The Mirror and the Garden

Table 2.a The propositional arc

It’s tricky to claim logical proof implications when so much of the argument has been subjective, analogous, almost emotional in its appeal. Faith is a tricky proposition if you’re also trying to speak logically, or at least reasonably. With this propositional arc, I’ve tried – amongst other objectives – to meet the faith/logic tension head-on, by logically tackling the consequences of an ultimate renunciation of faith. I think I met a solipsist once, or at least someone who thought he might be one: his reason for engaging with the real world was that acting out the illusion was easily the option most personally fulfilling, so that even in the absence of anti-sceptical faith, you may as well pretend belief. In any case, I hope that Proposition 3 reinforces the perception that there is no halfway house: you’re in the world or you’re in the absurd. Beyond that, in one sense all this is simply a reason-based game: when you embrace the anti-sceptical strategy, how far can you push that, if you’re willing to take some risks? In mathematics, if you haven’t proved it, it doesn’t count. Or does it? Fermat’s last ‘theorem’ was in actuality nothing but a conjecture for centuries, yet such was its imaginative hold on mathematicians over that period that entire areas of research mathematics have been spawned in a quest to prove the simple idea that, if the equation aⁿ + bⁿ = cⁿ can have a solution in which a, b and c are positive integers, the (integer) index n had better not be any larger than 2. I don’t mind leaving my propositional arc out there as a challenge either way, for ultimate proof or disproof of any part of it, but I suspect that – as in Descartes’ metatheological chess game – the logic only swings if you buy the assumptions, and for that I make no apologies. I don’t think metaphysical validity follows a 0–1 law – for example, I don’t entirely reject the ontological argument for the existence of God – because even the most easily attacked argument may have explanatory power beyond its susceptibility to systematic prosecution. I will try to show, in the sequence of chapters to come, that the work presented here has some genuine metaphysical reach, and ultimately that is a fairer test than logical sustainability, however much fun I’ve had playing the implication game.

As a philosopher, I try to comprehend the light for which I am, for which I believe we all are and in which it would be nice to think that most of us try to live. In identifying this light with emergence I am approaching as close as I dare to a direct answer to this chapter’s title, although in truth the rhetorical force of such a question may be diminished by any response that claims to be final. I make no such claim, because I want to keep asking, to keep experiencing the power of epiphany that uncertainty in the boundaries of consciousness releases. The most mysterious thing about epiphany, which literally means the experience of seeing the light, is its simplicity. When you let go of your old certainties, somehow the light floods in:

To all appearances he was just drifting. In actuality he was just drifting… The drift took him into the Army, which sent him to Korea. From his memory there’s a fragment… of a wall, seen from a prow of a ship, shining radiantly, like a gate of heaven, across a misty harbor…That wall in Korea that Phaedrus saw… was beautiful because the people who worked on it had a way of looking at things that made them do it right unselfconsciously… And what is good, Phaedrus, and what is not good – need we ask anyone to tell us these things?[28]

The question, ‘Why am I, if not for this?’ is worth asking, in any form, but if such questions were finally answerable, what price faith, however secular? Witness also, that in not quite answering the question – more holding it as valid-continuing – I have tackled major metaphysical questions that hinge on its impulse. Perhaps the meaning of life is the very question ‘What is the meaning of life?’ A big part of what I’d like to do in this philosophical project is to explore how the epiphanies of emergence arise in a continually dancing response to our continual questioning. But maybe they would remain just as true if we had never been. Meaning has a way of emerging … meaning in life is least tangible as a distant goal, and most present as a living force of connection between who we are and what we do, in this world that we have a chance, not only to comprehend to some extent, but also to recreate. Edith Wharton said: There are two ways of spreading light: to be the candle or the mirror that reflects it. Two ways perhaps, but one emergent light.

[1] I think that is why Shakespeare was right to have Cassius say: ‘The fault, dear Brutus, lies not in our stars, but in ourselves…’ – Julius Caesar, I:ii

[2] Schopenhauerian in terms of being beyond conventional knowing, but not in terms of being inherently evil.

