The Online Library of Liberty

A project of Liberty Fund, Inc.

• Introduction
• Textual Introduction
• Preface to the Third Edition[*]
• Chapter I: Introductory Remarks
• Chapter II: The Relativity of Human Knowledge
• Chapter III: The Doctrine of the Relativity of Human Knowledge, As Held By Sir William Hamilton
• Chapter IV: In What Respect Sir William Hamilton Really Differs From the Philosophers of the Absolute
• Chapter V: What Is Rejected As Knowledge By Sir William Hamilton, Brought Back Under the Name of Belief
• Chapter VI: The Philosophy of the Conditioned
• Chapter VII: The Philosophy of the Conditioned, As Applied By Mr. Mansel to the Limits of Religious Thought
• Chapter VIII: Of Consciousness, As Understood By Sir William Hamilton
• Chapter IX: Of the Interpretation of Consciousness
• Chapter X: Sir William Hamilton’s View of the Different Theories Respecting the Belief In an External World
• Chapter XI: The Psychological Theory of the Belief In an External World
• Chapter XII: The Psychological Theory of the Belief In Matter, How Far Applicable to Mind
• Chapter XIII: The Psychological Theory of the Primary Qualities of Matter
• Chapter XIV: How Sir William Hamilton and Mr. Mansel Dispose of the Law of Inseparable Association
• Chapter XV: Sir William Hamilton’s Doctrine of Unconscious Mental Modifications
• Chapter XVI: Sir William Hamilton’s Theory of Causation
• Chapter XVII: The Doctrine of Concepts, Or General Notions
• Chapter XVIII: Of Judgment
• Chapter XIX: Of Reasoning
• Chapter XX: On Sir William Hamilton’s Conception of Logic As a Science. Is Logic the Science of the Laws, Or Forms, of Thought?
• Chapter XXI: The Fundamental Laws of Thought According to Sir William Hamilton
• Chapter XXII: Of Sir William Hamilton’s Supposed Improvements In Formal Logic
• Chapter XXIII: Of Some Minor Peculiarities of Doctrine In Sir William Hamilton’s View of Formal Logic
• Chapter XXIV: Of Some Natural Prejudices Countenanced By Sir William Hamilton, and Some Fallacies Which He Considers Insoluble
• Chapter XXV: Sir William Hamilton’s Theory of Pleasure and Pain
• Chapter XXVI: On the Freedom of the Will
• Chapter XXVII: Sir William Hamilton’s Opinions On the Study of Mathematics
• Chapter XXVIII: Concluding Remarks
• Appendices
• Appendix A: Manuscript Fragments
• Appendix B: Textual Emendations
• Appendix C: Corrected References
• Appendix D: Bibliographic Index of Persons and Works Cited In the Examination, With Variants and Notes

CHAPTER VI

The Philosophy of the Conditioned

the “philosophy of the conditioned,” in its wider sense, includes all the doctrines that we have been discussing. In its narrower, it consists, I think, mainly of a single proposition, which Sir W. Hamilton often reiterates, and insists upon as a fundamental law of human intellect. Though suggested by Kant’s Antinomies of Speculative Reason, in the form which it bears in Sir W. Hamilton’s writings it belongs, I believe, originally to himself. No doctrine which he has anywhere laid down is more characteristic of his mode of thought, and none is more strongly associated with his fame.

For the better understanding of this theory, it is necessary to premise some explanations respecting another doctrine, which is also his, but not peculiar to him. He protests, frequently and with emphasis, against the notion that whatever is inconceivable must be false. “There is no ground,” he says, “for inferring a certain fact to be impossible, merely from our inability to conceive its possibility.”^* I regard this opinion as perfectly just. It is one of the psychological truths, highly important, and by no means generally recognised, which frequently meet us in his writings, and which give them, in my eyes, most of their philosophical value. I am obliged to add, that though he often furnishes a powerful statement and vindication of such truths, he seldom or never consistently adheres to them. Too often what he has affirmed in generals is taken back in details, and arguments of his own are found to rest on philosophical commonplaces which he has himself repudiated and refuted. I am afraid that the present is one of these cases, and that Sir W. Hamilton will sometimes be found contending that a thing cannot possibly be true because we cannot conceive it: but at all events he disclaims any such inference, and broadly lays down, that things not only may be, but are, of which it is impossible for us to conceive even the possibility.

Before showing how this proposition is developed into the “Philosophy of the Conditioned,” let us make the ground safe before us, by bestowing a brief consideration upon the proposition itself, its meaning, and the foundations on which it rests.

We cannot conclude anything to be impossible, because its possibility is inconceivable to us; for two reasons. First; what seems to us inconceivable, and, so far as we are personally concerned, may really be so, usually owes its inconceivability only to a strong association. When, in a prolonged experience, we have often had a particular sensation or mental impression, and never without a certain other sensation or impression immediately accompanying it, there grows up so firm an adhesion between our ideas of the two, that we are unable to think of the former without thinking the latter in close combination with it. And unless other parts of our experience afford us some analogy to aid in disentangling the two ideas, our incapacity of imagining the one fact without the other grows, or is prone to grow, into a belief that the one cannot exist without the other. This is the law of Inseparable Association, an element of our nature of which few have realized to themselves the full power. It was for the first time largely applied to the explanation of the more complicated mental phænomena by Mr. James Mill;^[*] and is, in an especial manner, the key to the phænomenon of inconceivability. As that phænomenon only exists because our powers of conception are determined by our limited experience, Inconceivables are incessantly becoming Conceivables as our experience becomes enlarged. There is no need to go farther for an example than the case of Antipodes. This physical fact was, to the early speculators, inconceivable: not, of course, the fact of persons in that position; this the mind could easily represent to itself; but the possibility that, being in that position, and not being nailed on, nor having any glutinous substance attached to their feet, they could help falling off. Here was an inseparable, though, as it proved to be, not an indissoluble association, which while it continued made a real fact what is called inconceivable; and because inconceivable, it was unhesitatingly believed to be impossible. Inconceivabilities of similar character have, at many periods, obstructed the reception of new scientific truths: the Newtonian system had to contend against several of them; and we are not warranted in assigning a different origin and character to those which still subsist, because the experience that would be capable of removing them has not occurred. If anything which is now inconceivable by us were shown to us as a fact, we should soon find ourselves able to conceive it. We should even be in danger of going over to the opposite error, and believing that the negation of it is inconceivable. There are many cases in the history of science (I have dilated on some of them in another work)^[*] where something which had once been inconceivable, and which people had with great difficulty learnt to conceive, becoming itself fixed in the bonds of an inseparable association, scientific men came to think that it alone was conceivable, and that the conflicting hypothesis which all mankind had believed, and which a vast majority were probably believing still, was inconceivable. In Dr. Whewell’s writings on the Inductive Sciences, this transition of thought is not only exemplified but defended.^[†] Inconceivability is thus a purely subjective thing, arising from the mental antecedents of the individual mind, or from those of the human mind generally at a particular period, and cannot give us any insight into the possibilities of Nature.

But, secondly, ^aeven assuming^a that inconceivability is not solely the consequence of limited experience, but that some incapacities of conceiving are inherent in the mind, and inseparable from it; this would not entitle us to infer, that what we are thus incapable of conceiving cannot exist. Such an inference would only be warrantable, if we could know à priori that we must have been created capable of conceiving whatever is capable of existing: that the universe of thought and that of reality, the Microcosm and the Macrocosm (as they once were called) must have been framed in complete correspondence with one another. That this is really the case has been laid down expressly in some systems of philosophy, by implication in more, and is the foundation (among others) of the systems of Schelling and Hegel: but an assumption more destitute of evidence could scarcely be made, nor can one easily imagine any evidence that could prove it, unless it were revealed from above.

What is inconceivable, then, cannot therefore be inferred to be false. But let us vary the terms of the proposition, and express it thus: what is inconceivable, is not therefore incredible. We have now a statement, which may mean either exactly the same as the other, or more. It may mean only that our inability to conceive a thing, does not entitle us to deny its possibility, nor its existence. Or it may mean that a thing’s being inconceivable to us is no reason against our believing, and legitimately believing, that it actually is. This is a very different proposition from the preceding. Sir W. Hamilton, as we have said, goes this length. It is now necessary to enter more minutely than at first seemed needful, into the meaning of “inconceivable;” which, like almost all the metaphysical terms we are forced to make use of, is weighed down with ambiguities.

Reid pointed out and discriminated two meanings of the verb “to conceive,”^* giving rise to two different meanings of inconceivable. But Sir W. Hamilton uses “to conceive” in three meanings, and has accordingly three meanings for Inconceivable; though he does not give the smallest hint to his readers, nor seems ever to suspect, that the three are not one and the same.

The first meaning of Inconceivable is, that of which the mind cannot form to itself any representation; either (as in the case of Noumena) because no attributes are given, out of which a representation could be framed, or because the attributes given are incompatible with one another—are such as the mind cannot put together in a single image. Of this last case numerous instances present themselves to the most cursory glance. The fundamental one is that of a simple contradiction. We cannot represent anything to ourselves as at once being something, and not being it; as at once having, and not having, a given attribute. The following are other examples. We cannot represent to ourselves time or space as having an end. We cannot represent to ourselves two and two as making five; nor two straight lines as enclosing a space. We cannot represent to ourselves a round square; ^bnor^b a body all black, and at the same time all white.

