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.


Does God believe in himself?

Rachel asked:

Does God believe in himself?

Answer by Peter Jones

What a good question. It opens a can of worms, as perhaps you already know or suspect.

Philosophers sometimes define knowledge as ‘justified true belief’. If it is, then God must believe in Himself in order to have knowledge of Himself, and if He ever stopped believing He would become ignorant of Himself.

And yet, how could He justify this belief? To know that His belief is justified He would have to have knowledge of Himself that is not merely justified true belief but is more secure than this, more directly known.

In this case, as well as justified true belief there is a stronger form of knowledge for which the knowledge simply is the justification, and the belief simply is the knowledge.

This is knowledge by identity. Aristotle proposes that it is the only form of true knowledge. Kant uses the phrase ‘non-intuitive immediate knowledge’ to mean what I imagine is the same thing.

If knowledge by identity is required in order to justify justified true belief then justified true belief is not knowledge but a conjectural theory. This would be my view, and it seems to be logically inevitable.

So God would have no need to believe anything about Himself, since He would know by being. Or, if we imagine that God has to believe things like we do, then His knowledge would justify his beliefs.

It is not irrelevant that the Sufi sage Al-Halaj was crucified not for claiming ‘I know the truth’, but for claiming ‘I am truth’. The difference between these claims is the difference between a belief that may or may not be justified and knowledge that is simply known and which therefore justifies the use of the phrase ‘true knowledge’ to describe it.

I do not think we have to believe in God to find a study of your question illuminating. A book could be written in reply but this may be a start. It seems a good example of the way that a study of God’s qualities and properties can be useful quite regardless of whether He exists.


Solipsism as a practical possibility

Jo asked:

I agree with Hume that extreme scepticism about the outside world isn’t practical. ARE there any good arguments against solipsism when not being practical?

Answer by Helier Robinson

In principle there are two ways to refute solipsism: show it to be self-contradictory, and prove that something outside your present consciousness (outside the content of solipsism) actually exists. My own view is that the first does not work because solipsism is consistent, but the other can be done with the following argument. The concept of ‘intrinsic necessary existence’ is not self-contradictory, so it must exist in at least one possible world; in that world it exists necessarily, and so that world exists necessarily (if a part of a whole exists then the whole exists); therefore at least one possible world exists necessarily, and so something exists outside your present consciousness. This necessary world is, of course, the world we live in.


Answer by Geoffrey Klempner

Whether or not solipsism can disproved by showing that it is self-contradictory or (as Helier claims) by showing that at least one thing exists outside your present consciousness, the question remains whether solipsism is a practical possibility. What is the difference between extreme scepticism about an external world and solipsism? If nothing exists outside my present consciousness, then a fortiori (from the stronger premiss) no other conscious beings exist apart from my present consciousness. So I would be interested in a version of solipsism which grants the existence of an external world, but denies that other consciousnesses exist, or are ‘real’. This would be equivalent to ‘extreme scepticism about other minds’.

This would be the belief demonstrated in action by an extreme psychopath who regards other persons or conscious beings as merely tools to use or obstacles to overcome. Whether such individuals are ever found in the ‘pure’ form is an empirical question. But there seems to be no reason why, in principle, a ‘practical solipsist’ could not live and function successfully – on ‘its’ own terms.


Descartes’ cosmological and ontological arguments

Cassie asked:

What exactly are Descartes’ cosmological and ontological arguments?

Answer by Craig Skinner

Traditional arguments for God’s existence include:

1. Cosmological argument (the world can’t be self-caused or uncaused, it needs a First Cause (God).

2. Ontological Argument (God’s existence provable from the very definition of God).

3. Design Argument (the universe shows evidence of design, a designer must exist).

4. Moral argument (God needed to underpin right and wrong).

All are flawed. Neither Descartes nor anybody else has proved that God exists. Belief in God is a matter of faith and revelation, but alleged revelations to date are wide open to doubt.

You refer to Descartes’ versions of the Cosmological (or Causality) argument (Meditation 3) and Ontological argument (Meditation 5).

