When I speak of ambiguity, I do not mean "living (existing) as a reflexive muddle", or vaguely and woolily (in the feminine style), or by mauvaise foi. What I want to refer to is the ambiguity that is perfectly clear doubleness (duplicity), which has to be unilaterally resolved by an act of choice (and belief) in order that existence may be. For instance: --

Which line is in front? (Muddle or vagueness here lies in forgetting the ambiguity; which is in front is quite ambiguous (objectively), and is, of course, part of an infinite hierarchy of ambiguities, an ambiguity of which hierarchy being whether it is infinite or has an horizon.) Again, . , is this a point en soi or a line pour moi? And so on. And the ambiguity of the "straight" stick seeming "crooked" in the water, which belief is normally withdrawn if [...several words illegible...] and granted to touch in order that the stick should be straight. Then the ambiguity of words qua words: are they mere sounds or symbols for a meaning? And (worst of all) the ambiguous ambiguity of identity: is self-identity one or two? Then is the Derivative of the Calculus a different entity or the same? etc. etc. All this is not mauvaise foi, which would be refusal to investigate one's suspicions about ambiguity and pretence that there was none (determinism, either scientific or of any kind), and at worst it is a sort of lunatic alternation between smug self-forgetting complacency and patches of hysterical shrieks and confusion: this is sammoha,[1] isn't it? (I think more people live and die like this than not, don't they?)

As to viññána "becoming" námarúpa, it all depends on what one means by "becoming" (and to "mean" is to be ambiguous, isn't it?), and I don't necessarily disagree with you here. (If I see where you keep your ambiguity in this.) It all depends, too, on what one defines as the self-identity of viññána and námarúpa, without which "constant under transformation" nothing can either become or be, very well, can it? Isn't viññána the "self-identity" of bhava?

I am at present inclined to define phassa "strictly" as a recul[2] (the recul). The recul from which there is always a new recul (in "memory") is then "seen" (with ambiguity and by identification) both (alternatively) as a line ______ and/or as an oscillation between points .     . , and so on. Hence the triadic relation here. The ramification is infinite, but beyond a limit these "memories" lapse. Hence the horizon of appearances. If your oscillation theory is right, then, in that analysis, only one point is "seen" with the eye, the other being "remembered" with the mind. But the ambiguity enters, and the "seeing and remembering" becomes "a line seen". This is the complementary theory, without which everything would ultimately be fixable by description into a kind of descriptive determinism, and all descriptions would then be definitions, and so non-existent: the essence of a description is that it is, or can be, one of a set of complementary (and I think necessarily partly incompatible) descriptions that can be multiplied ad infinitum. Existence fuses these and appearance clamps down an horizon.



[EL. 141]   1.i.1959

I said in my last letter that the formal logical principles derive from the structure of being itself. This is true, but needs a qualification. The formal logical principles, as formulated by the mathematical logicians (e.g. Stebbing), are the result of describing the structure of being (i.e. Kummer) from no point of view. That is to say, existing things are all taken at once and seen to form an "irreducible multiple relation" (Stebbing's phrase), and this "irreducible multiple relation" is the structure defined by the formal logical principles. But since no point of view is allowed to appear (the mathematical logicians being strictly scientific and objective), this structure or system is purely static. (The Principle of Deduction is then added to the Formal Principles, and this introduces some movement but quite arbitrary, of the wrong kind, and far too late.)

This, then, is half the picture. The other half consists in having a point of view, but not allowing an "irreducible multiple relation" to appear. This second half, I suspect, is what the metaphysical/idealist logicians are talking about (and they are strictly subjective). Kummer, however, has both aspects: -- (i) the sixteen operators can be seen to constitute an "irreducible multiple relation", and (ii) this system is "invariant under infinite bi-rational transformations" (according to the E.B. article).