These things are literally inconceivable to us, our minds and our experience being what they are. Whether they would be inconceivable if our minds were the same but our experience different, is open to discussion. A distinction may be made, which, I think, will be found pertinent to the question. That the same thing should at once be and not be—that identically the same statement should be both true and false—is not only inconceivable to us, but we cannot ^cimagine^c that it could be made conceivable. We cannot attach sufficient meaning to the proposition, to be able to represent to ourselves the supposition of a different experience on this matter. We cannot therefore even entertain the question, whether the incompatibility is in the original structure of our minds, or is only put there by our experience. The case is otherwise in all the other examples of inconceivability. Our incapacity of conceiving the same thing as A and not A, may be primordial; but our inability to conceive A without B, is because A, by experience or teaching, has become inseparably associated with B: and our inability to conceive A with C, is, because, by experience or teaching, A has become inseparably associated with some mental representation which includes the negation of C. Thus all inconceivabilities may be reduced to inseparable association, combined with the original inconceivability of a direct contradiction. All the cases which I have cited as instances of inconceivability, and which are the strongest I could have chosen, may be resolved in this manner. We cannot conceive a round square, not merely because no such object has ever presented itself in our experience, for that would not be enough. Neither, for anything we know, are the two ideas in themselves incompatible. To conceive a round square, or to conceive a body all black and yet all white, would only be to conceive two different sensations as produced in us simultaneously by the same object; a conception familiar to our experience; and we should probably be as well able to conceive a round square as a hard square, or a heavy square, if it were not that, in our uniform experience, at the instant when a thing begins to be round it ceases to be square, so that the beginning of the one impression is inseparably associated with the departure or cessation of the other.^* Thus our inability to form a conception always arises from our being compelled to form another contradictory to it. We cannot conceive time or space as having an end, because the idea of any portion whatever of time or space is inseparably associated with the idea of a time or space beyond it. We cannot conceive two and two as five, because an inseparable association compels us to conceive it as four; and it cannot be conceived as both, because four and five, like round and square, are so related in our experience, that each is associated with the cessation, or removal, of the other. We cannot conceive two straight lines as enclosing a space, because enclosing a space means approaching and meeting a second time; and the mental image of two straight lines which have once met is inseparably associated with the representation of them as diverging. Thus it is not wholly without ground that the notion of a round square, and the assertion that two and two make five, or that two straight lines can enclose a space, are said, in common and even in scientific parlance, to involve a contradiction. The statement is not logically correct, for contradiction is only between a positive representation and its negative. But the impossibility of uniting contradictory conceptions in the same representation, is the real ground of the inconceivability in these cases. And we should probably have no difficulty in putting together the two ideas supposed to be incompatible, if our experience had not first inseparably associated one of them with the contradictory of the other.^*

Thus far, of the first kind of Inconceivability; the first and most proper meaning in which the word is used. But there is another meaning, in which things are often said to be inconceivable which the mind is under no incapacity of representing to itself in an image. It is often said, that we are unable to conceive as possible that which, in itself, we are perfectly well able to conceive: we are able, it is admitted, to conceive it as an imaginary object, but unable to conceive it realized. This extends the term inconceivable to every combination of facts which to the mind simply contemplating it, appears incredible.^* It was in this sense that Antipodes were inconceivable. They could be figured in imagination; they could even be painted, or modelled in clay. The mind could put the parts of the conception together, but^g could not realize the combination as one which could exist in nature. The cause of the inability was the powerful tendency, generated by experience, to expect falling off, when a body, not of adhesive quality, was in contact only with the under side of another body. The association was not so powerful as to disable the mind from conceiving the body as holding on; doubtless because other facts of our experience afforded models on which such a conception could be framed. But though not disabled from conceiving the combination, the mind was disabled from believing it. The difference between belief and conception, and between the conditions of belief and those of simple conception, are psychological questions into which I do not enter. It is sufficient that inability to believe can coexist with ability to conceive, and that a mental association between two facts which is not intense enough to make their separation unimaginable, may yet create, and, if there are no counter associations, always does create, more or less of difficulty in believing that the two can exist apart: a difficulty often amounting to a local or temporary impossibility.

This is the second meaning of Inconceivability; which by Reid is carefully distinguished from the first,^[*] but his editor Sir W. Hamilton employs the word in both senses indiscriminately.^* How he came to miss the distinction is tolerably obvious to any one who is familiar with his writings, and especially with his theory of Judgment; but needs not be pointed out here. It is more remarkable that he gives ⁱtoⁱ the term a third sense, answering to a third signification of the verb “to conceive.” To conceive any thing, has with him not only its two ordinary meanings—to represent the thing as an image, and to be able to realize it as possible—but an additional one, which he denotes by various phrases. One of his common expressions for it is, “to construe to the mind in thought.” This, he often says, can only be done “through a higher notion.” “We think, we conceive, we comprehend a thing only as we think it as within or under something else.”^* So that a fact, or a supposition, is conceivable or comprehensible by us (conceive and comprehend being with him in this case synonymous) only by being reduced to some more general fact, as a particular case under it. Again, “to conceive the possibility” of a thing, is defined “conceiving it as the consequent of a certain reason.”^† The inconceivable, in this third sense, is simply the inexplicable. Accordingly all first truths are, according to Sir W. Hamilton, inconceivable. “The primary data of consciousness, as themselves the conditions under which all else is comprehended, are necessarily themselves incomprehensible . . . that is . . . we are unable to conceive through a higher notion how that is possible, which the deliverance avouches actually to be.”^‡ And we shall find him arguing things to be inconceivable, merely on the ground that we have no higher notion under which to class them. This use of the word inconceivable, being a complete perversion of it from its established meanings, I decline to recognise. If all the general truths which we are most certain of are to be called inconceivable, the word no longer serves any purpose. Inconceivable is not to be confounded with unprovable, or unanalysable. A truth which is not inconceivable in either of the received meanings of the term—a truth which is completely apprehended, and without difficulty believed, I cannot consent to call inconceivable merely because we cannot account for it, or deduce it from a higher truth.^§

These being Sir W. Hamilton’s three kinds of inconceivability; is the inconceivability of a proposition in any of these senses, consistent with believing it to be true? The third kind ^lis avowedly compatible not only with belief, but with our strongest and most natural beliefs^l . An inconceivable of the second kind can not only be believed, but believed with full understanding. In this case we are perfectly able to represent to ourselves mentally what is said to be inconceivable; only, from an association in our mind, it does not look credible: but, this association being the result of experience or of teaching, contrary experience or teaching is able to dissolve it; and even before this has been done—while the thing still feels incredible, the intellect may, on sufficient evidence, accept it as true. An inconceivable of the first kind, inconceivable in the proper sense of the term—that which the mind is actually unable to put together in a representation—may nevertheless be believed, if we attach any meaning to it, but cannot be said to be believed with understanding. We cannot believe it on direct evidence, i.e. through its being presented in our experience, for if it were so presented it would immediately cease to be inconceivable. We may believe it because its falsity would be inconsistent with something which we otherwise know to be true. Or we may believe it because it is affirmed by some one wiser than ourselves, who, we suppose, may have had the experience which has not reached us, and to whom it may thus have become conceivable. But the belief is without understanding, for we form no mental picture of what we believe. We do not so much believe the fact, as believe that we should believe it if we could have the needful presentation in our experience; and that some other being has, or may have, had that presentation. Our inability to conceive it, is no argument whatever for its being false, and no hindrance to our believing it, to the above-mentioned extent.

But though facts, which we cannot join together in an image, may be united in the universe, and though we may have sufficient ground for believing that they are so united in point of fact, it is impossible to believe a proposition which conveys to us no meaning at all. If any one says to me, Humpty Dumpty is an Abracadabra, I neither knowing what is meant by an Abracadabra, nor what is meant by Humpty Dumpty, I may, if I have confidence in my informant, believe that he means something, and that the something which he means is probably true: but I do not believe the very thing which he means, since I am entirely ignorant what it is. Propositions of this kind, the unmeaningness of which lies in the subject or predicate, are not those generally described as inconceivable. The unmeaning propositions spoken of under that name, are usually those which involve contradictions. That the same thing is and is not—that it did and did not rain at the same time and place, that a man is both alive and not alive, are forms of words which carry no signification to my mind. As Sir W. Hamilton truly says,^* one half of the statement simply sublates or takes away the meaning which the other half has laid down. The unmeaningness here resides in the copula. The word is has no meaning, except as exclusive of is not. The case is more hopeless than that of Humpty Dumpty, for no explanation by the speaker of what the words mean can make the assertion intelligible. Whatever may be meant by a man, and whatever may be meant by alive, the statement that a man can be alive and not alive is equally without meaning to me. I cannot make out anything which the speaker intends me to believe. The sentence affirms nothing of which my mind can take hold. Sir W. Hamilton, indeed, maintains the contrary. He says, “When we conceive the proposition that A is not A, we clearly comprehend the separate meaning on the terms A and not A, and also the import of the assertion of their identity.”^* We comprehend the separate meaning of the terms, but as to the meaning of the assertion, I think we only comprehend what the same form of words would mean in another case. The very import of the form of words is inconsistent with its meaning anything when applied to terms of this particular kind. Let any one who doubts this, attempt to define what is meant by applying a predicate to a subject, when the predicate and the subject are the negation of one another. To make sense of the assertion, some new meaning must be attached to is or is not, and if this be done the proposition is no longer the one presented for our assent. Here, therefore, is one kind of inconceivable proposition which nothing whatever can make credible to us. Not being able to attach any meaning to the proposition, we are equally incompetent to assert that it is, or that it is not, possible in itself. But we have not the power of believing it; and there the matter must rest.

