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 ; " 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
" what are called axioms in mathematics " (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>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,
