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 XXI

The Fundamental Laws of Thought According to Sir William Hamilton

having marked out, as the sole province of Logic, the “Laws of Thought,” Sir W. Hamilton naturally proceeds to specify what these are. The “Fundamental Laws of Thought,” of which all other laws that can be laid down for thought are but particular applications, are, according to our author, three in number: the Law of Identity; the Law of Contradiction; and the Law of Excluded Middle. In his Lectures he recognised a fourth, “the Law of Reason and Consequent,” which seems to be compounded of the Law of Causation, and the Leibnitzian “Principle of Sufficient Reason.”^[*] But as, in his later speculations, he no longer considered this as an ultimate law, it needs not be further spoken of.

These three laws he otherwise denominates “The Conditions of the Thinkable:”^* from which it might have been supposed that he regarded them as Laws of Thought in the scientific sense of the word law; conditions to which thought cannot but conform, and apart from which it is impossible. One would have said, à priori, that he could not mean anything but this: since otherwise the expression “Conditions of the Thinkable” is perverted from its meaning. Nevertheless, this is not what he means, at least in this place. It is on this very occasion that he disclaims, as applicable to laws of thought, the scientific meaning of the term, and declares them to be (like the laws made by Parliament) general precepts; not necessities of the thinking act, but instructions for right thinking. Yet it would not have been claiming too much for these three laws, to have regarded them as laws in the more peremptory sense; as actual necessities of thought. Our author could hardly have meant that we are able to disbelieve that a thing is itself, or to believe that a thing is, and at the same time that it is not. He not only, like other people, constantly assumes this to be an impossibility, but makes that impossibility the ground of some of his leading philosophical doctrines; as when he says that it is impossible for us to doubt the actual facts of consciousness “because the doubt implies a contradiction.”^* It is true that a person may, in one sense, believe contradictory propositions, that is, he may believe the affirmative at some times and the negative at others, alternately forgetting the two beliefs. It is also true that he may yield a passive assent to two forms of words, which, had he been fully conscious of their meaning, he would have known to be, either wholly or in part, an affirmation and a denial of the same fact. But when once he is made to see that there is a contradiction, it is totally impossible for him to believe it.

Now, to compel people to see a contradiction where a contradiction is, constitutes the entire office of Logic in the limited sense in which Sir W. Hamilton conceives it: and he is quite right in regarding the whole of Logic, in that narrow sense, as resting on the three laws specified by him. To call them the fundamental laws of Thought is a^a misnomer; but they are the laws of Consistency. All inconsistency is a violation of some one of these laws; an unconscious violation, for knowingly to violate them is impossible.

Something remains to be said respecting the three Laws considered singly, as well as respecting our author’s mode of regarding them.

The Law or Principle of Identity (Principium Identitatis) is no other than the time-honoured axiom, “Whatever is, is,” or, in another phraseology, “A thing is the same as itself:” the proposition which Locke, in his chapter on Maxims, treated with so much disrespect.^[*] Sir W. Hamilton, probably finding it difficult to establish the “principle of all logical affirmation” on such a basis as this, presents the axiom^† in a modified shape, as an assertion of the identity between a whole and its parts; or rather between a whole Concept, and its parts in Comprehension—the attributes which compose it; for Logic, as conceived by him, has nothing to do with any wholes but Concepts, abstracting altogether (as he asserts) from the reality of the things conceived.^‡