We are now prepared to enter on the peculiar doctrine of Sir W. Hamilton, called the Philosophy of the Conditioned. Not content with maintaining that things which from the natural and fundamental laws of the human mind are for ever inconceivable to us, may, for aught we know, be true, he goes farther, and says, we know that many such things are true. “Things there are which may, nay must, be true, of which the understanding is wholly unable to construe to itself the possibility.”^† Of what nature these things are, is declared in many parts of his writings, in the form of a general law. It is thus stated in the review of Cousin:

In the “Dissertations on Reid” he enunciates, in still more general terms, as “the Law of the Conditioned: That all positive thought lies between two extremes, neither of which we can conceive as possible, and yet as mutual contradictories, the one or the other we must recognise as necessary.” And it is (he says) “from this impotence of intellect” that “we are unable to think aught as absolute. Even absolute relativity is unthinkable.”^*

The doctrine is more fully expanded in the Lectures on Logic, from which I shall quote at greater length.

one or the other of them must be true.

In other passages our author applies the same order of considerations to Time, saying that we can neither conceive an absolute commencement, nor an infinite regress; an absolute termination, nor a duration infinitely prolonged; though either the one or the other must be true. And again, of the Will: we cannot, he says, conceive the Will to be Free, because this would be to conceive an event uncaused, or, in other words, an absolute commencement: neither can we conceive the Will not to be Free, because this would be supposing an infinite regress from effect to cause. The will, however, must be either free or not free; and in this case, he thinks we have independent grounds for deciding one way, namely, that it is free, because if it were not, we could not be accountable for our actions, which our consciousness assures us that we are.^[*]

This, then, is the Philosophy of the Conditioned: into the value of which it now remains to enquire.

In the case of each of the Antinomies which the author presents, he undertakes to establish two things: that neither of the rival hypotheses can be conceived by us as possible, and that we are nevertheless certain that one or the other of them is true.^o

To begin with his first position, that we can neither conceive an end to space, nor space without end.

That we are unable to conceive an end to space I fully acknowledge. To account for this there needs no inherent incapacity. We are disabled from forming this conception, by known psychological laws. We have never perceived any object, or any portion of space, which had not other space beyond it. And we have been perceiving objects and portions of space from the moment of birth. How then could the idea of an object, or of a portion of space, escape becoming inseparably associated with the idea of additional space beyond? Every instant of our lives helps to rivet this association, and we never have had a single experience tending to disjoin it. The association, under the present constitution of our existence, is indissoluble. But we have no ground for believing that it is so from the original structure of our minds. We can suppose that in some other state of existence we might be transported to the end of space, when, being apprised of what had happened by some impression of a kind utterly unknown to us now, we should at the same instant become capable of conceiving the fact, and learn that it was true. After some experience of the new impression, the fact of an end to space would seem as natural to us as the revelations of sight to a person born blind, after he has been long enough couched to have become familiar with them. But as this cannot happen in our present state of existence, the experience which would render the association dissoluble is never obtained; and an end to space remains inconceivable.

One half, then, of our author’s first proposition, must be conceded. But the other half? Is it true that we are incapable of conceiving infinite space? I have already shown strong reasons for dissenting from this assertion: and those which our author, in this and other places, assigns in its support, seem to me quite untenable.

He says, “we think, we conceive, we comprehend, a thing, only as we think it as within or under something else. But to do this of the infinite is to think the infinite as finite, which is contradictory and absurd.” When we come to Sir W. Hamilton’s account of the Laws of Thought, we shall have some remarks to make on the phrase “to think one thing within or under another;” a favourite expression with the Transcendental school, one of whose characteristics^p is, that they are always using the prepositions in a metaphorical sense. But granting that to think a thing is to think it under something else, we must understand this statement as it is ^qinvariably^q interpreted by those who employ it. According to them, we think a thing when we make any affirmation respecting it, and we think it under the notion which we affirm of it. Whenever we judge, we think the subject under the predicate. Consequently when we say “God is good,” we think God under the notion “good.” Is this, in our author’s opinion, to think the infinite as finite, and hence “contradictory and absurd?”

If this doctrine hold, it follows that we cannot predicate anything of a subject which we regard as being in any of its attributes, infinite. We are unable, without falling into a contradiction, to assert anything not only of God, but of Time, and of Space. Considered as a reductio ad absurdum, this is sufficient. But we may go deeper into the matter, and deny the statement that to think anything “under” the notion expressed by a general term is to think it as finite. None of our general predicates are, in the proper sense of the term, finite; they are all, at least potentially, infinite. “Good” is not a name for the things or persons possessing that attribute which exist now, or at any other given moment, and which are only a finite aggregate. It is a name for all those which ever did, or ever will, or even in hypothesis or fiction can, possess the attribute. This is not a limited number. It is the very nature and constituent character of a general notion that its extension (as Sir W. Hamilton would say) is ^rwithout limit^r .

But he might perhaps say, that though its extension, consisting of the possible individuals included in it, ^smay^s be infinite, its comprehension, the set of attributes contained in it (or as I prefer to say, connoted by its name) is a limited quantity. Undoubtedly it is. But see what follows. If, because the comprehension of a general notion is finite, anything infinite cannot without contradiction be thought under it, the consequence is, that a being possessing in an infinite degree a given attribute, cannot be thought under that very attribute. Infinite goodness cannot be thought as goodness, because that would be to think it as finite. Surely there must be some great confusion of ideas in the premises, when this comes out as the conclusion.

Our author goes on to repeat the argument used in his reply to Cousin, that Infinite Space is inconceivable, because all the conception we are able to form of it is negative, and a negative conception is the same as no conception. “The infinite is conceived only by the thinking away of every character by which the finite was conceived.” To this assertion I oppose my former reply. Instead of thinking away every character of the finite, we think away only the idea of an end, or a boundary. Sir W. Hamilton’s proposition is true of “The Infinite,” the meaningless abstraction; but it is not true of Infinite Space. In trying to form a conception of that, we do not think away its positive characters. We leave to it the character of Space; all that belongs to it as space; its three dimensions, with all their geometrical properties. We leave to it also a character which belongs to it as Infinite, that of being greater than any ^tfinite^t space. If an object which has these well-marked positive attributes is unthinkable, because it has a negative attribute as well, the number of thinkable objects must be remarkably small. Nearly all our positive conceptions which are at all complex, include negative attributes. I do not mean merely the negatives which are implied in affirmatives, as in saying that snow is white we imply that it is not black; but independent negative attributes superadded to these, and which are so real that they are often the essential characters, or differentiæ, of classes. Our conception of dumb, is of something which cannot speak; of the brutes, as of creatures which have not reason; of the mineral kingdom, as the part of Nature which has not organization and life; of immortal, as that which never dies. Are all these examples of the Inconceivable? So false is it that to think a thing under a negation is to think it as unthinkable.

In other passages, Sir W. Hamilton argues that we cannot conceive infinite space, because we should require infinite time to do it in. It would of course require infinite time to carry our thoughts in succession over every part of infinite space. But on how many of our finite conceptions do we think it necessary to perform such an operation? Let us try the doctrine upon a complex whole, short of infinite; such as the number 695, 788. Sir W. Hamilton would not, I suppose, have maintained that this number is inconceivable. How long did he think it would take to go over every separate unit of this whole, so as to obtain a perfect knowledge of that exact sum, as different from all other sums, either greater or less? Would he have said that we could have no conception of the sum until this process had been gone through? We could not, indeed, have an adequate conception. Accordingly we never have an adequate conception of any real thing. But we have a real conception of an object if we conceive it by any of its attributes that are sufficient to distinguish it from all other things. We have a conception of any large number, when we have conceived it by some one of its modes of composition, such as that indicated by the position of its digits. We seldom get nearer than this to an adequate conception of any large number. But for all intellectual purposes, this limited conception is sufficient: for it not only enables us to avoid confounding the number, in our calculations, with any other numerical whole—even with those so nearly equal to it that no difference between them would be perceptible by sight or touch, unless the units were drawn up in a manner expressly adapted for displaying it—but we can also, by means of this attribute of the number, ascertain and add to our conception as many more of its properties as we please. If, then, we can obtain a real conception of a finite whole without going through all its component parts, why deny us a real conception of an infinite whole because to go through them all is impossible? Not to mention that even in the case of the finite number, though the units composing it are limited, yet, Number being infinite, the possible modes of deriving any given number from other numbers are numerically infinite; and as all these are necessary parts of an adequate conception of any number, to render our conception even of this finite whole perfectly adequate would also require an infinite time.^*

But though our conception of infinite space can never be adequate, since we can never exhaust its parts, the conception, as far as it goes, is a real conception. We^x realize in imagination the various attributes composing it. We realize it as space. We realize it as greater than any given space. We even realize it as endless, in an intelligible manner, that is, we clearly represent to ourselves that however much of space has been already explored, and however much more of it we may imagine ourselves to traverse, we are no nearer to the end of it than we were at first^y; since^y , however often we repeat the process of imagining distance extending in any direction from us, that process is always susceptible of being carried further. This conception is both real and perfectly definite. ^zA merely negative notion may correspond to any number of the most heterogeneous positive things, but this notion corresponds to one thing only.^z We possess it as completely as we possess any of our clearest conceptions, and can avail ourselves of it as well for ulterior mental operations. As regards the Extent of Space, therefore, Sir W. Hamilton ^ahas not^a made out his point: one of the two contradictory hypotheses is not inconceivable.

