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Copyright Jonathan Bennett
[Brackets] enclose editorial explanations. Small dots enclose
material that has been added, but can be read as though it were
part of the original text. Occasional bullets, and also indenting
of passages that are not quotations, are meant as aids to grasping
the structure of a sentence or a thought. Four ellipses . . . .
indicate the omission of a brief passage that seems to present more
difficulty than it is worth.First launched: September 2004
* * * * * * *
Freedom and PossibilityBy G. W. Leibniz
In God everything is spontaneous. It can hardly be doubted that
in every human person there is the freedom to do what he wills to
do. A volition is an attempt to act of which we are conscious. An
act necessarily follows from a volition to do it and the ability to
do it. When all the conditions for willing to do something are
matched by equally strong conditions against willing to do it, no
volition occurs. Rather there is indifference [here = equilibrium].
Thus, even if someone accepts that all the conditions requisite for
acting are in place, he wont act if equal contrary conditions
obtain. Thats one way for a person to to act on reasons that he
has. Here is another: a person may be unmoved by reasons through
sheer forgetfulness, i.e. by turning his mind away from them. So it
is indeed possible to be unmoved by reasons. Unless this
proposition is accepted: There is nothing without reason. That is:
In every true proposition there is a connection between the subject
and the predicate, i.e. every true proposition can be proved a
priori. There are two primary propositions: one is the principle of
necessary things, that
whatever implies a contradiction is false, and the other is the
principle of contingent things, that
whatever is more perfect or has more reason is true. All truths
of metaphysics - indeed all truths that are absolutely necessary,
such as those of logic, arithmetic, geometry, and the like - rest
on the former principle, for someone who denies one of those truths
can always be shown that his denial implies a contradiction. All
contingent truths rest on the latter principle. (I mean truths that
are in themselves contingent. They may be
necessary-given-what-God-wills.) So the principle of contradiction
is the basis for all truths about possibilities or essences, and
all truths about a things impossibility or its necessity (that is,
the impossibility of its contrary). And the principle of perfection
is the basis for all truths about contingent things, that is, about
what exists. God is the only being whose existence is not
contingent. The reason why some particular contingent thing x
exists, and other possible things dont, shouldnt be sought in xs
definition alone. If xs definition did explain its existence, its
nonexistence would imply a contradiction; and those other things
wouldnt be possible, contrary to our hypothesis. For the reason why
x exists and those others dont, we must look to how x compares with
the others; the reason is that x is more perfect than the others
that are its rivals for existence.
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My over-riding thought here is a notion of possibility and
necessity according to which some things are not necessary and dont
actually exist but nevertheless are possible. It follows from this
that a reason that always brings it about that a free mind chooses
one thing rather than another (whether that reason derives from the
perfection of a thing, as it does in God, or from our imperfection)
doesnt take away our freedom. This also shows what distinguishes
Gods free actions from his necessary actions. Here is one example
of each kind of action. It is necessary that God loves himself, for
that can be demonstrated from the definition of God. But it cant be
demonstrated from that definition that God makes whatever is most
perfect, for theres nothing contradictory in the proposition that
he doesnt. If there were, it wouldnt be possible for him to make
something less perfect, and that is contrary to the hypothesis that
there are non-existent possibles. Moreover, this conclusion derives
from the notion of existence, for only the most perfect exists. Let
there be two possible things, A and B, such that necessarily one
and only one of them exists; and lets assume that A is more perfect
than B. Then we can certainly explain why A should exist rather
than B - this is a basis for us to predict which of the two will
exist. Indeed, As existing rather than Bs doing so can be
demonstrated, by which I mean that it can be rendered certain from
the nature of the case. Now, if being certain were the same as
being necessary then it would also be necessary for A to exist. But
As existence has merely what I call hypothetical necessity, meaning
that
it is necessary that: if God always chooses what is most
perfect, then A exists.That is to be distinguished from the
proposition that
it is necessary that: A exists.If it were absolutely and not
just hypothetically necessary that A exists, then B - which we have
stipulated cannot exist if A exists - would be absolutely
impossible, i.e. would imply a contradiction, which is contrary to
our stipulation that A and B are both possible. So we must hold
that anything that has some degree of perfection is possible, and
anything that is more perfect than its opposite actually exists -
not because of its own nature but because of Gods general resolve
to create the more perfect. Perfection (or essence) is an urge for
existence; it implies existence, not necessarily but through there
not being a more perfect thing that prevents it from existing. All
truths of physics are of this sort; for example, when we say that a
body persists in the speed with which it begins, we mean . . . if
nothing gets in its way. God produces the best - not necessarily,
but because he wills to do so. If you ask Does God will by
necessity? I ask you to explain what you mean by necessity,
spelling it out in detail so as to make clear what exactly you are
asking. For example, you might be asking:
Does God will by necessity or does he will freely?that is:
Does God will because of his nature or because of his will?My
answer to that is of course that God cant will voluntarily. That
is, it cant be the case that whenever God wills to do something, it
is because he has willed to will to do that thing; because that
would involve willing to will . . . to infinity. Rather, we must
say that it is Gods nature that leads him to will the best. So he
wills by necessity? you say, implying that I am demeaning God. I
reply with St. Augustine that such necessity is blessed. But surely
it follows from this that things exist by necessity. How so?
Because the nonexistence of what God wills to exist implies a
contradiction? I deny that this proposition is absolutely true. It
entails that what God doesnt will is not possible, and I deny that.
For things remain possible, even if God doesnt select them.
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Given that God doesnt will x to exist, it is still possible for
x to exist, because xs nature is such that x could exist if God
were to will it to exist. You will object: But God cant will it to
exist. Granted; yet x remains possible in its nature even if it is
not possible with respect to the divine will, since we have defined
as possible in its nature anything that in itself implies no
contradiction, even if its coexistence with God can in some way be
said to imply a contradiction. Well need to use unambiguous
meanings for words if we are to avoid every kind of absurd
locution. I start with the meaning I give to possible. I say:
a possible thing is something with some essence or reality, that
is, something that can be clearly understood.
For an illustrative example, let us pretend that nothing exactly
pentagonal ever did or will exist in nature. A pentagon would
nevertheless remain possible. However, if we are to maintain that
pentagons are possible, we should give some reason why no pentagon
ever did or will exist. The reason is simply the fact that the
pentagon is incompatible with other things that got into existence
ahead of it because they include more perfection, i.e. involve more
reality, than it does. Returning to your previous line of attack,
you will say: So according to you it is necessary that the pentagon
doesnt exist. I agree, if what you mean is that
The proposition No pentagon ever did or will exist is necessary.
But what you say is false if it is understood to mean that
The timeless proposition No pentagon exists is necessary,because
I deny that this timeless proposition can be demonstrated. The
pentagon is not absolutely impossible, and doesnt imply a
contradiction, even if it follows from the harmony of things that a
pentagon cant find a place among real things. The following
argument is valid (its second premise is the one we have been
pretending to be true):
If a pentagon exists, it is more perfect than other things.A
pentagon is not more perfect than other things.Therefore, a
pentagon does not exist.
But the premises dont imply that it is impossible for a pentagon
to exist. This is best illustrated by analogy with imaginary roots
in algebra, such as -1. For -1 does involve some notion, though it
cant be pictured . . . . But there is a great difference
between
problems that are insoluble because a solution requires
imaginary rootsand
problems that are insoluble because of their absurdity.An
example of the latter: Find a number which multiplied by itself is
9, and which added to 5 makes 9. Such a number implies a
contradiction, for it must be both 3 and 4, implying that 3 = 4, a
part equals the whole. An example of the former: Find a number x
such that x2 + 9 = 3x. Someone trying to solve this could certainly
never show that the solution would imply any such absurdity as that
the whole equals its part, but he could show that such a number
cannot be designated because the only solutions to the equation are
imaginary roots. To accompany the pentagon example, I now offer
another one, in which I use a real line to mean a line that really
bounds some body. If God had decreed that there should be no real
line that was incommensurable with other real lines, it wouldnt
follow that the existence of an incommensurable line implies a
contradiction, even if because of the principle of perfection God
couldnt have made such a line.
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All this removes the difficulties about the foreknowledge of
future contingents. For God, who foresees the future reasons or
causes for some things to exist and others not to, has certain
foreknowledge of future contingents through their causes. He
formulates propositions about them that are
necessary, given that the state of the world has been settled
once and for all,that is,
necessary, given the harmony of things.But the propositions
about future contingents are not necessary in the absolute sense,
as mathematical propositions are. This is the best answer to the
difficulty about how, if future contingents are not necessary, God
can have foreknowledge of them. It involves us in saying that it is
possible for the imperfect rather than the more perfect to exist.