Although our author still so far defers to the old version of the Principle of Identity, as to say that it is “expressed in the formula A is A, or A = A,”^[*] I must admit that while paying this tribute of respect to our ancient friend, he has taken a very substantial and useful liberty with him, and has made him mean much more than he ever meant before. The only fault that can be found (but that is a serious one) is, that if we accept this view of the maxim, we shall require many “principles of logical affirmation” instead of one. For if we are to make a separate principle for every mode in which we have occasion to re-affirm the same thing in different words, we need a large number of them. If we require a special principle to entitle us, when we have affirmed a set of attributes jointly, to affirm over again the same attributes severally, we require also a long list of such principles as these: When one thing is before another, the other is after. When one thing is after another, the other is before. When one thing is along with another, the other is along with the first. When one thing is like, or unlike, another, the other is like (or unlike) the first: in short, as many fundamental principles as there are kinds of relation. For we have need of all these changes of expression in our processes of thought and reasoning. What is at the bottom of them all is, that Logic (to borrow a phrase from our author)^[†] postulates to be allowed to assert the same meaning in any words which will, consistently with their signification, express it. The use and meaning of a Fundamental Law of Thought is, that it asserts in general terms the right to do something, which the mind needs to do in cases as they arise. It is in this sense that the Dictum de Omni et Nullo is called the fundamental law of the Syllogism. But, for this purpose, it is necessary that the Law or Postulate should be stated in so comprehensive and universal a manner as to cover every case in which the act authorized by it requires to be done. Looked at in this light, the Principle of Identity ought to have been expressed thus: Whatever is true in one form of words, is true in every other form of words which conveys the same meaning. Thus worded, it fulfils the requirements of a First Principle of Thought; for it is the widest possible expression of an act of thought which is always legitimate, and continually has to be done.^*

Understood in this sense, the Principle of Identity absorbs into itself a Postulate of Logic on which Sir W. Hamilton lays great stress, and which he did good service in making prominent, though we shall hereafter find that he sometimes misapplies it. He expresses it as follows: “The only Postulate of Logic which requires an articulate enouncement is the demand, that before dealing with a judgment or reasoning expressed in language, the import of its terms should be fully understood; in other words, Logic postulates to be allowed to state explicitly in language, all that is implicitly contained in the thought.”^* There cannot be a more just demand: but let us carefully note the terms in which our author enunciates it, that he may be held to them afterwards. Everything may be stated explicitly in language, which is “implicitly contained in the thought,” that is (according to his own interpretation) in the “import of the terms” used. In other words, we have a right to ^bexpress^b explicitly, what has already been asserted in terms which really mean, though they do not explicitly declare it. Observe, what has been already asserted; not what can be inferred from something that has been asserted. One proposition may imply another, but unless the implication is in the very meaning of the terms, it avails nothing. It may be impossible that the one proposition should be true without the other being true also, and yet Logic cannot “postulate” to be allowed to affirm this last; she must be required to prove it. Interpreted in this, its true sense, Sir W. Hamilton’s postulate is legitimate, but is only a particular case of the Principle of Identity in its most generalized shape. It is a case of postulating to be allowed to express a given meaning in another form of words.

As already mentioned, Sir W. Hamilton represents the Principle of Identity to be “the principle of all logical affirmation.” This I can by no means admit, whether the Principle in question is taken in Sir W. Hamilton’s narrower, or in my own wider sense. The reaffirmation in new language of what has already been asserted—or (descending to particulars and adopting our author’s phraseology) the thinking of a Concept through an attribute which is a part of itself—can, as I formerly observed, be admitted as a correct account of the nature of affirmation, only in the case of Analytical Judgments. In a Synthetical Judgment, the attribute predicated is thought not as part of, but as existing in a common subject along with, the group of attributes composing the Concept: and of this operation of thought it is plain that no principle of Identity can give any account, since there is a new element introduced, which is not identical with any part of what pre-existed in thought. This is clearly seen by Mr. Mansel, who expressly limits the dominion of the Law of Identity to analytical judgments;^* and, with perfect consistency, regards these as the only judgments with which Logic, as such, is concerned. If, then, the Law of Identity is to be upheld as the principle “of all logical affirmation,” we must understand that logical affirmation does not mean all affirmation, but only affirmations which communicate no fact, and merely assert that what is called by a name, is what the name declares it to be.

If our author had stated the Law of Identity to be the principle not of “logical affirmation,” but of affirmative Reasoning, he would have said something far more plausible, and which had been maintained by many of his predecessors. The truth is, however, that as far as that law is a principle of reasoning at all, it is as much a principle of negative, as of affirmative reasoning. In proving a negative, as much as in proving an affirmative, we require the liberty of exchanging a proposition for any other that is æquipollent with it, and of predicating separately of any subject, all attributes which have been predicated of it jointly. These liberties the mind rightfully claims in all its intellectual operations. The Principle of Identity is not the peculiar groundwork of any special kind of thinking, but an indispensable postulate in all thinking.

