From Leibniz’s fifth letter to Clarke (Aug. 18, 1716)
§ 47. I will here show, how men come to form to themselves the notion of space. They consider that many things exist at once and they observe in them a certain order of coexistence, according to which the relation of one thing to another is more or less simple. This order, is their situation or distance. When it happens that one of those coexistent things changes its relation to a multitude of others, which do not change their relation among themselves; and that another thing, newly come, acquires the same relation to the others, as the former had; we then say, it is come into the place of the former; and this change, we call a motion in that body, wherein is the immediate cause of the change. And though many, or even all the coexistent things, should change according to certain known rules of direction and swiftness; yet one may always determine the relation of situation, which every coexistent acquires with respect to every other coexistent; and even that relation which any other coexistent would have to this, or which this would have to any other, if it had not changed, or if it had changed any otherwise. And supposing, or feigning, that among those coexistents' there is a sufficient number of them, which have undergone no change; then we may say, that those which have such a relation to those fixed existents, as others had to them before. have now the same place which those others had. And that which comprehends all those places, is called space. Which shows, that in order to have an idea of place and consequently of space, it is sufficient to consider these relations, and the rules of their changes, without needing to fancy any absolute reality out of the things whose situation we consider. And, to give a kind of a definition: place is that, which we say is the same to A and, to B, when the relation of the coexistence of B, with C, E, F, G, etc.agrees perfectly with the relation of the coexistence, which A had with the same C, E, F, G, etc. supposing there has been no cause of change in C, E, F, G, etc. It may be said also, without entering into any further particularity, that place is that, which is the same in different moments to different existent things, when their relations of coexistence with certain other existents, which are supposed to continue fixed from one of those moments to the other, agree entirely together. And fixed existents are those, in which there has been no cause of any change of the order of their coexistence with others; or (which is the same thing,) in which there has been no motion. Lastly, space is that, which results from places taken together. And here it may not be amiss to consider the difference between place, and the relation of situation, which is in the body that fills up the place. For, the place of A and B is the same; whereas the relation of A to fixed bodies, is not precisely and individually the same, as the relation which B (that comes into its place) will have to the same fixed bodies; but these relations agree only. For, two different subjects, as A and B, cannot have precisely the same individual affection; it being impossible, that the same individual accident should be in two subjects, or pass from one subject to another. But the mind not contented with an agreement, looks for an identity, for something that should be truly the same; and conceives it as being extrinsic to the subjects: and this is what we call place and space. But this can only be an ideal thing; containing a certain order, wherein the mind conceives the application of relations. In like manner, as the mind can fancy to itself an order made up of genealogical lines, whose bigness would consist only in the number of generations. wherein every person would have his place: and if to this one should add the fiction of a metempsychosis, and bring in the same human souls again; the persons in those lines might change place; he who was a father, or a grandfather might become a son, or a grandson, etc. And yet those genealogical places, lines, and spaces, though they should express real truth, would only be ideal things. I shall allege another example, to show how the mind uses, upon occasion of accidents which are in subjects, to fancy to itself something answerable to those accidents out of the subjects. The ratio or proportion between two lines L and M, may be conceived three several ways: as a ratio of the greater L, to the lesser M; as a ratio of the lesser M, to the greater L; and lastly, as something abstracted from both, that is, as the ratio between L and M without considering which is the antecedent, or which the consequent; which the subject, and which the object. And thus it is, that proportions are considered in music. In the first way of considering them, L the greater; in the second M the lesser, is the subject of that accident, which philosophers call relation. But, which of them will be the subject in the third way of considering them? It cannot be said that both of them, L and M together, are the subject of such an accident; for if so, we should have an accident in two subjects, with one leg in one, and the other in the other; which is contrary to the notion of accidents. Therefore we must say, that this relation, in this third way of considering it, is indeed out of the subjects: but being neither a substance, nor an accident, it must be a mere ideal thing, the consideration of which is nevertheless useful. To conclude: I have here done much like Euclid, who not being able to make his readers well understand what ratio is absolutely in the sense of geometricians, defines what are the same ratios. Thus, in like manner, in order to explain what place is, I have been content to define what is the same place. Lastly; I observe that the traces of moveable bodies, which they leave sometimes upon the immovable ones on which they are moved; have given men occasion to form in their imagination such an idea, as if some trace did still remain, even when there is nothing unmoved. But this is a mere ideal thing, and imports only, that if there was any unmoved thing there, the trace might be marked out upon it. And it is this analogy, which makes men fancy places, traces and spaces; though those things consist only in the truth of relations, and not at all in any absolute reality.
Letter to Coste on Human Freedom (Dec. 19 1707)
I thank you very much for forwarding Mr. Locke's latest additions and
corrections, and I am also very pleased to learn about his last dispute
with Mr. Limborch. The freedom of indifference on which this dispute turned,
and about which you asked my opinion, contains a certain subtlety that
few take care to understand, although many people reason about it. It reduces
to the consideration of necessity and contingency.
A truth is necessary when its opposite implies a contradiction; and
when it is not necessary, it is called contingent. That God exists, that
all right angles are equal to one another, etc., are necessary truths,
but that I exist and that there are bodies in nature that actually appear
to have right angles are contingent truths. For the whole universe
could have been made otherwise, since time, space, and matter are absolutely
indifferent to motions and to shapes, and God has chosen from an infinity
of possibles that which he judged most suitable.