You may object: It is impossible for something to exist that God
doesnt will to exist. I deny that something that isnt going to
exist is thereby impossible in itself. So the proposition What God
doesnt will to exist doesnt exist should be accepted as true, but
its necessity should be denied.* * * *[Near the end of this paper
Leibniz has an incomplete sentence which he probably meant to turn
into something saying:] The only existential proposition that is
absolutely necessary is God exists.* * * *[Early in the paper,
Leibniz mentions indifference or equilibrium. He wrote the
following note in the margin about that:] If complete indifference
is required for freedom, then there is scarcely ever a free act,
since I think it hardly ever happens that everything on both sides
is equal. For even if the reasons happen to be equal, the passions
wont be. So why should we argue about circumstances that do not
arise? I dont think examples can be found in which the will chooses
- that is, where it arbitrarily breaks a deadlock by just choosing
- because there is always some reason for choosing one alternative
rather than the other. The followers of Aquinas place freedom in
the power of the will, which stands above every finite good in such
a way that the will can resist it. And so, in order to have
indifference of will, they seek indifference of intellect. They
think that necessity is consistent with freedom in God - for
example the free necessity of Gods loving himself. But (they hold)
with respect to creatures God does not decide with necessity. . .
.
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Copyright Jonathan Bennett
[Brackets] enclose editorial explanations. Small dots enclose
material that has been added, but can be read as though it were
part of the original text. Occasional bullets, and also indenting
of passages that are not quotations, are meant as aids to grasping
the structure of a sentence or a thought. Four ellipses . . . .
indicate the omission of a brief passage that seems to present more
difficulty than it is worth.First launched: September 2004
Meditations on Knowledge, Truth, and IdeasBy G. W. Leibniz
Controversies are boiling these days among distinguished men
over true and false ideas. This is an issue of great importance for
recognizing truth - an issue on which Descartes himself is not
altogether satisfactory. So I want to explain briefly what I think
can be established about the distinctions and criteria that relate
to ideas and knowledge. [Here and in the title, knowledge
translates cognitio, which means something weaker than knowledge
strictly so-called, involving certainty and guaranteed truth, for
which the Latin word is scientia]. Here is the skeleton of what I
have to say. Knowledge is either
dim or vivid;vivid knowledge is either
confused or clear;clear knowledge is either
inadequate or adequate;and adequate knowledge is either
symbolic or intuitive.Knowledge that was at the same time both
adequate and intuitive would be absolutely perfect. [Here and
throughout, vivid translates clarus. (The more usual rendering as
clear is no better from a dictionary point of view, and makes much
worse sense philosophically because it has Leibniz saying that
knowledge can be at once clear and confused.) This use of vivid
points to dim as the better translation of the contrasting term
obscurus, and liberates clear for use in translating distinctus.] A
dim notion is one that isnt sufficient for recognizing the thing
that it represents - i.e. the thing that it is a notion of.
Example: I once saw a certain flower but whenever I remember it I
cant bring it to mind well enough to recognize it, distinguishing
it from other nearby flowers, when I see it again. Another kind of
example: I have dim notions when I think about some term for which
there is no settled definition - such as Aristotles entelechy, or
his notion of cause when offered as something that is common to
material, formal, efficient and final causes. [For a coin, these
causes would be, respectively, the metal of which the coin is
composed, the coins shape, weight etc., the force of the die
against the hot metal, and the commercial purpose for which the
coin was made. Leibniz implies that these seem not to be four
species of a single genus.] And a proposition is dim if it contains
a dim notion as an ingredient. Accordingly, knowledge is vivid if
it gives me the means for recognizing the thing that is
represented.
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Vivid knowledge is either confused or clear. It is confused when
I cant list, one by one, the marks that enable me to differentiate
the represented thing from other things, even though the thing has
such marks into which its notion can be resolved [= analysed,
broken down into its simpler constituents]. And so we recognize
colours, smells, tastes, and other particular objects of the senses
vividly enough to be able to distinguish them from one another, but
only through the simple testimony of the senses, not by way of
marks that we could list. Thus we cant explain what red is to a
blind man; and we cant give anyone a vivid notion of things like
red except by leading him into the presence of the thing and
getting him to see, smell, or taste the same thing we do, or by
reminding him of some past perception of his that is similar. This
is so even though the notions of these qualities are certainly
composite and can be resolved - after all, they do have causes.
[Perhaps Leibnizs thought is that the complexity of the causes must
be matched by the complexity of the caused quality, and thus by the
complexity of the complete notion of it.] Similarly, we see that
painters and other skilled craftsmen can accurately tell well-done
work from what is poorly done, though often they cant explain their
judgments, and when asked about them all they can say is that the
works that displease them lack a certain je-ne-sais-quoi. But a
clear notion is like the one an assayer has of gold - that is, a
notion connected with listable marks and tests that are sufficient
to distinguish the represented thing from all other similar bodies.
Notions common to several senses - like the notions of number,
size, and shape - are usually clear. So are many notions of states
of mind, such as hope and fear. In brief, we have a clear notion of
everything for which we have a nominal definition (which is nothing
but a list of sufficient marks). Also, we have clear knowledge of
any indefinable notion, since such a notion is basic, something we
start with; it cant be resolved into marks or simpler constituents,
as it has none; so it has to serve as its own mark, and be
understood through itself. An inadequate notion is what you have
when
the notion is clear, meaning that you understand vividly the
individual marks composing it, but
the grasp of some or all of those marks is (though vivid)
confused, because you cant list the marks whereby you recognize
those marks.
For example, someones knowledge of gold may be clear yet
inadequate: he knows that heavi-ness, colour, solubility in aqua
fortis etc. are the marks of gold, but he cant produce a list of
the marks whereby he recognizes heaviness, yellowness, and all the
others. When every ingredient of a clear notion is itself clearly
known - that is, when the analysis of the original notion has been
carried to completion - then our knowledge of it is adequate. (I
dont know whether humans have any perfectly adequate knowledge,
though our knowledge of numbers certainly comes close.) Symbolic
notions are ones in which words stand in for thoughts. We dont
usually grasp the entire nature of a thing all at once, especially
one whose analysis is long; so in place of thoughts about the
things themselves we use thoughts about signs. In our thought we
usually omit the explicit explanation of what a sign means, knowing
or believing that we have the explanation at our command and could
produce it on demand. Thus, when I think about a chiliagon
[pronounced kill-ee-a-gon], that is, a polygon with a thousand
equal sides, I dont always
think about the nature of a side, or of equality, or of
thousandfoldedness . . . .; in place of such thoughts,
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in my mind I use the words side, equal and thousand.The meanings
of these words appear only dimly and imperfectly to my mind, but I
remember that I know what they mean, so I decide that I neednt
explain them to myself at this time. This kind of thinking is found
in algebra, in arithmetic, and indeed almost everywhere. I call it
blind or symbolic thinking. When a notion is very complex, we cant
bear in mind all of its component notions at the same time, and
this forces us into symbolic thinking. When we can keep them all in
mind at once, we have knowledge of the kind I call intuitive.
(Actually, I treat this as a matter of degree; so I should have
said: insofar as we can keep all that in mind at once, to that
extent our knowledge is intuitive.) Whereas our thinking about
composites is mostly symbolic, our knowledge of a clear basic
notion has to be intuitive. That is because symbolic knowledge
involves letting words stand in for components of a notion, and
basic notions dont have components. This shows that its only if we
use intuitive thinking that we have ideas in our minds, even when
we are thinking about something we know clearly. We often
mistakenly believe that we have ideas of things in our mind,
assuming that we have already explained to ourselves some of the
terms we are using, when really we havent explained any of them.
Some people hold that we cant understand what we are saying about a
thing unless we have an idea of it; but this is false or at least
ambiguous, because we can have understanding of a sort even when
our thinking is blind or symbolic and doesnt involve ideas. When we
settle for this blind thinking, and dont pursue the resolution of
notions far enough, we may have a thought that harbours a
contradiction that we dont see because it is buried in a very
complex notion. At one time I was led to consider this point more
clearly by an old argument for the existence of God . . . . that
Descartes revived. The argument goes like this:
Whatever follows from the idea or definition of a thing can be
predicated of the thing. God is by definition the most perfect
being, or the being nothing greater than which can be thought. Now,
the idea of the most perfect being includes ideas of all
perfections, and amongst these perfections is existence. So
existence follows from the idea of God. Therefore existence can be
predicated of God, which is to say that God exists.