The second of the “Fundamental Laws” is the Law or Principle of Contradiction (Principium Contradictionis); that two assertions, one of which denies what the other affirms, cannot be thought together. Most people would have said, cannot be believed together; but our author resolutely refuses to recognise belief as any element in the scientific analysis of a proposition. “This law,” he says, “is the principle of all logical negation and distinction,”^† and “is logically expressed in the formula, What is contradictory is unthinkable.” To this he subjoins, as an equivalent mathematical formula, “A = not A = o, or A - A = o:”^‡ a misapplication and perversion of algebraical symbols, not to be omitted among other evidences how little familiar he was with mathematical modes of thought.

Concerning the name of this law, Sir W. Hamilton observes that “as it enjoins the absence of contradiction as the indispensable condition of thought, it ought to be called, not the Law of Contradiction, but the Law of Non-Contradiction, or of non-repugnantia.”^§ It seems that no extent and accuracy of knowledge concerning the opinions of predecessors, can preserve a thinker from giving an erroneous interpretation of their meaning by antedating a confusion of ideas which exists in his own mind. The Law of Contradiction does not “enjoin the absence of contradiction;” it is not an injunction at all. If those who wrote before Sir W. Hamilton of the Law or Principle of Contradiction, had meant by those terms what he did, namely, a rule or precept, it would have been, no doubt, absurd in them to have given the name Law of Contradiction, to a Precept of Non-Contradiction. But I venture to assert that when they spoke of the Law of Contradiction (which most of them, I believe, never did, but called it the Principle) they were no more dreaming of enjoining anything, than when they spoke of the Law or Principle of Identity they intended to enjoin identity. They used those terms in their proper scientific, and not, as Sir W. Hamilton does, in their moral or legislative sense. By the Law of Identity they meant one of the properties of identity, namely, that a proposition which is identical must be true. And by the Law of Contradiction they meant one of the properties of contradiction, namely, that what is contradictory cannot be true. We should express their meaning better if instead of the word Law, we used the expressions, Doctrine of Identity, and Doctrine of Contradiction. This is what they had in their minds, and even expressed by their words; for the word Principle, with them, meant a particular kind of Doctrine, namely, one which is the groundwork, and justifying authority, of a whole class of operations of the mind. If the word Law is to be retained, Principium Contradictionis would be better translated, not Law of Contradiction but Law of Contradictory Propositions; were it not for the consideration, that the principle of Excluded Middle is also a law of contradictory propositions.

The Law of Contradiction, according to Sir W. Hamilton, is the “principle of all logical negation.”^* I do not see how it can be the principle of any negation except the denial that a thing is the contradictory of itself. That a sight is not a taste is a negation, and it must be a very narrow use of the term which refuses it the title of a logical negation. But there is no contradiction between a sight and a taste. That blue is not green, involves no logical contradiction. We could believe that a green thing may be blue, as easily as we believe that a round thing may be blue, if experience did not teach us the incompatibility of the former attributes, and the compatibility of the latter. The negative judgment, that a man is not a horse, may indeed be said to be grounded on the Principle of Contradiction, inasmuch as the opposite assertion, that a man is a horse, is in certain of its parts contradictory, though in others only false. The word man ^cmay be^c understood as signifying (in precise logical language, connoting) among ^dthe^d other properties, that of having exactly two legs—the word horse, that of having four; and in respect of this particular part of the meaning of the terms, the subject and the predicate are contradictory, the one affirming and the other denying the extra number of legs. But suppose the subject and predicate of the judgment to be names of classes constituted by positive attributes without negative, as mathematician and moralist, or merchant and philosopher. An affirmation uniting them may then be false, but cannot possibly be self-contradictory. The Law of Contradiction cannot be the ground on which it is asserted that a mathematician is not a moralist, for the two Concepts are only different, not contradictory, nor even repugnant.