The existence of God is crucial to Descartes because in the sustained argument of the Meditations, God is the bridge from the hyperbolic doubt of the Cogito back to knowledge of the empirical world and the abstract world of logic and mathematics.

Descartes does not set out his arguments in formal deductive terms (he antedates predicate logic and was no fan of syllogistic logic). He uses scholastic terminology. At times he seems to think that God’s existence is readily evident to any diligent, attentive meditator, and arguments are just heuristic devices to help the slower meditator to the almost self-evident truth that God’s existence is known by clear and distinct perception. For all these reasons, the meditator has to do some work to penetrate the arguments.

For each argument, I shall set out a fair construction and briefly consider objections.

Cosmological (Causality) Argument:

P1: I have the idea of a most perfect (infinite, eternal,omnipotent, benevolent) being (God).

P2: A cause must be at least as great (real) as its effect.

Conclusion: this idea of God can’t come from (imperfect) me. Its cause must be God (or, impossibly, greater). God exists.

P1 is clear.

P2 is less easy to grasp. Discussion is couched in technical, scholastic terms. Two types of reality (being) are distinguished regarding ideas. The existence of an idea (its formal reality) is distinguished from the content of the idea (its objective reality). “Objective” refers to the object contained in the idea, rather like the modern use of “subjective” – it refers to the tree (say) in the mind not the tree in the garden. The notion of degrees of reality is then introduced. Ideas all have the same degree of formal reality, all being states of mind, but they differ in degrees of objective reality – lowest in a “mode” (modification of a substance e.g. shape), intermediate in a finite substance, highest in an infinite substance.

So P2 expresses the Causal Principle that the degree of formal reality of the cause must be at least as great as the objective reality of the effect, leading to the conclusion that an idea whose content (objective reality) is infinite (such as my idea of God) can’t have its cause in a finite being (with less than infinite formal reality) such as me, only in God, so that God exists.


P1: I can claim not to have this idea.

P2: Whether expressed in scholastic or modern terms, P2 is simply an assertion. No evidence is given for it. To assume a finite mind needs an infinite mind to cause it begs the question as to God’s existence. As far as I can see simple things plus simple rules can lead to complex things e.g. laws of nature plus simple initial conditions has produced atoms, compounds, galaxies, life and minds, so that the Causal Principle is false.

The argument is valid but unsound.

Ontological Argument

Originally due to Anselm, declared invalid by Aquinas, the argument lapsed, and Descartes’ use of it surprised his contemporaries.

His version is as follows:

P1: I have a clear and distinct idea of a most perfect being.

P2: This idea includes necessary existence.

P3: God’s necessary existence is part of God’s essence.

Conclusion: God exists.


P1: again, I simply deny that I have this idea.

P2: this is fine if we mean that the conceived entity can be thought of AS IF it existed necessarily. It doesn’t mean that any such entity actually exists, or indeed could possibly exist.

P3: in support, Descartes makes a famous geometrical comparison, saying existence can no more be separated from the essence of God than the fact that its three angles make two right angles can be separated from the essence of a triangle.

To which Gassendi makes 2 penetrating objections (5th set of Objections).

1. The comparison is unfair. Like is not compared with like. Essence is (correctly) compared with essence, but then existence is not compared with existence. Rather existence (of God) is compared with property (of a triangle). A fair comparison would not show God necessarily exists any more than that a triangle necessarily exists.

2. Existence is placed among God’s, but not among the triangle’s perfection. Also existence is not a perfection, it is that without which no perfection (or other quality) can be present. Gassendi anticipates Kant’s view that existence is not a predicate.

Also, the traditional objection to the ontological argument applies, that we can prove the existence of anything e.g. I have a clear and distinct idea of a necessarily existing perfect pizza, holiday, partner etc.

The argument is invalid.

All we can really conclude from Ontological arguments is that if God exists his existence is necessary, if he doesn’t his existence is impossible, but we don’t know whether God exists or not.

