The principle of Contradiction and Reason

31. Our reasonings are grounded on 2 great principles.

• The principle of contradiction.

This lets us judge as false anything which involves a contradiction, and true anything which is the opposite of the false.

32. The other is the principle of sufficient reason

With this, we consider that no fact could be found to be genuine or existent, and no assertion true, without there being a sufficient reason why it is thus and not otherwise — even though we usually cannot know what these reasons are.

33. There are also 2 sorts of truths:

• those of reasoning
• those of fact

Truths of reasoning are necessary. Their opposite is impossible. Those of fact are contingent. Their opposite is possible. When a truth is necessary, you can find the reason by analysis, breaking it down into simpler ideas and truths, until you reach primary ones.

34. This is how mathematicians use analysis to reduce theorems about what is true, and rules for constructions, to definitions, axioms, and postulates.

35. Finally, there are simple ideas which cannot be defined; and there are also axioms and postulates — in a word, primary principles — which cannot be proved, and also do not need to be proved, since they are assertions of identity, of which the opposite contains an explicit contradiction.

36. But the sufficient reason must also be found in contingent truths, or truths of fact — that is to say, in the series of the things spread over the created universe.

Here, because of the immense variety of things in Nature, and because of the infinite division of body, the analysis into particular reasons could get more and more detailed without limit. An infinity of shapes and motions, present and past, come into the efficient cause of my present writing, and an infinity of tiny inclinations and dispositions of my soul, present and past, come into its final cause.

37. Since all this detail only includes other contingent things (whether previous or even more detailed), and since each of these still needs a similar analysis to find the reason for it, no progress has been made.

So the sufficient or ultimate reason must lie outside the sequence or series of these more and more detailed contingent things, however infinite it could be.

38. This is why the ultimate reason for things must lie in a necessary substance, in which the detail of changes exists only eminently, as in their source — and this is what we call ‘God’.

39. Now since this substance is a sufficient reason for all this detail, which is also completely interconnected, there is only one God, and this God is sufficient.

40. It can also be concluded that, since this Supreme Substance (which is unique, universal, and necessary) has nothing outside itself which could be independent of it, and since it is the simple consequence of possible being, then it must be incapable of having any limits, and must contain absolutely as much reality as is possible

41. From which it follows that God is absolutely perfect, since perfection is nothing other than magnitude of positive reality, taken in the precise sense of setting aside the limits or restrictions of things which are limited. And where there are no limits (i.e. in God), perfection is absolutely infinite.

42. It also follows that created things have their perfections infused into them by God, but that they owe their imperfections to their own nature, which is incapable of being unlimited. For this is what makes them distinct from God. This original imperfection of created things is evidenced by the natural inertia of bodies.

43. God is not only the source of existences, but also of essences in so far as they are real

He is the source of what reality there is in possibility. This is because God’s understanding is where eternal truths are located, or where the ideas on which they depend are. Without him, there would be no reality in possibilities, and not only would nothing exist, but nothing would even be possible.

44. For if there is any reality in essences or possibilities, or even in eternal truths, this reality must be grounded in something existent and actual, and consequently in the existence of the necessary being, in which essence includes existence, or which is such that its being possible is sufficient for its being actual.

45. Thus only God (or the necessary being) has this privilege, that he must exist if he is possible. And since nothing can prevent the possibility of that which includes no limits, no negation, and hence no contradiction, this alone is enough for us to know apriori that God exists. We have also proved his existence from the reality of eternal truths. But we have also just proved it aposteriori, since contingent beings exist, and they could only have their ultimate or sufficient reason in the necessary being, who has the reason for their existence in himself.

46. Meanwhile, one must not imagine (as some have) that, since eternal truths depend on God, they are arbitrary, and depend on his will.

This is how Descartes seems to have taken it, and subsequently Mr Poiret. It is only true of contingent truths, which depend on the principle of harmony, or the choice of the best; whereas necessary truths depend solely on his understanding, of which they are the internal object.

47. This God alone is the primary unity, or the original simple substance, which produces all created or derivative monads. To speak figuratively, they are born from one moment to the next by continual flashes of lightening from the divinity; and they are limited by the receptivity of that which is created, which is essentially bounded.

48. In God there is power, which is the source of everything; then there is knowledge, which contains the detailed system of ideas; and finally will, which changes or produces things in accordance with the principle of the best.

These correspond to what there is in created monads: the subject or basis, the faculty of perception, and the faculty of appetition. But in God these attributes are absolutely infinite, or perfect; whereas in created monads or entelechies (or ‘perfection-havers’, as Ermolao Barbaro translated this word) they are only imitations, which are closer the more perfection they have.

49. Created beings are said to act externally in so far as they have perfection, and to be acted upon by another in so far as they are imperfect.

Thus activity is attributed to monads in so far as their perceptions are distinct, and passivity in so far as their perceptions are confused.

50. One created being is more perfect than another in that it contains what is used to explain apriori what happens in the other; and this is why it is said to act on the other.

51. But among simple substances there is only an ideal influence of one monad on another. It can have its effect only by the intervention of God.

What happens is that, right from the beginning of things, among God’s ideas, one monad has reason to demand that he pays attention to it when organising the others. For since one created monad could not have any physical influence on the interior of another, this is the only means by which the one can have any dependence on the other.

52. This is how activity and passivity is mutual between created beings. For when God compares two simple substances, he finds reasons in each of them which oblige him to accommodate the one to the other.

Consequently, what is active in certain respects is passive from a different point of view. A created being is active in so far as what is known distinctly in it provides the reason for what happens in another created substance; and it is passive in so far as the reason for what happens in it is found in what is known distinctly in another.