Others have said, that the Law or Doctrine of Contradiction is the principle of Negative Reasoning. But the obvious truth is, that it is the principle of all Reasoning, so far as reasoning can be regarded apart from objective truth or falsehood. For, abstractedly from that consideration, the only meaning of validity in reasoning is that it neither involves a contradiction, nor infers anything the denial of which would not contradict the premises. Valid reasoning, from the point of view of merely Formal Logic, is a negative conception; it means, reasoning which is not self-destructive; which cannot be discovered to be worthless from its own data. It would be absurd to suppose that the validity of the reasoning process itself, either affirmative or negative, could be proved from the Doctrine of Contradiction; for though a given syllogism may be proved valid by showing that the falsity of the conclusion, combined with the truth of one premise, would contradict the truth of the other, this can only be done by another syllogism, so that the validity of Reasoning would be taken for granted in the attempt to prove it. The Law of Contradiction is a principle of reasoning in the same sense, and in the same sense only, as the Law of Identity is. It is the generalization of a mental act which is of continual occurrence, and which cannot be dispensed with in reasoning. As we require the liberty of substituting for a given assertion, the same assertion in different words, so we require the liberty of substituting, for any assertion, the denial of its contradictory. The affirmation of the one and the denial of the other are logical equivalents, which it is allowable and indispensable to make use of as mutually convertible.

The third “Fundamental Law” is the law or principle of Excluded Middle (principium Exclusi Medii vel Tertii), of which the purport is, that, of two directly contradictory propositions, one or the other must be true. I am now expressing the axiom in my own language, for the tortuous phraseology^* by which our author ^eescapes from^e recognising the ideas of truth and falsity, having already been sufficiently exemplified, may here be disregarded. This axiom is the other half of the doctrine of Contradictory Propositions. By the law of Contradiction, contradictory propositions cannot both be true; by the law of Excluded Middle, they cannot both be false. Or, to state the meaning in other language, by the law of Contradiction a proposition cannot be both true and false; by the law of Excluded Middle it must be either true or false—there is no third possibility.

Sir W. Hamilton says that this law is “the principle of disjunctive judgments.”^* By disjunctive judgments, logicians have always meant, judgments in this form: Either this is true or that is true. The law of Excluded Middle cannot be the principle of any disjunctive judgment but those in which the subject of both the members is the same, and one of the predicates a simple negation of the other: as, A is either B or not B. That indeed rests on the principle of Excluded Middle, or rather, is the very formula of that principle. It is here to be remarked that Sir W. Hamilton, after Krug, but by a very unaccountable departure from the common usage of logicians, confines the name of Disjunctive Judgments to those in which all the alternative propositions have the same subject: “D is either B, or C, or A.”^† This is not only an arbitrary change in the meaning of words, but renders the classification of propositions incomplete, leaving two kinds of disjunctive propositions (Either B, C, or D, is A, and Either A is B or C is D) unrecognised and without a name. But even in our author’s restricted sense of the word Disjunctive, I cannot see how the Law of Excluded Middle can be said to be the principle of all disjunctive judgments. The judgment that A is either B or not B, is warranted and its truth certified by the Law of Excluded Middle: but the judgment that A is either B or C, both B and C being positive, requires some other voucher than the law that one or other of two contradictories must be true. Thus, “X is either a man or a brute,” is not a judgment grounded on the principle of Excluded Middle, since brute is not a bare negation of man, but includes the positive attribute of being an animal, which X may possibly not be.

It might be said, with more plausibility, that the Law of Excluded Middle is the principle of Disjunctive Reasoning. Thus, in the last example, “X is either a man or a brute” may be a conclusion from two premises, that X is an animal, and that every animal is either a man or a brute: the latter of which is a disjunctive judgment grounded on the Law of Excluded Middle. But it is not the fact that all disjunctive conclusions are inferred from premises of this nature. Having been told that A has lost a son, I conclude that either B, C, or D (A having no other sons) is dead: what kind of reasoning is this? Disjunctive, surely: it has a disjunctive premise, and leads to a disjunctive conclusion. But the disjunctive premise (Every son of A is either B, C, or D) does not rest on the Law of Excluded Middle, or on any necessity of thought; it rests on my knowledge of the individual fact.

