The philosophy of the infinite; with special reference to the theories of Sir William Hamilton and M. Cousin

Preface

The work now presented to the public is intended as an illustration and defence of the proposition, that man has a positive conception of the Infinite. It is an attempt, by a careful analysis of consciousness, to prove that man does possess a notion of an Infinite Being, and, since such is the case, to ascertain the peculiar nature of the conception, and the particular relations in which it is found to arise. The discussion, therefore, belongs essentially to the sphere of the higher Metaphysics, and involves a course of speculation on many points not generally agitated by our Scotch philosophers, and even on some which have not hitherto, so far as I am aware, been contemplated in the philosophy of this country.

However great is the fondness for truth, and however strong the desire for its attainment, it is felt as an unfortunate characteristic of all our researches, that we have to advance to the determination of positive truth, in the midst of the conflict of contending opinions. This I have found to be painfully the case in the present instance. As I have prosecuted the argument in defence of what I firmly believe to be truth, I have found it necessary to differ from Sir William Hamilton to a degree which is

VI PREFACE.

painful to one who has been indebted to the instructions of that distinguished philosopher. I feel for Sir W. Hamilton a degree of esteem and respect .which can be thoroughly appreciated only by those who have listened to his prelections. Notwithstanding this, however, I have endeavoured to pursue my investigations concerning the Philosophy of the Infinite, with that love of mental science, and that independence of thought, which have been imbibed under his influence, and which it is his peculiar honour to cultivate. And, although I have come to results differing widely from those of Sir W. Hamilton, I know too much of the spirit of his philosophy to imagine that he will regard it as unbecoming or disrespectful.

I have not the presumption to suppose that I have completely examined, and unerringly determined, all the points involved in a question so difiicult and mysterious. My end has been gained, if I have made some contribution to the Philosophy of the Infinite, and have started speculations which may lead to the closer investigation of a theme so important and so grand.

H. C.

Edineuegh, September 1854.

Contents

PAOB

CHAPTER II. Examination of Sir William Hamilton's distinction of the Infinite

and Absolute, 16

CHAPTER in.

Examination of Sir AVilliam Hamilton's doctrine of a Negative Notion

of the Infinite 39

Note A. — ^Negative Thinking. Sir William Hamilton's Second

Edition of the " Discussions,'' 63

Chapter I. Statement Op The Question

In the midst of the various eflforts of the human intellect, the question is an interesting one, — what are the limits of our powers of thought 1 We make our observations in reference to the various phenomena presented in the external world, and in the world of thought. We speculate upon the many relations which present themselves around and within us, and we seek to discover what are the laws by which all things are regulated. Field after field of observation opens before us ; and the objects of our thought enlarge and increase, till the mind is startled by their magnitude. Still, these objects have their boundaries. Every thing before us is subject to conditions ; every visible object exists in certain relations. The same is true of the mind. Starting from a point, the circle of observation may go on enlarging; with vigorous effort the mind may endeavour

A to embrace the expanding objects of thought ; but still it is conscious of limits. Yet, its knowledge and belief rise above the things of matter. As it looks upon a finite world, and recognises that its own powers are limited, it is also conscious of the belief in an Infinite Being, who is subject to no restrictive conditions, but is all perfect in Himself.

Man exists in relation with the Infinite. The fact of his existence, and the end of his being, can be explained only on this admission. The union is indissoluble, and man -cannot sever it, even though he would. Limited though he be, he exists in relation with the unlimited ; nor can he, by any effort of the mind, conceive himself restricted to a relation with the merely finite. The Infinite is a prominent object in thought and feeling ; a-nd its recognition has exercised a powerful influence throughout the entire history of the race.