However, once he has chosen, we must confess that everything is included
in his choice and that nothing can be changed, since he has foreseen and
regulated everything once and for all, for he would not regulate things
by bits and pieces. Consequently, sins and evils, which he has judged permissible
in order to allow greater goods, are included in some way in his choice.
It is this necessity that we can now attribute to things to come, a necessity
which we call hypothetical or consequential, that is, necessity based on
a consequence of the hypothesis of the choice made. This necessity does
not destroy the contingency of things and does not produce the absolute
necessity that contingency cannot allow. And almost all theologians and
philosophers (that is, except the Socinians) acknowledge the hypothetical
necessity I have just explained and acknowledge that we cannot oppose it
without upsetting God's attributes and the very nature of things.
However, although all facts of the universe are now certain with respect
to God, or (what comes to the same thing) determined in themselves and
even linked among themselves, it does not follow that their interconnection
is always truly necessary, that is, that the truth which asserts that one
fact follows from another is necessary. And it is this fact we must especially
apply to the case of voluntary actions.
When we present a choice to ourselves, for example, whether to leave
or not to leave, given all the internal or external circumstances, motives,
perceptions, dispositions, impressions, passions, inclinations taken together,
there is a question as to whether I am still in a state of contingency,
or whether I make the choice to leave, for example, by-necessity, that
is, whether in fact this true and determined proposition, that in all these
circumstances taken together, I will choose to leave, is contingent or
necessary. I reply that it is contingent, because neither I nor any other
more enlightened mind could demonstrate that the opposite of this truth
implies a contradiction. And assuming that by freedom of indifference we
understand a freedom opposed to necessity (as I have just explained), I
agree about this freedom. For, I am actually of the opinion that our freedom,
as well as that of God and the blessed spirits, is not only exempt from
coercion, but also from absolute necessity, even though it cannot be exempt
from determination and certainty.
But I find that we need to be very cautious here so that we do not
fall into a chimera which clashes with the principles of good sense, namely,
what I call an absolute indifference or indifference of equilibrium, an
indifference that some people imagine freedom to involve, and that I believe
to be chimerical. We must therefore consider that this interconnection
about which I have just spoken is not necessary, absolutely speaking, but
that it is nevertheless certainly true, and that, in general, every time
that the circumstances taken together tip the balance of deliberation more
on one side than on the ocher, it is certain and infallible that the former
side will be chosen. God, or a perfectly wise person, will always
choose the best they know of, and if one side were not better than the
other, they would choose neither the one nor the other. The passions often
take the place of reason in other intelligent substances, and we can always
assert, with respect to the will in general, that choice follows the greatest
inclination (by which I understand both passions and reasons, true or apparent).
However, I see that there are people who imagine that sometimes we
set ourselves for the lesser option, that God sometimes chooses the lesser
good, everything considered, and that a person sometimes chooses without
grounds against all his reasons, dispositions, and passions, and finally,
that we sometimes choose without any reason determining the choice. But
I hold this to be false and absurd, because one of the greatest principles
of good sense is that nothing ever happens without a cause or determining
reason. Thus when God chooses, it is by reason of the best, and when a
person chooses, it is the option that struck him the most. If he chooses
what he sees as less useful and pleasant in some respects, perhaps it becomes
more agreeable to him through a whim, or contrariness, or for similar reasons
which belong to a depraved taste; these are determining reasons, even though
they are not conclusive reasons. And we will never be able to find a contrary
example.
Thus, although we have a freedom of indifference which saves us from
necessity, we never have an indifference of equilibrium which exempts us
from determining reasons. There is always something which inclines us and
makes us choose, but without being able to necessitate us. And just as
God is always infallibly led to the best, even though he is not led to
it necessarily (other than by a moral necessity), we are always infallibly,
but not necessarily, led to what strikes us the most; since the contrary
does not imply any contradiction, it was neither necessary nor essential
that God created, nor that he created this world in particular, even though
his wisdom and goodness led him to it.
That is what Mr. Bayle, subtle as he was, did not consider well enough
when he held that a case similar to Buridan's ass was possible, and that
a man placed in circumstances of perfect equilibrium could nevertheless
choose. For we must say that the case of a perfect equilibrium is chimerical,
and never happens, since the universe is incapable of being divided or
split into two equal and similar parts. The universe is not like an ellipse
or other such oval, where a straight line drawn through its center can
cut it into two congruent parts. The universe has no center, and its parts
are infinitely varied; thus the case never arises in which everything is
perfectly equal and strikes equally on all sides. And although we are not
always capable of perceiving all the small impressions that contribute
to determining us, there is always something that determines us to choose
between two contradictories, without the case ever being perfectly equal
on all sides.
However, although our choice ex datis, with respect to all internal
and external circumstances taken together, is always determined, and although,
for the present, we cannot alter our will, it nevertheless is true
that we have great power with respect to our future volitions, by choosing
to be attentive to certain objects and by accustoming ourselves to certain
ways of thinking. In this way we can accustom ourselves to resist impressions
better and have our reason behave better, so that we can contribute to
making ourselves will what we should. Moreover, I have also shown
that when we take things in a certain metaphysical sense, we are always
in a state of perfect spontaneity, and that what we attribute to the impressions
of external things arises only from confused perceptions in us corresponding
to them, perceptions that cannot fail to be given to us from the first
in virtue of pre-established harmony, which relates each substance to all
the others....