Finally, both arguments face the following objections:

1. Vicious circularity: the conclusion that a (non-deceiving) God exists is based on a clear and distinct idea, but the truth of clear and distinct ideas is guaranteed by the existence of a non-deceiving God.

2. No criteria for clear and distinct perception. No guide to recognizing slightly unclear or somewhat indistinct ideas which we can’t rely on. In any case, it’s quite common for people to have clear and distinct ideas which turn out to be wrong.

In the Meditations’ dedication (to a Faculty of Theology, he hoped to get the Churchmen on his side) Descartes says that although faith suffices for the faithful, proof is required by philosophers and for persuasion of infidels. He was no doubt disappointed by criticism, rather than acclamation, of his arguments by theologians (and others) which he published as Objections with his Replies along with the Meditations, and which are as worthy of study as the main text.


What is life?

Bob asked:

What is life?

Answer by Helier Robinson

The best answer I know of is due to the physicist Erwin Schroedinger, who said that life i.e. very high negative entropy in dynamic equilibrium. Entropy is a concept in physics usually popularised as disorder, so that negative entropy is order. So very high negative entropy is very high order. Dynamic equilibrium is moving equilibrium, as opposed to static equilibrium: a spinning top is in dynamic equilibrium, a brick wall is in static equilibrium. Entropy, as a concept, occurs in the second Law of Thermodynamics, which says that in any closed system entropy may increase to the maximum possible, but will not decrease. Living systems lose negative entropy all the time, according to this law, but replace it by feeding: either on sunlight or on other life. This steady loss and replacement is their dynamic equilibrium. Death is the failure of this equilibrium.


Choosing Philosophy as a major

Senaida asked:


I’m Senaida from Arizona, United States. I’m going back to school as admitted student. I’m considering what major that is possibly the best for me to a pursue degree in the future. So I’m seeking a right career for myself… I have questions to ask you if you don’t mind take your time answer those questions for me. Very basic questions.

What exactly do you do?
What do you like about your job?
What don’t you like?
What are the physical and mental stresses in your job?
Does philosophy prepare you for your career?
What are some values or attitudes needed for the job?
Wht is the work environment like?
What are the typical hours?
What are qualification requirement, including education and training?
Is there a career path in this field? If so, what does it lead to?
Did you take internship? If so, does it benefit you?
What are the opportunities for employment in this field?
Why did you study philosophy?
Are there tests or license needed?

Thank you for your time reading this.


Answer by Geoffrey Klempner

Hi Senaida,

Many of your questions are answered in my blog post, ‘Jobs for Philosophers’:

Philosophy is a terrific qualification for any career. As one commentator on the post noted:

I have a BA with two majors Philosophy and Public Speaking. Over the course of 13 years I have work in Public Education, Government, Health Care, Sales and finally; The Financial Investment Industry. This year I reached the 39% Fed income tax level. My studies in philosophy allow me to think circles around my peers. While most people focus on what and how; Philosophy separates me since I focus on the why.

My job is unusual, in that I am a philosopher by profession although I am not employed in any college or university department of philosophy. I run my own philosophy school, Pathways to Philosophy, founded in 1995 and launched on the web in 1997.

I love my job. I work whatever hours I like, I get to think about philosophical problems all the time. See my letters to students at

The down side is that it doesn’t bring in a lot of money. It seems people are more ready to splash out on a meal in a fancy restaurant than on a philosophy course which will change their life.

The stress of thinking about philosophical problems is not for everybody. One person I met remarked that, “Philosophy takes the roof off”. Can you live with that?

My work environment is my own study, surrounded by computers. But I can get out whenever I like.

To work professionally in philosophy you need a PhD. You start by getting a BA. There is no guarantee of a job at the end because competition is severe. But as I say in my blog post, you can follow any career after you have taken a Philosophy BA.

I haven’t heard of internship in philosophy, although the Pathways mentors who do some of the teaching could be described as interns. That sounds like a good idea, actually :-)

I studied philosophy because I needed to. No-one who has not felt the need for philosophy can understand what that means. You have to be gripped by the problems of philosophy. Are you?

Good luck!