What, then, is our knowledge of the Infinite, and what can we know of the Infinite God 1 This is the question upon the consideration of which we propose now to enter. It is the highest inquiry to which the mind can aspire. The question is intensely interesting, but, at the same time, it is confessedly the most difficult within the range of philosophical investigation, whether its purpose be to determine the precise limits by which the mind is regulated, or to discover what knowledge of the Infinite is competent to man, if, indeed, such a knowledge be at all possible. In

STATEMENT OF THE QUESTION. 3

advancing to such a consideration, we rise above the limits of this earthly scene ; we seek to obtain a notion of the mysterious Infinite ; our thoughts venture to approach the presence of that Being, who regulates all things, yet is Himself unrestricted ; and, we endeavour to obtain some knowledge of that God, who, as Infinite, can never be completely known. The diflSculties of the attempt are striking. The mind must be on the stretch ; the question is shrouded in mystery; and yet, possessing, as we consider, a necessary belief in the existence of an Infinite God, the question is a fair one, — what is our notion of that Being in whose existence we must believe ?

On the vpry threshold of our inquiry, we are met by such questions as these : — Can we have any notion of Infinite extension in space 1 Can we have any notion of Infinite duration in time 1 Can we have any knowledge of a God, Infinite in all his attributes 1

In endeavouring to answer such questions, it may seem that the decision of the judgment is at variance from the deliverance of consciousness ; that there is a want of harmony between the logical and psychological. If the question were presented, — have we any notion of the Infinite, or, still more, leaving the abstract and adopting the personal, have we any notion of an Infinite Deity 1 — the immediate deliverance of our consciousness would be, that we have a positive notion of the Infinite, and that it is not a mere negative notion ; that our notion of the Deity is not a mere negation of a finite creation, but something positive. If, however, on the other hand, the question be presented for determination by the judgment, — can the finite embrace the Infinite ■? the answer would as readily come forth that the thing is impossible. On the one hand, we would be ready to answer, that we have a positive conception of the Infinite Being ; and, on the other, we would as readily reply, that the Infinite cannot be embraced by the finite. In a psychological point of view, we might answer the question in the affirmative ; in a logical point of view, we might answer in the negative. Is there, then, any discrepancy in these decisions 1 Or, are these different results obtained by viewing the question in different aspects ? Is there a common stand-point from which both may be seen to harmonise 1 When we examine consciousness, do we find that we have a notion of the Infinite, though not a distinct conception, such as is obtained by embracing an object 1 And when we view it in a logical aspect, do we find that our decision only involves the conclusion, that we cannot embrace the Infinite in all its extent 1 If so, then the two positions are perfectly compatible.

We have not, however, raised these points for the purpose of giving them immediate attention, but simply with the view of bringing the subject more clearly before the mind of the reader, and revealing

STATEMENT OF THE QUESTION. 5

some of the points which will require careful consideration. The question is viewed in an aspect purely philosophical, and its determination must be based upon the deliverance of consciousness, and be in accordance with the conditions which regulate human thought.

The speculations of philosophers on this question have been various, and strongly conflicting. Some have asserted that a knowledge of the Infinite is possible, while others have resolutely maintained that it is entirely beyond the reach of human thought. Those who have admitted to man a knowledge of the Infinite, have adopted very different theories to account for its origin. Sir William Hamilton has given "a statement of the opinions which may be entertained regarding the Unconditioned, as an immediate object of knowledge and of thought," which we shall here quote, as presenting the matter with all the precision for which that philosopher is so distinguished.* He says : — " These opinions may be reduced to four, — \st. The Unconditioned is incognisable and inconceivable; its notion being only negative of the conditioned, which last can alone be positively known or conceived, ^d. It is not an object of knowledge ; but its notion, as a regulative

* For the sake of any reader who may be unacquainted witli tliu nomenclature of the question under discussion, we may remark that the terms Infinite, Absolute, and Unconditioned, are synonymous, and are used to designate what is subject to no conditions, limits, or restrictions. The terms will be fully discussed in the next Chapter, and Sir William lluniilton's definition of them considered.

principle of the mind itself, is more than a mere negation of the conditioned. 3d, It is cognisable, but not conceivable ; it can be known by a sinking back into identity with the Absolute, but it is incomprehensible by consciousness and reflection, which are only of the relative and the different. Ath, It is cognisable and conceivable by consciousness and reflediion, under relation, difference, and plurality."*

The^rst is the opinion maintained by Sir William Hamilton himself; the second is that adopted by Kant ; the third is the doctrine of Schelling ; and the fourth is that of M. Cousin.

