Extension

“ We conceive extension penetrable as easily as impenetrable, empty or full, white or green, with properties by which it can be placed in relation with our organs, as easily as without them. We can conceive extension in a body acting on another body, or in pure space; in the sun which enlightens and warms the world, or in the vague dimensions of an empty immensity. ”

“ Extension needs no other extension, in which to be placed, otherwise we should have a processus in infinitum: the succession of things, for the same reason, needs no other succession in which to succeed. ”

“ Extension, (1) in physics and metaphysics, that property of a body in virtue of which it occupies a portion of space. (2) In logic, extension is the extent of the application of a general term, that is, the objects collectively which are included under it; thus, the word figure is more extensive than triangle, circle, or parallelogram; European more extensive than French, Frenchman, German, &c. Matter and mind are the most extensive terms of which any definite conception can be formed. ”

“ Instead of its being true that all general ideas of extension are deducible to particular positive extension, the reverse proposition is I think demonstrable: that all particular extensions, the most positive and distinct, are never any thing else than a more or less vague notion of extension in general. In any given visible object we have always the general idea of something extended, and never of the precise length ”

“ The idea of extension is entirely acquired from the senses of sight and feeling; and if all the qualities, perceived by the senses, be in the mind, not in the object, the same conclusion must reach the idea of extension, which is wholly dependent on the sensible ideas or the ideas of secondary qualities. ”

“ It may be objected again that extension can never be built up out of the non-extended—that if one element of a given kind has, taken alone, no extension at all, two or more such elements together cannot have any extension either. ”

“ And I can no more conceive how a necessarily existing being can, on the same account or in the same manner as space and duration are, be needful in order to the existence of any other being, than I can conceive extension attributed to a thought: that idea no more belonging to a thing existing, than extension belongs to thought. ”

“ Just because both of us have subreptitiously restored the knowledge of extension in denying that extension itself would be annihilated. The knowledge of extension is extension, and extension is the knowledge of extension. Perhaps, in continuation, you will say, we have our own ideas, the secondary qualities are in truth our own ideas; but that besides these we have an idea of something existing externally to us which is not an idea, and that this something forms the aggregate of the primary qualities. ”

“ And therefore our very notion of extension is a sufficient proof of the existence of continuous matter.
We reply that this reason is even less plausible than the preceding one. To form the abstract notion of extension, we must first directly perceive some extension in the concrete, in the same manner as we must perceive concrete humanity in individual men before we conceive humanity in the abstract. But in all sensible movements we directly perceive extension through space and time. ”

“ But what else is the perception of extension than the perception of some parts beyond others? Is it not to perceive the difference of magnitude, to perceive some greater than others, and containing them? ”

“ What extension is, in relation to sensible intuitions, the idea of being is, in relation to conceptions. The intuition of extension, and the idea of being, are the two fundamental points in all ideological and ontological science ”

“ Extension is, so far as we are concerned, a determinate object, presented to us in the clearest intuition. The attribute of passive sensibility has ever been regarded as one of the most characteristic determinations ”

“ For example : there be that say that the essence of body is extension ; if it be so, we can never mistake in putting the essence of anything for the thing itself. Let us then in discourse put extension for body, and when we would say that body moves, let us say that extension moves, and see how ill it will look. He that should say that one extension by impulse moves another extension, would, by the bare expression, sufficiently show the absurdity of such a notion. ”

“ If the substance, the subject of extension is simple, the result will be a simple substance determined or modified by extension, a simple extended substance, which is a contradiction. A thing cannot be conceived as a modification of another unless it is modified by it ”

“ The idea of an abstract extension which is limited, is a contradiction. Limit takes from extension generality; and generality destroys the limit. There can, therefore, be no abstract idea of limited extension; but when we form an idea of extension in the abstract, we conceive it as unlimited, and the imagination attempting to follow the understanding, pictures to itself an indefinite space. ”

“ Before proceeding farther, in our inquiry with respect to the origin of the notion of extension, it may, however, be of advantage, to take a short retrospect of the progress which we have already made; for, if we have found nothing more, we have, at least, as I conceive, found reason to reject a considerable part of our former belief on the subject, which, though a negative acquisition, is yet a very important one. ”

“ But if the terms extension, parts, and the like, are taken in any sense conceivable—that is, for ideas,—then to say a finite quantity or extension consists of parts infinite in number is so manifest and glaring a contradiction, that every one at first sight acknowledges it to be so. And it is impossible it should ever gain the assent of any reasonable creature who is not brought to it by gentle and slow degrees, as a converted Gentile728 to the belief of transubstantiation. Ancient and rooted prejudices do often pass into principles. ”

“ Conversion offers a good illustration of the principle on which we have before insisted, namely, that in the ordinary form of proposition the subject is used in extension and the predicate in intension. For when by conversion we change the predicate into the subject, we are often obliged to attach a noun substantive to the predicate, in order that it may be taken in extension, instead of, as before, in intension, e.g.
Some mothers are unkind.
.'. Some unkind persons are mothers. ”

“ It is the same with the fourth proposition, that without the idea of extension, we can have no fixed idea of any thing corporeal, no fixed rule in relation to phenomena, but are like blind men. If, for an instant, we abstract the idea of extension, it is impossible for us to take a step in advance. ”

