CHAPTER VII.
OF PLACE AND TIME.
1. Things that have no existence, may nevertheless be understood and computed.—2. What is Space.—3. Time.—4. Part.—5. Division.—6. One.—7. Number.—8. Composition.—9. The whole.—10. Spaces and times contiguous, and continual.—11. Beginning, end, way, finite, infinite.—12. What is infinite in power. Nothing infinite can be truly said to be either whole, or one; nor infinite spaces or times, many.—13. Division proceeds not to the least.
[Sidenote: Things that have no existence, may nevertheless be understood and computed.]
1. In the teaching of natural philosophy, I cannot begin better (as I have already shewn) than from _privation_; that is, from feigning the world to be annihilated. But, if such annihilation of all things be supposed, it may perhaps be asked, what would remain for any man (whom only I except from this universal annihilation of things) to consider as the subject of philosophy, or at all to reason upon; or what to give names unto for ratiocination's sake.
I say, therefore, there would remain to that man ideas of the world, and of all such bodies as he had, before their annihilation, seen with his eyes, or perceived by any other sense; that is to say, the memory and imagination of magnitudes, motions, sounds, colours, &c. as also of their order and parts. All which things, though they be nothing but ideas and phantasms, happening internally to him that imagineth; yet they will appear as if they were external, and not at all depending upon any power of the mind. And these are the things to which he would give names, and subtract them from, and compound them with one another. For seeing, that after the destruction of all other things, I suppose man still remaining, and namely that he thinks, imagines, and remembers, there can be nothing for him to think of but what is past; nay, if we do but observe diligently what it is we do when we consider and reason, we shall find, that though all things be still remaining in the world, yet we compute nothing but our own phantasms. For when we calculate the magnitude and motions of heaven or earth, we do not ascend into heaven that we may divide it into parts, or measure the motions thereof, but we do it sitting still in our closets or in the dark. Now things may be considered, that is, be brought into account, either as internal accidents of our mind, in which manner we consider them when the question is about some faculty of the mind; or as species of external things, not as really existing, but appearing only to exist, or to have a being without us. And in this manner we are now to consider them.
[Sidenote: What is Space.]
2. If therefore we remember, or have a phantasm of any thing that was in the world before the supposed annihilation of the same; and consider, not that the thing was such or such, but only that it had a being without the mind, we have presently a conception of that we call _space_: an imaginary space indeed, because a mere phantasm, yet that very thing which all men call so. For no man calls it space for being already filled, but because it may be filled; nor does any man think bodies carry their places away with them, but that the same space contains sometimes one, sometimes another body; which could not be if space should always accompany the body which is once in it. And this is of itself so manifest, that I should not think it needed any explaining at all, but that I find space to be falsely defined by certain philosophers, who infer from thence, one, that the world is infinite (for taking _space_ to be the extension of bodies, and thinking extension may encrease continually, he infers that bodies may be infinitely extended); and, another, from the same definition, concludes rashly, that it is impossible even to God himself to create more worlds than one; for, if another world were to be created, he says, that seeing there is nothing without this world, and therefore (according to his definition) no space, that new world must be placed in nothing; but in nothing nothing can be placed; which he affirms only, without showing any reason for the same; whereas the contrary is the truth: for more cannot be put into a place already filled, so much is empty space fitter than that, which is full, for the receiving of new bodies. Having therefore spoken thus much for these men's sakes, and for theirs that assent to them, I return to my purpose, and define _space_ thus: SPACE _is the phantasm of a thing existing without the mind simply_; that is to say, that phantasm, in which we consider no other accident, but only that it appears without us.
[Sidenote: Time.]