The opinions of Sir William Hamilton and M, Cousin are those which are received at the present day, and divide philosophers generally. We intend, therefore, in the prosecution of our argument, to compare our ground especially with that maintained by these two philosophers. In the meantime, we shall make a few remarks on the other two theories, which have been more generally set aside.

Kant attributes to man the power of reason in two different relations ; the one is speculative reason, the other practical reason, and the results of both are combined by judgment. Speculative reason is conversantwith what man can know; practical reason, with what man ought to do. According to Kant, speculative reason does not give to man a knowledge of the Infinite God, but, on the contrary, expressly involves

* Sir 'WiUiam Hamilton's IHecussions on Philosophy, p. 12.

STATEMENT OF THE QUESTION. V

the impossibility of such knowledge. On the other hand, he asserts that practieal reason gives to man the recognition of God, and that as a necessary postulate for proper moral action. Reason, therefore, according to Kant, both denies to man the possibility of any knowledge of God, and, at the same time, affords to him a knowledge of God, as necessary to constitute him a moral being. The theory thus manifestly destroys itself, and in its nature tends to the destruction both of philosophy and religion. To make the statements of reason contradictory, is to prove it deceitful in a certain aspect, and, consequently, is to overturn the basis upon which a sound philosophy rests. To admit that reason is contradictory, and, therefore, deceitful, is to assert that God has given us a power which deceives us, and, consequently, is to shake the confidence of that faith in God, which is the foundation of true religion. We, therefore, set aside the doctrine of Kant as inconsistent with itself, and consequently untenable.

The doctrine of Schelling is that we obtain our knowledge of the Infinitive by sinking back into a state beyond consciousness, in which we are identified in being with the Absolute, and thus know it. We know not whether the presumption or the absurdity of this theory affords greater cause for astonishment. To retire from consciousness, and constitute oneself a part of the one Absolute Being, is venturing to a degree of presumption happily not very common. Viewed as a philosophical theory it. is baseless. If ScheUing thought fit to trust that he had obtained a knowledge of the Absolute, while he was not in a state of consciousness, — if he thought fit to trust that he had received a knowledge of the Infinite, which could not be retained on returning to a state of consciousness, — we do not imagine that he will obtain many supporters. Men are not accustomed to assert that they possess a knowledge of which they are not conscious. Nor need it much concern us how Schelling passed from the finite to the Infinite ; or, being once Infinite, how he again returned to the finite, since this important matter cannot be made known. This, at least, seems inconceivable.

Setting aside the theories of Kant and Schelling, there remain only those of M. Cousin and Sir William Hamilton : M. Cousin asserting that we have a knowledge of the Infinite by relation, difference, and plurality ; Sir William asserting that we can have no positive knowledge of the Unconditioned, its only notion being a negation of the Conditioned.

In reference to this question, Morell says, — " Here we have three minds standing severally at the head of the respective philosophies of Britain, France, and Germany, assuming each a different hypothesis on this subject, while Kant, the Aristotle of the modern world, assumes a fourth. Under such circumstances,

STATEMENT OP THE QUESTION. 9

he must be a bold tbinker who ventures to pronounce confidently upon the truth or error of any one of these opinions."* Now, we trust that we can lay no claim to the character of a bold thinker, — it is certainly our desire that our thinking should be characterised by all caution and humility ; at the same time, we trust that we have sufficient fidelity to recognised truth, to be earnest in maintaining it. We have no wish " to pronounce confidently" upon a subject so difficult. We present our observations as a contribution to the Philosophy of the Infinite, and if they tend in the slightest degree to instigate to its further study, they will have gained their end, though the result of the study thus increased, should leave them far behind.