But this argument shows only that if God is possible then it
follows that he exists. For we cant safely draw conclusions from
definitions unless we know first that they are real definitions,
that is, that they dont include any contradictions. If a definition
does harbour a contradiction, we can infer contradictory
conclusions from it, which is absurd. My favourite illustrative
example of this is the fastest motion, which entails an absurdity.
I now show that it does:
Suppose there is a wheel turning with the fastest motion. Anyone
can see that if a spoke of the wheel came to poke out beyond the
rim, the end of it would then be moving faster than a nail on the
rim of the wheel. So the nails motion is not the fastest, which is
contrary to the hypothesis.
Now, we certainly understand the phrase the fastest motion, and
we may think we have an idea corresponding to it; but we dont,
because we cant have an idea of something impossible. Similarly,
the fact that we think about a most perfect being doesnt entitle us
to claim that we have an idea of a most perfect being. So in the
above demonstration - the one revived by Descartes - in order
properly to draw the conclusion we must show or assume the
possibility of a most perfect being. It is indeed true - nothing
truer! - that we do have an idea of God and that a most perfect
being is possible, indeed, necessary. But that argument is not
sufficient for drawing the conclusion, and Aquinas rejected it.
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So we have a line to draw between nominal definitions, which
contain only marks that distinguish the thing from other things,
and real definitions, from which the thing can be shown to be
possible. And thats my answer to Hobbes, who claimed that truths
are arbitrary because they depend on nominal definitions. What he
didnt take into account was that a definitions being real is not
something we decide, and that not just any notions can be joined to
one another. Nominal definitions are insufficient for perfect
knowledge [scientia] except when the possibility of the thing
defined is established in some other way. Near the start of this
paper I listed four classifications of ideas, now at last we come
to a fifth - true and false. It is obvious what true and false
ideas are: an idea is true when it is a possible notion, and false
when it includes a contradiction. Somethings possibility can be
known either a priori or a posteriori. The possibility of a thing
is known a priori when we resolve a notion into its requisites,
i.e. into other notions that are known to be possible and to be
compatible with one another, and that are required if the notion is
to apply. [These requisita could be components of the notion:
closed is a component of circular, and could be called a logical
requisite for somethings being circular. In the very next sentence,
however, Leibniz also brings in causal requisites.] This happens,
for instance, when we understand how a thing can be produced, which
is why causal definitions are more useful than others. A things
possibility is known a posteriori when we know through experience
that it actually exists, for what did or does actually exist is
certainly possible! And, indeed, whenever we have adequate
knowledge we also have a priori knowledge of possibility: if an
analysis is brought to completion with no contradiction turning up,
then certainly the analysed notion is possible. For men to produce
a perfect analysis of their notions would be for them to reduce
their thoughts to basic possibilities and unanalysable notions,
which amounts to reducing them to the absolute attributes of God -
and thus to the first causes and the ultimate reason for things.
Can they do this? I shant venture to settle the answer to that now.
For the most part we are content to have learned through experience
that certain notions are real [here = possible], from which we then
assemble others following the lead of nature. All this, I think,
finally lets us understand that one should be cautious in claiming
to have this or that idea. Many people who use this glittering
title idea to prop up certain creatures of their imagination are
using it wrongly, for we dont always have an idea corresponding to
everything we consciously think of (as I showed with the example of
greatest speed). People in our own times have laid down the
principle:
Whatever I vividly and clearly perceive about a thing is true,
i.e. can be said of the thing;but I cant see that they have used
this principle well. [Leibniz is referring to a principle of
Descartess that is almost always translated in English as Whatever
I clearly and distinctly perceive . . ..] For people who are
careless in judgment often take to be vivid and clear what is
really dim and confused in their minds. So this axiom is useless
unless (1) explicitly stated criteria for vividness and clarity are
introduced, and (2) we have established the truth of the ideas that
are involved - in my sense, in which an idea is true if and only if
it is possible, i.e. could have instances. Furthermore, the rules
of common logic - which geometers use too - are not to be despised
as criteria for the truth of assertions: for example, the rule that
nothing is to be accepted as certain unless it is shown by careful
testing or sound demonstration - a sound demonstration being one
that follows the form prescribed by logic. Not that we always need
arguments to be in syllogistic order as in the Aristotelian
philosophy departments . . . .; but the argument must somehow
reach
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its conclusion on the strength of its form. Any correct
calculation provides an example of an argument conceived in proper
logical form. Such an argument should not omit any necessary
premise, and all premises should have been previously demonstrated
- or else have been assumed as hypotheses, in which case the
conclusion is also hypothetical. Someone who carefully observes
these rules will easily protect himself against deceptive ideas.
The highly talented Pascal largely agrees with this in his
excellent essay On the Geometrical Mind . . . . The geometer, he
says, must define all terms that are slightly obscure and prove all
truths that are slightly dubious. But I wish he had made precise
the line beyond which a notion or statement is no longer even
slightly obscure or dubious. Most of what matters regarding this
can be gathered from careful attention to what I have said above;
and I shant go further into it now, because I am trying to be
brief. Before finishing, I offer three further remarks, only
loosely connected with one another, but all having to do with
ideas. (1) There has been controversy over whether we see
everything in God - that is, perceive the world by sharing Gods
ideas with him - or whether we have our own ideas. The view that we
see everything in God, though recently made famous through
Malebranches defence of it, is an old opinion, and properly
understood it shouldnt be rejected completely. But the point I want
to make here is that even if we did see everything in God, we would
still also have to have our own ideas - not little sort-of copies
of Gods ideas, but states of our mind corresponding to the thing we
perceived in God. For when go from having one thought to having
another, there has to be some change in our mind - some alteration
of our minds state. (2) Dont think that in these changes of state
the previous ideas are entirely wiped out. In fact, the ideas of
things that we are not now actually thinking about are in our mind
now, as the figure of Hercules is in a lump of marble. In God, on
the other hand, all ideas are always actually engaged in his
thought: he must have not only an actually occurrent idea of
absolute and infinite extension but also an idea of each shape - a
shape being merely a modification of absolute extension [meaning
that a things having a certain shape is just its being extended in
a certain way]. (3) A final point: when we perceive colours or
smells, all that we really perceive - all! - are shapes and of
motions; but they are so numerous and so tiny that our mind in its
present state cant clearly attend to each one separately, so that
it doesnt notice that its perception is composed purely of
perceptions of minute shapes and motions. This is like what happens
when we perceive the colour green in a mixture of yellow powder and
blue powder. All we are sensing is yellow and blue, finely mixed,
but we dont notice this, and invent something new - the colour
green - for ourselves.
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Copyright Jonathan Bennett
[Brackets] enclose editorial explanations. Small dots enclose
material that has been added, but can be read as though it were
part of the original text. Occasional bullets, and also indenting
of passages that are not quotations, are meant as aids to grasping
the structure of a sentence or a thought. First launched: September
2004
ContingencyBy G. W. Leibniz
In God existence is the same as essence; or - the same thing put
differently - it is essential for God to exist. So God is a
necessary being, a being who exists necessarily. Created things are
contingent, i.e. their existence doesnt follow from their essence.
Necessary truths are ones that can be demonstrated through an
analysis of terms, so that they end up as identities. For example,
square analyses into figure that is plane, closed, equilateral, and
has four sides. Apply this analysis to the necessary truth
A square has four sidesand you get
A figure that is plane, closed, equilateral, and has four sides
has four sides,which is an identity. Similarly, in algebra when in
a correct equation you substitute values for the variables you get
an identity. For example, in the equation
(x + y)2 = x2 + 2xy + y2if we put 2 for x and 3 for y we get
(2 + 3)2 = 22 + 2(23) + 32which comes to
25 = 4 + 12 + 9which comes to 25 = 25,which is an identity.
Thus, necessary truths depend upon the principle of contradiction,
which says that the denial of an identity is never true. Contingent
truths cant be reduced to the principle of contradiction. If they
could, they wouldnt be contingent, and everything would be
necessary and nothing would be possible except what actually
exists. Nevertheless, since we say that both God and creatures
exist and that necessary propositions and some contingent ones are
true, there must be a notion of existence and one of truth that can
be applied both to what is contingent and what is necessary. What
is common to every truth, in my view, is that one can always give a
reason for a true proposition unless it is an identity. In
necessary propositions the reason necessitates, whereas in
contingent ones it inclines. Identical propositions are, as I have
said, the rock-bottom reasons for all necessary truths; we dont
have reasons why they are true. And it seems to be common to things
that exist, whether necessarily or contingently, that there is more
reason for their existing than there is for any others to exist in
their place. Every true universal affirmative proposition, whether
necessary or contingent, has some connection between subject and
predicate. In identities this connection is self-evident; in other
propositions it has to be brought out through the analysis of
terms.
