What Have the Greeks Done for Modern Civilisation?

by J. P. Mahaffy

Note.—I thought that I could not bring before the audience the character of this decoration adequately, except by showing some of the designs, and some of the furniture, on a screen. Some of the pictures were taken from Niccolini’s magnificent Art of Pompeii (Naples, 1876-92), the Curator having allowed me to use the expensive process of photographing in colours, in order to show not only the design, but the rich colours of the Pompeian walls.

VI
SCIENCE: GRAMMAR—LOGIC—MATHEMATICS—MEDICINE

WHEN I speak to you of Greek Science, of course I use the word in the old and proper sense to include all strict reasoning, especially of the deductive kind, particularly therefore pure Mathematics, and not merely the inferences from observation and experiment which now commonly assume and even monopolise the title of Science. I often see in educational programmes Science and Mathematics contrasted as distinct things, which indeed in this case they are, only because the Science so-called is often unworthy of the name. Sciences of observation were, I think, not formulated by the Greeks except in the case of Medicine, in which their results are still quoted with respect; in the case of Hydrostatics, as Heron’s great book shows; and in the case of Natural History, in which they made the first collection of facts that modern men of science can use; but we have lost what they said on their artistic observations, namely their minute observations of the anatomy of the human body, which, as I have told you, their sculptors learned to represent with such accuracy that no modern anatomist can find a flaw in their work. This was done by careful external observation, for the practice of dissecting the human body would have seemed to them impious and horrible. But, whenever it was possible, the Greeks went back to first principles and framed a theory from which they deduced the facts; and this it is which has made their science so valuable. It will not be hard to show you how in Logic—the Science of Reasoning,—in Arithmetic, and in Geometry—the science of the laws of lines, of figures, and of solid bodies in space—they are our teachers to the present day.

It is well to approach the subject of Logic through the avenue by which the Greeks approached it, through the analysis of ordinary language and as the natural expression of thinking. The early poets and great prose writers had so far perfected the use of language that the Greeks in the catalogue of human acquisitions came to put their speech on a very high pedestal. Delighted with it, and despising all other tongues as barbarous, they convinced themselves that the Greek word adequately expressed the nature of the thing it signified, and therefore that to understand their language properly was to understand the nature of things. Λὁγος meant not only speech (oratio), but reason (ratio), and so, after first seeking to obtain clear conceptions of abstract ideas, they advanced to the structure of sentences and analysed speech in so accurate a way that their technical terms are our technical terms of to-day. When you talk of infinitives, or genitives, or participles, you are only using words borrowed from Latin translations, often mistranslations, of the Greek. You find these logical studies in their beginning, but by no means in their infancy, in the Dialogues of Plato. Whole conversations are employed in trying to fix the connotation of important moral terms, such as holiness, or valour, or temperance. And we also find in some of the dialogues an appreciation of the difficulties contained in the form of simple propositions, the meaning of affirmation or negation, and the nature of the deduction of one proposition from another.

But I need not detain you with particulars about these early preparations for science, when we have before us in Aristotle various treatises on the analysis of speech from its logical side, and the laying down of the laws of formal thinking with such accuracy and completeness that nothing of importance has ever been added to it. We hear it often said that a single man apprehended and systematised these laws. That is not true; there were plenty of tentative essays before his time. But if there be one achievement which has made his name and fame everlasting, it is his treatment of the theory of Reasoning.

The mediæval universities knew this well, and so do the modern universities of Europe which are worthy of the name. I need not bear witness to the vast importance of common Logic by telling you that in my own youth nothing ever woke me up like having a good Logic put into my hands at the age of fourteen. For since that time I have been often teaching it and have watched its effects on hundreds of intelligent youths. Among all the subjects that we teach, not for the purpose of supplying mere facts, but for the purpose of training youth to judge facts and co-ordinate their knowledge, I know nothing that benefits the average student like the study of Aristotelian Logic. May I add that, so far as I know American education, the most serious defect I have observed in it is the small attention paid to this subject, and hence the vast number of your men and women who are unable to distinguish a sound from an unsound argument, still less to point out where the fallacy lies.

There are here present, I have no doubt, a large number of people, otherwise highly educated, who, were I to propose a stock example for their criticism, would feel at a loss how to deal with it. Let me give an illustration. “Every hen comes from an egg; every egg comes from a hen; therefore every egg comes from an egg.” Is this a correct argument? If not, where is it at fault? If you had all been trained in Whately’s Logic, or any other Logic of the kind, as we were in our youth, such a question would present no difficulty whatever.

But if you have failed to derive this lesson from the old Greeks, your English ancestors were better advised. All the subtlety of the mediæval schools, all the disputations of their universities, were based on Greek Logic; and, if they often wasted their time on idle problems, it must always be remembered that by this means Europe was trained to accuracy and subtlety in argument, and hence to weigh vague and random theorising and to make men competent critics of any new dogma. We often remark from our side of the Atlantic how many wild theories in religion, how many sham theories in science, blossom and flourish in this country, inhabited though it may be by a most shrewd and intelligent population. The simplest answer is to point to their ignorance of common Logic, and hence their liability to be deceived by the most vulgar fallacies. It would be easy to mention a book popular in this country, the pages of which any logically trained people would only use to wrap sardines or to heat a stove.

The Greeks do not parade their logic in their writings, though we know they were fond of subtleties; there are indeed examples of it in the Sophist of Plato, where this sort of thing is ridiculed in his travesty of two professional educators. But there are two great and solid proofs of the power which strict Logic had upon their minds. The first comes out in their literature. Wherever they undertake to argue an issue, whether political, social, or religious, their reasoning is clear and easily followed. They of course often start from traditional beliefs, which may not now command assent, but they always reason from these with clear and sober thinking. There was no more important cause for the permanence of that great literature. Its sound thinking has kept it from all extravagance and made it acceptable to educated men of all ages and nations. The second proof is my chief subject to-day: it is the peculiarly logical character of Greek mathematics which has made this too the model of the scientific thinking of the world.