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to Cyrus was what I have suggested. It is perfectly certain that very many persons believed this individual to be the genuine son of Cyrus, and perhaps with justice. Darius believed himself to be the only person cognizant of the death of the real Smerdis (Herod. iii. 71). Prexaspes must have believed the same (iii. 74). Otanes, in his turn, fancied the pretender's secret known only to him (iii. 68). One thing is clear, that it was absolutely necessary for the Persian party to destroy the Magian, and that they had the same motive for denying his claim to be the son of Cyrus that the Orange party in the reign of James II. had for trumping up the story of the warmingpan. The claim of legitimate succession has always been too powerful an engine not to be coveted by aspirants to power, and secured only too often, if necessary, by the commission of crime; and the removal of the only obstacle to Darius's accession (whether Gomates or Bartius) was at last achieved by a small band of conspirators *, who justified their act to the world by the equivocal evidence of producing the head of their victim and that of his brother† in public.

But by whatever means Darius may have acquired his power, it is plain from various incidents mentioned in the narrative of Herodotus, that he used it in a prudent and temperate manner. If he spared nothing to establish the supremacy of the religious party of which, according to the Behistun inscription, he was the champion, yet, that result having been obtained, he appears to have been at least tolerant of the conquered party. The fierce fanaticism which had served him excellently as a weapon of offence must have become very inconvenient when he had no longer rivals to overthrow; and it was only to be expected that he should revert to the policy of Cyrus and carefully avoid that of Cambyses. And hence, probably, arose that revival of Median customs and religious rites in the court of the new dynasty, which is indicated in the consultation of Magian soothsayers by his son Xerxest, the Magian hero-worship at Ilium §, the scrupulous reverence for Delos exhibited by the Median commander Datis ||, and (as it would seem) the recognition in later times of the necessity of a Magian priest even where the ceremonial belonged to a simple religious system¶. Indeed the remarkable tendency of the Persians to adopt foreign customs, which Herodotus himself remarks as an especial characteristic, would probably have baffled the attempt of Darius, had he even been desirous of making

*This is the statement of the Behistun tablets as well as of Herodotus.

I am much inclined to suspect that the two Magians of Herodotus's story (iii. 78, 79) grew out of the two pretenders, Gomates and Veisdates, of the Behistun annals. Each of these professed to be Bartius the son of Cyrus; but there seems to have been a considerable interval between their attempts,—the one being the first, the other the seventh of the nine figures which in the original bas-relief appear as conquered by Darius. An inverse mistake perhaps gave rise to the account of the protracted siege of Babylon (iii. 152). The Behistun inscription makes Darius twice take Babylon after a revolt. On the first occasion he commands in person; on the second the successful general is Intaphres, a Median. The former appears as the third, the latter as the ninth of the great successes recorded on the rock tablets. In each case the leader of the rebels professed "to be Nabokodrosor." Herodotus's informant seems to have compressed the two campaigns into one long one.

vii. 19, 37.

§ vii. 43.

vi. 97.

¶i. 132.

one, to retain them, after inheriting the wealth and civilization of their late masters, in the simplicity of their ancient manners and ancient faith. The more sagacious chiefs of the old school doubtless, like Artembares*, prophesied the degeneracy of a generation brought up in habits which would have excited the horror of Cyrus, but their protest was in vain; and in the time of Herodotus it can scarcely be doubted that the court of the Great King presented in morals, religion, and social indulgence of all kinds, a picture in no respect different from that which might have been seen in the worst days of the Median or Assyrian dynasties.

* ix. 122.

VOL. VI.

PHILOLOGICAL SOCIETY.

FEBRUARY 11, 1853.

No. 129.

THOMAS WATTS, Esq., in the Chair.

A paper was read entitled

"Some Suggestions in Logical Phraseology." De Morgan.

By Professor

Among the most unfortunate ambiguities of language only, unaccompanied by any confusion of thought, are those expressions which we so frequently qualify by the words exclusive and inclusive. Whether the termini or extreme cases are to be both taken in, both left out, or one taken in and one left out, is a matter which often requires an additional sentence. In mathematics, no ambiguity is more common than a statement about greater or less, which leaves it uncertain whether the extreme case, namely equality, is or is not included. In logic, the same thing occurs in the propositional forms. Every a is y' would be commonly understood as meaning that x is not coextensive with y, though the extreme case, that in which there are no more ys than rs, would not be held formally excluded. The distinction of these two cases led Aristotle to what have since been called the predicables. Returning to the master himself, and not attending to his followers, we find the distinction of genus, of definition or property (words the distinction of which is extra-logical), and of accident. When all the rs are some (only) of the ys, y is the genus of ; when all the rs, and no other things, are ys, y is the definition or property of x. (Thomson, Outlines, &c. p. 146.)

