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§5. Some Comments on Leibniz ’s Account of Truth

§5. Some Comments on Leibniz ’s Account of Truth

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Leibniz often uses this name, “the Principle of Sufficient Reason,” to refer

to various less general principles. The form above is, I think, the most

general form of the principle. Thus he says: “There are two first principles of all reasonings, the principle of contradiction . . . and the principle

that a reason must be given, that is, that every true proposition which is

known per se, has an a priori proof, or that a reason can be given for

every truth, or as is commonly said, that nothing happens without a cause.

Arithmetic and geometry do not need this principle, but physics and

mechanics do.”6

Another quotation brings out how contingent truths depend on God’s

decrees and choice of the best of all possible worlds.

The demonstration of this predicate of Caesar [that he resolved to cross

the Rubicon] is not as absolute as are those of numbers or of geometry,

but presupposes the series of things which God has chosen freely, and

which is founded on the first decree of God, namely to do always what

is most perfect, and on the decree which God has made [in consequence of the first], in regard to human nature, that man will always

do (though freely) what appears best. . . . [E]very truth which is

founded on decrees of this kind is contingent, although it is certain.

(Discourse:§ [Ariew and Garber:])

. A second comment on Leibniz’s account of truth is that today we

use the term “a priori” as an epistemological term. It says something about

how a proposition can be known, namely, that it can be known independently of experience. But this is not Leibniz’s idea of the a priori: when he

says that true propositions have an a priori proof, he means a proof based

on the ultimate reasons for their being true and not false. Clearly Leibniz

does not mean that we (human beings) can know contingent propositions

to be true independent of experience. The proofs he has in mind can be

known only by God, because only God sees by intuitive vision of the possible existences the answer to the requisite infinite analysis.

A further comment, related to the preceding one, is that Leibniz’s con6. Gerhardt, Philosophischen Schriften, VII:, in Leibniz Selections, ed. Philip R. Weiner (New

York: Scribners, ), p. .

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ception of the contingent is, we might say, proof-theoretic.7 That is, it draws

the distinction between necessary and contingent true propositions according to how they can be, or are, established by someone who is omniscient. This is seen from how he uses the conception of contingency and

by his saying, for example, in referring to the Principle of Sufficient Reason,

that “the principle that nothing ever happens without the possibility that

an omniscient mind could give some reason why it should have happened

rather than not” (Bodeman’s Catalogue of Leibniz’s MSS [], in Wiener:

). And he says in “Necessary and Contingent Truths” (.) that “existential

or contingent propositions differ entirely from these [the eternal truths

about essences]. Their truth is understood a priori by the infinite mind

alone, and cannot be demonstrated by any resolution.” These quotations

show the extent to which Leibniz’s distinction between necessary and contingent truths looks at the question from God’s point of view.

. A third comment: it is tempting to object that Leibniz’s account of

contingency in terms of proofs requiring an infinite analysis that only God

can see the answer to does not give us a real, bona fide conception of

contingency. The contingency that we complain is missing is perhaps that

of brute fact: that is, a fact that simply has no explanation even when everything is known, as, for example, the ultimate laws of nature, should there

be such. That conception of contingency, though, is precisely what Leibniz

rejects: it violates his principle of sufficient reason. This principle requires

that the world must be fully intelligible through and through, not to us,

admittedly, but to a perfect infinite intelligence. Thus the ultimate laws of

nature, even as subordinate maxims, will manifest an appropriate perfection. Leibniz believes that the laws of physics do this in the form of principles of conservation, for example, as well as of maximum and minimum

principles leading to the calculus of variations (Discourse:§§–). Nothing

is opaque to God. That our world satisfies this condition is part of Christian

faith (no doubt of other faiths as well). It is also a thesis of idealism.

A last comment: above we reviewed two beginnings for Leibniz’s account of the predicate-in-subject doctrine. One was the idea of a true proposition as one whose predicate concept is in the subject concept; the other

7. See R. M. Adams, “Leibniz’s Theory of Contingency,” in Leibniz: Critical and Interpretative

Essays, ed. M. Hooker (Minneapolis: University of Minnesota Press, ), pp. ff.

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was the idea of a monad as a windowless form of mental life specified

completely by a list of all its properties over time. It is natural to ask which

of these is better, and which came first in Leibniz’s mind.

Concerning the last question, I have no opinion, though a study of further texts might give an answer. I think, though, the second idea, beginning

with windowless monads, may be better: it goes deeper into Leibniz’s overall doctrine, and together with the idea of perfection it enables us to see

quite easily why the predicate-in-subject doctrine holds of all true affirmative contingent propositions. So I think it to be more instructive and in any

case sufficient to render Leibniz’s view intelligible. Certainly he has additional ideas in mind, as his use of the analogy to an infinite series shows;8

note his mention of surd relations and of showing that the error is less than

any assignable quantity (“Necessary and Contingent Truths,” paragraph ).

