Descartes on self-knowledge and Leibniz on indiscernibles

Eric asked:

In my Modern Philosophy class we have touched on Leibniz and Descartes, from the readings I have a few questions.

The contradiction found in Descartes’ Meditations II and III. In Meditations II Descartes says that he cannot doubt that he is a thinking thing. However in Meditations III, it appears that he does doubt it because he believes that God may be tricking him. How is it possible for him to believe both of these things?

What for Leibniz, is the status for the Principle for the Identity of Indiscernibles? Is it a Necessary Truth? a contingent truth? a truth about any world God might create?

Answer by Jürgen Lawrenz

You will be aware that this point provoked a deluge of academic argument. But I am of the view that we can get around it by Descartes’ own principle of reduction. This led him in the first place to the irreducibility of thinking as the bedrock of existence. Being tricked makes no difference at all, because it still implies the existence of a thinking thing. So there is no contradiction.

The major problem is something quite different. Namely: Who is this “I”? And what exactly does it mean that this “I” is thinking thing? What is thinking?

This is where the limitations of Descartes’ objectivity and his prejudices interfere. His notorious claim that animals are mere automatons amounts almost to a disqualification of his whole train of argument. However, it is not a contradiction, just deficient knowledge.

It is perfectly obvious that animals are intentional creatures, so for him to ignore or dispute the plain-speaking phenomenology of living things is not acceptable. Yet if we go that one step further and acknowledge that mice and mackerels, birds and bees all possess some kind of survival knowledge and the skills to ensure it, then we rescue that part of his argument by simply replacing ‘thinking’ with ‘intentionality’ as the bedrock of existence. For just as the thinking thing is irreducible, so the intentional aspect of all living things is irreducible. We may also admit that, to the best of our knowledge, ‘thinking’ is a high level of intentionality that includes self-reflexive thinking and therefore enables a conscious grasp of an “I” as the bearer of this form of intentionality.

Under the same criterion of irreducibility Leibniz’s indiscernibility principle is a necessary truth. No two existents can share the same soul, the same space, the same identity; and this implies further that no soul can comprise two identities, nor occupy two different spaces simultaneously.

The monad, from which this argument begins, is a ‘simple thing’, indivisible. The problem for us is to conceive of such a monad. Clearly it cannot be a thing, because all things are reducible (divisible). Hence the idea of a smallest particle is self-contradictory; and the notion of two particles being identical in every respect except location is also self-contradictory. We can resolve this issue by noting the limitations of observership: A human observer does not have the infinite capacity of differentiation to discern the differences in this seeming identicalness.

In part this is a logical argument. Every existing composite can in principle be decomposed into monads. Accordingly (as in Leibniz’s famous ‘cosmic equation’) every existent in the world is a composite string of 1 and 0. Would it not be possible for the monadic ensemble 1101001 to occur twice, i.e. in different composites? Leibniz says ‘no’, because it already exists; and every monad is a unique instance of existence.

Behind this rests the ‘principle of sufficient reason’. Since non-existence is prior to existence, a sufficient reason must be given for every existent to exist. This can only refer to creation. But creation (whether by God or a Big Bang) is ineluctably differentiation from nondifferentiation. If identicals are created, then differentiation has not occurred; and this means that no creation has transpired.

I have described a pretty complex metaphysical argument here in the simplest way I can. Both Descartes and Leibniz spent most of their lives defending their respective theses against attacks; and objections to them continue to this day. But they persist nonetheless, because it is difficult (perhaps impossible) to refute them, given the nature and scope of the human intellect. A great deal of today’s theoretical physics is devoted to the same issues, because sub-nuclear science is constantly running up against identical discernibles. As mentioned, however, in this department the conflict between what can be observed and what can be argued (for or against) intellectually cannot be bridged by appealing to empirical features. They remain ambiguous, precisely because experiments that can be conceived (thought experiments) and those that can be implemented, rarely give the same answers.


Answer by Craig Skinner

Good, perceptive questions.

The short answers are that indeed Descartes can’t believe both these things at the same time, the anomaly is unresolved; and Leibniz vacillates as to the status of his Principle.

It comes as a surprise to the reader that Descartes establishes the cogito in Med 2 only to retract it in Med 3 without comment or explanation.

Thus in Med 2, after doubting all that can be doubted, he concludes that because he doubts, he thinks, and thus exists as a thinking thing, and he can be absolutely certain about this. He makes it clear that a malicious god or demon might fool him about everything else, but not about this. He says

“let him deceive me as much as he will, he can never cause me to be nothing so long as I think that I am something.”

But in Med 3 he takes it back, saying

“I must inquire whether there is a God….I must also inquire whether He may be a deceiver; for without a knowledge of these two truths I do not see that I can ever be certain of anything.”

He doesn’t say that he can never be certain of anything except his existence, as we would expect. No, he says that without a prior clear and distinct idea of a non-deceiving God, he can never be certain of anything.

It is inconceivable that he simply made a mistake, and doesn’t mention it even in the section including his Replies to Objections. Also he can hardly have changed his mind between one chapter and the next, and say nothing about it into the bargain. So it remains an anomaly as to why there is this contradiction by such a clear, systematic thinker and writer. So much so that scholars have tried to explain it away, suggesting he has different notions of certainty (logical and psychological) or of clear and distinct perception in different chapters, or that his cogito is sometimes inferential, sometimes intuitive knowledge. I find this unconvincing, but have no better explanation. It seems you can go with Med 3 and require God to guarantee absolutely all knowledge, or with Med 2 where God guarantees all else but the cogito stands.