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This little-known fact reveals the distinction between necessary
and contingent truths. It is hard to grasp unless one has some
knowledge of mathematics, because it goes like this. When the
analysis of a necessary proposition is continued far enough it
arrives at an identical equation; thats what it is to demonstrate a
truth with geometrical rigour. But the analysis of a contingent
proposition continues to infinity, giving reasons (and reasons for
the reasons (and reasons for those reasons . . .)), so that one
never has a complete demonstration. There is always an underlying
complete and final reason for the truth of the proposition, but
only God completely grasps it, he being the only one who can whip
through the infinite series in one stroke of the mind. [This
paragraph expands Leibnizs compact formulation in ways that cant be
flagged by dots. For more on incommensurables, see pages 4-5 of his
Dialogue on human freedom.] I can illustrate this with a good
example from geometry and numbers. In necessary propositions, as I
have said, a continual analysis of the predicate and the subject
can eventually get us to the point where we can see that the notion
of the predicate is in the subject. For a numerical analogue of
this, consider the process of getting an exact comparison between
two numbers: we repeatedly divide each until we arrive at a common
measure. For example, wanting to compare 24.219 with 12.558, we
find that each can be divided by 3 then by 13 then by 23, giving us
the more graspable relationship of 27 to 14. But that doesnt work
with an incommensurable pair of numbers such as any whole number
and 2: as Euclid has demonstrated, there is no fraction F (however
tiny) such that (FF) = 2. We can work along a series of fractions,
squaring as we go, and get ever nearer to 2, but it is
mathematically impossible for us to end the series by finding a
fraction whose square exactly equals 2. Still, there is a
proportion or relation between (say) 3 and 2; we cant express it
exactly in terms of fractions, but we know that it exists: 3 is a
certain determinate definite amount larger than 2. I offer this as
analogous to the situation with contingent truths: in them there is
a connection between the terms - i.e. there is truth - even if that
truth cant be reduced to the principle of contradiction or
necessity through an analysis into identities. Here are two
questions that can be asked about the necessity of certain
propositions. Is this proposition:
God chooses the bestnecessary? Or is it one - indeed, the first
- of his free decrees? Again, is this proposition:
Whatever exists, there is a greater reason for it to exist than
for it not to existnecessary? I answer that the former proposition
is not necessary: God always chooses the best because he decrees
that thats what hell do. It follows that the latter proposition is
not necessary either: there is always a greater reason for the
existence of an actual thing than for any possible rival to it, but
only because God has freely decided always to choose the best. It
is certain that there is a connection between subject and predicate
in every truth. So the truth of Adam, who sins, exists requires
that the possible notion of Adam, who sins involves something by
virtue of which he is said to exist. It seems that we must concede
that God always acts wisely, i.e. in such a way that anyone who
knew his reasons would know and worship his supreme justice,
goodness, and wisdom. And it seems that God never acts in a certain
way just because it pleases him to act in this way, unless there is
a good reason why it is pleasing. Thus, something may be done at
Gods pleasure (as we say), but that is never an alternative to its
being done for a reason. Since we cant know the true formal reason
for the existence of any particular thing, because that would
involve an infinite series of reasons, we have to settle for
knowing contingent truths a posteriori, i.e. through experience.
But we must at the same time hold the general principle,
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implanted by God in our minds and confirmed by both reason and
experience, that nothing happens without a reason, as well as the
principle of opposites, that of rival possibilities the one for
which there is more reason always happens. (I said confirmed by
experience, but treat that cautiously. I meant only that experience
confirms the principle to the extent that we can discover reasons
through experience.) And just as God decreed that he would always
act in accordance with true reasons of wisdom, so too he created
rational creatures in such a way that they act in accordance with
prevailing or inclining reasons - reasons that are true or, failing
that, seem to them to be true. Unless there were such a principle
as this one about reasons, there would be no principle of truth in
contingent things, because to them the principle of contradiction
is certainly irrelevant. Not all possibles come to exist - we have
to accept that, because if it were false you couldnt think up any
story that wasnt actually true somewhere at some time! Anyway, it
doesnt seem possible for all possible things to exist, because they
would get in one anothers way. There are, in fact, infinitely many
series of possible things, no one of which can be contained within
any other, because each of them is complete. From the following two
principles, the others follow:
1. Whatever God does bears the mark of perfection or wisdom.2.
Not every possible thing comes to exist.
To these one can add:3. In every true universal affirmative
proposition the predicate is in the subject, i.e. there is a
connection between predicate and subject.
[In this next paragraph, Leibniz wrote of a propositions
existing, apparently meaning its being true.] Assuming that this
proposition:
The proposition P that has the greater reason for being true is
trueis necessary, we must see whether it then follows that P itself
is necessary. It isnt. If by definition a necessary proposition is
one whose truth can be demonstrated with geometrical rigour, then
indeed it could be the case that these two propositions are
demonstrable and thus necessary:
Every truth and only a truth has greater reason.God always acts
with the highest wisdom.
But from these one cant demonstrate any proposition of the form
Contingent proposition P has greater reason for being true than has
contingent proposition not-P or of the form Contingent proposition
P is in conformity with divine wisdom. So it doesnt follow from the
above two displayed propositions that any contingent proposition P
is necessary. Thus, although one can concede that it is necessary
for God to choose the best, or that the best is necessary, it
doesnt follow that P is necessary, where P is something that has
been chosen; for there is no demonstration that P is the best. This
can be put in terms of the technical distinction between necessity
of the consequence and necessity of the consequent - that is,
between P necessarily follows from Q and P is itself necessary.
Assuming that the best is necessarily chosen, we have
From P is the best it follows necessarily that P is true,but we
do not have
Necessarily P is true,because we have no demonstration that P is
the best. Though I have been exploring the implications of the
thesis that necessarily God always chooses the best, I dont assert
it. I say only that it seems safer to attribute to God the most
perfect way possible of operating. When it comes to creatures, one
cant be as sure as we can
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with God that they will act in accordance with even the most
obvious reason; with respect to creatures, this proposition - that
they will always so act - cant be demonstrated.
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Copyright Jonathan Bennett
[Brackets] enclose editorial explanations. Small dots enclose
material that has been added, but can be read as though it were
part of the original text. Occasional bullets, and also indenting
of passages that are not quotations, are meant as aids to grasping
the structure of a sentence or a thought. Bold type is used where
Leibniz used italics, apparently for emphasis.First launched:
September 2004
First TruthsBy G. W. Leibniz
First truths are the ones that assert something of itself or
deny something of its opposite. For example,
A is AA is not not-AIf it is true that A is B, then it is false
that A isnt B (i.e. false that A is not-B)Everything is as it
isEverything is similar or equal to itselfNothing is bigger or
smaller than itself
and others of this sort. Although they may have a rank-ordering
among themselves, they can all be lumped together under the label
identities. Now, all other truths are reducible to first ones
through definitions, that is, by resolving notions into their
simpler components. Doing that is giving an a priori proof - a
proof that doesnt depend on experience. From among the axioms that
are accepted by mathematicians and by everyone else, I choose as an
example this:
A whole is bigger than its part, orA part is smaller than the
whole.
This is easily demonstrated from the definition of smaller or
bigger together with the basic axiom, that is, the axiom of
identity. Here is a definition of smaller than:
For x to be smaller than y is for x to be equal to a part of y
(which is bigger).This is easy to grasp, and it fits with how
people in general go about comparing the sizes of things: they take
away from the bigger thing something equal to the smaller one, and
find something left over. With that definition in hand, here is an
argument of the sort I have described:
1. Everything is equal to itself
.................................................... (axiom of
identity)2. A part is equal to itself
.........................................................................
(from 1)3. A part is equal to a part of the whole
.................................................... (from 2)4. A
part is smaller than the whole ....... (from 3 by the definition of
smaller than).
Because all truths follow from first truths with the help of
definitions, it follows that in any true proposition the predicate
or consequent is always in the subject or antecedent. It is just
this - as Aristotle observes - that constitutes the nature of truth
in general, or the true-making connection between the terms of a
statement. In identities the connection of the predicate with the
subject (its inclusion in the subject) is explicit; in all other
true propositions it is implicit, and has to be shown through the
analysis of notions; a priori demonstration rests on this.