[3] To digress somewhat technically for a minute, for me the noumenality of consciousness can be grounded in the characterisation of sentience as an (elegant? Of course we would find it so) evolutionary response to the question constantly posed by and interpreted in reality: the question of this chapter’s title. We as a species evolved our extraordinary mentalities – we are, as humans – because (in the teleological sense of that word) of our quest for meaning, for a reconciliation of consciousness with its noumenal roots. This drive is what I mean, when I talk about nostalgia for significance of being. Without it, how are we any different from the upright apes from whence we evolved?

[4] The subset of metaphysical philosophy which addresses what we can know, and how we can know it. Plato wrote a fascinating though ultimately inconclusive dialogue on the nature of knowledge, the Theaetetus. Epistemology itself may arguably have been ‘founded’ a generation or two earlier by Protagoras, whose ideas Plato’s protagonists in the Theaetetus debate and ultimately reject. The dialogue is fruitful and puzzling in equal measure, and since its inconclusiveness is surely part of Plato’s intent, I had better not try to summarize it here. Myles Burnyeat has done a thoughtful modern edition.

[5] The title of Chapter 3 being What is emergence?, I am obviously getting a little ahead of myself here. More later…

[6] In a way, my concept of the noumenal aspect of consciousness is a more spiritual ‘take’ on this idea. In any case, let’s say that there is an unassailable realness to personal thought.

[7] How deeply problematic all this must be for a Cartesian atheist, of whom there might not have been many in Descartes’ own time, but try walking into any university science faculty now and not finding one! This is the kind of thing I meant when I suggested in Chapter 1 that unitary entities – like God – are tough to incorporate into mirror-type dualistic systems. I am more of an agnostic than an atheist, I suppose (though I don’t really know…), but rather than buy Descartes’ logic wholesale, I would drop the first two moves and essentially base my response only on an agnosticised move three, leaving God out of it until I had my metaphysics more fully established. You’ll see what I mean later on in the chapter. I do agree with Descartes in spirit, if not entirely in approach. Above all I believe tremendously in ‘move zero’, the Cogito. You’ll also see, as we go on, how it pervades and enriches my own enquiry.

There are grounds for wondering whether Descartes’ logic convinced even himself. Well, perhaps that’s not fair, but it is the case that, having erected a wall between mind and matter so high that only God could help you over it, he was at a loss to explain the connection by which the mind might experience the material world in any concrete way, let alone act upon it. As Gottfried Leibniz later remarked, ‘Monsieur Descartes seems to have given up the game so far as we can see.’ Slightly embarassingly, Descartes postulated a sort of ‘gland’ in the brain – actually the pineal gland – which might accomplish the uplink. But this only muddles the mystery, which I think is a profound one, and to which I’ll devote much of Chapters 4, 5 and 6.

[8] Locke’s influence on political thought, in an age of revolutions, was particularly profound. A characteristic part of his ‘common-sense’ empiricism was to limit faith in convention or authority well short of dogma, but rather to rely also – really, primarily – on a reasoned analysis of the facts of the case. Historically, this position starts from the intellectual freedom that post-feudal/-Catholic England offered (Jacob Bronowski suggests in The Ascent of Man that the passing of the torch of modern physics from Galileo to Newton was highly significant in this regard), and leads to the recognition of ‘the rights of man’ that in different ways drove both the American and French Revolutions. Certainly Voltaire was an enthusiastic promoter of Locke’s ideas, and the Founding Fathers kept him very much in mind as they drafted their bill of rights.

[9] A digression from epistemology into pure logic comes to mind here. I remember once waiting for a graduate seminar to begin, while next to me Alex Selby, a white-hot mathematician and something of an iconoclast, was apparently railing against the ‘indoctrination’ of students that modus ponens was an invariable law of logic. Modus ponens, or ‘bridging method’, basically says that if A is true, and (A implies B) is true, then B is true – it allows mathematicians to do joined-up logic. It seems so obvious, and the consequences of abandoning it so dire, that but for my respect for Alex’s intellect I would have dismissed this rant out of hand. However, evidently it stuck in my memory, and it occurs to me now that there are certain parallels between Alex’s scepticism (though for all I know he has moved on from this position by now) and the classic scepticism about external reality. The key is the little phrase ‘is true’, which in some accounts of logic has been scrubbed out altogether but in fact may hint at some profound assumption level about any kind of external reality in which an abstract proposition may be tested. If you’re sceptical about that, I guess you would be sceptical about modus ponens. Moreover, if even logic is directly experienced only as part of internal reality, even logic must be subject to meta-epistemological question, which could be awkward to the extent that a given epistemology is founded on logic.

