Fundamental Philosophy, Vol. 2 (of 2)

17. The predicate is, then, in every affirmative proposition, identified with the subject. When we perceive, therefore, we affirm the identity. Judgment, then, is the perception of the identity. We do not, however, deny that in what we call assent there is often something more than the simple perception of identity; but we do not understand how we need any thing more than to see it evidently in order to assent to it. What we call assent, adhesion of the understanding, seems to be a kind of metaphor, as if the understanding would adhere, would yield itself to the truth, if it were presented; but in reality we very much doubt if, with respect to what is evident, there be any thing but perception of the identity.

18. Hence it follows, that if the same ideas were to correspond in the very same manner to the same words, the opposition and diversity of judgments in different understandings would be impossible. When, then, this diversity or opposition does exist, there is always a discrepancy in the ideas.

19. We conceive of things, and reason upon them abstracted from their existence or non-existence; or we even suppose them not to exist, that is, conceive of relations between predicates and subjects without the existence of either predicates or subjects. And as all contingent beings may either be or cease to be, and even the first moment of their being be designated, it follows that science, or the knowledge of the nature and relations of beings, founded upon certain and evident principles, has nothing contingent for its object inasmuch as it exists. There is, then, an infinite world of truths beyond contingent reality.

We conclude, from our reflections upon this, that there must be beyond the contingent world a necessary being in which may be founded that necessary truth which is the object of science. Science cannot have nothing for its object; but contingent beings, if we abstract their existence, are pure nothing. There can be no essence, no properties, no relations in what is pure nothing; something therefore is necessary whereon to base the necessary truth of those natures, properties, and relations which the understanding conceives of in contingent beings themselves. There is, then, a God; and to deny him, is to make science a pure illusion. The unity of human reason furnishes us one proof of this truth; the necessity of human science furnishes a second, and confirms the first.19

20. We find a conditional proposition involved in every necessary proposition, wherein substantive being is not affirmed nor denied, but the relative, as in this; all the diameters of a circle are equal. Thus, the one we have just cited is equivalent to this one; if there exists a circle all its diameters are equal. For in reality did no circle exist, there would be no diameters, no equality, or any thing else; nothing can have no properties; wherefore in all that is thus affirmed we must understand the condition of its existence.

21. In general propositions the union conceived of two objects is affirmed; but we must take good care to notice that although we are wont to say that what is affirmed is the union of two ideas; this is not, therefore, perfectly exact. When we assert that all the diameters of a circle are equal, we do not mean that this is so only in ideas, that we conceive it so to be, but that it really is so, beyond our own understanding and in reality, and this abstracting our ideas and even our own existence. Our understanding sees then a relation, a union of the objects; and it affirms that whenever these exist, there will also really exist the union, provided the conditions under which the object is conceived be fulfilled.

CHAPTER IV.

BEING, THE OBJECT OF THE UNDERSTANDING, IS NOT THE POSSIBLE, INASMUCH AS POSSIBLE

22. One very important point concerning the idea of being remains to be illustrated, and that is, whether this idea has possible or real being for its object. The scholastics taught that the object of the understanding was being; nor were they altogether without reason in so doing, since one of the things we conceive of with the greatest distinctness, and which is found to be the most fundamental in all our ideas, is the idea of being, containing as it does in a certain manner all other ideas. But as being is distinguished into actual and possible, a difficulty occurs as to which of these categories the idea of being, the chief object of our understanding, is applicable to.

23. The Abbate Rosmini, in his Nuovo Saggio sull' origine delle idee, pretends that the form and the light of our understanding, and the origin of all our ideas, consists in the idea, not of real, but of possible being. "The simple idea of being," he says, "is not the perception of any existing thing, but the intuition of some possible thing; it is no more than the idea of the possibility of the thing."20

I very much doubt the truth of this; and there seems also to be some confusion of ideas here. He ought to have defined possibility itself for us, before making the idea of it enter into that of being. I will myself give a definition of it, and this may serve greatly to facilitate the understanding of the whole matter.

24. What is possibility? The idea of possibility, abstracted from its classifications, offers us a general idea of the non-repugnance, or non-exclusion, of two things with respect to each other; just as the idea of impossibility presents us such a repugnance or exclusion. A triangle cannot be a circle. A triangle may be equilateral. In the former case we affirm the repugnance of the ideas of the triangle and of the circle: in the latter, the non-repugnance of a triangle having its three sides equal. It may be said that in these cases there is no question of the existence of the triangle or of the circle; and that the possibility or impossibility is referred to the repugnance of their essences, abstracted from their existence or non-existence, although ideal impossibility draws along with it real impossibility.