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This is true for every affirmative truth - universal or
particular, necessary or contingent - and it holds when the
predicate is relational as well as when it isnt. And a wonderful
secret lies hidden in this, a secret that contains the nature of
contingency, i.e. the essential difference between necessary and
contingent truths, and removes the difficulties concerning the
necessity - and thus the inevitability - of even those things that
are free. These considerations have been regarded as too simple and
straightforward to merit much attention; but they do deserve
attention because many things of great importance follow from them.
One of their direct consequences is the received axiom Nothing is
without a reason, or There is no effect without a cause.If that
axiom were false, there would be a truth that couldnt be proved a
priori, that is, a truth that couldnt be resolved into identities,
contrary to the nature of truth, which is always an explicit or
implicit identity. Thus, if the axiom were false, my account of
truth would be false; which is why I say that (the truth of) the
axiom follows from (the truth of) my account. It also follows that
when there is a perfect balance or symmetry in a physical set-up
there will also be a balance or symmetry in what follows from it.
Stated more abstractly: when there is symmetry in what is given,
there will be symmetry in what is unknown. This is because any
reason for an asymmetry in the unknown must derive from the
givens., and in the case as stated there is no such reason. An
example of this is Archimedes postulate at the beginning of his
book on statics, that if there are equal weights on both sides of a
balance with equal arms, everything is in equilibrium. There is
even a reason for eternal truths. Suppose that the world has
existed from eternity, and that it contains nothing but little
spheres; for such a world we would still have to explain why it
contained little spheres rather than cubes. From these
considerations it also follows that In nature there cant be two
individual things that differ in number alone,i.e. that dont differ
in any of their qualities, and differ only in being two things
rather than one. For where there are two things it must be possible
to explain why they are different - why they are two, why it is
that x is not y - and for that explanation we must look to
qualitative differences between the things. St. Thomas said that
unembodied minds never differ by number alone - that is, no two of
them are qualitatively exactly alike; and the same must also be
said of other things, for we we never find two eggs or two leaves
or two blades of grass that are exactly alike. So exact likeness is
found only in notions that are incomplete and abstract. In that
context things are considered only in a certain respect, not in
every way - as, for example, when we consider shapes alone,
ignoring the matter that has the shape. And so it is justifiable to
consider two perfectly alike triangles in geometry, even though two
perfectly alike triangular material things are not found anywhere.
Gold and other metals, also salts and many liquids, are taken to be
homogeneous, which implies that two portions of gold could be
qualitatively exactly alike. This way of thinking and talking is
all right if it is understood as referring only to differences that
our senses can detect; but really none of these substances is
strictly homogeneous. [Leibniz is about to use the phrase purely
extrinsic denomination. This means purely relational property,
meaning a relational property that isnt grounded in any
non-relational property. It might seem to us that a things spatial
relations to other things constitute such an extrinsic
denomination: the thing could be moved without being in anyway
altered in itself. That is what Leibniz is going to deny. The word
denomination (and Leibnizs corresponding Latin) mark the fact that
he wavers between making this a point about the properties and
relations a
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thing can have, and the linguistic expressions that can be used
in talking about a thing. Although basically an external
denomination is meant to be a relational property, Leibniz
sometimes writes as though it were a relational predicate.] It also
follows that
There are no purely extrinsic denominations- that is,
denominations having absolutely no foundation in the denominated
thing. For the notion of the denominated subject must contain the
notion of the predicate; and, to repeat what I said at the top of
page 2, this applies to relational predicates as well as
qualitative ones, i.e. it applies to extrinsic as well as to
intrinsic denominations. So whenever any denomination of a thing is
changed, there must be an alteration in the thing itself. The
complete notion of an individual substance contains all its
predicates - past, present, and future. If a substance will have a
certain predicate, it is true now that it will, and so that
predicate is contained in the notion of the thing. Thus, everything
that will happen to Peter or Judas - necessary events and also free
ones - is contained in the perfect individual notion of Peter or
Judas, and is seen there by God. [The next two sentences expand a
condensed clause of Leibnizs.] To grasp how the concept of the
complete notion of Judas is being used here, think of it as the
complete total utterly detailed specifications for Judas, viewed as
a possibility without any thought of whether God has chosen to make
the possibility actual. That is the notion that God employed when
deciding to make Judas actual: he pointed to the possibility Judas
and said Let him come into existence, which means that he pointed
to that complete notion and said Let that be actualized. This makes
it obvious that out of infinitely many possible individuals God
selected the ones he thought would fit best with the supreme and
hidden ends of his wisdom. Properly speaking, he didnt decide
that
Peter would sinor that
Judas would be damned.All he decreed was that two possible
notions should be actualized - the notion of
Peter, who would certainly sin (but freely, not necessarily)and
the notion of
Judas, who would suffer damnation - which is to decree that
those two individuals should come into existence rather than other
possible things. Dont think that Peters eventual salvation occurs
without the help of Gods grace, just because it is contained in the
eternal possible notion of Peter. For what that complete notion of
Peter contains is the predicate achieves salvation with the help of
Gods grace. [Leibniz says, puzzlingly, that the complete notion
contains this predicate sub notione possibilitatis = under the
notion of possibility. That seems to say where in the complete
notion the predicate will be found - Look it up in the file
labelled Possibility, as it were - but that cant be right.] Every
individual substance contains in its complete notion the entire
universe and everything that exists in it - past, present, and
future. [The next sentence is stronger than what Leibniz wrote, but
it seems to express what he meant.] That is because: for any given
things x and y, there is a true proposition about how x relates to
y, if only a comparison between them. And there is no purely
extrinsic denomination, which implies that every relational truth
reflects non-relational truths about the related things. I have
shown this in many ways, all in harmony with one another.
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Indeed, all individual created substances are different
expressions of the same universe and of the same universal cause,
namely God. But the expressions vary in perfection, as do different
pictures of the same town drawn or painted from different points of
view. Every individual created substance exercises physical action
and passion on all the others. Any change made in one substance
leads to corresponding changes in all the others, because the
change in the one makes a difference to the relational properties
of the others. For example, a pebble on Mars becomes colder, so
that you move from having the property
...has spatial relation R to a pebble that is at 5Cto having the
property
...has spatial relation R to a pebble that is at 2C;and, because
there are no purely extrinsic denominations, that change in your
relational properties will be backed by a change in your intrinsic
properties. This fits with our experience of nature. In a bowl
filled with liquid, a movement of the liquid in the middle is
passed on out to the edges, becoming harder and harder to detect
the further it gets from the centre but never being wiped out
altogether. Well, the whole universe is just such a bowl! Strictly
speaking, one can say that no created substance exercises a
metaphysical action or influence on anything else. [Leibniz is
saying that no real causal force or energy passes from one
substance to another. Influence here translates the Latin influxus
[= in-flow], which reflects one view about what would have to
happen for one substance to act on another: according to this view,
when the hot poker heats the water, some of its heat literally
passes from one to the other; when a man falls against a wall and
knocks it down, some his motion passes to the wall. The basic idea
is that of an accident - a property-instance - travelling from one
substance to another. The pokers heat is an accident in this sense;
it is to be distinguished from the poker (an individual substance)
and from heat (a universal property); it is
the-present-heat-of-this-particular-poker, an individualized
property. Leibniz is sceptical about the transfer of accidents from
one thing to another, but since he thinks that substances dont act
on one another, he doesnt mind implying that if they did act on one
another it would have to be by the transfer of accidents.] For one
thing, there is no explanation of how something -an accident -
could pass from one thing into the substance of another; but Ill
let that pass. I have already shown that there is no work for
inter-substance causation to do, because all a things states follow
from its own complete notion. What we call causes are, speaking
with metaphysical strictness, only concurrent requirements. This
too is illustrated by our experience of nature. For bodies really
rebound from others through the force of their own elasticity, and
not through the force of other things, even if a body other than x
is required in order for xs elasticity to be able to act. Assuming
that soul and body are distinct, from the foregoing we can explain
their union, without appealing to the popular but unintelligible
idea of something in-flowing from one to the other, and without the
hypothesis occasional causes, which appeals to God as a kind of
puppet-master. [Leibniz says Deus ex machina - a God who comes
on-stage by being winched down from the ceiling of the theatre. The
phrase occasional causes refers to the view that minds cant
literally act on bodies, and that when I will to raise my arm that
act of my mind is the prompt or occasion for God to raise my arm.]
