The Critique of Pure Reason Part 22

But if any one could free himself entirely from all considerations of interest, and weigh without partiality the a.s.sertions of reason, attending only to their content, irrespective of the consequences which follow from them; such a person, on the supposition that he knew no other way out of the confusion than to settle the truth of one or other of the conflicting doctrines, would live in a state of continual hesitation. Today, he would feel convinced that the human will is free; to-morrow, considering the indissoluble chain of nature, he would look on freedom as a mere illusion and declare nature to be all-in-all. But, if he were called to action, the play of the merely speculative reason would disappear like the shapes of a dream, and practical interest would dictate his choice of principles. But, as it well befits a reflective and inquiring being to devote certain periods of time to the examination of its own reason--to divest itself of all partiality, and frankly to communicate its observations for the judgement and opinion of others; so no one can be blamed for, much less prevented from, placing both parties on their trial, with permission to end themselves, free from intimidation, before intimidation, before a sworn jury of equal condition with themselves--the condition of weak and fallible men.

SECTION IV. Of the necessity imposed upon Pure Reason of presenting a Solution of its Transcendental Problems.

To avow an ability to solve all problems and to answer all questions would be a profession certain to convict any philosopher of extravagant boasting and self-conceit, and at once to destroy the confidence that might otherwise have been reposed in him. There are, however, sciences so const.i.tuted that every question arising within their sphere must necessarily be capable of receiving an answer from the knowledge already possessed, for the answer must be received from the same sources whence the question arose. In such sciences it is not allowable to excuse ourselves on the plea of necessary and unavoidable ignorance; a solution is absolutely requisite. The rule of right and wrong must help us to the knowledge of what is right or wrong in all possible cases; otherwise, the idea of obligation or duty would be utterly null, for we cannot have any obligation to that which we cannot know. On the other hand, in our investigations of the phenomena of nature, much must remain uncertain, and many questions continue insoluble; because what we know of nature is far from being sufficient to explain all the phenomena that are presented to our observation. Now the question is: Whether there is in transcendental philosophy any question, relating to an object presented to pure reason, which is unanswerable by this reason; and whether we must regard the subject of the question as quite uncertain, so far as our knowledge extends, and must give it a place among those subjects, of which we have just so much conception as is sufficient to enable us to raise a question--faculty or materials failing us, however, when we attempt an answer.

Now I maintain that, among all speculative cognition, the peculiarity of transcendental philosophy is that there is no question, relating to an object presented to pure reason, which is insoluble by this reason; and that the profession of unavoidable ignorance--the problem being alleged to be beyond the reach of our faculties--cannot free us from the obligation to present a complete and satisfactory answer. For the very conception which enables us to raise the question must give us the power of answering it; inasmuch as the object, as in the case of right and wrong, is not to be discovered out of the conception.

But, in transcendental philosophy, it is only the cosmological questions to which we can demand a satisfactory answer in relation to the const.i.tution of their object; and the philosopher is not permitted to avail himself of the pretext of necessary ignorance and impenetrable obscurity. These questions relate solely to the cosmological ideas. For the object must be given in experience, and the question relates to the adequateness of the object to an idea. If the object is transcendental and therefore itself unknown; if the question, for example, is whether the object--the something, the phenomenon of which (internal--in ourselves) is thought--that is to say, the soul, is in itself a simple being; or whether there is a cause of all things, which is absolutely necessary--in such cases we are seeking for our idea an object, of which we may confess that it is unknown to us, though we must not on that account a.s.sert that it is impossible.* The cosmological ideas alone posses the peculiarity that we can presuppose the object of them and the empirical synthesis requisite for the conception of that object to be given; and the question, which arises from these ideas, relates merely to the progress of this synthesis, in so far as it must contain absolute totality--which, however, is not empirical, as it cannot be given in any experience. Now, as the question here is solely in regard to a thing as the object of a possible experience and not as a thing in itself, the answer to the transcendental cosmological question need not be sought out of the idea, for the question does not regard an object in itself.

The question in relation to a possible experience is not, "What can be given in an experience in concreto" but "what is contained in the idea, to which the empirical synthesis must approximate." The question must therefore be capable of solution from the idea alone. For the idea is a creation of reason itself, which therefore cannot disclaim the obligation to answer or refer us to the unknown object.