I raise this point; first because it seems to suggest that official Western thinking is perhaps not confined to inductive and deductive logic, and that we have been neglecting the idealist philosophers (who, though admittedly just as one-sided as the mathematical logicians, are at least the other side) in our recent correspondence; and secondly because a passage in Stebbing throws light upon a certain incident about two years ago. The passage is from her preface, and states that the metaphysical logicians (Bradley and Bosanquet) were dissatisfied with traditional Logic in that it was 'formal' (i.e. static -- see above) and severed from 'reality', that they were concerned with the relation between the knowing mind and what it knows, and that he (Stebbing's) book has nothing in common with such views. She adds that none of this school of Idealist Logicians has ever made clear exactly what is meant by the principle of identity-in-difference upon which their logic based. (My underlining.) Surely the principle of identity-in-difference is nothing but the principle of invariance-under-transformation, is it not? And this latter is the dynamic aspect of Kummer. Naturally Stebbing has never been able to understand this -- she is strictly objective, and this is subjectivity, which she will have no part of. Now the incident in question was this. The last time I met the Ven. Soma Thera was at the Hermitage (as you will remember) and on that occasion we all had a discussion in the dánasála about (roughly) 'being and logic' in which sharp differences of view became apparent. I made a remark to the effect that if change is to be perceived it must be perceived by a percipient (or against a background) who, during the change, does not himself change (i.e. invariance-under-transformation). Immediately, the Ven. One, in a tone of great finality, said "Oh, that's just Bradley!", after which there was nothing more to be said. Though I once read Bradley's Appearance and Reality I can remember nothing about it, and have (at least until reading this passage of Stebbing's) no idea what views Bradley held. Now, however, the situation is clear -- (i) the Ven. One would probably agree with practically everything Stebbing says, and (ii) I am just an idealist. It is noteworthy that Stebbing deliberately avoids discussion of quantum phenomena (she says as much, though without giving a reason), and that Dirac says that quantum theory reveals that the 'things' in the world are the invariants of transformations. Stebbing's view -- that of the mathematical logicians -- is that there is no point of view and that all things are on an equal footing; both what is present and what is absent alike exist -- sabbam atthíti --; and 'to exist' becomes synonymous with 'to be real', which is why this view is sometimes called Realism. Bradley's view -- that of the metaphysical logicians -- is, presumably, that there is (what is at) the point of view and nothing else; what is present (i.e. perceived at, or by, the point of view) exists (esse est percipi[1]), what is absent does not, and when a thing ceases to be present it ceases to exist -- sabbam natthíti; and here, since it is the subject -- the point of view -- that confers existence, the object is reduced to a mere 'idea' -- whence Idealism. This, no doubt, is obvious enough. But it now occurs to me that to affirm sabbam atthíti -- the absolutely real objective existence of things independent of any observer -- is precisely to deny the existence of a subject or self, natthi attáti; and conversely, to deny objective existence to things, sabbam natthíti, is, precisely, to affirm the existence of the subject or self, atthi attáti. There is, however, another point: an oriented world (which is the maning of loka in the Suttas) is the correlative of a point of view (there is a Samyutta Sutta[2] that specifically identifies the world with the eye, ear, nose, and so on), and consequently to deny self is to deny the world, and to assert self is to assert the world (so loko so attá). Thus we have the following scheme: --

Sassataváda	Ucchedaváda
Asserts a point of view;	Denies a point of view;
Asserts self -- atthi attáti;	Denies self -- natthi attáti;
Asserts the world;	Denies the world;
Denies the objective existence	Asserts the objective existence
of things -- sabbam natthíti	of things -- sabbam atthíti
Is an Idealist (Bradley, Berkeley)	Is a Realist (Stebbing, Russell)

If this analysis is correct it would explain why a scientist, though apparently asserting the permanence of the Universe, is, in fact, an ucchedavádin -- the Universe he asserts is without a point of view, and is the negation of the world (= loka). I have never been quite happy with your statement that the scientist is a concealed sassatavádin, though at the same time I have always had to admit (even if not to you) that there is something in what you say. It seems to me that this resolves the paradox: the scientist is, actually, ucchedavádin, since he denies his own existence, but he thereby asserts the absolutely objective existence of things, and since this is equivalent to asserting the absolute objective existence of his own non-existence (which he is -- the scientist is non-existent) he gives the impression of asserting his own permanence -- his ucchedaváda is sassata. (The natural assumption that sabbam atthíti = atthi attáti forgets that self, the subject, is the negative of the object, and that to assert the subject as a positive entity is to deny positive existence to the object. To assert the subject is to assert orientation, and consequently to deny there is any content to be oriented; and conversely, to assert the object is to assert the content, and consequently to deny that it has any orientation. But existence is a relation between orientation and content; and neither can be unilaterally asserted. The Idealist says there is choice but no thing to choose, and the Realist says there are things but no choice of them.)