In entering upon a subject so difficult as the Philosophy of the Infinite, we are conscious not only of feelings of diffidence, but of regret that we are constrained to take up a position opposed to that of Sir Wilham Hamilton. Let us at once confess, that this fact, on the one hand, causes us the deepest regret ; and on the other, strongly convinces us of the necessity for taking the step. Respected and admired, as Sir William is, and possessing, as we rejoice to acknowledge, the very highest claims to such esteem, we cannot but regard it as unfortunate that he has propounded a doctrine concerning the Infinite so startling and hazardous. We regret that

* History of Modern Philosophy, vol. ii. p. 504, second edition.

the influence of the first philosopher of the present day, should be given so strongly to maintain the doctrine that we can have no notion of the Infinite. And when we hear around us the oft repeated admission that the arguments of Sir William on this question are unanswerable;' when we hear from others, only the feeble expression of a doubt that there may be error somewhere ; and when we find some taking up an opposite doctrine without being able to give a suflBcient reason ; it is obvious that there is room for further investigation, and the importance of the question demands that such investigation be careful and minute.

As a specimen of the manner in which the doctrine of Sir William has been received by many, we may take the following quotation from Morell. Considering the article on the Infinite as it first appeared in the Edinburgh Review, he makes the following observations, — " We freely confess that we are not yet prepared to combat, step by step, the weighty arguments by which the Scottish metaphysician seeks to establish the negative character of this great fundamental conception ; neither, on the other hand, are we prepared to admit his inference. We cannot divest our mind of the belief, that there is something positive in the glance which the human soul casts upon the world of eternity and infinity."''- We find this statement made by Morell in the first

* History of Modern Philosophy, vol. ii. p. 501, second 'edition.

STATEMENT OP THE QUESTION. 11

edition of hiis History of Philosophy, and again repeated in the second edition, and it is only a specimen of what has been commonly felt and expressed on the point. We confess to similar uneasiness in reference to the conclusion at which Sir William Hamilton- has arrived — that man can have no knowledge of the Infinite God — and we readily admit thai; it is mainly to test the validity of this conclusion that we have entered upon a strict examination of the arguments adduced. M. Cousin has himself presented some defence of his position, but it is only partial, and cannot be regarded as a sufficient answer to the very formidable arguments of the philosopher of Edinburgh.

3ir William Hamilton bases his doctrine of- the inconceivability of the Infinite upon the constitution of the mind. He says that the conditions of thought are such as 'to render a conception of the Infinite impossible. The condition of Relativity is that which, according to this doctrine, is regarded as excluding the -possibiUty of a knowledge of the Infinite. Let us take a passage from Sir William. He says, — " Thought cannot transcend consciousness ; consciousness is only possible under the antithesis of a subject and an object of thought, known only in correlation, and mutually limiting each other ; while, independently of all this, all that we know either of subject or object, either of mind or matter, is only a knowledge in each of the particular, of the plural, of the different, of the modified, of the phenomenal."* Now, we grant all that is here said concerning the relative character of our knowledge. We grant that " consciousness is only possible under the antithesis of a subject and an object of thought known only in correlation ;" but, is it true that the subject and object limit each other 1 We do not admit it. We grant that the mind is limited, but does it thence follow that the object of thought must be limited'? We think not. We grant that the mind cannot embrace the Infinite, but we nevertheless consider that the mind may have a notion of the Infinite. No more do we believe that the mind, as finite, can only recognise finite objects, than we believe that the eye, because limited in its power, can only recognise those objects whose entire extension comes within the range of vision. Ah well tell us that because a mountain is too large for the eye of a mole, therefore the mole can recognise no mountain : as well tell us that because the world is too large for the eye of a man, therefore man can recognise no world — as tell us that because the Infinite cannot be embraced by the finite mind, therefore the mind can recognise no Infinite. We altogether deny the assertion of Sir William Hamilton, that " the Absolute can only be known, if adequately known ;" though we admit that " it can only be adequately known by the Absolute itself." We

* Discussions, p. 1-J.