[*Footnote: The question, "What is the const.i.tution of a transcendental object?" is unanswerable--we are unable to say what it is; but we can perceive that the question itself is nothing; because it does not relate to any object that can be presented to us. For this reason, we must consider all the questions raised in transcendental psychology as answerable and as really answered; for they relate to the transcendental subject of all internal phenomena, which is not itself phenomenon and consequently not given as an object, in which, moreover, none of the categories--and it is to them that the question is properly directed--find any conditions of its application. Here, therefore, is a case where no answer is the only proper answer. For a question regarding the const.i.tution of a something which cannot be cogitated by any determined predicate, being completely beyond the sphere of objects and experience, is perfectly null and void.]

It is not so extraordinary, as it at first sight appears, that a science should demand and expect satisfactory answers to all the questions that may arise within its own sphere (questiones domesticae), although, up to a certain time, these answers may not have been discovered. There are, in addition to transcendental philosophy, only two pure sciences of reason; the one with a speculative, the other with a practical content--pure mathematics and pure ethics. Has any one ever heard it alleged that, from our complete and necessary ignorance of the conditions, it is uncertain what exact relation the diameter of a circle bears to the circle in rational or irrational numbers? By the former the sum cannot be given exactly, by the latter only approximately; and therefore we decide that the impossibility of a solution of the question is evident. Lambert presented us with a demonstration of this. In the general principles of morals there can be nothing uncertain, for the propositions are either utterly without meaning, or must originate solely in our rational conceptions. On the other hand, there must be in physical science an infinite number of conjectures, which can never become certainties; because the phenomena of nature are not given as objects dependent on our conceptions. The key to the solution of such questions cannot, therefore, be found in our conceptions, or in pure thought, but must lie without us and for that reason is in many cases not to be discovered; and consequently a satisfactory explanation cannot be expected. The questions of transcendental a.n.a.lytic, which relate to the deduction of our pure cognition, are not to be regarded as of the same kind as those mentioned above; for we are not at present treating of the certainty of judgements in relation to the origin of our conceptions, but only of that certainty in relation to objects.

We cannot, therefore, escape the responsibility of at least a critical solution of the questions of reason, by complaints of the limited nature of our faculties, and the seemingly humble confession that it is beyond the power of our reason to decide, whether the world has existed from all eternity or had a beginning--whether it is infinitely extended, or enclosed within certain limits--whether anything in the world is simple, or whether everything must be capable of infinite divisibility--whether freedom can originate phenomena, or whether everything is absolutely dependent on the laws and order of nature--and, finally, whether there exists a being that is completely unconditioned and necessary, or whether the existence of everything is conditioned and consequently dependent on something external to itself, and therefore in its own nature contingent. For all these questions relate to an object, which can be given nowhere else than in thought. This object is the absolutely unconditioned totality of the synthesis of phenomena. If the conceptions in our minds do not a.s.sist us to some certain result in regard to these problems, we must not defend ourselves on the plea that the object itself remains hidden from and unknown to us. For no such thing or object can be given--it is not to be found out of the idea in our minds.

We must seek the cause of our failure in our idea itself, which is an insoluble problem and in regard to which we obstinately a.s.sume that there exists a real object corresponding and adequate to it. A clear explanation of the dialectic which lies in our conception, will very soon enable us to come to a satisfactory decision in regard to such a question.

The pretext that we are unable to arrive at certainty in regard to these problems may be met with this question, which requires at least a plain answer: "From what source do the ideas originate, the solution of which involves you in such difficulties? Are you seeking for an explanation of certain phenomena; and do you expect these ideas to give you the principles or the rules of this explanation?" Let it be granted, that all nature was laid open before you; that nothing was hid from your senses and your consciousness. Still, you could not cognize in concreto the object of your ideas in any experience. For what is demanded is not only this full and complete intuition, but also a complete synthesis and the consciousness of its absolute totality; and this is not possible by means of any empirical cognition. It follows that your question--your idea--is by no means necessary for the explanation of any phenomenon; and the idea cannot have been in any sense given by the object itself.