But I don’t think that these other things are necessary to give sense to the

predicate-in-subject doctrine. The elementary intuitive idea of monads as

discussed above seems sufficient to do that.

Note in conclusion that obviously Leibniz’s theory of truth is framed

for his philosophical theology and its apologetic aims. It is not an account

of how we, human beings, learn the meaning and reference of the terms

in our language and apply them in everyday life. Certainly Leibniz could

not have been unaware of this. But for him, that is not the point. He is

not trying to explain our use of language, how its terms get their meaning

and reference. Rather, he wants to maintain certain very general considerations about all truths seen as fully accessible only from God’s point of

view. He thinks that our actual language hooks up suitably in some way

with these truths; and this enables us to understand his theory. And that

is enough for his purposes. It is not what we think of today as philosophy

of language, however suggestive and valuable it might be for that.

8. What these ideas might be are instructively discussed by John Carriero in “Leibniz on Infinite

Resolution and Intra-mundane Contingency, Part One: Infinite Resolution,” Studia Leibnitiana 

(), pp. –.

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Spirits as Active Substances: Their Freedom

§. The Complete Individual Concept Includes Active Powers

. Leibniz’s predicate-in-subject account of truth, which we took up last time

in sections –, with its distinction between necessary and contingent truths,

serves his purposes provided that it helps him to maintain two things:

(a) The world is freely created by God, who has attributes of reason,

moral perfection, and will, and who creates the world for the best of reasons, not arbitrarily or by logical necessity.

(b) This requires that the actual world must be the best of all possible

worlds, and that the created things that make up the world—the complete

substances—must be genuinely created things, having their own active

forces and tendencies that move them to act in accordance with their own


Now, Leibniz believes that to speak of God’s, or anyone’s, free choice,

there must exist alternatives: this is a necessary condition of freedom. Thus

he thinks of the best of all possible worlds, and other less favored worlds,

including ones with much evil, as possible and of God’s choice of the best

as contingent. But how are we to understand a possible world?

Following Robert Adams’s suggestion, perhaps the clearest explanation

is to form the basic concept of a possible world just as we form the complete

concept of an individual.1 Such a concept of an individual contains in itself

1. See R. M. Adams, “Leibniz’s Theory of Contingency,” in Hooker, Leibniz: Critical and Interpretative Essays, pp. f.

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no contradiction: it has a consistent description. We get the basic concept

of a possible world by combining into a world a plurality of individuals, or

monads, and by supposing relations between the monads to be arranged

by preestablished harmony. Should this be done so that the world so conceived has a consistent description and contains no contradiction, then Leibniz says it is possible in itself. So long as we specify possible worlds without

bringing in God’s choice of the best, we avoid any complications arising

from the fact that God’s choice of the best possible world is in some way

necessary. It is at least morally necessary, that is, practically necessary as

required by moral reasons or by God’s moral perfections. But I avoid the

tangles of this question, which troubled Leibniz and which he seems never

to have resolved.2 I don’t know if he thought that the proposition that

God creates the best world is contingent, though he did think it morally


. To satisfy condition (b) above, Leibniz hopes his predicate-in-subject

view of truth enables him to regard complete individual substances as genuinely created things, and for this they must have active powers of their

own. This is essential for him in the case of spirits (minds with reason and

will), for it enables them to think, deliberate, and act on their own, and to

be spontaneously active, voluntarily moved, and able to follow the dictates

of their reason. The succession of thoughts, feelings, and actions that they

undergo must not be merely lifeless happenings—simply part of the divine

picture show—as Leibniz thinks is the case, in their different ways, with

Descartes and Spinoza.

To explain Leibniz’s criticisms of Descartes and Spinoza, let’s begin by

asking what a complete individual concept, where the substance in question

is a spirit, is a concept of. Suppose first that we think of the complete individual concept of Caesar as a complete story of Caesar’s life. (Let’s restrict

ourselves to this for simplicity.) The story starts with Caesar’s birth at such

and such a time, his crossing the Rubicon, his assassination, and the rest.

To this we add the story of Caesar’s thoughts, feelings, desires, perceptions,

and so on. And much else: the story recounts a complete and full sequence

of events over the life of Caesar. Think of this life as the complete film of

Caesar, as it were. Given this story, we suppose that when God creates

2. See ibid., pp. –.

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§5. Some Comments on Leibniz ’s Account of Truth

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