relation of number to something else which is counted, we find that an interminable series of groups of three is necessarily possible. It may be said that number must always be the number of something. In a sense, this is true. But the something may be anything whatever if only it is capable of being numbered. Thus pure number is not considered as an adjective of anything except of the numerable as such. This is equivalent to making it merely an adjective of itself and therefore not an adjective at all. It is not an adjective because the conception of the numerable as such is included in the abstract conception of number itself. Now pure number thus defined is certainly real inasmuch as it has a positive and determinate nature to which our thought concerning it may or may not conform. We can discover arithmetical truths and we can make arithmetical blunders. Further the field for thought which has pure number for its object is inexhaustible in range and complexity. A mind such as that of Aristotle's deity might occupy itself for ever with abstract number and nothing else to all eternity without exhausting its resources. So long as it was interested in this object there would be no reason why it should turn to any other.

IX. CERTAINTY

§ 10. In the initial statement of our problem stress was laid on the apparent fact that the unreal in erroneous belief is present to consciousness in the same manner as the real in true belief. We have now to point out that this is not always so. It is not so where the essential conditions of the possibility of error are absent. For, in such cases, a question answers itself so as to render doubt meaningless. This holds good for my assertion of my own existence as a conscious being and for such propositions as " 2 + 1 = 3 3" or "Trilateral figures are triangular." In instances of this kind we can raise a doubt only by abandoning the proper question for another which is irrelevant. We may, for instance, ask: How far can we trust our faculties ? But

inquiries of this sort are futile and even nonsensical. They presuppose a meaningless separation of the thinking process from what is thought of, and then proceed to ask how far the thinking process, regarded merely as someone's private psychical affection can be "trusted" to reveal a reality extraneous to it. In all cognition, what we "trust" is not the psychical process of thinking or perceiving, but the thing itself which is thought of or perceived the thing concerning which we raise a question.

It is urged by Mr. Bradley that all propositions, except perhaps certain assertions concerning the Absolute as such, must be more or less erroneous. His reason is that they are all conditional and that their conditions are never fully known. Whatever exists, exists within the universe and it is conditioned by the whole constitution of the universe. But if what exists within a whole is conditioned by so existing, no assertion as to what exists is true if stated apart from this condition. This argument seems to involve a confusion. It confuses conditions of the truth of a proposition with conditions of that which is stated in the proposition. When I say,-"If this witness is to be trusted, Jones committed the theft," the "if" introduces a condition of the first kind. It suggests uncertainty. When I say, "If a figure is trilateral it is triangular," the "if" introduces a condition of the second kind. It does not suggest uncertainty. My own existence as a conscious being has conditions far too complex and obscure for me to discover. But these conditions do not condition the truth of the proposition that I exist. The inverse is the case. Because I am certain that I exist, I am certain that all the conditions of my existence, whatever they may be, exist also. Be they what they may, they are all logically included in the import of my thought when I affirm my own existence.

Mr. Bradley's contention seems to rest on the assumption that, unless the universe is completely known, every

1 This distinction corresponds in principle with that drawn by Mr. W. E. Johnson, between Conditional and Hypothetical propositions. Cf. Keynes, Formal Logic, pp. 271 seq.

assertion or denial about its contents must be liable to the error of ignorance, or rather, must actually incur the error of ignorance. Since we do not know everything, it is assumed that there always may be, or rather, must be something unknown which would be seen to falsify our judgment if we knew it. But this view is untenable if we are right in maintaining that there are limits to the possibility of error. Unexplored conditions can affect the truth of a statement only in so far as they are relevant, and their relevancy in each case depends on the nature of the question raised. Suppose the question to be, What is the sum of two and two? By the very nature of the problem there can be no relevant data except just two and two considered as forming a sum of countable units. It may be urged that perhaps the numbers to be added do not exist, or that they may be incapable of forming a But these doubts become meaningless as soon as we try to count. If there is nothing to count there can be no counting. But the supposition is absurd. Suppose, per impossibile, that we fail to find anything to count in the first instance. Our failure may then be counted as one thing and the act of counting it may be counted as another, and this second act of counting as yet another, and so on ad infinitum.

sum.