3. As a body leaves a phantasm of its magnitude in the mind, so also a moved body leaves a phantasm of its motion, namely, an idea of that body passing out of one space into another by continual succession. And this idea, or phantasm, is that, which (without receding much from the common opinion, or from _Aristotle's_ definition) I call _Time_. For seeing all men confess a year to be time, and yet do not think a year to be the accident or affection of any body, they must needs confess it to be, not in the things without us, but only in the thought of the mind. So when they speak of the times of their predecessors, they do not think after their predecessors are gone, that their times can be any where else than in the memory of those that remember them. And as for those that say, days, years, and months are the motions of the sun and moon, seeing it is all one to say, motion _past_ and motion _destroyed_, and that _future_ motion is the same with motion which _is not yet begun_, they say that, which they do not mean, that there neither is, nor has been, nor shall be any time: for of whatsoever it may be said, _it has been_ or _it shall be_, of the same also it might have been said heretofore, or may be said hereafter, _it is_. What then can days, months, and years, be, but the names of such computations made in our mind? _Time_ therefore is a phantasm, but a phantasm of motion, for if we would know by what moments time passes away, we make use of some motion or other, as of the sun, of a clock, of the sand in an hour-glass, or we mark some line upon which we imagine something to be moved, there being no other means by which we can take notice of any time at all. And yet, when I say _time_ is a phantasm of motion, I do not say this is sufficient to define it by; for this word _time_ comprehends the notion of _former_ and _latter_, or of _succession_ in the motion of a body, in as much as it is first _here_ then _there_. Wherefore a complete definition of _time_ is such as this, TIME _is the phantasm of before and after in motion_; which agrees with this definition of _Aristotle_, _time is the number of motion according to former and latter_; for that numbering is an act of the mind; and therefore it is all one to say, _time is the number of motion according to former and latter_; and _time is a phantasm of motion numbered_. But that other definition, _time is the measure of motion_, is not so exact, for we measure time by motion and not motion by time.
[Sidenote: Part.]
4. One space is called _part_ of another space, and one time _part_ of another time, when this contains that and something besides. From whence it may be collected, that nothing can rightly be called a PART, but that which is compared with something that contains it.
[Sidenote: Division.]
5. And therefore to _make parts_, or to _part_ or DIVIDE space or _time_, is nothing else but to consider one and another within the same; so that if any man _divide_ space or time, the diverse conceptions he has are more, by one, than the parts he makes; for his first conception is of that which is to be divided, then of some part of it, and again of some other part of it, and so forwards as long as he goes on in dividing.
But it is to be noted, that here, by _division_, I do not mean the severing or pulling asunder of one space or time from another (for does any man think that one hemisphere may be separated from the other hemisphere, or the first hour from the second?) but diversity of consideration; so that division is not made by the operation of the hands but of the mind.
[Sidenote: One.]
6. When space or time is considered among other spaces or times, it is said to be ONE, namely _one of them_; for except one space might be added to another, and subtracted from another space, and so of time, it would be sufficient to say space or time simply, and superfluous to say one space or one time, if it could not be conceived that there were another. The common definition of _one_, namely, that _one is that which is undivided_, is obnoxious to an absurd consequence; for it may thence be inferred, that whatsoever is divided is many things, that is, that every divided thing, is divided things, which is insignificant.
[Sidenote: Number.]
7. NUMBER is _one_ and _one_, or _one one_ and _one_, and so forwards; namely, _one_ and _one_ make the number _two_, and _one one_ and _one_ the number _three_; so are all other numbers made; which is all one as if we should say, _number is unities_.
[Sidenote: Composition.]
8. To COMPOUND space of spaces, or time of times, is first to consider them one after another, and then altogether as one; as if one should reckon first the head, the feet, the arms, and the body, severally, and then for the account of them all together put _man_. And that which is so put for all the severals of which it consists, is called the WHOLE; and those severals, when by the division of the whole they come again to be considered singly, are parts thereof; and therefore the _whole_ and _all the parts taken together_ are the same thing. And as I noted above, that in _division_ it is not necessary to pull the parts asunder; so in _composition_, it is to be understood, that for the making up of a whole there is no need of putting the parts together, so as to make them touch one another, but only of collecting them into one sum in the mind. For thus all men, being considered together, make up the whole of mankind, though never so much dispersed by time and place; and twelve hours, though the hours of several days, may be compounded into one number of twelve.
[Sidenote: The whole.]
9. This being well understood, it is manifest, that nothing can rightly be called a whole, that is not conceived to be compounded of parts, and that it may be divided into parts; so that if we deny that a thing has parts, we deny the same to be a whole. For example, if we say the soul can have no parts, we affirm that no soul can be a whole soul. Also it is manifest, that nothing has parts till it be divided; and when a thing is divided, the parts are only so many as the division makes them. Again, that a part of a part is a part of the whole; and thus any part of the number _four_, as _two_, is a part of the number _eight_; for _four_ is made of _two_ and _two_; but _eight_ is compounded of _two_, _two_, and _four_, and therefore _two_, which is a part of the part _four_, is also a part of the whole _eight_.
