Polytropy

Index to this series

A certain person says,

I am not better than you or more virtuous than you. If you see me on the right path, help me. If you see me on the wrong path, advise me and halt me. And obey me as far as I obey God.

How should one hear these words: as an eminently reasonable expression of benevolent humility such as any of us might honorably make? Well, no matter how qualified, the command obey me might be a warning sign. The words are in fact from a recently published video, as quoted in the Guardian Weekly (Vol 190 No 5, 11–17 July 2014, p. 4). The speaker is the man whose nom de guerre is Abu Bakr al-Baghdadi, on whose head the Department of State of the United States of America placed a ten-million-dollar bounty in 2011. He now styles himself Ibrahim, Caliph of the Islamic State, a new entity that is supposed to restore the lost Muslim glory of past centuries. This restoration is to be achieved through war. War requires military discipline, with punishments meted out for infractions like insubordination, not to mention the slaughter of those perceived as enemies. So al-Baghdadi’s request to be advised and halted if seen to be in the wrong must be interpreted rather carefully.

It is difficult to know how to interpret somebody’s words. With that I pass to the transitional chapter in the first part, “Man,” of Collingwood’s New Leviathan.

Collingwood constructs his book on what Locke called the historical plain method (9. 1), and

9. 11. The essence of this method is concentration upon facts. Facts is a name for what history is about: facta, gesta, things done, πεπραγμένα, deeds.

(In an earlier article I also made this quotation.) Collingwood’s care with the word fact has induced a corresponding vigilance in me. Plato induces a similar vigilance about the word idea; and Aristotle, essence. In mathematics, if we state a known theorem that we do not want to be bothered to re-prove, we may call the theorem a fact. Are we correct in so doing? Collingwood elaborates further upon fact in his criticism of positivism in Part II, Anti-Metaphysics, of An Essay on Metaphysics (1940: pp. 144f.). As is so often the case, it seems worthwhile here to quote at length; I emphasize the part that I shall want to concentrate on:

In suggesting that [the positivists’ theory] is too naïve a theory of scientific method I have especially in mind two shortcomings. In the first place it was not very acute in the positivists to think that the facts of which a scientist speaks are observed by the mere action of our senses. The science of psychology had been founded centuries ago on the recognition that by means of our senses we never observe any facts at all, we only undergo feelings. Here positivism ignored the whole history of modern thought and reverted in a single jump to a long-exploded error of the Middle Ages. It was one example of a medievalist tendency which crops out not infrequently among the manifestations of the positivist mind.

This is not to suggest that the positivists were wrong to insist as they did on the importance of facts, and in particular upon their importance in the economy of natural science. What they failed to see was that fact is a term belonging to the vocabulary of historical thought. Properly speaking a fact is a thing of the kind which it is the business of historians to ascertain. The word is sometimes used in another sense, as if it were merely a synonym for truth; there are people who will not shrink from calling it a fact that twice two is four; but no such misuse of the word is implied when facts are spoken of in the vocabulary of natural science. Here facts are always and notoriously historical facts. It is a fact for the astronomer that at a certain time on a certain day a certain observer saw a transit of Venus taking place. If it is of any interest for this observer or any one else to know subsequently that the transit took place then, the only way in which he can know it is by knowing the historical fact that it was observed; and historical facts are not apprehensible to our senses. Positivism thus implied, but did not attempt to furnish, a theory of historical knowledge as a foundation for its theory of natural science. Failing that, it was bankrupt from the start. It had staked its solvency on assets it did not possess.

In the second place it was rash of the positivists to maintain that every notion is a class of observable (if you like, historical) facts. This amounted to saying, what in fact positivists have always tried more or less consistently to say, that scientific thought has no presuppositions. For if the function of thought is to classify observed facts, there must be facts available for classification before thought can begin to operate. And once facts are available there is no need to presuppose anything. You just set to work and classify them. This would be a tenable position if the work of observing facts were done by the senses without any assistance from the intellect. but as this is not the case, as what the positivists called observing facts is really historical thinking, which is a complex process involving numerous presuppositions, it is far from tenable.

Is it really notorious that scientific facts are historical facts? Here is a case where Collingwood’s words must be interpreted with care. I do not suppose that most scientists think of themselves as historians; and if they do, they probably do it in the wrong sense. For scientists are not historians of nature, natural historians. Nature as such has no history. What has a history is humanity’s study of nature, and the working scientist studies this history, even while creating it. A laboratory notebook is an historical record. If it records a transit of Venus, then you can read this record with your eyes, but not merely your eyes. You have to make various assumptions, as, most basically, that the record is written in a language that you can understand.