25. Since, whenever impossibility is asserted, repugnance also, is asserted, and there can be no repugnance of a thing with itself, it follows that impossibility is only possible when two or more ideas are compared. On the other hand, when there is no repugnance there is possibility; then, no simple idea, of itself alone, can offer to us an impossible object. The object, therefore, of every simple idea is always possible, that is, is not repugnant.

26. Those things only are intrinsically impossible which involve the being and the not-being of the same thing; wherefore they are styled contradictory. When an absurdity of this nature is presented to us, we at once recollect the principle of contradiction, and say, this cannot be, "since it would be and would not be at the same time." Why is a circular triangle impossible? Because it would be and it would not be a triangle at one and the same time.

The idea of not-being does then enter into that of impossibility: without it, there can be no exclusion of being, and consequently, neither contradiction nor impossibility.

27. Possibility may be understood in two ways: I., inasmuch as it expresses only simple non-repugnance; and then what does not exist, is not only possible when it does not involve any contradiction, but also, the existing, the actual; II., inasmuch as it expresses non-repugnance, united to the idea of not being realized; and then it is only applicable to non-existing things. The possible taken in the former sense, is opposed to the impossible; in the latter, it is opposed to the existing; it involves, however, the condition of non-repugnance. In the former case we have possibility simply so called; in the second, pure possibility.

From these remarks we conclude that the idea of possibility adds something to that of being, that is, non-repugnance, non-exclusion; and if there be question of pure possibility, the non-existence of the possible being is likewise added.

28. When the understanding perceives being in itself, it cannot distinguish whether there is or is not repugnance; this is only discoverable by comparison; for the idea of being, in itself simple, does not include comparable terms. The idea of being can encounter no repugnance if it be not applied to some determinate thing, to an essence in which contradictory conditions are imagined, as may be verified by seeking to apply being to a circular triangle.

29. So far is the idea of being in itself from being susceptible of abstraction from the idea of existence, that it is rather the idea itself of existence. When we conceive of being, in all its abstractness, we conceive of nothing else than of existence; these two words denote one and the same idea.

30. We can, in determinate things, conceive of the essence without existence; thus also we can very easily consider all imaginable geometrical figures and examine their properties and relations, abstracted from their existence or non-existence; but the idea of being, as something absolutely indeterminate, if it be abstracted from existence, is also abstracted from itself, is annihilated.

I should be much obliged to any one who would tell me to what the idea of being in general corresponds, abstracted from existence. If, after abstracting all determination, we also abstract being itself, what remains? Some one may answer, there remains a thing which may be. What does a thing mean? In case we abstract every thing determinate, thing can only signify a being; we should have a thing which may be, and this is equivalent to a being which may be. This is very well: but when we speak of a being which may be, is there only a question of an impure possibility? then we do not abstract existence, and the conditions of the supposition are not kept. Is there question of pure possibility? then existence is denied, and the proposition is equivalent to this: a being which is not, but which involves no repugnance. Let us examine the meaning of this expression: "a being which is not." What does the subject, a being, mean? a thing, or rather, that which is. What does a thing mean? a being: then abstraction is made from every thing determinate. Therefore, either the subject of the proposition means nothing, or the proposition is absurd, since it is equivalent to this, a thing which is, which is not, but which involves no repugnance.

31. The origin of the equivocation we combat consists in applying to the idea itself of being that which belongs only to things that are something determinate, conceivable without existence. Pure being, in all its abstractness, is inconceivable without actual being, it is existence itself.

32. Nor does pure possibility mean any thing except in order to existence. What is possible being if it cannot be realized, cannot exist? The idea of being is therefore independent of the idea of possibility; and the latter is only applicable in relation to the former.

33. The idea, then, of being is the very idea of existence, of realization. If we conceive of pure being, without mixture or modification, and subsisting in itself, we conceive of the infinite, we conceive of God: but if we consider the idea of being as participated in a contingent manner, by application to finite things, we then conceive of their actuality or realization.

34. When we apply the idea of being to things, we have no intention of applying to them that of possibility, but that of reality. If we say the desk is, we affirm of the subject desk the predicate contained in the idea of being: and still we do not mean to say that the desk is possible, but that it really exists.

35. Nevertheless, the idea of being excludes that of not-being, in such a way that if the idea of being were only of the possible, it would not exclude that of not-being, since the purely possible even includes not-being; possibility, therefore, does not enter into the sole idea of being; and this idea expresses simply existence, reality.

CHAPTER V.

A DIFFICULTY SOLVED

36. What means the idea of purely possible being? If we maintain that the object of the idea of being is reality, these two ideas, being, and purely possible, would seem to be contradictory: reality is not purely possible, for were it purely possible, it would not exist, and in the non-existing there is no reality. Let us examine this difficulty, and investigate the origin of the idea of pure possibility.