Of course, he may have changed his mind about things over the years. Thus in the earlier Discourse on Method, he establishes the cogito in the inferential formula forever associated with his name (“I think therefore I am”) and runs with it. But in Meditations, he doesn’t use this formula and may there be claiming it as an intuitive rather than inferential truth. Also, in his later Principles of Philosophy he explains that

“When I said that the proposition I think therefore I exist is the first and most certain… I did not thereby deny that one must first know what thought is, what existence is, and what certainty is, and that it cannot happen that what thinks does not exist… these are simple notions, I did not think they needed to be listed.”

So it seems he has to know quite a bit before concluding I think therefore I am, but how can he be sure that his ideas of thought, existence, and certainty can be relied on, if not guaranteed by God.

Leibniz, unusually, is a great philosopher who didn’t write a magnum opus, and his scattered writings need to be scoured for his views.

As regards his Principle of the Identity of Indiscernibles, his comments in The Leibniz-Clarke Correspondence are helpful.

Leibniz and Newton disagreed about the nature of space. Newton was a Substantivist – space was a something, a substance, the arena in which things were placed and events occurred, and if everything in the universe disappeared, empty space (or spacetime) would remain. Leibniz was a Relationist – there is no such Thing as space, it’s a way of describing the relations between things, and if all the things in the universe disappeared, there would be absolutely nothing left. Their debate was carried on as correspondence between Leibniz and Newton’s representative, Samuel Clarke, and includes mention of the Principle.

Leibniz says that the Principle follows from his conception of an individual as something which has a “complete notion”. This would make it a necessary truth (at least as applied to substances). But then he wavers, saying it’s not “absolutely impossible to suppose….two things perfectly indiscernible”, only that it is contrary to God’s wisdom to create two such things. So it appears he thinks it a truth about any world that God would create (although God could create a different world). Also he appeals to empirical fact to support it, suggesting he thinks it contingent, as in an anecdote about a man running all over a garden to find two identical leaves; and saying that two apparently indistinguishable water drops will differ under the microscope.

There is still debate as to the nature of spacetime, although most are Substantivists.

As regards the Principle, again there is debate. Weak and a Strong versions applied to substances and to states of affairs are now recognized, and most think these contingently true. But in the quantum realm, the Principle doesn’t hold.



Answer by Helier Robinson

When Descartes described himself as a thinking being he meant, in modern language, a conscious being. He could not doubt his own consciousness because he had to be conscious in order to doubt. What he doubts if he is being tricked is the content of his consciousness, not the fact of his consciousness. So there is no conflict between these two beliefs.

The key to understanding Leibniz is the single axiom to his whole philosophy: all truth is analytic. (See Bertrand Russell, A critical exposition of the Philosophy of Leibniz, 2nd. ed., Allen and Unwin, 1951, Introduction. N.B. not the first ed.) All truth being analytic meant that every true proposition had to be a categorical proposition, with the predicate contained in the subject. (Categorical propositions are the propositions of Aristotelian logic: All S are P, No S are P, Some S are P, and Some S are not P, where S stands for subject and P for predicate.) Leibniz was dealing with metaphysics, which concerns itself with everything that exists that is not known through the senses, all of non-empirical reality. The only beginning for metaphysics is to assume that it is rational: both in the sense of not containing any contradictions, and of containing causes corresponding to logical necessities.

(Note that causes are not empirical, and are essential to explanation, since to describe causes is to explain their effects. These days theoretical physicists will tell you that they explain empirical phenomena by describing their underlying (non-empirical) causes.)

But Leibniz realised that there is a problem with Aristotelian logic: the logic cannot handle relations. So he tried to develop a metaphysics without relations, based on subjects and predicates. Subjects became substances, and predicates became attributes. And there are no relations inside the substances, or between them. The substances are monads, and no two are alike. This is his Principle of the Identity of Indiscernibles. If there were no discernible differences between two monads then there would be a relation of similarity between them, and these do not exist. So every monad differs from every other, its characteristic difference being its viewpoint. (Dissimilarities are not relations, they are only the absence of similarities.)

Causations are relations so do not exist between substances, so every monad is Windowless. Space and time are relational, so do not exist between substances: they exist in the mind of each monad in order to organise its perceptions (you may recognise Leibniz’ influence on Kant here). Each monad organises its perceptions on a basis of here and now, and the here and now is its viewpoint. Every monad is conscious, and its perceptions, or empirical world, are a mirroring of the viewpoints of nearby monads; this mirroring occurs because all these perceptions are attributes of the substance that is the monad; they were created when God created the universe, with the infinity of monads in it, each with an infinity of attributes, ordered in advance by God, Who, being good, desired the best of all possible worlds. This ordering of all the attributes of all the monads is Leibniz’ Pre-established Harmony. Leibniz was widely misunderstood on this matter of the best of all possible worlds: he was thought to be talking of the empirical world, not the metaphysical world. In fact, the best of all possible worlds is the best of all possible pre-establish harmonies. It is ironic that Leibniz did not succeed in abolishing relations, he only succeeded is combining all of them into one Harmony, an infinite-adic relation.

So your three questions about the Principle of the Identity of Indiscernibles can be answered in the affirmative, given Leibniz’ axiom.


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