A reason why I can have difficulty making myself understood in Turkey is that people assume my speech is not Turkish. If they could just accept that it is Turkish, they might get past the peculiar pronunciation and odd choice of words. I can even address somebody in Turkish and be understood, but find my interlocutor tongue-tied, because he does not realize that the language he has just heard and understood is Turkish, and he thinks he must respond in English. (I discount the possibility that my Turkish is so bad that my interlocutor presumes that I would not be able to understand his or her Turkish.)

Because of such examples, it might be said that presuppositions are not needed for understanding language. We can hear and understand without thinking about it. Obviously conscious presuppositions are not needed. But a theme of An Essay on Metaphysics is that presuppositions are usually unconsious and difficult to tease out; and I think this is correct.

Again, I do not suppose that most scientists think of themselves as historians, at least not in Collingwood’s sense. But I suppose that, when questioned, they will acknowledge that their work relies on historical records. I suppose this can make it notorious that scientific facts are historical facts. But if scientists are serious about their work, they will just want to get back to it and not be bothered further by the philosopher’s questions.

Is it not a fact that two plus two is four? It is at least a truth; but more than that, it is a truth universally acknowledged. Jane Austen’s Pride and Prejudice (1813) begins notoriously,

It is a truth universally acknowledged, that a single man in possession of a good fortune must be in want of a wife.

However little known the feelings or views of such a man may be on his first entering a neighborhood, this truth is so well fixed in the minds of the surrounding families that he is considered as the rightful property of some one or other of their daughters.

I think Ms Austen could just as well have said, It is a fact that a single man in possession of a good fortune must be in want of a wife. To say a fact universally acknowledged would have been redundant; for a fact can be understood as a universally acknowledged truth. Now, if she had read Collingwood (having looked into the future to do so), Ms Austen might have written fact with irony, sharing with an inner circle of cognoscenti the understanding that the word fact is commonly misused. But then her words as they are are already ironic, like the title of the painting of William Merritt Chase (1849–1916) in the National Gallery of Art, Washington: A Friendly Call (1895).

It may be acknowledged in drawing rooms everywhere that a wealthy single man needs a wife; but the acknowledgement is nonetheless foolish. At least that is how I read Jane Austen.

I think it is not just a truth, but a fact, that twice two is four, or that the second powers of three and four sum to the second power of five: 3² + 4² = 5². However, it is perhaps not quite a fact that such equations are impossible for all higher powers. It is a fact that Andrew Wiles has proved this impossibility—Fermat’s so-called Last Theorem—to the satisfaction of those interested mathematicians who are able to check his work. But if you are looking for an example of an indubitable truth, I do not think you will use Wiles’s Theorem.

Wiles’s Theorem and the equation 3² + 4² = 5² are equally true. But here I have to acknowledge a certain possibility that there is an undiscovered error in Wiles’s proof. Indeed, Wiles had to acknowledge an error in an earlier proof. Here is the wonderful feature of mathematics, that errors are universally recognized, even by those people who made them. Disagreements are resolved peacefully; it is understood that all parties to a dispute must ultimately agree, or else nobody can claim to be correct. In the present case, if Wiles’s proof should indeed still be in error, and if moreover his supposed theorem is false, then some equation will serve as a counterexample to the supposed theorem, and this equation will be as true as 3² + 4² = 5².

Mathematical truth is hypothetical, not just in the sense discussed by Collingwood in An Essay on Philosophical Method, Chapter VI, Philosophy As Categorical Thinking, §1, Preliminary statement of the principle, subsection 1, The judgements composing the body of mathematics are hypothetical,, pp. 117f.:

In order to assert a proposition in mathematics, it is not necessary to believe that the subject of discourse has any actual existence. We say that every square has its diagonals equal; but to say this we need not think that we have any acquaintance with actual squares …

Nor need we hold that, though in the perceptible world no squares are to be found, they exist in an intelligible world. That is a metaphysical conception full of difficulties; a thing far harder to conceive than the notions of elementary geometry; a theory to which the Greeks were driven by reflection on their mathematical knowledge, but one which to the Greeks as a people, and to each of ourselves as individuals, came after a grounding in mathematics, not before it.

What is necessary is not to believe that a square anywhere or in any sense exists, but to suppose it … In mathematics we frame a supposition and then see what follows from it; this complex thought is called in logic a hypothetical proposition; and it is of such propositions that the body of mathematical knowledge is composed.

Such a complex thought, a hypothetical proposition, may in turn be made to serve as the hypothesis of a further complex. But we make it serve as a hypothesis in this sense with more or less confidence: more when it is the equation 3² + 4² = 5²; less when it is Wiles’s Theorem. The greater our confidence, the more likely we are to refer to the hypothesis as a fact. And I think this usage of fact is not really in disagreement with Collingwood’s. Confidence is a human achievement. It is something we work to attain. It is something we do; it is something done: a fact.