Similar ambiguities exist as to negative propositions; but Aristotle does not take notice of them, as he would have done, if he had

admitted contrary or privative terms. The universe of the proposition being either the whole universe of thought, or a given portion of it, all that is not r may be called the contrary of x. If y be a name entirely external to x, so that no x is y, then y may either apply to the whole contrary of x, or only to a part of it. We owe to this omission of Aristotle the want of clear phraseology by which to express relations of disagreement, in terms as familiar to us as genus, species, and property. I dissent from the general opinion that Aristotle confined himself to the common modes of thought, and maintain that it was the common mode of thought which confined itself to Aristotle. We owe the capability of our modern languages, as vehicles of abstract science of all kinds, to the scholastic followers of the Greek philosopher; and I, for one, am persuaded that the difficulty of certain existing and therefore possible forms of thought is due solely to neglect of cultivation; and that this neglect has been most injurious to the progress of mental power. My present object is to invite criticism and suggestion with respect

VOL. VI.

E

to an attempt to construct language expressive of extension, and of distinction of extension to privative or contrary notions, and of distinction between what, relatively to each other, we may call unambiguous and ambiguous predication.

In my work on Logic I designated terms which are coextensive as identical, and the contained and containing terms as subidentical and superidentical: while terms which are contained in and contain the contrary were called subcontrary and supercontrary. With these terms, as expressing the relations of extent, I am well satisfied. Any one who will learn to recall their meaning will very easily make axioms of those compositions of relations on the perception of which the complex syllogism depends. For instance, in the assertion 'A subcontrary (or contrary) of a supercontrary of is a subidentical of z,' will be seen the mode of inference contained in the following:If no x be y (whether there be other things or not which are not ys), and if y contain all that is not z (and also some things that are zs), then (and other things besides) must always be z.' Reserving this language for comparison of extents, I now propose the following extended table of predicables, to express every way in which we can predicate or deny one notion of another, in which some is not all.

Let that which can be said of all be an attribute; of some and some only, an accident; of none, an excludent. Observe that the accident is also, by definition, non-accident: the former in relation to the part of which it can be said; the latter in relation to the part of which it cannot. Let each of these be divided into universal, generic, and specific. Let any predicable be universal when it applies in the same manner both to the subject of predication and to its contrary. Let it be generic when, not being universal, by enlarging the subject of predication from a species into some higher genus, the additional extent contains matter to which the predicable is applicable, or which contributes towards the name. it be specific when no such thing can happen in any genus into which the subject of predication can be enlarged. The application of the three adjectives to each of the three substantives will give nine predicables, which are all that can be, so long as we do no more than annex the privative notion to the form of thought on which Aristotle distinguished genus, property, and accident.

Let

I take a descriptive example of each, the universe in question being animal, that is, all the names of which we predicate being species of animals, and each species having all other animals in its contrary.

1. Universal attribute.-The term organized, as applied to man, in the universe animal, is a universal attribute, because, besides applying to all men, it applies to all the contrary, or to all other animals.

2. Generic attribute (superidentical).-The term warm-blooded, as applied to all men, is a generic attribute, because, without being an attribute of all the contrary, it is of some, so that a larger genus, containing man, can be formed, of which the term in question shall still be an attribute.

3. Specific attribute (identical).-The term rational is a specific attribute of man, because, applying to all men, it applies to nothing else, so that no additional extent contained in any genus of which man is a species, has anything to which it is applicable.

4. Specific accident and generic non-accident (subidentical).—The term lawyer is a specific accident of man, inasmuch as no genus of man contains it except as man contains it. The species is called an accident of the genus even by Aristotle.

5. Universal accident and universal non-accident.-The term darkcoloured, an accident of man, is a universal accident, because it is an accident of the class not-man. The word universal, it must be remembered, is used strictly according to definition. The universe, animal, is divided, as a subject of predication, into man and not-man, and the predicable which applies in the same manner to both man and not-man, is therefore called universal. But the phrase 'universal accident,' sounds like 'total part,' or 'permanent casualty.' One of the questions to which I wish to draw attention is the following:When a word applies in a natural and vernacular sense to all subdivisions except one, which should be preferred-the extension of the word to that one exceptional subdivision, which we are obliged to do in mathematics, or the introduction of another and, for the present time, more natural, expression?

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6. Generic accident and specific non-accident (supercontrary).— The term unclothed (by art) is a generic accident of man, because, being an attribute of some races, and not being universal (for it is not an accident, but an attribute, of the contrary), a genus containing man can be formed, of which genus the term is still an accident, the term applying also to the part of the genus which is not

man.

7. Specific excludent (contrary).—The term dumb (in the sense of not capable of speaking and understanding language) is, as predicated with respect to man in the universe animal, a specific excludent; because, not applying to man at all, but to all other animals, it cannot be predicated excludently of any genus of which man is a species.

8. Generic excludent (subcontrary).-The term quadruped is a generic excludent of man, because it is also an excludent of genera in which man is contained.

9. Universal excludent.-The term mineral is a universal excludent of man, because it excludes also every animal which is not man.

The preceding cases include all the forms in which one term can be predicated of another without terminal ambiguity in the meaning of the word some. Here, some means not none and not all. In the sense in which it is used in the common proposition, it only means not none.

And in passing to this common proposition, we see that the mode of predication affirms, not one of the preceding, but one of two. There are eight modes of connexion, for which eight distinct terms are absolutely requisite: these must be of that degree of clearness which will make axioms of the compositions of relations which take

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