For such an object can never be presented to us, because it cannot be given by any possible experience. Whatever perceptions you may attain to, you are still surrounded by conditions--in s.p.a.ce, or in time--and you cannot discover anything unconditioned; nor can you decide whether this unconditioned is to be placed in an absolute beginning of the synthesis, or in an absolute totality of the series without beginning.

A whole, in the empirical signification of the term, is always merely comparative. The absolute whole of quant.i.ty (the universe), of division, of derivation, of the condition of existence, with the question--whether it is to be produced by finite or infinite synthesis, no possible experience can instruct us concerning. You will not, for example, be able to explain the phenomena of a body in the least degree better, whether you believe it to consist of simple, or of composite parts; for a simple phenomenon--and just as little an infinite series of composition--can never be presented to your perception. Phenomena require and admit of explanation, only in so far as the conditions of that explanation are given in perception; but the sum total of that which is given in phenomena, considered as an absolute whole, is itself a perception--and we cannot therefore seek for explanations of this whole beyond itself, in other perceptions. The explanation of this whole is the proper object of the transcendental problems of pure reason.

Although, therefore, the solution of these problems is unattainable through experience, we must not permit ourselves to say that it is uncertain how the object of our inquiries is const.i.tuted. For the object is in our own mind and cannot be discovered in experience; and we have only to take care that our thoughts are consistent with each other, and to avoid falling into the amphiboly of regarding our idea as a representation of an object empirically given, and therefore to be cognized according to the laws of experience. A dogmatical solution is therefore not only unsatisfactory but impossible. The critical solution, which may be a perfectly certain one, does not consider the question objectively, but proceeds by inquiring into the basis of the cognition upon which the question rests.

SECTION V. Sceptical Exposition of the Cosmological Problems presented in the four Transcendental Ideas.

We should be quite willing to desist from the demand of a dogmatical answer to our questions, if we understood beforehand that, be the answer what it may, it would only serve to increase our ignorance, to throw us from one incomprehensibility into another, from one obscurity into another still greater, and perhaps lead us into irreconcilable contradictions. If a dogmatical affirmative or negative answer is demanded, is it at all prudent to set aside the probable grounds of a solution which lie before us and to take into consideration what advantage we shall gain, if the answer is to favour the one side or the other? If it happens that in both cases the answer is mere nonsense, we have in this an irresistible summons to inst.i.tute a critical investigation of the question, for the purpose of discovering whether it is based on a groundless presupposition and relates to an idea, the falsity of which would be more easily exposed in its application and consequences than in the mere representation of its content. This is the great utility of the sceptical mode of treating the questions addressed by pure reason to itself. By this method we easily rid ourselves of the confusions of dogmatism, and establish in its place a temperate criticism, which, as a genuine cathartic, will successfully remove the presumptuous notions of philosophy and their consequence--the vain pretension to universal science.

If, then, I could understand the nature of a cosmological idea and perceive, before I entered on the discussion of the subject at all, that, whatever side of the question regarding the unconditioned of the regressive synthesis of phenomena it favoured--it must either be too great or too small for every conception of the understanding--I would be able to comprehend how the idea, which relates to an object of experience--an experience which must be adequate to and in accordance with a possible conception of the understanding--must be completely void and without significance, inasmuch as its object is inadequate, consider it as we may. And this is actually the case with all cosmological conceptions, which, for the reason above mentioned, involve reason, so long as it remains attached to them, in an unavoidable antinomy. For suppose:

First, that the world has no beginning--in this case it is too large for our conception; for this conception, which consists in a successive regress, cannot overtake the whole eternity that has elapsed. Grant that it has a beginning, it is then too small for the conception of the understanding. For, as a beginning presupposes a time preceding, it cannot be unconditioned; and the law of the empirical employment of the understanding imposes the necessity of looking for a higher condition of time; and the world is, therefore, evidently too small for this law.

The same is the case with the double answer to the question regarding the extent, in s.p.a.ce, of the world. For, if it is infinite and unlimited, it must be too large for every possible empirical conception.

If it is finite and limited, we have a right to ask: "What determines these limits?" Void s.p.a.ce is not a self-subsistent correlate of things, and cannot be a final condition--and still less an empirical condition, forming a part of a possible experience. For how can we have any experience or perception of an absolute void? But the absolute totality of the empirical synthesis requires that the unconditioned be an empirical conception. Consequently, a finite world is too small for our conception.