The same thing may be said, equally decidedly, respecting the Divisibility of Space. According to our author, a minimum of divisibility, and a divisibility without limit, are both inconceivable. I venture to think, on the contrary, that both are conceivable. Divisibility, of course, does not here mean physical separability of parts, but their mere existence; and the question is, can we conceive a portion of extension so small as not to be composed of parts, and can we, on the other hand, conceive parts consisting of smaller parts, and these of still smaller, without end? As to the latter, smallness without limit is as positive a conception as greatness without limit. We have the idea of a portion of space, and to this we add that of being smaller than any given portion. The other side of the alternative is still more evidently conceivable. It is not denied that there is a portion of extension which to the naked eye appears an indivisible point; it has been called by philosophers the minimum visibile. This minimum we can indefinitely magnify by means of optical instruments, making visible the still smaller parts which compose it. In each successive experiment there is still a minimum visibile, anything less than which, cannot be discerned with that instrument, but can with one of a higher power. Suppose, now, that as we increase the magnifying ^bpowers^b of our instruments, and before we have reached the limit of possible increase, we arrive at a stage at which that which seemed the smallest visible space under a given microscope, does not appear larger under one which, by its mechanical construction, is adapted to magnify more—but still remains apparently indivisible. I say, that if this happened, we should believe in a minimum of extension; ^cand as we should be unable to conceive, that is, to represent to ourselves in an image, anything smaller, any further divisibility would be as inconceivable to us as it would be unbelievable^c .

There would be no difficulty in applying a similar line of argument to the case of Time, or to any other of the Antinomies, (there is a long list of them,^* to some of which I shall have to return for another purpose,) but it would needlessly encumber our pages. In no one case mentioned by Sir W. Hamilton do I believe that he could substantiate his assertion, that “the Conditioned,” by which he means every object of human knowledge, lies between two “inconditionate” hypotheses, both of them inconceivable. Let me add, that even granting the inconceivability of the two opposite hypotheses, I cannot see that any distinct meaning is conveyed by the statement that the Conditioned is “the mean” between them, or that “all positive thought,” “all that we can positively think,” “lies between” these two “extremes,” these “two opposite poles of thought.” The extremes are, Space in the aggregate considered as having a limit, Space in the aggregate considered as having no limit. Neither of these, says Sir W. Hamilton, can we think. But what we can positively think (according to him) is not Space in the aggregate at all; it is some limited Space, and this we think as square, as circular, as triangular, or as elliptical. Are triangular and elliptical a mean between infinite and finite? They are, by the very meaning of the words, modes of the finite. So that it would be more like the truth to say that we think the pretended mean under one of the extremes; and if infinite and finite are “two opposite poles of thought,” then in this polar opposition, unlike voltaic polarity, all the matter is accumulated at one pole. But this counter-statement would be no more tenable than Sir W. Hamilton’s; for in reality, the thought which he affirms to be a medium between two extreme statements, has no correlation with those statements at all. It does not relate to the same object. The two counter-hypotheses are suppositions respecting Space at large, Space as a collective whole. The “conditioned” thinking, said to be the mean between them, relates to parts of Space, and classes of such parts: circles and triangles, or planetary and stellar distances. The alternative of opposite inconceivabilities never presents itself in regard to them; they are all finite, and are conceived and known as such. What the notion of extremes and a mean can signify, when applied to propositions in which different predicates are affirmed of different subjects, passes my comprehension: but it served to give greater apparent profundity to the “Fundamental Doctrine,” in the eyes not of disciples (for Sir W. Hamilton was wholly incapable of quackery) but of the teacher himself.

^dIf these arguments are valid, the “Law of the Conditioned” rests on no rational foundation. The proposition that the Conditioned lies between two hypotheses concerning the Unconditioned, neither of which hypotheses we can conceive as possible,^d must be placed in that numerous class of metaphysical doctrines, which have a magnificent sound, but are empty of the smallest substance.^*

[* ]Discussions, [App. I (A),] p. 624.

[[*] ]Analysis of the Phenomena of the Human Mind, 2 vols. (London: Baldwin and Cradock, 1829).

[[*] ]See Logic, Bk. II, Chap. v, §6, and Bk. V, Chap. iii, §3, in Collected Works, Vol. VII, pp. 238ff.; Vol. VIII, pp. 752ff.

[[†] ]See William Whewell, History of the Inductive Sciences, 3rd ed., 3 vols. (London: Parker, 1857); History of Scientific Ideas, 3rd ed., 2 vols. (London: Parker, 1858); Novum Organon Renovatum, 3rd ed. (London: Parker, 1858); and On the Philosophy of Discovery (London: Parker, 1860).

[a-a]651, 652 were it granted

[* ]“To conceive, to imagine, to apprehend, when taken in the proper sense, signify an act of the mind which implies no belief or judgment at all. It is an act of the mind by which nothing is affirmed or denied, and which, therefore, can neither be true nor false. But there is another and a very different meaning of these words, so common and so well authorized in language that it cannot be avoided; and on that account we ought to be the more on our guard, that we be not misled by the ambiguity. . . . When we would express our opinion modestly, instead of saying, ‘This is my opinion,’ or ‘This is my judgment,’ which has the air of dogmaticalness, we say, ‘I conceive it to be thus—I imagine, or apprehend it to be thus;’ which is understood as a modest declaration of our judgment. In like manner, when anything is said which we take to be impossible, we say, ‘We cannot conceive it:’ meaning that we cannot believe it. Thus we see that the words conceive, imagine, apprehend, have two meanings, and are used to express two operations of the mind, which ought never to be confounded. Sometimes they express simple apprehension, which implies no judgment at all; sometimes they express judgment or opinion. . . . When they are used to express simple apprehension they are followed by a noun in the accusative case, which signifies the object conceived; but when they are used to express opinion or judgment, they are commonly followed by a verb in the infinitive mood. ‘I conceive an Egyptian pyramid.’ This implies no judgment. ‘I conceive the Egyptian pyramids to be the most ancient monuments of human art.’ This implies judgment. When they are used in the last sense, the thing conceived must be a proposition, because judgment cannot be expressed but by a proposition.” (Reid, [Essays] on the Intellectual Powers [of Man], p. 223 of Sir W. Hamilton’s edition [Edinburgh: Maclachlan and Stewart, 1846], to which edition all my references will be made.)

[b-b]651, 652, 67 or

[c-c]651, 652 conceive

[* ][72] It has been remarked to me by a correspondent, that a round square differs from a hard square or a heavy square in this respect, that the two sensations or sets of sensations supposed to be joined in the first-named combination are affections of the same nerves, and therefore, being different affections, are mutually incompatible by our organic constitution, and could not be made compatible by any change in the arrangements of external nature. This is probably true, and may be the physical reason why when a thing begins to be perceived as round it ceases to be perceived as square; but it is not the less true that this mere fact suffices, under the laws of association, to account for the inconceivability of the combination. I am willing, however, to admit, as suggested by my correspondent, that “if the imagination employs the organism in its representations,” which it probably does, “what is originally unperceivable in consequence of organic laws” may also be “originally unimaginable.”

[* ]That the reverse of the most familiar principles of arithmetic and geometry might have been made conceivable, even to our present mental faculties, if those faculties had coexisted with a totally different constitution of external nature, is ingeniously shown in the concluding paper of a recent volume, anonymous, but of known authorship, Essays, by a Barrister.

“Consider this case. There is a world in which, whenever two pairs of things are either placed in proximity or are contemplated together, a fifth thing is immediately created and brought within the contemplation of the mind engaged in putting two and two together. This is surely neither inconceivable, for we can readily conceive the result by thinking of common puzzle tricks, nor can it be said to be beyond the power of Omnipotence. Yet in such a world surely two and two would make five. That is, the result to the mind of contemplating two two’s would be to count five. This shows that it is not inconceivable that two and two might make five: but, on the other hand, it is perfectly easy to see why in this world we are absolutely certain that two and two make four. There is probably not an instant of our lives in which we are not experiencing the fact. We see it whenever we count four books, four tables or chairs, four men in the street, or the four corners of a paving stone, and we feel more sure of it than of the rising of the sun to-morrow, because our experience upon the subject is so much wider and applies to such an infinitely greater number of cases. Nor is it true that every one who has once been brought to see it, is equally sure of it. A boy who has just learnt the multiplication table is pretty sure that twice two are four, but is often extremely doubtful whether seven times nine are sixty-three. If his teacher told him that twice two made five, his certainty would be greatly impaired.

It would also be possible to put a case of a world in which two straight lines should be universally supposed to include a space. Imagine a man who had never had any experience of straight lines through the medium of any sense whatever, suddenly placed upon a railway stretching out on a perfectly straight line to an indefinite distance in each direction. He would see the rails, which would be the first straight lines he had ever seen, apparently meeting, or at least tending to meet at each horizon; and he would thus infer, in the absence of all other experience, that they actually did enclose a space, when produced far enough. Experience alone could undeceive him. A world in which every object was round, with the single exception of a straight inaccessible railway, would be a world in which every one would believe that two straight lines enclosed a space. In such a world, therefore, the impossibility of conceiving that two straight lines can enclose a space would not exist.” [James Fitzjames Stephen, “Mr. Mansel’s Metaphysics,” in Essays by a Barrister (London: Smith, Elder, 1862), pp. 333-4.]