STATEMENT OF THE QUESTION. 18

deny that we must have either an adequate notion of the Absolute, or no notion of it at all. There is nothing in our mental constitution to prevent us having an indefinite conception of an object of which we can form no adequate conception. On the contrary, our experience presents proof, both abundant and convincing, of the possibility of indefinite and inadequate conceptions of objects not fully recognised. With these convictions, we find ourselves shut up to an opposite theory from that which affii'ms that we can have no knowledge of the Infinite. Yet, though this be the case, we are willing to admit that our knowledge is only of the relative. That is to say, we admit that an object must come into relation with the mind in order to be known, and that even when an object is thus presented, we can recognise only its relative manifestations or properties. We do not profess a system of Ontology, nor do we think this at all necessary in order to establish the possibility of a knowledge of the Infinite. When, therefore. Sir William, in laying down the conditions of thought, restricts us to a knowledge of the relative, we perfectly concur in the restriction, but we think this restriction is carried too far, when it is maintained that nothing can exist in relation to our mind as an object of thought, except the finite. It is possible to confine us by a theory to an extent much greater than we are in reality restricted ; it is possible to raise barriers which may seem to establish the irapossibility of our obtaining, or possessing any knowledge of what we can know ; nay, of what we do know. This we consider Sir William Hamilton has done in asserting the impossibility of our obtaining any knowledge of the Infinite. In treating of the Infinite, he has dealt with a mere abstraction, for the knowledge of which no one contends, which does not even exist, and by arguments, which are sufficiently valid as applied to the abstraction which he has himself enunciated, he has seemed to establish the impossibility of our obtaining any knowledge of the Infinite. To vindicate for man a knowledge of the Infinite, and remove the objections thus urged against it, is the purpose of the present Treatise.

We consider that the balance of truth in this case is to be found with M. Cousin, though we think it necessary to premise, that in upholding the French philosopher, we do so only to a limited extent, and that merely in reference to this individual doctrine, and not in reference to the relation which that doctrine holds in his system. Nor are we to be understood as tending towards a system of Eclecticism, with which we have little sympathy. We certainly believe that M. Cousin is right in maintaining that we have a positive notion of the Infinite, but we are not by any means persuaded that he has strictly confined himself to a delineation of consciousness. On the contrary, we consider that he has encumbered the doctrine with matter altogether untenable, and

STATEMENT OF THE QUESTION. 15

has thus laid it open to assault, so that, at a cursory glance, it might seem that even the citadel itself l^ad been considerably shaken. We admire the great central truth in the philosophy of M. Cousin, but we. regard the various points of Eclecticism, which he has made to cluster around it, as so many outposts, worse than useless, which ought to fall to atoms, and which have so fallen under the effective assaults of the Scottish metaphysician. ,

Chapter II

EXAMINATION OF 8IE WILLIAM HAMILTON'S DISTINCTION OF THE INFINITE AND ABSOLUTE.

Before entering upon a consideration of the respective theories in reference to the Infinite, it is necessary that we precisely determine what we understand by the terms employed ; for even here there is a diversity between Sir William Hamilton and other philosophers. On this point there are three terms in common use — the Infinite, the Absolute, and the Unconditioned. In the ordinary language of philosophers, these three terras are regarded as synonymous ; the Infinite is that which is absolute, that which is unconditioned, that which is limited or restricted by no conditions. But in the language of Sir William, the Infinite is the " unconditionally unlimited," the Absolute is the " unconditionally limited," and the Unconditioned is the genus of which the Infinite and Absolute are the species. According to this distinction, the Infinite is that which is without beginning or termination, — which is circumscribed by no boundaries, which is determined by no limits. The Absolute is that which, while limited, is finished, perfect, or complete in itself ; and, consequently, is subject to no conditions. The two constitute, according to this theory, the opposite poles, between which alone all thought, as conditioned, is possible. To both of these extremes or poles belongs the characteristic of being unconditioned, and they are, therefore, taken together to constitute one genus under this title.