The third Law, however, like the two others, is one of the principles of all reasonings, being the generalization of a process which is liable to be required in all of them. As the Doctrine of Contradiction authorizes us to substitute for the assertion of either of two contradictory propositions, the denial of the other, so the doctrine of Excluded Middle empowers us to substitute for the denial of either of two contradictory propositions, the assertion of the other. Thus all the three principles which our author terms the Fundamental Laws of Thought, are universal postulates of Reasoning; and as such, are entitled to the conspicuous position which our author assigns to them in Logic: though it is evident that they ought not to be placed at the very beginning of the subject, but at the earliest, in its Second Part, the theory of Judgments, or Propositions: since they essentially involve the ideas of Truth and Falsity, which are attributes only of judgments, not of names, or concepts.

It is another question altogether, what we ought to think of these three principles, considered not as general expressions of legitimate intellectual processes, but as themselves speculative truths. Sir W. Hamilton considers them to be such in a very universal sense indeed, since he thinks we are bound to regard them as true beyond the sphere of either real or imaginable phænomenal experience—to be true of Things in Themselves—of Noumena. “Whatever,” he says,

And in another place: “If the true character of objective validity be universality, the laws of Logic are really of that character, for those laws constrain us, by their own authority, to regard them as the universal laws not only of human thought, but of universal reason.”^† A few pages before, our author took pains to impress upon us that we were not to regard these laws as necessities of thought, but as general precepts “which we are able to violate:”^[*] but they now appear to be necessities of thought and something more.

I readily admit that these three general propositions are universally true of all phænomena. I also admit that if there are any inherent necessities of thought, these are such. I express myself in this qualified manner, because whoever is aware how artificial, modifiable, the creatures of circumstances, and alterable by circumstances, most of the supposed necessities of thought are (though real necessities to a given person at a given time), will hesitate to affirm of any such necessities that they are an original part of our mental constitution. Whether the three so-called Fundamental Laws are laws of our thoughts by the native structure of the mind, or merely because we perceive them to be universally true of observed phænomena, I will not positively decide: but they are laws of our thoughts now, and invincibly so. They may or may not be capable of alteration by experience, but the conditions of our existence deny to us the experience which would be required to alter them. Any assertion, therefore, which conflicts with one of these laws—any proposition, for instance, which asserts a contradiction, though it were on a subject wholly removed from the sphere of our experience, is to us unbelievable. The belief in such a proposition is, in the present constitution of nature, impossible as a mental fact.^*

But Sir W. Hamilton goes beyond this: he thinks that the obstacle to belief does not lie solely in an incapacity of our believing faculty, but in objective incapacities of existence; that the “Fundamental Laws of Thought” are laws of Existence too, and may be known to be true not only of Phænomena but also of Noumena. Of this, however, as of all else relating to Noumena, the verdict of philosophy, I apprehend, must be that we are entirely ignorant. The distinction itself is but an idle one; for since Noumena, if they exist, are wholly unknowable by us, except phænomenally, through their effects on us; and since all attributes which exist for us, even in our fancy, are but phænomena, there is nothing for us either to affirm or deny of a Noumenon except phænomenal attributes: existence itself, as we conceive it, being merely the power of producing phænomena. Now in respect to phænomenal attributes, no one denies the three “Fundamental Laws” to be universally true. Since then they are laws of all Phænomena, and since Existence has to us no meaning but one which has relation to Phænomena, we are quite safe in looking upon them as laws of Existence. This is sufficient for those who hold the doctrine of the Relativity of human knowledge. But Sir W. Hamilton, as has been seen, does not hold that doctrine, though he holds a verbal truism which he chooses to call by the same name. His opinion is that we do know something more than phænomena: that we know the Primary Qualities of Bodies as existing in the Noumena, in the things themselves, and not as mere powers of affecting us. Sir W. Hamilton, therefore, needs another kind of argument to establish the doctrine that the Laws of Identity, Contradiction, and Excluded Middle, are laws of all existence: and here we have it:

This proves only that a contradiction is unthinkable, not that it is impossible in point of fact. But what follows goes more directly to the mark.