Secondly, if every phenomenon (matter) in s.p.a.ce consists of an infinite number of parts, the regress of the division is always too great for our conception; and if the division of s.p.a.ce must cease with some member of the division (the simple), it is too small for the idea of the unconditioned. For the member at which we have discontinued our division still admits a regress to many more parts contained in the object.

Thirdly, suppose that every event in the world happens in accordance with the laws of nature; the causality of a cause must itself be an event and necessitates a regress to a still higher cause, and consequently the unceasing prolongation of the series of conditions a parte priori. Operative nature is therefore too large for every conception we can form in the synthesis of cosmical events.

If we admit the existence of spontaneously produced events, that is, of free agency, we are driven, in our search for sufficient reasons, on an unavoidable law of nature and are compelled to appeal to the empirical law of causality, and we find that any such totality of connection in our synthesis is too small for our necessary empirical conception.

Fourthly, if we a.s.sume the existence of an absolutely necessary being--whether it be the world or something in the world, or the cause of the world--we must place it in a time at an infinite distance from any given moment; for, otherwise, it must be dependent on some other and higher existence. Such an existence is, in this case, too large for our empirical conception, and unattainable by the continued regress of any synthesis.

But if we believe that everything in the world--be it condition or conditioned--is contingent; every given existence is too small for our conception. For in this case we are compelled to seek for some other existence upon which the former depends.

We have said that in all these cases the cosmological idea is either too great or too small for the empirical regress in a synthesis, and consequently for every possible conception of the understanding. Why did we not express ourselves in a manner exactly the reverse of this and, instead of accusing the cosmological idea of over stepping or of falling short of its true aim, possible experience, say that, in the first case, the empirical conception is always too small for the idea, and in the second too great, and thus attach the blame of these contradictions to the empirical regress? The reason is this. Possible experience can alone give reality to our conceptions; without it a conception is merely an idea, without truth or relation to an object. Hence a possible empirical conception must be the standard by which we are to judge whether an idea is anything more than an idea and fiction of thought, or whether it relates to an object in the world. If we say of a thing that in relation to some other thing it is too large or too small, the former is considered as existing for the sake of the latter, and requiring to be adapted to it. Among the trivial subjects of discussion in the old schools of dialectics was this question: "If a ball cannot pa.s.s through a hole, shall we say that the ball is too large or the hole too small?"

In this case it is indifferent what expression we employ; for we do not know which exists for the sake of the other. On the other hand, we cannot say: "The man is too long for his coat"; but: "The coat is too short for the man."

We are thus led to the well-founded suspicion that the cosmological ideas, and all the conflicting sophistical a.s.sertions connected with them, are based upon a false and fict.i.tious conception of the mode in which the object of these ideas is presented to us; and this suspicion will probably direct us how to expose the illusion that has so long led us astray from the truth.

SECTION VI. Transcendental Idealism as the Key to theSolution of Pure Cosmological Dialectic.

In the transcendental aesthetic we proved that everything intuited in s.p.a.ce and time, all objects of a possible experience, are nothing but phenomena, that is, mere representations; and that these, as presented to us--as extended bodies, or as series of changes--have no self-subsistent existence apart from human thought. This doctrine I call Transcendental Idealism.* The realist in the transcendental sense regards these modifications of our sensibility, these mere representations, as things subsisting in themselves.

[*Footnote: I have elsewhere termed this theory formal idealism, to distinguish it from material idealism, which doubts or denies the existence of external things. To avoid ambiguity, it seems advisable in many cases to employ this term instead of that mentioned in the text.]

It would be unjust to accuse us of holding the long-decried theory of empirical idealism, which, while admitting the reality of s.p.a.ce, denies, or at least doubts, the existence of bodies extended in it, and thus leaves us without a sufficient criterion of reality and illusion. The supporters of this theory find no difficulty in admitting the reality of the phenomena of the internal sense in time; nay, they go the length of maintaining that this internal experience is of itself a sufficient proof of the real existence of its object as a thing in itself.

