Page:Encyclopædia Britannica, Ninth Edition, v. 3.djvu/174

Rh aud comprises the parishes of Althorpa, Belton, Epworth, Haxey, Luddington, Owston, and Crowle ; the total area being about 47,000 acres. At a very early period it would appear to have been covered with forest ; but this having been in great measure destroyed, it sank into a comparative swamp. In 1627 King Charles I., who was lord of the island, entered into a contract with Cornelius Vermuyden, a Dutchman, for reclaiming the meres and marshes, and rendering them fit for tillage. This undertaking led to the introduction of a large number of Flemish workmen, who settled in the district, and, in spite of the violent measures adopted by the English peasantry to expel them, retained their ground in sufficient numbers to affect the physical appearance and the accent of the inhabitants to this day. Elaborate volumes have been published on the island by Peck (1815), Stonehouse, and Read. (See paper, by E. Peacock, in Anthropological Review, 1870.)

 AXIOM, from the Greek [Greek], is a word of great import both in general philosophy and in special science ; it also has passed into the language of common life, being applied to any assertion of the truth of which the speaker happens to have a strong conviction, or which is put forward as beyond question. The scientific use of the word is most familiar in mathematics, where it is customary to lay down, under the name of axioms, a number of propositions of which no proof is given or considered necessary, though the reason for such procedure may not be the same in every case, and in the same case may be vari ously understood by different minds. Thus scientific axioms, mathematical or other, are sometimes held to carry with them an inherent authority or to be self-evident, wherein it is, strictly speaking, implied that they cannot be made the subject of formal proof ; sometimes they are held to admit of proof, but not within the particular science in which they are advanced as principles ; while, again, some times the name of axiom is given to propositions that admit of proof within the science, but so evidently that they may be straightway assumed. Axioms that are genuine principles, though raised above discussion within the science, are not therefore raised above discussion alto gether. From the time of Aristotle it has been claimed for general or first philosophy to deal with the principles of special science, and hence have arisen the questions concerning the nature and origin of axioms so much debated among the philosophic schools. Besides, the general philo sopher himself, having to treat of human knowledge and its conditions as his particular subject-matter, is called to determine the principles of certitude, which, as there can be none higher, must have in a peculiar sense that character of ultimate authority (however explicable) that is ascribed to axioms; and by this name, accordingly, such highest principles of knowledge have long been called. In the case of a word so variously employed there is, perhaps, no batter way of understanding its proper signification than by considering it first in the historical light not to say that there hangs about the origin and early use of the name an obscurity which it is of importance to dispell. The earliest use of the word in a logical sense appears in the works of Aristotle, though, as will presently be shown, it had probably acquired such a meaning before his time, find only received from him a more exact determination. In his theory of demonstration, set forth in the Posterior Analytics, he gives the name of axiom to that immediate principle of syllogistic reasoning which a learner must bring with him (i. 2, 6) ; again, axioms are said to be the common principles from which all demonstration takes place com mon to all demonstrative sciences, but varying in expression according to the subject-matter of each (i. 10, 4). The principle of all other axioms the surest of all principles is that called later the principle of Contradiction, in demonstrable itself, and thus fitted to be the ground of all demonstration (Metaph., iii. 2, iv. 3). Aristotle s fol lowers, aud, later on, the commentators, with glosses of their own, repeat his statements. Thus, according to Themistius (ad Post. Anal.), two species of axioms were distinguished by Theophrastus one species holding of all things absolutely, as the principle (later known by the name) of Excluded Middle, the other of all things of the same kind, as that the remainders of equals are equal. These, adds Themistius himself, are, as it were, connate and com mon to all, and hence their name Axiom ; &quot; for what is put over either all things absolutely or things of one sort universally, we consider to have precedence with respect to them. ; The same view of the origin of the name reappears in Boethius s Latin substitutes for it dignitas zudmaxima (propositio), the latter preserved in the word Maxim, which is often used interchangeably with Axiom. In Aristotle, however, there is no suggestion of such a meaning. As the verb diow changes its original meaning of deem worthy into think fit, think simply, and also claim or require, it might as well be maintained that do/m which Aristotle himself employs in its original ethical sense of worth, also in the secondary senses of opinion or dictum (Metaph., iii. 4), and of simple proposition (Topics, viii. 1) was conferred upon the highest principles of reasoning and science because the teacher might require them to be granted by the learner. In point of fact, later writers, like Proclus and others quoted by him, did attach to Axiom this particular meaning, bringing it into relation with Postulate (atrr//xa), as defined by Aristotle in the Posterior Analytics, or as understood by Euclid in his Elements. It may here be added that the word was used regularly in the sense of bare proposition by the Stoics (Diog. Laert., vii. 65, though Simplicius curiously asserts the contrary, ad Epict. Ench., c. 58), herein followed in later times by the Ilamist logicians, and also, in effect, by Bacon. That Aristotle did not originate the use of the term axiom in the sense of scientific first principle, is the natural conclusion to be drawn from the reference he makes to &quot; what are called axioms in mathematics &quot; (Metapli., iv. 3). Sir William Hamilton (Note A, Reid s Works, p. 765) would have it that the reference is to mathematical works of his own now lost, but there is no real ground for such a supposition. True though it be, as Hamilton urges, that the so-called axioms standing at the head of Euclid s Elements acquired the name through the influence of the Aristotelian philosophy, evidence is not wanting that by the time of Aristotle, a generation or more before Euclid, it was already the habit of geometricians to give definite expression to certain fixed principles as the basis of their science. Aristotle himself is the authority for this asser tion, when, in his treatise De Coelo, iii. 4, he speaks of the advantage of having definite principles of demonstration, and these as few as possible, such as are postulated by mathematicians (xaddirep dio&amp;gt;cri KOL ol ev TCHS {jiaO^ao-iv}, who always have their principles limited in kind or num ber. The passage is decisive on the point of general mathematical usage, and so distinctly suggests the very word axiom in the sense of a principle assumed or postulated, that Aristotle s repeated instance of what he himself calls by the name If equals be taken from equals, the remainders are equal can hardly be regarded otherwise than as a citation from recognised mathematical treatises. The conclusion, if warranted, is of no small interest, in view of the famous list of principles set out by Euclid, which has come to be regarded in modern times as the typical specimen of axiomatic foundation for a science. Euclid, giving systematic form to the elements of geome trical science in the generation after the death of Aristotle, 