In the “Geometry of Visibles” which forms part of Reid’s Inquiry into the Human Mind, it is contended that if we had the sense of sight, but not that of touch, it would appear to us that “every right line being produced will at last return into itself,” and that “any two right lines being produced will meet in two points.” [In Works, ed. Hamilton,] Chap. vi, §9 (p. 148.) The author adds, that persons thus constituted would firmly believe “that two or more bodies may exist in the same place.” For this they would “have the testimony of sense,” and could “no more doubt of it than they can doubt whether they have any perception at all, since they would often see two bodies meet and coincide in the same place, and separate again, without having undergone any change in their sensible qualities by this penetration.” (Ibid., p. 151.)

dHardly any part of the present volume has been so maltreated, by so great a number of critics, as the illustrations here quoted from an able and highly instructed cotemporary thinker; which, as they were neither designed by their author nor cited by me as anything more than illustrations, I do not deem it necessary to take up space by defending. When a selection must be made, one is obliged to consider what one can best spare.

eSome of my correspondents, looking upon the illustrations by “A Barrister” as (what they are not) an essential part of my argument, think me bound either to defend them or to give them up. As they are, in my opinion, perfectly defensible, I am ready, thus challenged, to stand up for them. And I select, among the attacks made on them, that of Dr. M‘Cosh (Examination of Mr. J. S. Mill’s Philosophy, pp. 209-11), as one of the fairest, and including what is most worthy of notice in the others. Of the first illustration, Dr. M‘Cosh says:

“Were we placed in a world in which two pairs of things were always followed by a fifth thing, we might be disposed to believe that the pairs caused the fifth thing, or that there was some prearranged disposition of things producing them together; but we could not be made to judge that 2 + 2 = 5, or that the fifth thing is not a different thing from the two and the two. On the other supposition put, of the two pairs always suggesting a fifth, we should explain their recurrence by some law of association, but we would not confound the 5 with the 2 + 2, or think that the two pairs could make five.” [P. 210.]

This passage is a correct description of what would happen if the presentation of the fifth thing were posterior, by a perceptible interval, to the juxtaposition of the two pairs, so that we should have time to judge that the two and two make four previously to perceiving the fifth. But the supposition is that the production of the fifth is so instantaneous in the very act of seeing, that we never should see the four things by themselves as four: the fifth thing would be inseparably involved in the act of perception by which we should ascertain the sum of the two pairs. I confess it seems to me that in this case we should have an apparent intuition of two and two making five.

To the second illustration, Dr. M‘Cosh replies: “I allow that this person as he looked one way, would see a figure presented to the eye of two straight lines approaching nearer each other; and that as he looked the other way he would see a like figure. But I deny that in combining the two views he would ever decide that the four lines seen, the two seen first and the two seen second, make only two straight lines. In uniting the two perceptions in thought, he would certainly place a bend or a turn somewhere, possibly at the spot fromwhich he took the two views. He would continue to do so till he realized that the lines seen on either side did not in fact approach nearer each other. Or, to state the whole phenomenon with more scientific accuracy: Intuitively, and to a person who had not acquired the knowledge of distance by experience, the two views would appear to be each of two lines approaching nearer each other; but without his being at all cognisant of the relation of the two views, or of one part of the lines being further removed from him than another. As experience told him that the lines receded from him on each side, he would contrive some means of combining his observations, probably in the way above indicated; but he never could make two straight lines enclose a space.” [Pp. 210-11.]

Now it seems to me that the supposed percipient could not account for his apparent perceptions in the manner indicated; he could not believe that there was a turn or a bend anywhere. “At the spot from which he took the two views” he would have the evidence of his senses that there was no bend. Looking along the interval between the lines, he would again have the evidence of sense that they were not deflected either way, but maintained an uniform direction. Until therefore, experience of the laws of perspective had corrected his judgment, he would have the apparent evidence of his senses that two straight lines met in two points. This appearance, until shown by further experience to be an illusion, would probably decide his belief: and any doubts that might be raised by a contemplation of straight lines which were nearer to him, would be silenced by the supposition that two straight lines will inclose a space if only they are produced far enough.

Dr. M‘Cosh may himself be cited as a witness to the intrinsic possibility of conceiving combinations which I should have thought were universally regarded as inconceivable. When distinguishing between the two meanings of inconceivable (in pp. 235-6 of his book) he says: “We cannot be made to decide or believe that Cleopatra’s Needle should be in Paris and Egypt at the same time; yet with some difficulty we can simultaneously image it in both places.” Now when we consider that in order really to image the same Needle (and not two Needles exactly similar) in two places at once we must actually imagine the two places, Paris and Alexandria, superposed upon one another and occupying the same portion of space, it seems to me that this conception is quite as impossible to us as the reverse of a geometrical axiom; and is, indeed, of much the same character.e

The “Geometry of Visibles” has been noticed only by Dr. M‘Cosh (pp. 211-13), who rejects it, as founded on the erroneous doctrine (as he considers it) that we cannot perceive by sight the third dimension of space. I regard this, on the contrary, as not only a true doctrine, but one from which Dr. M‘Cosh’s own opinion does not materially differ: and if it be true, it is impossible to resist Reid’s conclusion [see Inquiry, pp. 149-50], that to beings possessing only the sense of sight, the paradoxes here quoted, and several others, would be truths of intuition—selfevident truths.d

fDr. Ward, in the Dublin Review, contests this doctrine [“Mr. Mill’s Denial of Necessary Truth,” pp. 304-5]; and an argument against it has been sent to me by the intelligent and instructed correspondent already once referred to. For a reply I might refer them to the chapter on the Geometry of Visibles, in Reid’s work; but I will point out, in few words, where I think they are in error. They contend that Reid’s Idomenians would not possess the notion which we attach to the term straight line, but would call by that name what they would really image to themselves as a circular arc. But Reid’s position (and he assigns good reasons for it) is the reverse of this; that what we, who have the sense of touch, perceive as a circular arc with ourselves in the centre, Idomenians could only perceive as a straight line; and that, consequently, all the appearances which Reid enumerates would be by them apprehended, and, as they would think, perceived, as phenomena of straight lines.

Dr. M‘Cosh also returns to the charge, but holds a different doctrine from my other two critics, being of opinion that the Idomenians would really have the notion of a straight line. [See “Mill’s Reply,” p. 356.] For the consequences of this I refer him back to Reid. He adds, that as touch alone can reveal to us impenetrability, the Idomenians could argue nothing as to bodies penetrating one another. [See Inquiry, pp. 150-2.] But, they could have the conception of the only penetration Reid contended for, namely, of bodies meeting and coinciding in the same place, and separating again without alteration. And for this they would have the evidence of sense. The fact is literally true of the visual images, which to them would be the whole bodies; and as they could form no notion of one thing passing behind another, their only impression would be of penetration.f

[* ][72] I do not mean, which is really incredible, as Mr. Mansel, in his rejoinder, supposes I do, and consequently charges me with imputing to Sir W. Hamilton that in the Law of the Conditioned he maintains that of two incredible alternatives one must be believed. [“Supplementary Remarks,” p. 27.]

[g]651, 652 it

[[*] ]See On the Intellectual Powers, pp. 375-9.

[* ][67] It is curious that Dr. M‘Cosh, with this volume before him, and occupied in criticizing it, did not find out until his book was passing through the press, and then only from the sixth edition of my System of Logic, that I was aware of the difference between these two meanings of “to conceive.” (M‘Cosh, [Examination,] p. 241n. [See System of Logic, Bk. II, Chap. vii, §3, in Collected Works, Vol. VII, p. 269.]) He consequently thought it necessary to tell me, what I had myself stated in the text, that Antipodes were inconceivable only in the second sense. [McCosh, Examination, pp. 240-1.]

hDr. M‘Cosh continually charges me with confounding the two meanings, and arguing from one of them to the other. [See “Mill’s Reply,” pp. 357-8.] But he must be well aware that intuitional philosophers in general (I do not say that Dr. M‘Cosh) assign as the sufficient, and conclusive proof of inconceivability in the one sense, inconceivability in the other. They argue that a proposition must be true, and ought to be believed—on the ground that we cannot conceive its opposite, meaning that we cannot frame a mental representation of it. It is therefore quite pertinent to show (when it can be done) that this inability to join the ideas together is not inherent in our constitution, but is accounted for by the conditions of our experience; for to shew this, is to destroy the argument principally relied on as a proof that the judgment is a necessary one.h

[i-i]+67, 72

[* ]Lectures, Vol. III, p. 102.

[† ]Ibid., p. 100.

[‡ ]“Dissertations on Reid,” [Note A,] p. 745.