“ NOT CONCLUSIVE AS TO EXTENSION.--In short, let any one consider those arguments which are thought manifestly to prove that colours and taste exist only in the mind, and he shall find they may with equal force be brought to prove the same thing of extension, figure, and motion. ”

“ For, any of those things that caused an object to be thought greater than in proportion to its visible extension being either omitted, or applied without the usual circumstances, the judgment depends more entirely on the visible extension ”

“ But what possible meaning has it to say that, when we think of a foot-rule or a square yard, extension is not attributable to our thought? Of every extended object the adequate mental picture must have all the extension of the object itself. The difference between objective and subjective extension is one of relation to a context solely. In the mind the various extents maintain no necessarily stubborn order relatively to each other, while in the physical world they bound each other stably, and, added together, make the great enveloping Unit which we believe in and call real Space. ”

“ The difficulty arises from the very nature of extended things, whether realized or only conceived; the real order escapes none of the difficulties of the ideal. If ideal extension cannot be constituted out of unextended points, neither can real extension; if ideal extension has no limit to its divisibility until we come to simple points, the same is also true of real extension; for in both it is a result of the essence of extension, and inseparable from it. ”

“ Inclusiveness, exclusiveness, and intersection, are three different aspects of the purely formal relation of extension, and are therefore equally free of all spatial and temporal content.
12. Every entity is defined by a number of attributes, by the totality of which it is distinguished from all entities not identical with it. These attributes can be divided into two classes: those attributes which are common to all parts of a given entity, and by virtue of which (with respect to which) this entity has extension ”

“ As becoming is the foundation of the become, continuous living history that of fulfilled dead nature, the organic that of the mechanical, destiny that of causal law and the causally-settled, so too direction is the origin of extension. ”

“ When we think of that possibility as antecedent to all creation, we are thinking of bodies, and of their extension, as possible; and the concept of their total extension as possible is the concept of ideal or possible space. ”

“ Carry the process in thought as far as we may, until the extension of the parts is less than can be imagined, we still cannot escape the admission of forces by which the extension is upheld; and we can find no limit until we arrive at the conception of centres of force without any extension. ”

“ No one is less inclined than I am to place any limit upon the extension of human knowledge. Yet the extension of our scientific knowledge, in the widest sense of the term, is always subordinate to certain conditions. ”

“ A root plus one extension may be translated quite differently from the same root with another extension.
3. Unlike the prefixes, some of the extensions vary markedly in their form.
78/ Nevertheless, extensions are in some ways of as much potential Value to a student as the prefixes are. ”

“ Since we discover extension in the whole of our perceptual data, it follows that of parts of the world as such we can predicate everything which we can predicate of an entity having extension, i.e., inclusiveness, exclusiveness, and intersection of its various parts, and that we can postulate in them the existence of elementary parts, i.e., parts which have no extension as regards any attribute by virtue of which they are parts of our perceptual data. ”

“ A term is used in extension when it is employed with reference to the objects for which the term stands. A term is used in intension when it is employed with reference to the qualities for which the term stands. ”

“ It is no longer a subject of doubt, in the minds of savants who have got beyond experimentation, that extension is an image and a show rather than an essential constituent property of bodies. The extension of bodies is a phenomenon which takes its rise in the collision of force with our minds. ”

“ If, in one indivisible act of consciousness, we immediately perceive extended matter exterior to our percipient mind, then Extension exists objectively; and if Extension exists objectively, then Space, its conditio sine qua non, also exists objectively. ”

“ These various operations might be brought within the compass of the science, and the additional advantage be obtained of a very simple definition, if, by an extension of the term, sanctioned by high authorities, we were to define logic as the science which treats of the operations of the human understanding in the pursuit of truth. ”

“ He maintains that force is the cause of extension, meaning by that that the sensation of extension is a modification of our sensibility, occasioned by forces analogous to those which produce sensations of a more complex kind. ”

“ Hence the true account of abstract terms seems to me to be that we have in them another limiting case, a case in which the extension and the intension are coincident. Incidentally, by illustrating the ambiguity of the principle that attributes have no attributes of their own, our discussion seems to indicate the advantage of taking the purely extensional view is opposed to the predicative view of the import of propositions as the basis of an elementary treatment of logical doctrine. ”

“ No priestly dogmas, invented on purpose to tame and subdue the rebellious reason of mankind, ever shocked common sense more than the doctrine of the infinitive divisibility of extension, with its consequences; as they are pompously displayed by all geometricians and metaphysicians, with a kind of triumph and exultation. A real quantity, infinitely less than any finite quantity, containing quantities infinitely less than itself, and so on in infinitum; ”

“ A privative term, on the other hand, restricts us within a definite sphere. The term 'empty' restricts us within the sphere of things which are capable of fulness, that is, if the term be taken in its literal sense, things which possess extension in three dimensions. ”

“ No definition can be expected to exhaust the whole intension of a term, and there will always be room for varying definitions of the same thing, according to the different points of view from which it is approached.
§ 366. Names of attributes lend themselves to definition far more easily than names of substances. The reason of this is that names of attributes are primarily intensive in force, whereas substances are known to us in extension before they become known to us in intension. ”