In making this distinction, its author finds in the two extremes which he has indicated as the Infinite and the Absolute, the character of being unconditioned, or destitute of any conditions or relations which affect their existence. This ia what they possess in common, and what renders them capable of being classified under one genus, which is thus called the Unconditioned. That which distinguishes them from each other, is that, while both are unconditioned, the Infinite is unlimited, the Absolute is limited, hut perfect. In contradistinction to this, other philosophers have regarded the Infinite and Absolute as one and the same, and have not recognised the possibility of any other Absolute than the Infinite. With all deference to Sir William, we consider that the problem of the Unconditioned is one, and not twofold as he has maintained ; and, in confirmation of our opinion, we shall endeavour to show that the Infinite is also Absolute, and that the Absolute postulated by him is not really absolute.

B

I. In entering upon this point, o\xv first question is, — Are philosophers in general wrong in regarding the Infinite as in its nature also Absolute 1 Does that quality which we distinguish by the name of Absolute, belong, or not belong, to the Infinite 1 Sir William distinguishes the Infinite and Absolute, not only as essentially distinct, but also as contradietory opposites, consequently, it seems from this doctrine, that philosophers in regarding the Infinite as at the same time Absolute, must have been attributing to it that which does not belong to it. Our question, therefore, is, — Do philosophers in general include in the Infinite that which does not pertain to it ; or, does the author of this distinction exclude from it that which ought to belong to it 1

Let us first define the term Absolute. The plain and etymological meaning of the term is freed or loosed, and hence it means freed from restriction or condition. In this sense it is evident that the Infinite must be absolute ; that that which has no limitation does not afford the possibility of restriction. This is the sense in which philosophers have uniformly used the word ; and, in this sense. Sir William admits that " the Absolute is not opposed to the Infinite."* Thus far, then, there is no difference. If philosophers, therefore, are chargeable in the matter, it is not in respect of positive error, but in respect of neglect. One question, however, is

Discussions, page 18.

DISTINCTION OP THE INFINITE AND ABSOLUTE. 19

open at this point, — Is it warrantable in Sir William to take a term which naturally, and by common consent, expresses a certain notion, and apply it to that which is entirely distinct 1 Is it warrantable to make such an unusual application of a term in common use, and thereby cause it to appear as if philosophers had entirely mistaken the character of the Absolute, and had ascribed to the Infinite that which does not belong to it 1 If it be true, as our author admits, that, in the primary sense of the word absolute, the Infinite, from its very nature, is absolute, is it warrantable to take the word absolute and apply it to that which is asserted to be contradictory of the Infinite 1 We might push our question farther and say, if the Infinite be necessarily absolute, can that be really absolute which is contradictory of the Infinite 1 But this is to anticipate what shall be afterwards considered. The meaning of the term absolute, as employed by Sir William, will shortly appear ; but what we wish observed in the flieantime, is that he admits that philosophers are correct in regarding the Infinite and Absolute as convertible, if the latter term be used as expressive of entire freedom from all restriction. His objection is, not that philosophers have put their Absolute in the wrong place, but that they have failed to recognise an Absolute in another sense which he marks out. We have deemed these remarks necessary, since at a cursory glance it might seem that our author considers that philosophers have blundered in asserting that the Infinite is also Absolute.

The sense in which Sir William employs the term absolute, when he distinguishes it as a contradictory of the Infinite, is what is finished, perfected, completed ; so that the absolute in this sense is " what is out of relation, &c., as finished, perfect, complete, total."*