[§ ][67] Mr. Mansel refuses to admit ([Philosophy of the Conditioned,] pp. 131ff.) that Sir W. Hamilton confounds these different senses of the word Conception, and asserts that he always adheres to the meaning indicated by him in a foot-note to Reid (p. 377n), and answering to the first meaning of inconceivable, namely, unimaginable. Of the second meaning Mr. Mansel says, “When Hamilton speaks of being ‘unable to conceive as possible,’ he does not mean, as Mr. Mill supposes, physically possible under the law of gravitation or some other law of matter, but mentally possible as a representation or image; and thus the supposed second sense is identical with the first.” (P. 132n.) According to this interpretation, when Sir W. Hamilton says of anything that it cannot be conceived as possible, he does not mean possible in fact, but possible to thought, in other words, that it cannot be conceived as conceivable. I, however, do Sir W. Hamilton the justice of believing, that when he added the words “as possible” to the word conceive, he intended to add something to the idea. Accordingly he uses the phrases “to understand as possible,” “to comprehend as possible,” as equivalents for “to conceive as possible.” [See, e.g., Discussions, p. 15; Lectures, Vol. III, p. 101.] I believe that by “possible” he meant, as people usually do, possible in fact. And I have the authority of Mr. Mansel himself for so thinking. Mr. Mansel, in another place expresses what was probably the real meaning of Sir W. Hamilton, and laments that Sir W. Hamilton did not state it distinctly. “To conceive a thing as possible,” says Mr. Mansel, “we must conceive the manner in which it is possible; but we may believe in the fact without being able to conceive the manner.” ([Philosophy of the Conditioned,] p. 36n.) jThis makes no sense if understood as Mr. Mansel, in his rejoinder, says that it ought to be—“mentally possible as a notion, not physically possible as a fact.” [“Supplementary Remarks,” p. 27.] There is no manner of being possible as a mere notion: the elements of the notion can be put together in the mind, or they cannot. A manner of being possible can only refer to possibility as a fact.j When people say that they cannot conceive how a thing is possible, they always mean, that but for evidence to the contrary, they should have supposed it impossible. And this I always find to be the case when Sir W. Hamilton uses the phrase. I know not of any manner of a possibility that would enable us to conceive the thing “as possible” unless it removed some obstacle to believing that the thing is possible. Such, for instance, would be the case, if we have found or imagined something which is capable of causing the thing; or some means or mechanism by which it could be brought about (the desideratum in Mr. Mansel’s illustration of a being who sees without eyes [Philosophy of the Conditioned, p. 126n]); or if we have had an actual intuition of the thing as existing: which, when sufficiently familiar, makes it no longer seem to require any ground of possibility beyond the fact itself. In short, the how of its existence, which enables us to conceive it as possible, must be a how which affords at least a semblance of explanation of Mr. Mansel’s that. This is distinctly recognised by Sir W. Hamilton in one of the passages I have quoted, in which “to conceive the possibility” of a thing is defined “conceiving it as the consequent of a certain reason.” By conceiving a thing as possible, he meant apprehending some fact, or imagining some hypothesis, which would explain its possibility; which would be, in the Leibnitzian sense, its Sufficient Reason. For, an explanation, even hypothetical, of a thing which previously seemed to admit of none, removes a difficulty in believing it. kWe have a natural tendency to disbelieve anything which, while it has never been presented in our experience, also contradicts our habitual associations: but the suggestion to our mind of some possible conditions which would be a Sufficient Reason for its existence, takes away its incredibility, and enables us to “conceive it as possible.” This view of Sir W. Hamilton’s meaning explains, though it does not justify, his using the term in its third signification; which Mr. Mansel also endeavours to reduce to the first ([ibid.,] p. 132n), but which may be better identified with the second: for of First Truths also it is impossible to assign any Sufficient Reason.k

[l-l]651, 652 we may disregard, not only as inadmissible, but as avowedly compatible with belief

[* ]Lectures, Vol. III, p. 99.

[* ]Ibid., p. 113.

[† ]Discussions, [App. I (A),] p. 624.

[‡ ]Ibid., p. 15.

[* ]“Dissertations on Reid,” [Note D***,] p. 911.

[† ]To save words in the text, I shall simply indicate in foot-notes the places at which the author passes from one of the three meanings of the word Inconceivable to another. In this place he is using it in the first or second meaning, probably in the first.

[‡ ]First mand second senses confused togetherm .

[§ ]First sense.

[¶ ]First sense.

[∥ ]Third sense.

[* ]Third sense, gliding back into the first.

[† ]Here the return to the first sense is completed.

[‡ ]nSecond sensen .

[§ ]Second sense.

[¶ ]First sense.

[∥ ]Lectures, Vol. III, pp. 100-4.

[[*] ]See ibid., Vol. II, pp. 404-13.

[o]651, 652 I think he has failed to make out either point. [Cf. 87-8c-cand 88n below.]

[p]651, 652 it

[q-q]+67, 72

[r-r]651, 652 infinite

[s-s]+67, 72

[t-t]651, 652 other

[* ][67] Mr. Manselu replies that our system of numeration enables us to “exhaust any finite number, by dealing with its items in large masses,” but that no such process can “exhaust the infinite.” ([Philosophy of the Conditioned,] p. 134.) vMy argument isv that we need not exhaust the infinite to be enabled to conceive it; since, in point of fact, we do not exhaust the finite numbers which it is admitted that we can and do conceive. wMr. Mansel says we do [“Supplementary Remarks,” p. 27]; which reduces the question to a difference in the meaning of the word exhaust. In the only sense that is of importance to the argument, we do not mentally exhaust any large number, since we do not acquire an adequate idea of it.w

[x]651, 652 completely

[y-y]651, 652 time [printer’s error?]

[z-z]651, 652 It is not vague and indeterminate, as a merely negative notion is.

[a-a]651, 652 does not seem to have

[b-b]651, 652 power

[c-c]651, 652 or, if some à priori metaphysical prejudice prevented us from believing it, we should at least be enabled to conceive it

[* ]See the catalogue at length, in the Appendix [iii] to the second volume of the Lectures, pp. 527-9.

[d-d]651, 652 We have now to examine the second half of the “Law of the Conditioned,” namely, that although the pair of contradictory hypotheses in each Antinomy are both of them inconceivable, one or the other of them must be true.

I should not, of course, dream of denying this, when the propositions are taken in a phænomenal sense; when the subjects and predicates of them are interpreted relatively to us. The Will, for example, is wholly a phænomenon; it has no meaning unless relatively to us; and I of course admit that it must be either free or caused. Space and Time, in their phænomenal character, or as they present themselves to our perceptive faculties, are necessarily either bounded or boundless, infinitely or only finitely divisible. The law of Excluded Middle, as well as that of Contradiction, is common to all phænomena. But it is a doctrine of our author that these laws are true, and cannot but be known to be true, of Noumena likewise. It is not merely Space as cognisable by our senses, but Space as it is in itself, which he affirms must be either of unlimited or of limited extent. Now, not to speak at present of the Principle of Contradiction, I demur to that of Excluded Middle as applicable to Things in themselves. . . . [Here appear, in immediate succession, the two passages JSM quotes from himself in the footnote above.] As already observed, the only contradictory alternative of which the negative side contains nothing positive is that between Entity and Non-entity, Existing and Non-existing; and so far as regards that distinction, I admit the law of Excluded Middle as applicable to Noumena; they must either exist or not exist. But this is all the applicability I can allow to it.

If the preceding arguments are valid, the “Law of the Conditioned” breaks down in both its parts. It is not proved that the Conditioned lies between two hypotheses concerning the Unconditioned, neither of which hypotheses we can conceive as possible. And it is not proved, that, as regards the Unconditioned, one or the other of these hypotheses must be true. Both propositions

[* ][67] In the first edition, besides denying the inconceivability of the pairs of contradictory hypotheses in Sir W. Hamilton’s Antinomies, I also contested the assertion that one or other of them must be true; arguing, that the law of Excluded Middle, though true of all phænomena, and therefore of Space and Time in their phænomenal character, is not a law of Things. “The law of Excluded Middle is, that whatever predicate we suppose, either that or its negative must be true of any given subject: and this I do not admit when the subject is a Noumenon; inasmuch as every possible predicate, even negative, except the single one of Non-entity, involves, as a part of itself, something positive, which part is only known to us by phænomenal experience, and may have only a phænomenal existence.” This, being an overstatement, and, when reduced to its proper bounds, not necessarily conflicting with anything said by Sir W. Hamilton on the present subject, I abandon. But I retain a portion of my remarks, illustrative of the abusive application of which the Principle of Excluded Middle is susceptible. “The universe, for example, must, it is affirmed, be either infinite or finite: but what do these words mean? That it must be either of infinite or finite magnitude. Magnitudes certainly must be either infinite or finite, but before affirming the same thing of the Noumenon Universe, it has to be established that the universe as it is in itself is capable of the attribute magnitude. How do we know that magnitude is not exclusively a property of our sensations—of the states of subjective consciousness which objects produce in us? Or if this supposition displeases, how do we know that magnitude is not, as Kant considered it eto bee , a form of our minds, an attribute with which the laws of thought invest every conception that we can form, but to which there may be nothing analogous in the Noumenon, the Thing in itself? The like may be said of Duration, whether infinite or finite, and of Divisibility, whether stopping at a minimum or prolonged without limit. Either the one proposition or the other must of course be true of duration and of matter as they are perceived by us—as they present themselves to our faculties; but duration itself is held by Kant to have no real existence out of our minds; and as for matter, not knowing what it is in itself, we know not whether, as affirmed of matter in itself, the word divisible has any meaning. Believing divisibility to be an acquired notion, made up of the elements of our sensational experience, I do not admit that the Noumenon Matter must be either infinitely or finitely divisible.” [Cf. 87d-d above.]

[* ]That the reverse of the most familiar principles of arithmetic and geometry might have been made conceivable, even to our present mental faculties, if those faculties had coexisted with a totally different constitution of external nature, is ingeniously shown in the concluding paper of a recent volume, anonymous, but of known authorship, Essays, by a Barrister.

“Consider this case. There is a world in which, whenever two pairs of things are either placed in proximity or are contemplated together, a fifth thing is immediately created and brought within the contemplation of the mind engaged in putting two and two together. This is surely neither inconceivable, for we can readily conceive the result by thinking of common puzzle tricks, nor can it be said to be beyond the power of Omnipotence. Yet in such a world surely two and two would make five. That is, the result to the mind of contemplating two two’s would be to count five. This shows that it is not inconceivable that two and two might make five: but, on the other hand, it is perfectly easy to see why in this world we are absolutely certain that two and two make four. There is probably not an instant of our lives in which we are not experiencing the fact. We see it whenever we count four books, four tables or chairs, four men in the street, or the four corners of a paving stone, and we feel more sure of it than of the rising of the sun to-morrow, because our experience upon the subject is so much wider and applies to such an infinitely greater number of cases. Nor is it true that every one who has once been brought to see it, is equally sure of it. A boy who has just learnt the multiplication table is pretty sure that twice two are four, but is often extremely doubtful whether seven times nine are sixty-three. If his teacher told him that twice two made five, his certainty would be greatly impaired.