Of this favourite style of argument with our author we have already had many specimens, and have said so much about them, that we can afford to be brief in the present instance. Assuming it to be true that “to deny the universal application of the three laws” as laws of existence “is to subvert the reality of thought:” is anything added to the force of this consideration by saying that “this subversion is itself an act of thought?” If the reality of thought can be subverted, is there any peculiar enormity in doing it by means of thought itself? In what other way can we imagine it to be done? And if it were true that thought is an invalid process, what better proof of this could be given than that we could, by thinking, arrive at the conclusion that our thoughts are not to be trusted? Sir W. Hamilton always seems to suppose that the imaginary sceptic, who doubts the validity of thought altogether, is obliged to claim a greater validity for his subversive thoughts than he allows to the thoughts they subvert. But it is enough for him to claim the same validity, so that all opinions are thrown into equal uncertainty.^* Sir W. Hamilton, of all men, ought to know this, for when he is himself on the sceptical side of any question, as when speaking of the Absolute, or anything else which he deems inaccessible to the human faculties, this is the very line of argument he employs. He proves the invalidity, as regards those subjects, of the thinking process, by showing that it lands us in contradictions.^†

But it is entirely inadmissible that to suppose that a law of thought need not necessarily be a law of existence, invalidates the thinking process. If, indeed, there were any law necessitating us to think a relation between phænomena which does not in fact exist between the phænomena, then certainly the thinking process would be proved invalid, because we should be compelled by it to think true something which would really be false. But if the mind is incapable of thinking anything respecting Noumena except the Phænomena which it considers as proceeding from them, and to which it can appeal to test its thoughts; and if we are under no necessity of thinking these otherwise than in conformity to what they really are; we may refuse to believe that our generalizations from the Phænomenal attributes of Noumena can be applied to Noumena in any other aspect, without in the least invalidating the operation of thought in regard to anything to which thought is applicable. We may say to Sir W. Hamilton what he says himself in another case: “I only say that thought is limited; but, within its limits, I do not deny, I do not subvert, its truth.”^* As he elsewhere observes, translating from Esser, truth consists “solely in the correspondence of our thoughts with their objects.”^† If the only real objects of thought, even when we are nominally speaking of Noumena, are Phænomena, our thoughts are true when they are made to correspond with Phænomena: and, the possibility of this being denied by no one, the thinking process is valid whether our laws of thought are laws of absolute existence or not.

[[*] ]See, e.g., Leibniz, Essais de théodicée sur la bonté de Dieu, la liberté de l’homme, et l’origine du mal (Amsterdam: Troyel, 1710), pp. 114-15, 156-7 (I, §§7, 44).

[* ]Lectures, Vol. III, p. 79. In the Appendix to the Lectures he calls them the Laws of the Thinkable; and the laws of Conception, Judgment, and Reasoning he distinguishes from them under the name of “the laws of Thinking in a strict sense.” (Ibid., Vol. IV, App. iv, pp. 244-5.)

[* ]Foot-note to Reid, p. 713n, and in many other places.

[a]651, 652 mere

[[*] ]See Essay Concerning Human Understanding, Works, Vol. III, pp. 23-5 (Bk. IV, Chap. vii, §4).

[† ]Lectures, Vol. III, pp. 79-80.

[‡ ]We here see our author by implication admitting that a Concept has no parts except its parts in Comprehension; what he elsewhere calls its parts in Extension being in no sense parts of the Concept, but parts of something else, namely, of the aggregate of concrete objects to which the Concept corresponds. Had Sir W. Hamilton adhered to this rational doctrine, he must have given up his Judgments in Extension: instead of which he not only retains them, but considers them as also founded on the Principle of Identity: though he has expressly limited that principle in a manner inconsistent with founding any judgments on it save Judgments in Comprehension. This contradiction was worth pointing out, but is not worth insisting on, since it may be rectified by extending the scope of the First Law to the identity of any whole with its parts, instead of limiting it to the identity of a Concept with its parts in Comprehension only.

[[*] ]Lectures, Vol. III, pp. 79-80.

[[†] ]See ibid., p. 114.

[* ][67] This principle provides for the whole of what Kant terms Conclusions of Understanding [Kritik der Reinen Vernunft, pp. 245-7], and Dr. M‘Cosh Implied or Transposed Judgments. ([Examination,] p. 296.) They are not conclusions, nor fresh acts of judgment, but the original judgment, expressed in other words.