In L'Être et le Néant Sartre claims that he goes between Idealism and Realism, but it is clear that he is well on the side of Realism. His statement that I quoted to you the other day, to the effect that we always perceive more and other than we see, reveals his fundamentally Realist outlook; and it may be compared with the following from Stebbing: 'What is normally presented to us is always less than what we correctly say we see.' Allowing for a difference i n usage, these statements are identical. It is true that Stebbing is making an excursion into "psychology" (as she calls it), but the fact that both she and Sartre are in full agreement on such a point is very significant. You said the other day that Sartre suffered from concealed deduction, but it seems to me that if this is so it is only because he allows himself to use a measure of induction.

I now think that the principle of identity has been totally misconceived by the Realists. In her discussion of it Stebbing is rather at a loss to know what to make of it, suggesting rather vaguely that it means "given p". It now seems to me that the principle of identity, normally expressed as "A is A", or "p implies p", means nothing else than "either p or not-p, excluding both", or in other words "p is defined by its negative". But this is equivalent to saying that you must have a point of view, which is strenuously denied by the Realists. In my last letter I said that the three Laws of Thought -- the Principles of Identity, Excluded Middle, and Contradiction -- define the negative; and I gave as illustration the following figure: -- p.___.not-p. This needs correction and elaboration. We can simply have the Principle of Identity "either p or not-p, excluding both": -- Or we can start with the Principle of Excluded Middle, which is formulated thus: "either p or not-p, not excluding both". This can be represented so: --

  (either p or not-p)
  (both p and not-p)

and we then also have the Principle of Contradiction, which excludes "both p and not-p" (without excluding neither). So we are again left with this: -- , which as you will recognize is the basic triangle in the tetrahedon, and therefore in Kummer. The second two Principles, as you will observe, define the first, which is the fundamental disjunction or negative -- Kierkegaard's Either/Or -- p/not-p. (Further discussion later in this letter.)

Just as the Idealists were ousted by the Realists, so, in their turn, the Realists have apparently been ousted by what we might describe as the Philosophers of English (or in the case of Ducasse, American) Usage. And in reaction to all this there is Colin Wilson who, even as a pimple, has achieved eminence. The surrounding countryside must be very flat indeed.

Before I change the subject or come to a stop, it occurs to me that the distinction between a Realist and an Idealist can be summed up thus: an Idealist has a point but no view ('a point of view without a view'), and a Realist has a view but no point ('a view without a point of view'). Viññána, however, requires a point and a view.

This, for the moment, and also because I don't know more about Bradley, seems to exhaust what I have to say about Logic. "And high time too!" no doubt you are thinking. It is satisfactory, in a way, to be able to round it off and see that it is not of further interest, but I had long ago come to that conclusion, and I do not feel at all the sense of stimulation that I had upon reading Dirac and discovering (to my astonishment) that the Quantum Theory held no terrors for me (and also to a lesser exte nt with Sartre; but this was more gradual, since I was learning from him and being disillusioned about him at the same time). This rather final statement will not, of course, prevent me from finding something else to say about Logic in a few days'time and writing it to you at great length. (Having been given some stamps of peculiarly repellent design I feel an urge to use them up as fast as possible.)

...I wonder if Bradley is available anywhere. Also McTaggart's Nature of Existence might be of interest, in view of Prof. Broad's statement that McTaggart held that he could demonstrate, from purely philosophical considerations, that conscious existence is beginningless and endless and requires a body. The fact that Stebbing refers to McTaggart only once, and then rather unfavourably, is in his favour. But I don't know whether he was an Idealist or not.