37. Surrounded as we are by contingent beings, contingent beings ourselves, we are incessantly aware of the destruction of some, and the production of others, that is to say, of the transition from being to not-being, and from not-being to being. Our inward sense attests to us this transition from not-being to being; we have ourselves experienced it; all our recollections are limited to a very brief term, before which the world already existed. Thus, then, reason, experience, and inward sense show us that there are some objects which are, and then disappear, and that others, which before were not, now appear. In those things in which we witness this change, we perceive properties and relations which give occasion to a certain combination of our ideas, and this combination subsists whether the objects to which they refer continue or cease to exist. In this way we form a general idea of things which, although they do not exist, may exist; but this subject things, does not express being, but in general finite, determinate objects.

38. Here, then, is the solution of the difficulty. Purely possible being, such as we conceive it to be in the manner explained, involves no contradiction; it does not denote a reality which is not a reality, but an object, or a finite, determinate thing, the idea of which we have, although it do not exist, and whose existence involves no contradiction, or repugnance with any of the conditions contained in its idea. The expression, then, purely possible being, if it be explained in this manner, is nothing more than the generalization of these and other similar propositions. A desk which is not is possible. What do we mean by this? Simply that in the idea of desk there is nothing repugnant to its existing; and purely possible being signifies nothing more than that we have many ideas of finite things which may exist without repugnance. The expression refers to determinate things conceived of by us, but we abstract in this case whether this or that be the essence of which we speak, and comprise all those which offer no repugnance.

39. If it be objected that an infinite, non-existing being would then be a contradictory thing, we admit it without hesitation. If an infinite being do not exist it is an absurdity; and if, when we compare these two ideas, infinity and non-existence, we do not see the repugnance between them with perfect clearness, it is because we do not comprehend the nature of infinity. This is the only reason why the demonstration of the existence of God founded simply on his idea, has been and still is exposed to difficulties. But it is certain that if the infinite being did not exist, it would be impossible. For that is impossible which cannot exist; and did it not already exist it could not exist. This existence could not come from another, since the infinite cannot be a being produced; nor from itself, since it would not exist. We do, it is true, imagine the infinite in its essence, abstracted from its existence; but I repeat that this abstraction is only possible to us because we cannot well comprehend the infinite; could we comprehend it, we should see the repugnance between these terms, infinity and non-existence, with the same clearness as we see that of the triangle and circle.

CHAPTER VI.

IN WHAT SENSE THE IDEA OF BEING IS THE FORM OF THE UNDERSTANDING

40. When it is asserted that the object of the understanding is being, there is room to doubt whether it is meant that the idea of being is the general form of all conceptions, or only that all the understanding conceives is being; or, in other words, whether the quality of object is attributed to being, as being, in such a way that under this form alone objects are conceivable, or only that the quality of being belongs to all that the understanding conceives.

In the first case the proposition might be taken in a reduplicative sense, and would then be equivalent to this: "The understanding conceives nothing save inasmuch as it is being;" in the second it might be taken formally, and be equivalent to this: "whatever the understanding conceives is being."

41. We are of opinion that it cannot be said that the object of the understanding is being only inasmuch as being; in such a way as to make the idea of being the only form of the understanding's conceiving; but that this form is an essential condition to all perception.

42. If we remark that the idea of being, in itself considered, neither includes any determination or variety, nor expresses any thing more than being, in its greatest abstractness, we shall not fail clearly to perceive that this idea of being is not the only form conceived by the understanding; if, therefore, the understanding do not perceive any thing besides this idea in its objects, it cannot know their differences; nor can its perception go beyond that which is common to all, being.

43. If it be said that the differences perceived are modes of being, modifications of that which is represented in the general idea, it is at once agreed that being in itself is not the only form perceived; since both modification and mode of being add something to the idea of being. The rectangular triangle is a kind of triangle: its idea is a modification of the general idea, and no one will pretend that the idea of rectangular adds nothing to that of triangle, or that they are both the same thing. The same is verified in the idea of being and its modifications.

44. We have already seen21 that indeterminate ideas by themselves alone do not lead to positive cognitions; and certainly no idea better merits the name of indeterminate than that of being. Were our understanding limited to it, perception would be nothing but a vague conception, incapable of any combination.

45. Negation itself, as we shall hereafter see, is known to us, but this it could not be were we to admit that the understanding knows nothing save inasmuch as it is being; in which case the indispensable condition of all cognition, the principle of contradiction, would deceive us.

