Elements of philosophy the first section, concerning body / written in Latine by Thomas Hobbes of Malmesbury ; and now translated into English ; to which are added Six lessons to the professors of mathematicks of the Institution of Sr. Henry Savile, in the University of Oxford.

CHAP. VII. Of Place and Time.

• 1 Things that have no existence, may neverthelesse be under stood and compu∣ted.
• 2 What is space.
• 3 Time.
• 4 Part.
• 5 Division.
• 6 One
• 7 Num∣ber.
• 8 Composition.
• 9 The Whole.
• 10 Spaces and Times Contiguous, and Continuall.
• 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.

1 IN the Teaching of Naturall Philoso∣phy, I cannot begin better (as I have al∣ready shewn) then from Privation; that is, from feigning the World to be anni∣hilated. But if such annihilation of all things be supposed, it may perhaps be asked, what would remain for any Man (whom onely 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 Ratiocina∣tions 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 eies, or perceived by any other Sense; that is to say, the Memory and Imagination of Magnitudes, Motions, Sounds, Co∣lours, &c. as also of their order & parts. All w^ch things though they be nothing but Ideas & Phantasms▪ hapning internally to him that imagineth; yet they will appear as if they were externall, and not at all depending upon any power of the Mind. And these are

the things to which he would give Names, and substract 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 thinkes, imagines, and remembers, there can be nothing for him to thinke of but what is Past; Nay, if we do but observe diligently what it is we doe 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 Phantasmes. For when we calculate the magnitude and motions of Heaven or Earth, we doe not ascend into Heaven that we may divide it into parts, or measure the motions thereof, but we doe it sitting still in our Closets or in the Darke. 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 onely to exist, or to have a Be∣ing without Us. And in this manner we are now to consider them.

2 If therefore we remember, or have a Phantasme 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 onely that it had a Being without the Mind, we have presently a Conception of that we call Space: an Imaginary Space indeed, because a meere Phantasme, 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 alwayes accompany the Body which is once in it. And this is of it selfe so manifest, that I should not thinke it need∣ed any explaining at all, but that I finde Space to be falsely defi∣ned by certaine Philosophers, who inferre from thence, One, that the world is Infinite; for taking Space to be the Extension of Bo∣dies, and thinking Extension may encrease continually, he in∣ferres that Bodies may be infinitely Extended; and Another from the same Definition concludes rashly, that it is impossible even to God himselfe to create more Worlds then one; for if ano∣ther World were to be created, he sayes, that seeing there is no∣thing without this world, and therefore (according to his

Definition) no Space, that new world must be placed in no∣thing; but in nothing nothing can be placed; which he affirms onely, without shewing any reason for the same; whereas the contrary is the truth: for more cannot be put into a Place allready filled, so much is Empty Space fitter then that which is Full for the receiving of new Bodies. Having therefore spoken thus much for these mens sakes, and for theirs that assent to them, I return to my purpose, and define Space thus, SPACE is the Phantasme of a Thing existing without the Mind simply; that is to say, that Phantasme, in which we consider no other Accident, but onely that it ap∣pears without us.

3 As a Body leaves a Phantasme of its Magnitude in the mind, so also a Moved Body leaves a Phantasme of its Motion, namely an Idea of that Body passing out of one Space into another by con∣tinuall succession. And this Idea or Phantasme, is that which (without receding much from the common opinion, or from Ari∣stotles Definition) I call Time. For seeing all men confesse a Yeare to be Time, and yet do not think a Year to be the Accident or Af∣fection of any Body, they must needs confesse it to be, not in the things without Us, but only in the Thought of the Mind. So when they speake of the Times of their Predecessors, they do not think after their Predecessors are gone, that their Times can be any where else then in the Memory of those that remember them. And as for those that say, Dayes, Years and Moneths are the Mo∣tions of the Sunne 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 meane, 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 here∣after, It is. What then can Dayes, Moneths and Yeares be, but the Names of such Computations made in our Mind? Time there∣fore is a Phantasme, but a Phantasme 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∣glasse, 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 Phantasme

of Motion, I doe not say this is sufficient to define it by; for this word Time comprehends the notion of Former and Later, or of Succession in the motion of a Body, in as much as it is first Here then There. Wherefore a compleat Definition of Time is such as this, TIME is the Phantasme of Before and After in Motion; which agrees with this Definition of Aristotle, Time is the Number of Motion accord∣ing to Former and Later; for that Numbring is an act of the Mind; and therefore it is all one to say, Time is the Number of Motion accord∣ing to Former and Later; and Time is a Phantasme of Motion Numbred. But that other Definition, Time is the Measure of Motion, is not so ex∣act; for we measure Time by Motion and not Motion by Time.

4 One Space is called Part of another Space, and one Time Part of another Time, when this containes that and something besides. From whence it may be collected, that nothing can right∣ly be called a PART, but that which is compared with something that contains it.

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 Con∣ceptions he has are more by one, then 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 doe 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.

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 substracted 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 ob∣noxious to an absurd Consequence; for it may thence be inferred, that whatsoever is Divided, is many things, that is, that every Di∣vided

thing, is Divided Things, which is Insignificant.

7 NUMBER is. One and One, or One One and One, and so for∣wards; namely One and One make the Number Two, and One One and One, the Number Three; and so are all other Numbers made; which is all one as if we should say, Number is Unities.

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 Armes and the Body severally, and then for the account of them all together put Man. And that which is so put for all the severalls of which it consists, is called the WHOLE; and those severalls, 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 onely of collecting them into one summe in the Mind. For thus all Men being considered together, make up the Whole of Mankind, though never so much disper∣sed by Time and Place; and twelve Hours, though the hours of severall dayes, may be Compounded into one Number of Twelve.

9 This being well understood, it is manifest, that nothing can rightly be called a Whole, that is not conceived to be compound∣ed 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 affirme that no soul can be a Whole soul. Also it is manifest, that No∣thing has Parts till it be Divided; and when a Thing is Divided, the Parts are onely so many as the Division makes them. Againe, that a Part of a Part is a Part of the Whole; & 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.

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, A—B—C as AB, BC. And any two Spaces as well as Times are said to be CONTINUALL, when they have one common part, A—B—C—D as AC, BD, where the part BC is common; and more Spaces and Times are Continual, when every two which are next one another are Continual.

11 That Part which is between two other Parts, is called a MEAN; & 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 Begin∣ning and End; as also that every thing is FINITE or INFINITE, acording as we imagine or not imagine it Limited or Terminated eve∣ry 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 In∣finite, 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.

12 Space or Time is said to be 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 Num∣ber 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 then any number that can be assigned, yet their number will alwayes 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 In∣finite number of Paces: But no such Part can be taken; wherefore the

world is not infinite; because that Consequence of the Major Propo∣sition is false; for in an Infinite space, whatsoever we take, or de∣sign 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 whch we our selves are the Beginning, and whatsoever any man with his Mind cuts off both wayes from Infi∣nite, 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 al∣so 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 Minde 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 thousanth Sphere. The meaning of the Question is this onely, whether God has actually made so great an Addition of Body to Body, as we are able to make of Space to Space.

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, Whatsover is Divided, is divided into such Parts as may again be Divided; or thus, The Least Divisible thing is not to be gi∣ven; or as Geometricians have it, No Quantity is so small, but a Less may be taken; which may easily be demonstrated in this man∣ner. 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 ei∣ther 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 (be∣ing greater then 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 Di∣visible.