To return (I'm afraid) to discussion of the Laws of Thought. A further investigation of the relation between the three Laws (which may be stated clearly thus: -- (i) [EXCLUSION or IDENTITY] p/not-p, either p or not-p exclusively, i.e. excluding the possibility of both p and not-p [this Law, the Principle of Identity, I have restated -- Stebbing gives it as: "if p, then p"; the other two Laws are as Stebbing gives them]; (ii) [ALTERNATION or EXCLUDED MIDDLE] p v not-p, either p or not-p, non-exclusively, or not excluding the possibility of both, and (iii) [DISJUNCTION or CONTRADICTION] (), not both p and not-p, non-exclusively, or not excluding the possibility of neither) clearly shows that the fundamental difference between p and not-p can be expressed as the difference between both and neither. That is, p is related to not-p as both is related to neither. But both what? And neither what? Answer: -- both (both and neither); neither (both nor neither). You will see at once that this can be extended infinitely without ever requiring us to specify either both or neither except in terms of themselves. (BOTH = both and neither; NEITHER = neither and both.) This shows that difference or the negative is absolute. The exclusion either/or is simply (at each level) the mediation (shades of Hegel!) between both and neither: either/or is the invariant of the transformation consisting of the interchange of both and neither; and the reason for this is absurdly simple: -- the negative of the exclusive "either p or not-p" is "either not-p or p", which (to be Idealist for the moment) is an admirable example of identity-in-difference. But what, you might ask, is p? The answer is that p is a relation. What relation? The relation between both and neither. And what is not-p? It is the relation that is not p -- i.e. the relation between neither and both. But surely p is "both" and not-p is "neither"? Correct, except that there is a difference in order of generality to be taken into account. (The Logicians are correct in defining p as a proposition, except that it is not a proposition -- i.e. a relation but the proposition -- i.e. the relation of relation.) What, then, is a "thing"? Answer: -- a thing is "either-p-or-not-p", which must be carefully distinguished from "either p, or not-p" -- in other words, a thing is (= exists as) an exclusion between the positive and the negative, a thing is either/or (naturally we are speaking of a thing in so far as it is a thing, not in so far as it is this or that). A conjunction between a positive and a negative, which are themselves relations, is simply a relation between relations, or another, more general relation. If, now, I represent both and neither by vectors, so: --

= BOTH. I can also represent the negative of this by vectors, so: --

= NEITHER. I can now conjoin these, by adding NEITHER to BOTH, and changing the direction of NEITHER's arrows: --

giving me BOTH and NEITHER (which =

B O T H

N E I T H E R

If I conjoin these two (and changing N E I T H E R's arrow[a]) I get the following:

(giving me B O T H). But if, instead, I exclude them (by not changing arrows) I get:

and from my earlier post card you will remember that this is equivalent to

[b], or, to complete the picture, to which is the invariant of the transformation or exclusion. It is simply

E I T H E R / O R.

Correction to the above. Upon referring again to Stebbing I see that she says that the traditional interpretation of the Laws of Identity is metaphysical, that it expresses a theory (sic) with regard to the nature of persistent individuality; it is 'the persistence of something through change' (apparently it has, traditionally, to do with substance-and-attribute [as you asked a few weeks ago], though not as I have analyzed it). But she adds that this could not properly be regard ed as a fundamental principle of logical thinking, and so need not be further discussed. No wonder Bradley complained that formal logic is 'severed from reality'! No wonder Stebbing is unable to tell us what 'p implies p' does mean!

But now quite enough and to spare.

P.S. Stebbing, quoting somebody, says that Idealist Logic ends in shipwreck. This sounds rather a recommendation. Perhaps I should find that dolce m'e il naufragio in questo mar.[3]

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[140a.1] Bewilderment, confusion. [Back to text]

[140a.2] Backward-movement ('recoil'). [Back to text]

[141.1] What is is perceived. [Back to text]

[141.2] Cf. S. XXXV,82 (iv,52) [Back to text]

[141.a] By changing the arrows an order of priority is given, and one diagonal qualifies the other yielding a relation. [Back to text]

[141.b] By failing to change to arrows, neither diagonal has priority (neither qualifies the other) and they are thus excluded. [Back to text]

[141.3] Sweet for me is shipwreck in that sea. [Back to text]