To pursue this topic farther would lead outside the limits of the present essay. It is enough here to insist that there is such a thing as logically unconditioned truth. In order to attain absolute knowledge, it is by no means necessary to wait until we have attained an adequate knowledge of the absolute. The truth of judgments concerning what is real is not logically dependent on the truth of judgments concerning "Reality" with a capital R.1

1 I am aware that this essay is likely to raise more questions in the reader's mind than it even attempts to solve. Some of these I hope to deal with in the future; e.g. the relation of the universal to the particular, the nature of the material world, and the nature and possibility of thought as dependent on the constitution of the Absolute. In dealing with these topics, I hope to develop more fully the grounds of that divergence from Mr. Bradley which is referred to in § 10 and implied elsewhere.

1. Agreement that the world is experience + connecting principles-why we should start rather than conclude with this.

2. But (a) whose experience? Ours. Why self cannot be analysed away; why knowledge of self depends on experience.

3. (6) Experience of what? The world.

yet possible to say completely.

But what the world is, it is not

4. (1) The World not ready-made datum but constructed by a process of evolution,

5. (2) i.e. of trial or experiment-original flexibility or indeterminateness of world. Experiment suggested by practical needs-conscious and unconscious experimenting.

6. (3) Limits of experimenting-'matter' as resisting medium-impossibility of saying what it is in itself. Conception of material world developing in experience. Value of Aristotelian description of a

An capable of being moulded.

7. (4) The World,' therefore, is what is made of it-plastic. How far, to be determined only by trying. But methodologically plasticity assumed to be complete. Provisional character of our 'facts.'

axioms.

8. Bearing of this 'pragmatism' or 'radical empiricism' on the nature of Their origin as postulates to which we try to get world to Contrast with the old empiricism and apriorism.

conform.

II. CRITICISM OF EMPIRICISM

9. (1) Its standpoint psychological, (2) intellectualist, (3) axioms presupposed in the experience which is supposed to impress them on us— Mill's admissions, (4) derivation not historical, but ex post facto reconstruction, (5) its incompleteness, (6) impossibility of really tracing development of axioms and so unprogressiveness.

III. CRITICISM OF APRIORISM

10-25. Its superficial plausibility and real obscurity.

from § 9 (3) that there are a priori truths.

Fallacy of inferring

11. How postulates also yield 'universality' and 'necessity.' 'Necessity'

and need.

12. 'Condition of all possible experience' means? Might be (1) cause or psychical antecedent, (2) presupposition of reflection (logical), or (3) ethical or asthetical. Objections.

13. Meaning of ‘a priori'; (1) logical or (2) psychological? Equivocations of apriorist authority.

14-18. The a priori as logical. But why analyse in Kant's way? Exclusive correctness of Kantian analysis not to be based either (1) on its a priori truth, or (2) on experience of its satisfactory working. Else why should Kantians have tried to better it?

15. Kant's derivation of his analysis from psychology.

16. Even if it were satisfactory, no proof that it would be the only or the best possible.

17. If a priori is not in time, its superiority to the a posteriori merely honorific.

18. Kant's analysis neither simple nor lucid.

19-22. A priori as psychical fact. But if so, has it (1) been correctly described? (2) how is it distinguished from innate idea? (3) does not epistemology merge in psychology?

20. As facts a priori truths have a history, which must be inquired into.

21. A priori faculties tautologous, and

22. should not be treated as ultimate.

23. Result that science of epistemology rests on systematic confusion of alternative interpretations of apriority. The proper extension of logic and psychology.

24. Intellectualism of both apriorism and empiricism incapacitates them from recognising unity and activity of organism. How this may be recognised by deriving axioms from a volitional source by postulation.

25. Kant's recognition of postulation in ethics-its conflict with his 'critical' theory of knowledge-resulting dualism intolerable. Hence either (1) suppress the Practical Reason or preferably (2) extend postulation to Theoretic Reason.

IV. SOME CHARACTERISTICS OF POSTULATION

26. Postulates at first tentative and not always successful-their various stages and common origin—the theoretic possibility of changing axioms not practically to be feared.

27. Postulates not a coherent system inter se except as rooted in personality.

V. THE POSTULATION OF IDENTITY

28. Not to be derived out of nothing, but out of a prior psychical fact on the sentient level of consciousness-why consciousness itself cannot be derived-its characteristics on the sentient level.

29. Hence identity (of self) first felt in the coherence and continuity of mental processes, and forms basis for the postulation of identity-the practical necessity of recognising the same' in the 'like.'

30. Once postulated, identity proves a great success, though never completely realised in fact. Stages of identity - postulation: (1) recognition of others and objects of perception. But these change and so do not provide a stable standard of comparison. Hence (2) postulation of ideally identical selves.

31. (3) Meaning demands absolute identity and recognition leads to cognition-advantage of classification by 'universals' which abstract from differences.