[* ]Lectures, Vol. III, p. 114.

[b-b]651 assert

[* ]Prolegomena Logica, pp. 196-7.

[† ]Lectures, Vol. III, p. 82.

[‡ ]Ibid., p. 81.

[§ ]Ibid., p. 82.

[* ]Ibid.

[c-c]651, 652, 67 is

[d-d]+72

[* ]Ibid., p. 83.

[e-e]651, 652 evades

[* ]Ibid., p. 84.

[† ]Ibid., p. 239. [Cf. Krug, Logic, §57.]

[* ]Ibid., p. 98.

[† ]Ibid., Vol. IV, p. 65.

[[*] ]Ibid., p. 79.

[* ][67] “When remembering a certain thing as in a certain place, the place and the thing are mentally represented together; while to think of the non-existence of the thing in that place, implies a consciousness in which the place is represented but not the thing. Similarly, if instead of thinking of an object as colourless, we think of it as having colour, the change consists in the addition to the concept of an element that was before absent from it—the object cannot be thought of first as red and then as not red, without one component of the thought being totally expelled from the mind by another. The law of the Excluded Middle, then, is simply a generalization of the universal experience that some mental states are directly destructive of other states. It formulates a certain absolutely constant law, that the appearance of any positive mode of consciousness cannot occur without excluding a correlative negative mode: and that the negative mode cannot occur without excluding the correlative positive mode: the antithesis of positive and negative being, indeed, merely an expression of this experience. Hence it follows that if consciousness is not in one of the two modes, it must be in the other.” (Mr. Herbert Spencer, [“Mill versus Hamilton,”] in Fortnightly Review for July 15, 1865 [p. 533].)

[f-f]Source, 651 this

[* ]Lectures, Vol. III, pp. 99-100.

[* ]The principal extant interpreter of the ancient Scepticism, Sextus Empiricus, expressly defines as its essence and scope, τὸ παντὶ λόγῳ λόγον ἴσον ἀντικεῖσθαι. (Pyrrh. Hypot.) [Sextus Empiricus, Outlines of Pyrrhonism, in Sextus Empiricus, Vol. I, p. 8 (Chap. vi).] It is, indeed, impossible to conceive Scepticism otherwise. Anything more would not be Scepticism, but Negative Dogmatism.

[† ]“If I,” says our author, “have done anything meritorious in philosophy, it is in the attempt to explain the phænomena of these contradictions, in showing that they arise only when intelligence transcends the limits to which its legitimate exercise is restricted.” (Lectures, Vol. I, App. i, p. 402.) “In generating its antinomies, Kant’s Reason transcended its limits, violated its laws. . . . Reason is only self-contradictory when driven beyond its legitimate bounds.” (Ibid., Vol. II, App. iv, p. 543.) “It is only when transcending that sphere, when founding on its illegitimate as on its legitimate exercise, that it affords a contradictory result. . . . The dogmatic assertion of necessity—of Fatalism, and the dogmatic assertion of Liberty, are the counter and equally inconceivable conclusions from reliance on the illegitimate and one-sided.” (Ibid., Vol. I, App. i, p. 403.) To the same effect Mr. Mansel, throughout his Limits of Religious Thought.

In one of the Appendices to the Lectures on Metaphysics (Vol. II, App. iii, pp. 527-9), Sir W. Hamilton makes out a long list of contradictions or antinomies (of which we shall have something to say hereafter) involved, as he thinks, in the attempt to conceive the Infinite, and which he considers as evidence that the notion is beyond the reach of the human faculties. Yet he will not allow that the fact of leading to contradictions, which he habitually urges as an argument against the validity of some thought, would be admissible as an argument against Thought in general, if it could be brought home to it. At least he will not allow it in this place: for in his theory of the veracity of Consciousness he does (ibid., Vol. I, p. 277).

[* ]Ibid., Vol. III, p. 100.

[† ]Ibid., p. 107 [cf. Esser, Logik, pp. 65-6]; see also Vol. IV, p. 61.