Transcendental idealism allows that the objects of external intuition--as intuited in s.p.a.ce, and all changes in time--as represented by the internal sense, are real. For, as s.p.a.ce is the form of that intuition which we call external, and, without objects in s.p.a.ce, no empirical representation could be given us, we can and ought to regard extended bodies in it as real. The case is the same with representations in time. But time and s.p.a.ce, with all phenomena therein, are not in themselves things. They are nothing but representations and cannot exist out of and apart from the mind. Nay, the sensuous internal intuition of the mind (as the object of consciousness), the determination of which is represented by the succession of different states in time, is not the real, proper self, as it exists in itself--not the transcendental subject--but only a phenomenon, which is presented to the sensibility of this, to us, unknown being. This internal phenomenon cannot be admitted to be a self-subsisting thing; for its condition is time, and time cannot be the condition of a thing in itself. But the empirical truth of phenomena in s.p.a.ce and time is guaranteed beyond the possibility of doubt, and sufficiently distinguished from the illusion of dreams or fancy--although both have a proper and thorough connection in an experience according to empirical laws. The objects of experience then are not things in themselves, but are given only in experience, and have no existence apart from and independently of experience. That there may be inhabitants in the moon, although no one has ever observed them, must certainly be admitted; but this a.s.sertion means only, that we may in the possible progress of experience discover them at some future time. For that which stands in connection with a perception according to the laws of the progress of experience is real. They are therefore really existent, if they stand in empirical connection with my actual or real consciousness, although they are not in themselves real, that is, apart from the progress of experience.

There is nothing actually given--we can be conscious of nothing as real, except a perception and the empirical progression from it to other possible perceptions. For phenomena, as mere representations, are real only in perception; and perception is, in fact, nothing but the reality of an empirical representation, that is, a phenomenon. To call a phenomenon a real thing prior to perception means either that we must meet with this phenomenon in the progress of experience, or it means nothing at all. For I can say only of a thing in itself that it exists without relation to the senses and experience. But we are speaking here merely of phenomena in s.p.a.ce and time, both of which are determinations of sensibility, and not of things in themselves. It follows that phenomena are not things in themselves, but are mere representations, which if not given in us--in perception--are non-existent.

The faculty of sensuous intuition is properly a receptivity--a capacity of being affected in a certain manner by representations, the relation of which to each other is a pure intuition of s.p.a.ce and time--the pure forms of sensibility. These representations, in so far as they are connected and determinable in this relation (in s.p.a.ce and time) according to laws of the unity of experience, are called objects. The non-sensuous cause of these representations is completely unknown to us and hence cannot be intuited as an object. For such an object could not be represented either in s.p.a.ce or in time; and without these conditions intuition or representation is impossible. We may, at the same time, term the non-sensuous cause of phenomena the transcendental object--but merely as a mental correlate to sensibility, considered as a receptivity. To this transcendental object we may attribute the whole connection and extent of our possible perceptions, and say that it is given and exists in itself prior to all experience. But the phenomena, corresponding to it, are not given as things in themselves, but in experience alone. For they are mere representations, receiving from perceptions alone significance and relation to a real object, under the condition that this or that perception--indicating an object--is in complete connection with all others in accordance with the rules of the unity of experience. Thus we can say: "The things that really existed in past time are given in the transcendental object of experience." But these are to me real objects, only in so far as I can represent to my own mind, that a regressive series of possible perceptions--following the indications of history, or the footsteps of cause and effect--in accordance with empirical laws--that, in one word, the course of the world conducts us to an elapsed series of time as the condition of the present time. This series in past time is represented as real, not in itself, but only in connection with a possible experience. Thus, when I say that certain events occurred in past time, I merely a.s.sert the possibility of prolonging the chain of experience, from the present perception, upwards to the conditions that determine it according to time.

If I represent to myself all objects existing in all s.p.a.ce and time, I do not thereby place these in s.p.a.ce and time prior to all experience; on the contrary, such a representation is nothing more than the notion of a possible experience, in its absolute completeness. In experience alone are those objects, which are nothing but representations, given. But, when I say they existed prior to my experience, this means only that I must begin with the perception present to me and follow the track indicated until I discover them in some part or region of experience.