[Sidenote: Spaces and times contiguous and continual.]
10. Two spaces are said to be CONTIGUOUS, when there is no other space betwixt them. But two times, betwixt which there is no other time, are called immediate, as A B, B C.[Sidenote: A B C] And any two spaces, as well as times, are said to be CONTINUAL, when they have one common part, as A C, B D, where the part B C is common; [Sidenote: A B C D] and more spaces and times are continual, when every two which are next one another are continual.
A B C D -------------
A B C ------------
[Sidenote: Beginning, end, way, finite, infinite.]
11. That part which is between two other parts, is called a MEAN; and that which is not between two other parts, an EXTREME. And of extremes, that which is first reckoned is the BEGINNING, and that which last, the END; and all the means together taken are the WAY. Also, _extreme parts_ and _limits_ are the same thing. And from hence it is manifest, that _beginning_ and _end_ depend upon the order in which we number them; and that to _terminate_ or _limit_ space and time, is the same thing with _imagining their beginning and end_; as also that every thing is FINITE or INFINITE, according as we imagine or not imagine it _limited_ or _terminated_ every way; and that the _limits_ of any number are _unities_, and of these, that which is the first in our numbering is the _beginning_, and that which we number last, is the _end_. When we say number is _infinite_, we mean only that no number is expressed; for when we speak of the numbers _two_, _three_, _a thousand_, &c. they are always _finite_. But when no more is said but this, _number is infinite_, it is to be understood as if it were said, this name _number_ is an _indefinite_ name.
[Sidenote: What is infinite in power. Nothing infinite can be truly said to be either whole or one; nor infinite spaces or times, many.]
12. Space or time is said to _finite in power_, or _terminable_, when there may be assigned a number of finite spaces or times, as of paces or hours, than which there can be no greater number of the same measure in that space or time; and _infinite in power_ is that space or time, in which a greater number of the said paces or hours may be assigned, than any number that can be given. But we must note, that, although in that space or time which is infinite in power, there may be numbered more paces or hours than any number that can be assigned, yet their number will always be finite; for every number is finite. And therefore his ratiocination was not good, that undertaking to prove the world to be finite, reasoned thus; _If the world be infinite, then there may be taken in it some part which is distant from us an infinite number of paces: but no such part can be taken; wherefore the world is not infinite_; because that consequence of the major proposition is false; for in an infinite space, whatsoever we take or design in our mind, the distance of the same from us is a finite space; for in the very designing of the place thereof, we put an end to that space, of which we ourselves are the beginning; and whatsoever any man with his mind cuts off both ways from infinite, he determines the same, that is, he makes it finite.
Of infinite space or time, it cannot be said that it is a _whole_ or _one_: not a _whole_, because not compounded of parts; for seeing parts, how many soever they be, are severally finite, they will also, when they are all put together, make a whole finite: nor _one_, because nothing can be said to be one, except there be another to compare it with; but it cannot be conceived that there are two spaces, or two times, infinite. Lastly, when we make question whether the world be finite or infinite, we have nothing in our mind answering to the name _world_; for whatsoever we imagine, is therefore finite, though our computation reach the fixed stars, or the ninth or tenth, nay, the thousandth sphere. The meaning of the question is this only, whether God has actually made so great an addition of body to body, as we are able to make of space to space.
[Sidenote: Division proceeds not to the least.]
13. And, therefore, that which is commonly said, that space and time may be divided infinitely, is not to be so understood, as if there might be any infinite or eternal division; but rather to be taken in this sense, _whatsoever is divided, is divided into such parts as may again be divided_; or thus, _the least divisible thing is not to be given_; or, as geometricians have it, _no quantity is so small, but a less may be taken_; which may easily be demonstrated in this manner. Let any space or time, that which was thought to be the least divisible, be divided into two equal parts, A and B. I say either of them, as A, may be divided again. For suppose the part A to be contiguous to the part B of one side, and of the other side to some other space equal to B. This whole space, therefore, being greater than the space given, is divisible. Wherefore, if it be divided into two equal parts, the part in the middle, which is A, will be also divided into two equal parts; and therefore A was divisible.
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