It would also be possible to put a case of a world in which two straight lines should be universally supposed to include a space. Imagine a man who had never had any experience of straight lines through the medium of any sense whatever, suddenly placed upon a railway stretching out on a perfectly straight line to an indefinite distance in each direction. He would see the rails, which would be the first straight lines he had ever seen, apparently meeting, or at least tending to meet at each horizon; and he would thus infer, in the absence of all other experience, that they actually did enclose a space, when produced far enough. Experience alone could undeceive him. A world in which every object was round, with the single exception of a straight inaccessible railway, would be a world in which every one would believe that two straight lines enclosed a space. In such a world, therefore, the impossibility of conceiving that two straight lines can enclose a space would not exist.” [James Fitzjames Stephen, “Mr. Mansel’s Metaphysics,” in Essays by a Barrister (London: Smith, Elder, 1862), pp. 333-4.]

In the “Geometry of Visibles” which forms part of Reid’s Inquiry into the Human Mind, it is contended that if we had the sense of sight, but not that of touch, it would appear to us that “every right line being produced will at last return into itself,” and that “any two right lines being produced will meet in two points.” [In Works, ed. Hamilton,] Chap. vi, §9 (p. 148.) The author adds, that persons thus constituted would firmly believe “that two or more bodies may exist in the same place.” For this they would “have the testimony of sense,” and could “no more doubt of it than they can doubt whether they have any perception at all, since they would often see two bodies meet and coincide in the same place, and separate again, without having undergone any change in their sensible qualities by this penetration.” (Ibid., p. 151.)

dHardly any part of the present volume has been so maltreated, by so great a number of critics, as the illustrations here quoted from an able and highly instructed cotemporary thinker; which, as they were neither designed by their author nor cited by me as anything more than illustrations, I do not deem it necessary to take up space by defending. When a selection must be made, one is obliged to consider what one can best spare.

eSome of my correspondents, looking upon the illustrations by “A Barrister” as (what they are not) an essential part of my argument, think me bound either to defend them or to give them up. As they are, in my opinion, perfectly defensible, I am ready, thus challenged, to stand up for them. And I select, among the attacks made on them, that of Dr. M‘Cosh (Examination of Mr. J. S. Mill’s Philosophy, pp. 209-11), as one of the fairest, and including what is most worthy of notice in the others. Of the first illustration, Dr. M‘Cosh says:

“Were we placed in a world in which two pairs of things were always followed by a fifth thing, we might be disposed to believe that the pairs caused the fifth thing, or that there was some prearranged disposition of things producing them together; but we could not be made to judge that 2 + 2 = 5, or that the fifth thing is not a different thing from the two and the two. On the other supposition put, of the two pairs always suggesting a fifth, we should explain their recurrence by some law of association, but we would not confound the 5 with the 2 + 2, or think that the two pairs could make five.” [P. 210.]

This passage is a correct description of what would happen if the presentation of the fifth thing were posterior, by a perceptible interval, to the juxtaposition of the two pairs, so that we should have time to judge that the two and two make four previously to perceiving the fifth. But the supposition is that the production of the fifth is so instantaneous in the very act of seeing, that we never should see the four things by themselves as four: the fifth thing would be inseparably involved in the act of perception by which we should ascertain the sum of the two pairs. I confess it seems to me that in this case we should have an apparent intuition of two and two making five.

To the second illustration, Dr. M‘Cosh replies: “I allow that this person as he looked one way, would see a figure presented to the eye of two straight lines approaching nearer each other; and that as he looked the other way he would see a like figure. But I deny that in combining the two views he would ever decide that the four lines seen, the two seen first and the two seen second, make only two straight lines. In uniting the two perceptions in thought, he would certainly place a bend or a turn somewhere, possibly at the spot fromwhich he took the two views. He would continue to do so till he realized that the lines seen on either side did not in fact approach nearer each other. Or, to state the whole phenomenon with more scientific accuracy: Intuitively, and to a person who had not acquired the knowledge of distance by experience, the two views would appear to be each of two lines approaching nearer each other; but without his being at all cognisant of the relation of the two views, or of one part of the lines being further removed from him than another. As experience told him that the lines receded from him on each side, he would contrive some means of combining his observations, probably in the way above indicated; but he never could make two straight lines enclose a space.” [Pp. 210-11.]

Now it seems to me that the supposed percipient could not account for his apparent perceptions in the manner indicated; he could not believe that there was a turn or a bend anywhere. “At the spot from which he took the two views” he would have the evidence of his senses that there was no bend. Looking along the interval between the lines, he would again have the evidence of sense that they were not deflected either way, but maintained an uniform direction. Until therefore, experience of the laws of perspective had corrected his judgment, he would have the apparent evidence of his senses that two straight lines met in two points. This appearance, until shown by further experience to be an illusion, would probably decide his belief: and any doubts that might be raised by a contemplation of straight lines which were nearer to him, would be silenced by the supposition that two straight lines will inclose a space if only they are produced far enough.

Dr. M‘Cosh may himself be cited as a witness to the intrinsic possibility of conceiving combinations which I should have thought were universally regarded as inconceivable. When distinguishing between the two meanings of inconceivable (in pp. 235-6 of his book) he says: “We cannot be made to decide or believe that Cleopatra’s Needle should be in Paris and Egypt at the same time; yet with some difficulty we can simultaneously image it in both places.” Now when we consider that in order really to image the same Needle (and not two Needles exactly similar) in two places at once we must actually imagine the two places, Paris and Alexandria, superposed upon one another and occupying the same portion of space, it seems to me that this conception is quite as impossible to us as the reverse of a geometrical axiom; and is, indeed, of much the same character.e

The “Geometry of Visibles” has been noticed only by Dr. M‘Cosh (pp. 211-13), who rejects it, as founded on the erroneous doctrine (as he considers it) that we cannot perceive by sight the third dimension of space. I regard this, on the contrary, as not only a true doctrine, but one from which Dr. M‘Cosh’s own opinion does not materially differ: and if it be true, it is impossible to resist Reid’s conclusion [see Inquiry, pp. 149-50], that to beings possessing only the sense of sight, the paradoxes here quoted, and several others, would be truths of intuition—selfevident truths.d

fDr. Ward, in the Dublin Review, contests this doctrine [“Mr. Mill’s Denial of Necessary Truth,” pp. 304-5]; and an argument against it has been sent to me by the intelligent and instructed correspondent already once referred to. For a reply I might refer them to the chapter on the Geometry of Visibles, in Reid’s work; but I will point out, in few words, where I think they are in error. They contend that Reid’s Idomenians would not possess the notion which we attach to the term straight line, but would call by that name what they would really image to themselves as a circular arc. But Reid’s position (and he assigns good reasons for it) is the reverse of this; that what we, who have the sense of touch, perceive as a circular arc with ourselves in the centre, Idomenians could only perceive as a straight line; and that, consequently, all the appearances which Reid enumerates would be by them apprehended, and, as they would think, perceived, as phenomena of straight lines.

Dr. M‘Cosh also returns to the charge, but holds a different doctrine from my other two critics, being of opinion that the Idomenians would really have the notion of a straight line. [See “Mill’s Reply,” p. 356.] For the consequences of this I refer him back to Reid. He adds, that as touch alone can reveal to us impenetrability, the Idomenians could argue nothing as to bodies penetrating one another. [See Inquiry, pp. 150-2.] But, they could have the conception of the only penetration Reid contended for, namely, of bodies meeting and coinciding in the same place, and separating again without alteration. And for this they would have the evidence of sense. The fact is literally true of the visual images, which to them would be the whole bodies; and as they could form no notion of one thing passing behind another, their only impression would be of penetration.f

[* ][67] It is curious that Dr. M‘Cosh, with this volume before him, and occupied in criticizing it, did not find out until his book was passing through the press, and then only from the sixth edition of my System of Logic, that I was aware of the difference between these two meanings of “to conceive.” (M‘Cosh, [Examination,] p. 241n. [See System of Logic, Bk. II, Chap. vii, §3, in Collected Works, Vol. VII, p. 269.]) He consequently thought it necessary to tell me, what I had myself stated in the text, that Antipodes were inconceivable only in the second sense. [McCosh, Examination, pp. 240-1.]

hDr. M‘Cosh continually charges me with confounding the two meanings, and arguing from one of them to the other. [See “Mill’s Reply,” pp. 357-8.] But he must be well aware that intuitional philosophers in general (I do not say that Dr. M‘Cosh) assign as the sufficient, and conclusive proof of inconceivability in the one sense, inconceivability in the other. They argue that a proposition must be true, and ought to be believed—on the ground that we cannot conceive its opposite, meaning that we cannot frame a mental representation of it. It is therefore quite pertinent to show (when it can be done) that this inability to join the ideas together is not inherent in our constitution, but is accounted for by the conditions of our experience; for to shew this, is to destroy the argument principally relied on as a proof that the judgment is a necessary one.h