46. These reasons suffice to place beyond all doubt what we have proposed to show, but as this point is intimately connected with what is most transcendental in logic and metaphysics, we will endeavor to explain it more at large in the following chapter.

CHAPTER VII.

ALL SCIENCE IS FOUNDED IN THE POSTULATE OF EXISTENCE

47. We have said that the idea of being is not the sole form perceived, but that it is a form necessary to all perception. We do not mean by this to say that we cannot perceive without the actually existing; but that existence enters in some degree as a condition of every thing perceived. We will explain ourselves. When we simply perceive an object, and affirm nothing of it, it is always offered to us as a reality. Our idea certainly expresses something, but it has nothing excepting reality. Even the perception of the essential relations of things involves the condition that they exist. Thus, when we say that in the same circle or in equal circles equal arcs are subtended by equal chords, we suppose impliedly this condition, "if a circle exists."

48. Since this manner of explaining the cognition of the essential relations of things may seem far-fetched, we will endeavor to present it under the clearest possible point of view. When we affirm or deny an essential relation of two things, do we affirm or deny it of our own ideas or of the things? Clearly of the things, not of our ideas. If we say, "the ellipse is a curve," we do not say this of our idea, but of the object of our idea. We are well aware that our ideas are not ellipses, that there are none in our head, and that when we reflect, for example, upon the orbit of the earth, that this orbit is not within us. Of what, then, do we speak? Not of the idea, but of its object; not of what is in us, but of what is without us.

49. Nor do we mean that we see it thus, but that it is thus; when we say the circumference is greater than the diameter, we do not mean that we see it thus, but that it is thus. So far are we from speaking of our idea, that we should assert it to be true although we did not see it, and even although it were not to exist. We speak of our idea only when we doubt of its correspondence with the object; then we do not speak of reality, but of appearance, and in such cases our language is admirably exact, for we do not say, it is, but, it seems to us.

50. Our affirmations and negations, therefore, refer to their objects. Now, we argue thus: what does not exist is pure nothing, and nothing can either be affirmed or denied of nothing, since it has no property or relation of any kind, but is a pure negation of every thing; therefore, nothing can be affirmed or denied; there can be no combination, no comparison, no perception, except on condition of existence.

We say on condition, because we know the properties and relations of many things which do not exist; but in all that we do know of them, this condition always enters: if they exist.

51. Hence it follows that our science rests always on a postulate; and we purposely use this mathematical expression in order to show that those sciences which are called exact by antonomasy do not disdain this condition which we exact from all science. The greater part of them commence with this postulate: "Let a line be drawn, &c.," "Suppose B to be a right angle, &c.," "Take a quantity A greater than B, &c." This is the way the mathematician, with all his rigor, always supposes the condition of existence.

52. It is necessary to suppose this existence, otherwise nothing could be explained. Common sense teaches us what has escaped some metaphysicians. To prove it, let us see how a mathematician, who never dipped into metaphysics, would talk. We will suppose the interlocutor to set out to demonstrate to us that in a rectangular triangle the square of the hypothenuse is equal to the sum of the squares of the base and perpendicular; and that we, in order to exercise his intelligence, or rather to make him show us, without himself being aware of it, what is passing in his own mind with respect to the perception of its object, put various questions to him, in reality searching, although apparently asked out of ignorance. We will adopt the form of a dialogue for the sake of greater clearness, and will suppose the demonstration to be given from memory, without the aid of figures.

Demonstration. Drop a perpendicular from the right angle to the hypothenuse.

Where?

Why, in the triangle of which we speak, of course.

But, sir, if there be no such triangle —

Why then, what are we talking of?

We are talking of a rectangular triangle, and the case supposed is that there is none.

Is not, but can be. Take paper, a pencil, and ruler, and we will have one right away.

That is to say, you speak of the triangle we may make?

Yes, sir.

Ah, I understand; but then we should have it; now, we have not got it.

All in good time. But if we had drawn it, could we not drop the perpendicular?

Certainly.

That is all I meant to say.

But you were saying drop —

No doubt we cannot drop a perpendicular in a triangle unless the triangle exists, since then there is neither vertex of a right angle, hypothenuse, nor any thing else; but when I say, drop a perpendicular, I always suppose a triangle; and as it is evident that the triangle may exist, I do not express the supposition, but understand it.

I comprehend this; but then we should drop the perpendicular only in this triangle, but you spoke as if we might drop it in all triangles.

I only took this triangle for an example; we can clearly do with all others what we can do with this one.

With all?

Certainly. Can you not see how, in every rectangular triangle, a perpendicular may be drawn from the right angle to the hypothenuse?

Yes, in your figure; but since what is in my head is not a triangle, for I imagine some with sides a thousand miles long, and there is not in my head room enough —