For Gods wisdom and workmanship enabled him to set up the soul and
the body, at the outset, in such a way that from the first
constitution or notion of each of them everything that happens in
it through itself corresponds perfectly to everything that happens
in the other through itself, just as if something - some accident -
passed from one to the other. This hypothesis of mine (which I call
the hypothesis of
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concomitance) is true for all substances in the whole universe,
but it cant be sensed in all of them as it can in the case of the
soul and the body. There is no vacuum. For if there were empty
space, two different parts of it could be perfectly similar and
congruent and indistinguishable from one another. Thus, they would
differ in number alone - differ in being two, but not in any other
way - which is absurd. One can also prove that time is not a thing,
in the same way as I just did for space, namely arguing that if
time were a thing there could be stretches of empty time, i.e. time
when nothing happens; and two parts of such empty time would be
exactly alike, differing only in number, which is absurd. There is
no atom, which means that any body could be split. In fact, every
body, however small, is actually subdivided. Because of that, each
body, while it constantly changes because it is acted on by
everything else in the universe in ways that make it alter, also
preserves all the states that have been impressed on it in the past
and contains in advance all that will be impressed on it in the
future. You might object:
Your view that every body is affected by every other body, and
that each body contains information about all its past and all its
future states, could be true even if there were atoms. It could be
that other bodies affect an atom by making it move in certain ways
and by changing its shape, and these are effects that the atom can
receive as a whole, without being divided.
I reply that not only must there be effects produced in an atom
from all the impacts of the universe upon it, but also conversely
the state of the whole universe must be inferable from the states
of the atom - the cause must be inferable from the effect. However,
any given motion of an atom and any given shape could have come
about through different impacts, so there is no way to infer from
the present shape and motion of the atom what effects have been had
upon it. And there is a different objection to atoms, independent
of my metaphysics, namely the fact that one couldnt explain why
bodies of a certain smallness couldnt be further divided - that is,
there couldnt be an explanations of why there are any atoms. From
this it follows that every particle in the universe contains a
world of an infinity of creatures. However, the continuum is not
divided into points, because points are not parts but boundaries;
nor is it divided in all possible ways, because the contained
creatures are not all separately there. Its just that a series of
divisions could go on ad infinitum separating some from others at
each stage. But no such sequence separates out all the parts, all
the contained creatures, because every division leaves some of them
clumped together - just as someone who bisects a line leaves
clumped together some parts of it that would be separated if the
line were trisected. There is no determinate shape in actual
things, for no determinate shape can be appropriate for infinitely
many effects. So neither a circle, nor an ellipse, nor any other
definable line exists except in the intellect; lines dont exist
until they are drawn, and parts dont exist until they are separated
off. Extension and motion, are not substances, but true phenomena
(like rainbows and reflections). The same holds for bodies, to the
extent that there is nothing to them but extension and motion. For
there are no shapes in reality, and if we think about bodies purely
as extended, each of them is not one substance but many. Something
unextended is required for the substance of bodies. Without that
there would be no source for the reality of phenomena or for true
unity. There is always a plurality of bodies, never just one (so
that really there isnt a plurality either, because a many must
consist of many
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ones). Cordemoy used a similar line of thought as an argument
for the existence of atoms. But since I have ruled out atoms, all
that remains as a source of unity is something unextended,
analogous to the soul, which they once called form or species.
Corporeal substance cant come into existence except through
creation or go out of existence except through annihilation,
because once a corporeal substance exists it will last for ever,
since there is no reason for it not to do so. Any body may come
apart - its parts may come to be scattered - but this has nothing
in common with its going out of existence. Therefore, animate
things dont come into or go out of existence, but are only
transformed.
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Copyright Jonathan Bennett[Brackets] enclose editorial
explanations. Small dots enclose material that has been added, but
can be read as though it were part of the original text. Occasional
bullets, and also indenting of passages that are not quotations,
are meant as aids to grasping the structure of a sentence or a
thought. The division into sections is Leibnizs; the division of
some sections into paragraphs is not. Leibniz wrote brief summaries
of the 37 sections of this work, but did not include them in the
work itself. Some editors preface each section with its summary,
but that interrupts the flow. In this version the summaries are
given at the end.First launched: July 2004 Amended: November
2004
* * * * * * * * *
Discourse on Metaphysicsby G.W. Leibniz
1. The most widely accepted and sharpest notion of God that we
have can be expressed like this: God is an absolutely perfect
being;
but though this is widely accepted, its consequences havent been
well enough thought out. As a start on exploring them, let us note
that there are various completely different ways of being perfect,
and that God has them all, each in the highest degree. We also need
to understand what a perfection is. Here is one pretty good
indicator: a property is not a perfection unless there is a highest
degree of it; so number and shape are not perfections, because
there cannot possibly be a largest number or a largest thing of a
given shape - that is, a largest triangle, or square, or the like.
But there is nothing impossible about the greatest knowledge or
about omnipotence [here = greatest possible power]. So power and
knowledge are perfections, and God has them in unlimited form. It
follows that the actions of God, who is supremely - indeed
infinitely - wise, are completely perfect. This is not just
metaphysical perfection, but also the moral kind. His moral
perfection, so far as it concerns us, amounts to this: the more we
come to know and understand Gods works, the more inclined we shall
be to find them excellent, and to give us everything we could have
wished.2. Some people - including Descartes - hold that there are
no rules of goodness and perfection in the nature of things, or in
Gods ideas of them, and that in calling the things God made good
all we mean is that God made them. I am far from agreeing with
this. If it were right, then God would not have needed after the
creation to see that they were good, as Holy Scripture says he did,
because he already knew that the things in question were his work.
In saying this - And God saw everything that he had made, and,
behold, it was very good (Genesis 1:31) - Scripture treats God as
like a man; but its purpose in doing this appears to be to get
across the point that a things excellence can be seen by looking
just at the thing itself, without reference to the entirely
external fact about what caused it. Reinforcing that point is this
one: the works must bear the imprint of the workman, because we can
learn who he was just by inspecting them. I have to say that the
contrary opinion strikes me as very dangerous, and as coming close
to the view of the Spinozists that the beauty of the universe, and
the goodness we attribute to Gods works, are merely the illusions
of people who conceive God as being like themselves. Furthermore,
if you say as Descartes did that things are good not because they
match up to objective standards of goodness, but only because God
chose them, you will unthinkingly destroy all Gods love and all
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his glory. For why praise him for what he has done, if he would
be equally praiseworthy for doing just the opposite? Where will his
justice and wisdom be,
if there is only a kind of despotic power, if reasons place is
taken by will, and if justice is tyrannically defined as what best
pleases the most powerful?
[Leibniz here relies on his view that it is through reason that
we learn what things are good.] And another point: it seems that
any act of the will presupposes some reason for it - a reason which
naturally precedes the act - so that Gods choices must come from
his reasons for them, which involve his knowledge of what would be
good; so they cant be the sources of the goodness of things. That
is why I find it weird when Descartes says that the eternal truths
of metaphysics and geometry, and therefore also the rules of
goodness, justice, and perfection, are brought about by Gods will.
Against this, they seem to me to be results of his understanding,
and no more to depend on his will than his intrinsic nature does.3.
Nor could I ever accept the view of some recent philosophers who
have the nerve to maintain that Gods creation is not utterly
perfect, and that he could have acted much better. This opinion, it
seems to me, has consequences that are completely contrary to the
glory of God. Just as a lesser evil contains an element of good, so
a lesser good contains an element of evil. To act with fewer
perfections than one could have done is to act imperfectly; showing
an architect that he could have done his work better is finding
fault with it. Furthermore, this opinion goes against holy
scriptures assurance of the goodness of Gods works. That goodness
cant consist simply in the fact that the works could have been
worse; and here is why. Whatever Gods work was like, it would
always have been good in comparison with some possibilities,
because there is no limit to how bad things could be. But being
praiseworthy in this way is hardly being praiseworthy at all! I
believe one could find countless passages in the holy scriptures
and the writings of the holy fathers that support my opinion, and
hardly any to support the modern view to which I have referred - a
view that I think was never heard of in ancient times. It has
arisen merely because we are not well enough acquainted with the
general harmony of the universe and of the hidden reasons for Gods
conduct; and that makes us recklessly judge that many things could
have been improved. Furthermore, these moderns argue - subtly but
not soundly - from the false premiss that however perfect a thing
is, there is always something still more perfect. They also think
that their view provides for Gods freedom, through the idea that if
God is free, it must be up to him whether he acts perfectly or not;
but really it is the highest freedom to act perfectly, in
accordance with sovereign reason. For the view that God sometimes
does something without having any reason for his choice, besides
seeming to be impossible, is hardly compatible with his glory.
