triangles, &c., and the body of the science consists of propositions about triangles, &c., in logic the subject-matter is propositions, and the body of the science consists of propositions about propositions. In geometry the body of the science is heterogeneous with its subject-matter; in logic they are homogeneous, and more than homogeneous, they are identical; for the propositions of which logic consists must conform to the rules which logic lays down, so that logic is actually about itself; not about itself exclusively, but at least incidentally about itself.

It follows that logic cannot be in substance merely hypothetical. Geometry can afford to be indifferent to the existence of its subject-matter; so long as it is free to suppose it, that is enough. But logic cannot share this indifference, because, by existing, it constitutes an actually existing subject-matter to itself. Thus, when we say ‘all squares have their diagonals equal’, we need not be either explicitly or implicitly asserting that any squares exist; but when we say ‘all universal propositions distribute their subject’, we are not only discussing universal propositions, we are also enunciating a universal proposition; we are producing an actual instance of the thing under discussion, and cannot discuss it without doing so. Consequently no such discussion can be indifferent to the existence of its own subject-matter; in other words, the propositions which constitute the body of logic cannot ever be in substance hypothetical. A logician who lays it down that all universal propositions are merely hypothetical is showing a true insight into the nature of science, but he is undermining the very possibility of logic; for his assertion cannot be true consistently with the fact of his asserting it.

Similarly with inference. Logic not only discusses, it also contains, reasoning; and if a logician could believe that no valid reasoning anywhere actually existed, he would merely be disbelieving his own logical theory. For logic has to provide not only a theory of its subject-matter, but in the same breath a theory of itself; it is an essential part of its proper task that it should consider not only how other kinds of thought proceed, and on what principles, but how and on what principles logic proceeds. If it had only to consider other kinds of thought, it could afford to deal with its subject-matter in a way either merely normative or merely descriptive; but towards itself it can only stand in an attitude that is both at once. It is obliged to produce, as constituent parts of itself, actual instances of thought which realize its own ideal of what thought should be.

Logic, therefore, stands committed to the principle of the Ontological Proof. Its subject-matter, namely thought, affords an instance of something which cannot be conceived except as actual, something whose essence involves existence.

I think Collingwood’s argument hinges on the notion that to assert something is to assert it as being true, just as to conceive of a deity is to conceive of that deity as existing. There is no similar obligation in the conception of a unicorn. Unicorns do exist, after a fashion, in Medieval tapestries, but we read the associated stories with a different frame of mind than we read a newspaper article.

The Lady and the Unicorn (image from Wikimedia)

It would seem then that by asserting, we do not always assert as true. A unicorn story takes the form of assertions, but not true ones. In the passage from The Idea of History that started this article, it is observed that we do not always intend the results of our actions, for the simple reason that we do not know what the results will be. Our actions may be, so to speak, hypothetical. But this makes sense, only because there is a possibility of acting with full deliberation.

Collingwood himself observes that, in one popular sense of the word, a categorical statement is a statement made with conviction. Philosophical statements are often not so made; but this is irrelevant:

The question I am discussing is what logical form philosophical knowledge would take if we could achieve it, not the question how easy it is to achieve.

Since the ramifications of Collingwood’s original thought above have ended up in logic, I close by looking at two popular accounts of the subject. In A Very Short Introduction to Logic (Oxford, 2000), Graham Priest reduces the Ontological Proof, first to a syllogism:

God is the being with all the perfections.

Being is a perfection.

So God possesses existence.

This in turn reduces to,

The object which is omniscient, omnipotent, morally perfect, … and exists, exists.

And this is not merely vacuous, but possibly false, because it assumes that there is such an object.

Priest has perverted the Ontological Proof. It is an argument about us, even a psychological argument. We can understand a unicorn as an imaginary beast; but not so a deity. Priest writes, “there were, in reality, no Greeks gods. They did not in fact exist.” All I take this to mean is that Zeus is not a deity for Priest.

The very first exercise of Wilfrid Hodges in Introduction to Elementary Logic (2nd edition, Penguin, 2001) is:

You know that human beings normally have two legs. Try to convince yourself that normally they have five. (Allow yourself at least a minute.)

The answer at the back of the book is,

If you think you succeeded, you probably overlooked the difference between believing a thing and imagining it.

I suppose then we can imagine unicorns without believing in them; but—the argument might run—we cannot imagine a deity as such without believing in it.

Note added May 23, 2018: I considered the Ontological Proof in detail in “NL II: ‘The Relation Between Body and Mind.’ ”