[§ ][67] Mr. Mansel refuses to admit ([Philosophy of the Conditioned,] pp. 131ff.) that Sir W. Hamilton confounds these different senses of the word Conception, and asserts that he always adheres to the meaning indicated by him in a foot-note to Reid (p. 377n), and answering to the first meaning of inconceivable, namely, unimaginable. Of the second meaning Mr. Mansel says, “When Hamilton speaks of being ‘unable to conceive as possible,’ he does not mean, as Mr. Mill supposes, physically possible under the law of gravitation or some other law of matter, but mentally possible as a representation or image; and thus the supposed second sense is identical with the first.” (P. 132n.) According to this interpretation, when Sir W. Hamilton says of anything that it cannot be conceived as possible, he does not mean possible in fact, but possible to thought, in other words, that it cannot be conceived as conceivable. I, however, do Sir W. Hamilton the justice of believing, that when he added the words “as possible” to the word conceive, he intended to add something to the idea. Accordingly he uses the phrases “to understand as possible,” “to comprehend as possible,” as equivalents for “to conceive as possible.” [See, e.g., Discussions, p. 15; Lectures, Vol. III, p. 101.] I believe that by “possible” he meant, as people usually do, possible in fact. And I have the authority of Mr. Mansel himself for so thinking. Mr. Mansel, in another place expresses what was probably the real meaning of Sir W. Hamilton, and laments that Sir W. Hamilton did not state it distinctly. “To conceive a thing as possible,” says Mr. Mansel, “we must conceive the manner in which it is possible; but we may believe in the fact without being able to conceive the manner.” ([Philosophy of the Conditioned,] p. 36n.) jThis makes no sense if understood as Mr. Mansel, in his rejoinder, says that it ought to be—“mentally possible as a notion, not physically possible as a fact.” [“Supplementary Remarks,” p. 27.] There is no manner of being possible as a mere notion: the elements of the notion can be put together in the mind, or they cannot. A manner of being possible can only refer to possibility as a fact.j When people say that they cannot conceive how a thing is possible, they always mean, that but for evidence to the contrary, they should have supposed it impossible. And this I always find to be the case when Sir W. Hamilton uses the phrase. I know not of any manner of a possibility that would enable us to conceive the thing “as possible” unless it removed some obstacle to believing that the thing is possible. Such, for instance, would be the case, if we have found or imagined something which is capable of causing the thing; or some means or mechanism by which it could be brought about (the desideratum in Mr. Mansel’s illustration of a being who sees without eyes [Philosophy of the Conditioned, p. 126n]); or if we have had an actual intuition of the thing as existing: which, when sufficiently familiar, makes it no longer seem to require any ground of possibility beyond the fact itself. In short, the how of its existence, which enables us to conceive it as possible, must be a how which affords at least a semblance of explanation of Mr. Mansel’s that. This is distinctly recognised by Sir W. Hamilton in one of the passages I have quoted, in which “to conceive the possibility” of a thing is defined “conceiving it as the consequent of a certain reason.” By conceiving a thing as possible, he meant apprehending some fact, or imagining some hypothesis, which would explain its possibility; which would be, in the Leibnitzian sense, its Sufficient Reason. For, an explanation, even hypothetical, of a thing which previously seemed to admit of none, removes a difficulty in believing it. kWe have a natural tendency to disbelieve anything which, while it has never been presented in our experience, also contradicts our habitual associations: but the suggestion to our mind of some possible conditions which would be a Sufficient Reason for its existence, takes away its incredibility, and enables us to “conceive it as possible.” This view of Sir W. Hamilton’s meaning explains, though it does not justify, his using the term in its third signification; which Mr. Mansel also endeavours to reduce to the first ([ibid.,] p. 132n), but which may be better identified with the second: for of First Truths also it is impossible to assign any Sufficient Reason.k

[‡ ]First mand second senses confused togetherm .

[‡ ]nSecond sensen .

[* ][67] Mr. Manselu replies that our system of numeration enables us to “exhaust any finite number, by dealing with its items in large masses,” but that no such process can “exhaust the infinite.” ([Philosophy of the Conditioned,] p. 134.) vMy argument isv that we need not exhaust the infinite to be enabled to conceive it; since, in point of fact, we do not exhaust the finite numbers which it is admitted that we can and do conceive. wMr. Mansel says we do [“Supplementary Remarks,” p. 27]; which reduces the question to a difference in the meaning of the word exhaust. In the only sense that is of importance to the argument, we do not mentally exhaust any large number, since we do not acquire an adequate idea of it.w

[* ][67] In the first edition, besides denying the inconceivability of the pairs of contradictory hypotheses in Sir W. Hamilton’s Antinomies, I also contested the assertion that one or other of them must be true; arguing, that the law of Excluded Middle, though true of all phænomena, and therefore of Space and Time in their phænomenal character, is not a law of Things. “The law of Excluded Middle is, that whatever predicate we suppose, either that or its negative must be true of any given subject: and this I do not admit when the subject is a Noumenon; inasmuch as every possible predicate, even negative, except the single one of Non-entity, involves, as a part of itself, something positive, which part is only known to us by phænomenal experience, and may have only a phænomenal existence.” This, being an overstatement, and, when reduced to its proper bounds, not necessarily conflicting with anything said by Sir W. Hamilton on the present subject, I abandon. But I retain a portion of my remarks, illustrative of the abusive application of which the Principle of Excluded Middle is susceptible. “The universe, for example, must, it is affirmed, be either infinite or finite: but what do these words mean? That it must be either of infinite or finite magnitude. Magnitudes certainly must be either infinite or finite, but before affirming the same thing of the Noumenon Universe, it has to be established that the universe as it is in itself is capable of the attribute magnitude. How do we know that magnitude is not exclusively a property of our sensations—of the states of subjective consciousness which objects produce in us? Or if this supposition displeases, how do we know that magnitude is not, as Kant considered it eto bee , a form of our minds, an attribute with which the laws of thought invest every conception that we can form, but to which there may be nothing analogous in the Noumenon, the Thing in itself? The like may be said of Duration, whether infinite or finite, and of Divisibility, whether stopping at a minimum or prolonged without limit. Either the one proposition or the other must of course be true of duration and of matter as they are perceived by us—as they present themselves to our faculties; but duration itself is held by Kant to have no real existence out of our minds; and as for matter, not knowing what it is in itself, we know not whether, as affirmed of matter in itself, the word divisible has any meaning. Believing divisibility to be an acquired notion, made up of the elements of our sensational experience, I do not admit that the Noumenon Matter must be either infinitely or finitely divisible.” [Cf. 87d-d above.]

[dHardly any part of the present volume has been so maltreated, by so great a number of critics, as the illustrations here quoted from an able and highly instructed cotemporary thinker; which, as they were neither designed by their author nor cited by me as anything more than illustrations, I do not deem it necessary to take up space by defending. When a selection must be made, one is obliged to consider what one can best spare.]74+67, 72

[eSome of my correspondents, looking upon the illustrations by “A Barrister” as (what they are not) an essential part of my argument, think me bound either to defend them or to give them up. As they are, in my opinion, perfectly defensible, I am ready, thus challenged, to stand up for them. And I select, among the attacks made on them, that of Dr. M‘Cosh (Examination of Mr. J. S. Mill’s Philosophy, pp. 209-11), as one of the fairest, and including what is most worthy of notice in the others. Of the first illustration, Dr. M‘Cosh says:]+72

[fDr. Ward, in the Dublin Review, contests this doctrine [“Mr. Mill’s Denial of Necessary Truth,” pp. 304-5]; and an argument against it has been sent to me by the intelligent and instructed correspondent already once referred to. For a reply I might refer them to the chapter on the Geometry of Visibles, in Reid’s work; but I will point out, in few words, where I think they are in error. They contend that Reid’s Idomenians would not possess the notion which we attach to the term straight line, but would call by that name what they would really image to themselves as a circular arc. But Reid’s position (and he assigns good reasons for it) is the reverse of this; that what we, who have the sense of touch, perceive as a circular arc with ourselves in the centre, Idomenians could only perceive as a straight line; and that, consequently, all the appearances which Reid enumerates would be by them apprehended, and, as they would think, perceived, as phenomena of straight lines.]+72

[hDr. M‘Cosh continually charges me with confounding the two meanings, and arguing from one of them to the other. [See “Mill’s Reply,” pp. 357-8.] But he must be well aware that intuitional philosophers in general (I do not say that Dr. M‘Cosh) assign as the sufficient, and conclusive proof of inconceivability in the one sense, inconceivability in the other. They argue that a proposition must be true, and ought to be believed—on the ground that we cannot conceive its opposite, meaning that we cannot frame a mental representation of it. It is therefore quite pertinent to show (when it can be done) that this inability to join the ideas together is not inherent in our constitution, but is accounted for by the conditions of our experience; for to shew this, is to destroy the argument principally relied on as a proof that the judgment is a necessary one.h]+72

[jThis makes no sense if understood as Mr. Mansel, in his rejoinder, says that it ought to be—“mentally possible as a notion, not physically possible as a fact.” [“Supplementary Remarks,” p. 27.] There is no manner of being possible as a mere notion: the elements of the notion can be put together in the mind, or they cannot. A manner of being possible can only refer to possibility as a fact.j]67 This is reducible to my second meaning of inconceivable, that which is synonymous with incredible.

[kWe have a natural tendency to disbelieve anything which, while it has never been presented in our experience, also contradicts our habitual associations: but the suggestion to our mind of some possible conditions which would be a Sufficient Reason for its existence, takes away its incredibility, and enables us to “conceive it as possible.” This view of Sir W. Hamilton’s meaning explains, though it does not justify, his using the term in its third signification; which Mr. Mansel also endeavours to reduce to the first ([ibid.,] p. 132n), but which may be better identified with the second: for of First Truths also it is impossible to assign any Sufficient Reason.k][manuscript fragment exists; see Appendix A below.]

[mand second senses confused togetherm]651, 652 sense

[nSecond sensen]651, 652 Here the second sense makes its appearance

[u]67 , entirely missing the point of this argument,

[vMy argument isv]67 If Mr. Mansel had considered a little, he would have seen my argument to be

[wMr. Mansel says we do [“Supplementary Remarks,” p. 27]; which reduces the question to a difference in the meaning of the word exhaust. In the only sense that is of importance to the argument, we do not mentally exhaust any large number, since we do not acquire an adequate idea of it.w]+72

[eto bee]+67, 72