Suppose that God, facing a choice between A and B, opts for A
without having any reason for preferring it to B. I see nothing to
praise in that, because all praise should be grounded in some
reason, and in this case we have stipulated that there is none. By
contrast, I hold that God does nothing for which he does not
deserve to be glorified.4. The love that we owe to God, above all
things, is based (I think) on our grasp of the great truth that God
always acts in the most perfect and desirable way possible. For a
lover looks for satisfaction in the happiness or perfection of the
loved one and of his actions. Friendship is wanting the same things
and not-wanting the same things. And I think it will be hard to
love God properly without being disposed to want what he wants,
even if one had the power to get something different. Indeed, those
who are not satisfied with what God does strike me as being
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like malcontent subjects whose set of mind is not much different
from a rebels. These principles lead me to maintain that loving God
requires a certain attitude to everything that happens to us
through his will: not merely accepting it patiently because one has
no alternative, but being truly satisfied with it. I am saying this
about the past; for we shouldnt be quietists about the future,
stupidly waiting with folded arms for what God will do, as in the
fallacy of the argument for idleness (as the ancients called it).
So far as we can judge what God wants, in a general way, we should
act in accordance with that, doing our very best to contribute to
the general good, and in particular to adorning and perfecting the
things that concern us - what is close to us, within reach (so to
speak). The outcome may show that in a particular instance God
didnt want our good will to have its effect, but it doesnt follow
that he didnt want us to do what we did. On the contrary, as he is
the best of masters, he never asks more than the right intention,
and it is up to him to know when and where good intentions should
succeed.5. So it is enough to be sure of this about God: that he
does everything for the best, and that nothing can harm those who
love him. But to know in detail his reasons for ordering the
universe as he has, allowing sin, and granting his saving grace in
one way rather than another, is beyond the power of a finite mind,
especially one that has not yet attained the delight of seeing God.
Still, some general remarks can be made about how God goes about
governing things. Thus, we can liken someone who acts perfectly to
an expert geometer who knows how to find the best construction for
a problem; to a good architect who exploits the location and the
budget for his building to the best advantage, not allowing
anything nasty, or less beautiful than it could be; to a good head
of a household, who manages his property so that no ground is left
uncultivated or barren; to a clever special-effects technician in
the theatre, who produces his effect by the least awkward means
that can be found; or to a learned author, who gets the largest
amount of subject-matter into the smallest space he can. Now, minds
are the most perfect of all things, occupying the least space and
thus providing the least hindrance to one another because they dont
take up space at all; and their perfections are virtues. That is
why we should be sure that the happiness of minds is Gods principal
aim, which he carries out as far as the general harmony will
permit. Ill say more about this later. The simplicity of Gods ways
relates to the means he adopts, while their variety, richness or
abundance relate to ends or effects. These should be in balance
with one another, as the money for putting up a building has to be
balanced against its desired size and beauty. Admittedly, whatever
God does costs him nothing - even less than it costs a philosopher
or scientist to invent theories out of which to build his imaginary
world - for God can bring a real world into existence merely by
decreeing it. But in the exercise of wisdom by God or a scientist
there is something analogous to the cost of a building, namely the
number of independent decrees or theories that are involved. For
Gods creative activity to be economical is for it to involve very
few separate decrees; for a scientific theory to be economical in
its means is for it to have very few basic principles or axioms.
Reason requires that multiplicity of hypotheses or principles be
avoided, rather as the simplest system is always preferred in
astronomy.6. Gods wishes or actions are usually divided into the
ordinary and the extraordinary. But we should bear in mind that God
does nothing that isnt orderly. When we take something to be out of
the ordinary, we are thinking of some particular order that holds
among created things. We do not, or ought not to, mean that the
thing is absolutely extraordinary or disordered, in the sense of
being outside every order; because there is a universal order to
which everything conforms.
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Indeed, not only does nothing absolutely irregular ever happen
in the world, but we cannot even feign [= tell a consistent
fictional story about] such a thing. Suppose that someone
haphazardly draws points on a page, like people who practise the
ridiculous art of fortune-telling through geometrical figures. I
say that it is possible to find a single formula that generates a
geometrical line passing through all those points in the order in
which they were drawn. And if someone drew a continuous line which
was now straight, now circular, now of some other kind, it would be
possible to find a notion or rule or equation that would generate
it. The contours of anyones face could be traced by a single
geometrical line governed by a formula. But when a rule is very
complex, what fits it is seen as irregular. So one can say that no
matter how God had created the world, it would have been regular
and in some general order. But God chose the most perfect order,
that is, the order that is at once simplest in general rules and
richest in phenomena - as would be a geometrical line whose
construction was easy yet whose properties and effects were very
admirable and very far-reaching. These comparisons help me to
sketch some imperfect picture of divine wisdom, and to say
something that might raise our minds to some sort of conception, at
least, of what cannot be adequately expressed. But I dont claim
that they explain this great mystery of creation on which the whole
universe depends.7. Now, because nothing can happen that isnt
orderly, miracles can be said to be as orderly as natural events.
The latter are called natural because they conform to certain
subordinate rules - ones that are not as general and basic as Gods
fundamental creative decrees - which we call the nature of things.
This Nature is only a way in which God customarily goes about
things, and he can give it up if he has a reason for doing so - a
reason that is stronger than the one that moved him to make use of
these subordinate maxims in the first place. General acts of the
will are distinguished from particular ones. Using one version of
this distinction, we can say that God does everything according to
his most general will, which conforms to the most perfect order
that he has chosen; but that he also has particular wills, which
are exceptions (not to the most general of Gods laws, which
regulates the whole order of the universe, and to which there are
no exceptions, but) to the subordinate maxims I have mentioned, the
ones that constitute Nature. Any object of Gods particular will is
something he can be said to want. But when it comes to the objects
of his general will - such as are actions of created things
(especially rational ones) which God chooses to allow - we cannot
say that God wants them all, and must make a distinction. (1) If
the action is intrinsically good, we can say that God wants it, and
sometimes commands it, even if it doesnt happen. (2) But an action
may be intrinsically bad, and only incidentally good because later
events - especially ones involving punishment and reparations -
correct its wickedness and make up for the bad with some to spare,
so that eventually there is more perfection overall than if this
bad thing had not been done. In a case like that we must say that
God allows the action but not that he wants it, even though he goes
along with it because of the laws of Nature that he has established
and because he sees how to derive from it a greater good.8. It is
quite hard to distinguish Gods actions from those of created
things. Some believe that God does everything, and others suppose
that he only conserves the force he has given to created things,
allowing them to decide in what directions the force shall be
exercised. We shall see later on what truth there is in each of
these. Now since actions and passions properly belong to individual
substances (when there is an action there is something, some
subject, that acts), I have to explain what such a substance is.
This much is certain: when several predicates are attributed to
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the same subject, and this subject is not attributed to any
other, it is called an individual substance. For example, we call
John a substance because we can attribute to him honesty,
intelligence, and so on; but we dont call his honesty a substance
because, although we can attribute predicates to it (His honesty is
charming, and surprising) we can attribute it to something else,
namely to John. In contrast, John cannot be attributed to anything
else. But that explanation is only nominal - all it does is to
relate our calling a thing a substance to other facts concerning
what we say about it. Beyond that, we need to think about what it
is for something to be truly attributed to a certain subject - e.g.
what it is for honesty to be a property of John. Now it is certain
that all true predication is founded in the nature of things, and
when a proposition is not identical, that is, when the predicate is
not explicitly included in the subject as in The man who governs
Somalia governs Somalia, it must be implicitly included in it. This
is what philosophers call in-esse [being-in] when they say that the
predicate is in the subject. So the notion of the subject term must
always include that of the predicate, so that anyone who understood
the subject notion perfectly would also judge that the predicate
belongs to it. We can therefore say that the nature of an
individual substance or of a complete being is to have a notion so
complete that it is sufficient to include, and to allow the
deduction of, all the predicates of the subject to which that
notion is attributed. An accident, on the other hand, is a being
whose notion doesnt involve everything that can be attributed to
the subject to which that notion is attributed. Thus Alexander the
Greats kinghood is an abstraction from the subject, leaving out
much detail, and so is not determinate enough to pick out an
individual, and doesnt involve the other qualities of Alexander or
everything that the notion of that prince includes; whereas God,
who sees the individual notion or thisness of Alexander, sees in it
at the same time the basis and the reason for all the predicates
that can truly be said to belong to him, such as for example that
he would conquer Darius and Porus, even to the extent of knowing a
priori (and not by experience) whether he died a natural death or
by poison - which we can know only from history. Furthermore, if we
bear in mind the interconnectedness of things, we can say that
Alexanders soul contains for all time traces of everything that did
and signs of everything that will happen to him - and even marks of
everything that happens in the universe, although it is only God
who can recognise them all.9. Several considerable paradoxes follow
from this, amongst others that it is never true that two substances
are entirely alike, differing only in being two rather than one. It
also follows that a substance cannot begin except by creation, nor
come to an end except by annihilation; and because one substance
cant be destroyed by being split up, or brought into existence by
the assembling of parts, in the natural course of events the number
of substances remains the same, although substances are often
transformed. Moreover, each substance is like a whole world, and
like a mirror of God, or indeed of the whole universe, which each
substance expresses in its own fashion - rather as the same town
looks different according to the position from which it is viewed.