The cause of the empirical condition of this progression--and consequently at what member therein I must stop, and at what point in the regress I am to find this member--is transcendental, and hence necessarily incognizable. But with this we have not to do; our concern is only with the law of progression in experience, in which objects, that is, phenomena, are given. It is a matter of indifference, whether I say, "I may in the progress of experience discover stars, at a hundred times greater distance than the most distant of those now visible," or, "Stars at this distance may be met in s.p.a.ce, although no one has, or ever will discover them." For, if they are given as things in themselves, without any relation to possible experience, they are for me non-existent, consequently, are not objects, for they are not contained in the regressive series of experience. But, if these phenomena must be employed in the construction or support of the cosmological idea of an absolute whole, and when we are discussing a question that oversteps the limits of possible experience, the proper distinction of the different theories of the reality of sensuous objects is of great importance, in order to avoid the illusion which must necessarily arise from the misinterpretation of our empirical conceptions.

SECTION VII. Critical Solution of the Cosmological Problem.

The antinomy of pure reason is based upon the following dialectical argument: "If that which is conditioned is given, the whole series of its conditions is also given; but sensuous objects are given as conditioned; consequently..." This syllogism, the major of which seems so natural and evident, introduces as many cosmological ideas as there are different kinds of conditions in the synthesis of phenomena, in so far as these conditions const.i.tute a series. These ideas require absolute totality in the series, and thus place reason in inextricable embarra.s.sment. Before proceeding to expose the fallacy in this dialectical argument, it will be necessary to have a correct understanding of certain conceptions that appear in it.

In the first place, the following proposition is evident, and indubitably certain: "If the conditioned is given, a regress in the series of all its conditions is thereby imperatively required." For the very conception of a conditioned is a conception of something related to a condition, and, if this condition is itself conditioned, to another condition--and so on through all the members of the series.

This proposition is, therefore, a.n.a.lytical and has nothing to fear from transcendental criticism. It is a logical postulate of reason: to pursue, as far as possible, the connection of a conception with its conditions.

If, in the second place, both the conditioned and the condition are things in themselves, and if the former is given, not only is the regress to the latter requisite, but the latter is really given with the former. Now, as this is true of all the members of the series, the entire series of conditions, and with them the unconditioned, is at the same time given in the very fact of the conditioned, the existence of which is possible only in and through that series, being given. In this case, the synthesis of the conditioned with its condition, is a synthesis of the understanding merely, which represents things as they are, without regarding whether and how we can cognize them. But if I have to do with phenomena, which, in their character of mere representations, are not given, if I do not attain to a cognition of them (in other words, to themselves, for they are nothing more than empirical cognitions), I am not ent.i.tled to say: "If the conditioned is given, all its conditions (as phenomena) are also given." I cannot, therefore, from the fact of a conditioned being given, infer the absolute totality of the series of its conditions. For phenomena are nothing but an empirical synthesis in apprehension or perception, and are therefore given only in it. Now, in speaking of phenomena it does not follow that, if the conditioned is given, the synthesis which const.i.tutes its empirical condition is also thereby given and presupposed; such a synthesis can be established only by an actual regress in the series of conditions. But we are ent.i.tled to say in this case that a regress to the conditions of a conditioned, in other words, that a continuous empirical synthesis is enjoined; that, if the conditions are not given, they are at least required; and that we are certain to discover the conditions in this regress.

We can now see that the major, in the above cosmological syllogism, takes the conditioned in the transcendental signification which it has in the pure category, while the minor speaks of it in the empirical signification which it has in the category as applied to phenomena.

There is, therefore, a dialectical fallacy in the syllogism--a sophisma figurae dictionis. But this fallacy is not a consciously devised one, but a perfectly natural illusion of the common reason of man. For, when a thing is given as conditioned, we presuppose in the major its conditions and their series, unperceived, as it were, and unseen; because this is nothing more than the logical requirement of complete and satisfactory premisses for a given conclusion. In this case, time is altogether left out in the connection of the conditioned with the condition; they are supposed to be given in themselves, and contemporaneously. It is, moreover, just as natural to regard phenomena (in the minor) as things in themselves and as objects presented to the pure understanding, as in the major, in which complete abstraction was made of all conditions of intuition. But it is under these conditions alone that objects are given. Now we overlooked a remarkable distinction between the conceptions. The synthesis of the conditioned with its condition, and the complete series of the latter (in the major) are not limited by time, and do not contain the conception of succession. On the contrary, the empirical synthesis and the series of conditions in the phenomenal world--subsumed in the minor--are necessarily successive and given in time alone. It follows that I cannot presuppose in the minor, as I did in the major, the absolute totality of the synthesis and of the series therein represented; for in the major all the members of the series are given as things in themselves--without any limitations or conditions of time, while in the minor they are possible only in and through a successive regress, which cannot exist, except it be actually carried into execution in the world of phenomena.