In a way, then, the universe is multiplied as many times as there
are substances, and in the same way the glory of God is magnified
by so many quite different representations of his work. It can even
be said that each substance carries within it, in a certain way,
the imprint of Gods infinite wisdom and omnipotence, and imitates
him as far as it is capable of doing so. For it expresses (though
confusedly) everything that happens in the universe - past,
present, and future - and this is a little like infinite perception
or knowledge. And as all the other substances express this one in
their turn, and adapt themselves to it - that is, they are as they
are because it is as it is - it can be said to have power over all
the others, imitating the creators omnipotence.
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10. The ancients, as well as many able teachers of theology and
philosophy a few centuries ago - men accustomed to deep thought,
and admirable in their holiness - seem to have had some knowledge
of the things I have been saying, and to have been led by that to
introduce and defend substantial forms. These are much sneered at
today, but they are not so far from the truth, nor so ridiculous,
as the common run of our new philosophers suppose. I agree that
these forms have no work to do in explaining particular events, and
thus no role in the details of physics. That is where our
scholastics [= mediaeval Christian philosophers influence by
Aristotle, Thomas Aquinas being the most famous example] went
wrong, and the physicians of the past followed them into error:
they thought they could invoke forms and qualities to explain the
properties of bodies, without bothering to find out how the bodies
worked - like settling for saying that a clocks form gives it a
time-indicative quality, without considering what all that consists
in - that is, without considering what mechanisms are involved.
Actually, that might be all the clocks owner needs to know, if he
leaves the care of it to someone else. But this misuse and
consequent failure of forms shouldnt make us reject them.
Metaphysics needs a knowledge of them, so much so that without that
knowledge - I maintain - we couldnt properly grasp the first
principles of metaphysics, and couldnt raise our minds to the
knowledge of immaterial natures and the wonders of God. However,
important truths need not be taken into account everywhere. A
geometer need not worry about the famous labyrinth of the
composition of the continuum [that is, the puzzles that arise from
the idea that a line has no smallest parts]; and the huge
difficulties to be found in trying to reconcile free will with Gods
providence need not trouble a moral philosopher, still less a
lawyer or politician; for the geometer can do all his proofs, and
the politician can complete his plans, without getting into those
debates, necessary and important though they are in philosophy and
theology. In the same way a physicist can explain his experiments -
sometimes using simpler experiments he has already made, sometimes
proofs in geometry and mechanics - without needing to bring in
general considerations belonging to another sphere. And if he does
go outside his sphere, and appeal to Gods co-operation, or to some
soul or spiritual force or other thing of that kind, he is talking
nonsense, just as much as someone who drags large-scale reflections
about the nature of destiny and our freedom into an important
practical deliberation. Indeed men often enough unthinkingly make
this mistake, when they let the idea of what is fated to happen
tangle their thoughts, and sometimes are even deterred by that idea
from some good decision or some important precaution.11. I know I
am putting forward a considerable paradox in claiming to
rehabilitate the ancient philosophy, in a way, and to re-admit
substantial forms when they have been all but banished. But perhaps
you wont just brush me off if you realize that I have thought a lot
about the modern philosophy, that I have spent much time on
experiments in physics and proofs in geometry, and that for a long
time I was sure that these entities [substantial forms] are futile.
Eventually I had to take them up again - against my will, as though
by force - after my own researches made me recognize that thinkers
these days do less than justice to St. Thomas and to other great
men of his time, and that the views of scholastic philosophers and
theologians contain much more good stuff than people suppose,
provided they are used relevantly and in their right place. I am
convinced, indeed, that if some exact and thoughtful mind took the
trouble to clarify and digest their thoughts, in the way the
analytic geometers do, he would find them to be a treasure-house of
important and completely demonstrable truths.
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12. Picking up again the thread of our reflections, I believe
that anyone who thinks about the nature of substance, as I have
explained it above, will find that there is more to the nature of
body than extension (that is, size, shape, and motion), and that we
cant avoid attributing to body something comparable with a soul,
something commonly called substantial form - though it has no
effect on particular events, any more than do the souls of animals,
if they have souls. It can be proved, indeed, that the notion of
size-shape-movement is less sharp and clear than we imagine, and
that it includes an element that belongs to imagination and the
senses, as do - to a much greater degree - colour, heat, and other
such qualities, which we can doubt are really there in the nature
of external things. That is why qualities of such kinds could never
constitute the basic nature of any substance. Moreover, if there is
nothing but size-shape-movement to make a body the thing that it
is, then a body can never persist for more than a moment because
bodies constantly gain and lose tiny bits of matter. However, the
souls and substantial forms of bodies other than ours are quite
different from our thinking souls. Only the latter know their own
actions; and they dont naturally go out of existence, but last for
ever and always retain the foundation of the knowledge of what they
are. This is what makes them alone liable to punishment and reward,
and what makes them citizens of the republic of the universe, of
which God is the monarch. It also follows that all other creatures
must serve them. I shall say more about that later.13. The
foundations that I have laid down give rise to a big problem, which
I must try to solve before moving on. I have said that the notion
of an individual substance involves, once and for all, everything
that can ever happen to it; and that by looking into that notion
one can see in it everything that will ever be truly sayable of the
substance, just as we can see in the nature of a circle all the
properties that are deducible from it. But this seems to destroy
the difference between contingent and necessary truths, to rule out
human freedom, and to imply that all the events in the world -
including our actions - are governed by an absolute fate. To this I
reply that we have to distinguish what is certain from what is
necessary. Everyone agrees that future contingents are assured,
because God foresees them; but we dont infer from this that they
are necessary. You may say:
But if some conclusion can be infallibly deduced from a
definition or notion, it is necessary. And you contend that
everything that happens to a person is already included implicitly
in his nature or notion, just as a circles properties are contained
in its circle; so you are still in trouble.
I shall now resolve this problem completely. To that end, I
remark that there are two kinds of connection or following-from.
One is absolutely necessary, and its contrary implies a
contradiction; such deduction pertains to eternal truths, such as
those of geometry. The other is necessary not absolutely, but only
ex hypothesi, and, so to speak, accidentally. It doesnt bring us to
It is necessary that P, but only to Given Q, it follows necessarily
that P. This is contingent in itself, and its contrary does not
imply a contradiction. This second kind of connection is based not
purely on ideas and on Gods understanding alone, but also on his
free decrees, and on the history of the universe. Let us take an
example. Since Julius Caesar will become the permanent dictator and
master of the Republic, and will overthrow the freedom of the
Romans, these actions are comprised in his perfect or complete
notion; because we are assuming that it is the nature of such a
perfect notion of a subject to include everything, so that the
predicate can be contained in the subject. It could be put like
this: it is not because of that notion or idea that Caesar will
perform the action, since that notion applies to him only because
God knows everything. You may
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object: But his nature or form corresponds to that notion, and
since God has imposed this character or nature or form on him, from
then on he must necessarily act in accordance with it. I could
reply to that by bringing up the case of future contingents: they
have as yet no reality except in Gods understanding and will, yet
since God has given them that form in advance, they will
nevertheless have to correspond to it. So I could counter-attack by
challenging you to choose between two options, each of which you
will find uncomfortable: either (1) say that future contingents are
really necessary, and not contingent, or (2) say that God does not
know them in advance. But I prefer to resolve difficulties rather
than excusing them by likening them to other similar ones; and what
I am about to say will throw light on both of the above problems.
Applying now the distinction between different kinds of connection,
I say that whatever happens in accordance with its antecedents is
assured but is not necessary; for someone to do the contrary of
such an assured outcome is not impossible in itself, although it is
impossible ex hypothesi - that is, impossible given what has gone
before. For if you were capable of carrying through the whole
demonstration proving that this subject (Caesar) is connected with
this predicate (his successful power-grabbing enterprise), this
would involve you in showing that Caesars dictatorship had its
foundation in his notion or nature, that a reason can be found
the