After this proof of the viciousness of the argument commonly employed in maintaining cosmological a.s.sertions, both parties may now be justly dismissed, as advancing claims without grounds or t.i.tle. But the process has not been ended by convincing them that one or both were in the wrong and had maintained an a.s.sertion which was without valid grounds of proof. Nothing seems to be clearer than that, if one maintains: "The world has a beginning," and another: "The world has no beginning," one of the two must be right. But it is likewise clear that, if the evidence on both sides is equal, it is impossible to discover on what side the truth lies; and the controversy continues, although the parties have been recommended to peace before the tribunal of reason. There remains, then, no other means of settling the question than to convince the parties, who refute each other with such conclusiveness and ability, that they are disputing about nothing, and that a transcendental illusion has been mocking them with visions of reality where there is none. The mode of adjusting a dispute which cannot be decided upon its own merits, we shall now proceed to lay before our readers.

Zeno of Elea, a subtle dialectician, was severely reprimanded by Plato as a sophist, who, merely from the base motive of exhibiting his skill in discussion, maintained and subverted the same proposition by arguments as powerful and convincing on the one side as on the other. He maintained, for example, that G.o.d (who was probably nothing more, in his view, than the world) is neither finite nor infinite, neither in motion nor in rest, neither similar nor dissimilar to any other thing. It seemed to those philosophers who criticized his mode of discussion that his purpose was to deny completely both of two self-contradictory propositions--which is absurd. But I cannot believe that there is any justice in this accusation. The first of these propositions I shall presently consider in a more detailed manner. With regard to the others, if by the word of G.o.d he understood merely the Universe, his meaning must have been--that it cannot be permanently present in one place--that is, at rest--nor be capable of changing its place--that is, of moving--because all places are in the universe, and the universe itself is, therefore, in no place. Again, if the universe contains in itself everything that exists, it cannot be similar or dissimilar to any other thing, because there is, in fact, no other thing with which it can be compared. If two opposite judgements presuppose a contingent impossible, or arbitrary condition, both--in spite of their opposition (which is, however, not properly or really a contradiction)--fall away; because the condition, which ensured the validity of both, has itself disappeared.

If we say: "Everybody has either a good or a bad smell," we have omitted a third possible judgement--it has no smell at all; and thus both conflicting statements may be false. If we say: "It is either good-smelling or not good-smelling (vel suaveolens vel non-suaveolens),"

both judgements are contradictorily opposed; and the contradictory opposite of the former judgement--some bodies are not good-smelling--embraces also those bodies which have no smell at all. In the preceding pair of opposed judgements (per disparata), the contingent condition of the conception of body (smell) attached to both conflicting statements, instead of having been omitted in the latter, which is consequently not the contradictory opposite of the former.

If, accordingly, we say: "The world is either infinite in extension, or it is not infinite (non est infinitus)"; and if the former proposition is false, its contradictory opposite--the world is not infinite--must be true. And thus I should deny the existence of an infinite, without, however affirming the existence of a finite world. But if we construct our proposition thus: "The world is either infinite or finite (non-infinite)," both statements may be false. For, in this case, we consider the world as per se determined in regard to quant.i.ty, and while, in the one judgement, we deny its infinite and consequently, perhaps, its independent existence; in the other, we append to the world, regarded as a thing in itself, a certain determination--that of finitude; and the latter may be false as well as the former, if the world is not given as a thing in itself, and thus neither as finite nor as infinite in quant.i.ty. This kind of opposition I may be allowed to term dialectical; that of contradictories may be called a.n.a.lytical opposition. Thus then, of two dialectically opposed judgements both may be false, from the fact, that the one is not a mere contradictory of the other, but actually enounces more than is requisite for a full and complete contradiction.