[10] Loosely, you could say that philosophy with Husserl reached the limits of its concern with knowing, with Heidegger passed from knowing to being as a central concern, and with Wittgenstein passed from knowing to meaning.

[11] The concept is also quite reminiscent of another Hindu/Bhuddist doctrine, tat tvam asi or ‘you are that’, in which sense of self dissolves in an egoless identification with brahman reality.

[12] I think ‘superficial’ is the right judgement, because Heidegger’s actual philosophy does not smell of Nazism in any way, being rather apolitical in its content and anyway about a billion times too sophisticated in its sensibility. After the war, Heidegger was scarcely able to deny some rather public pro-Nazi utterances but at least did not pretend that he had made them only for expediency’s sake, instead explaining that he now viewed Nazism as a kind of mass social experiment that had gone catastrophically wrong. The whole business leaves a bad taste, of course, but let’s face it, bigger villains have grown old in Paraguay. As for Heidegger’s focus on practical activity, that makes at least as much sense as expressed in Roosevelt’s New Deal as it does in the context of Hitler’s work programmes of the early 1930s, which in reality were no more than thinly disguised war preparations.

[13] At the end of this sequence I have provided a table that sets out the logical connections, some playful but also I believe valid adaptations of the Cogito to individual propositions, and some identifications with the fourfold diagrammatic process. You may find it interesting to refer to this table as you read through the text of the propositions.

[14] I’d better deal here with a slight whiff of logical circularity. I am essentially defining ‘internal reality’ as ‘what I experience directly’, which does presuppose a certain metaphysical conclusion that, by contrast, ‘external reality’ is not thus directly experienced. That for me is an axiomatic or perhaps definitional structure – I am not going to try to prove it, from this proposition where I have certainly assumed it or from anywhere else in the propositional sequence. Rather the aim of this sequence is to clarify what is inferrable about external reality. As a first step, let’s figure out what we can know about the boundary – which is, I shall be saying, quite a lot.

[15] Hume would probably say that I am committing a ‘causal fallacy’ here: why does my mental content need to be caused or stimulated, even if its intentional aspect tells me it is? I can best respond to that by relying as closely as possible on direct experience. In using the topological metaphor for intentionality I am quite deliberately aiming to capture something of its experiential essence, which is that perceptions and experiences, and maybe much more, reach me across it. I’m saying the intentional boundary acts as a causal vector because I directly experience it as such, not because there has to be one out of some logical necessity. In all of this work I am actually more interested in remaining true to actual experience than I am in establishing airtight logic, which I suspect is ultimately impossible. What I can do is use logic, as far as appropriate, to make sense of this experience, to try to understand the metaphysical big picture that emerges from it.

[16] The Spectrum had been the leading home computer in the UK about five to ten years previously, and so despite its severe limitations there had been some wonderful games written for it: hence the emulator craze. You now see downloadable emulators of early arcade machines on gaming sites, for just the same reason.

[17] I concede this is another argument by analogy but I think it’s a good one, and again, as true to the nuts and bolts of how mentality and especially intentionality is experienced as I can make it.

[18] I say ‘pseudo-’ because, as mentioned earlier, I don’t want to push Berkeley’s philosophy to the point where I claim he was definitely saying this – in fact I suspect that he wasn’t.

[19] I am implicitly using Proposition 5 to guarantee that we actually have some phenomena and noumena to consider. In mathematics, you can’t have a meaningful mapping from region A to region B unless A and B are both non-empty. Another mathematical point: a mapping is useful because it gives specific correspondences, not just a general link.

[20] I mean ‘objective’ is in the sense of ‘of or relating to objects’, rather than ‘not subjectively interpreted’.

[21] The full implications of this idea will have to wait until Chapter 3.

[22] In a sense this is even true of ideas about ideas, because thanks to Proposition 7, ideas can be viewed as noumenal as well as internal. That is, ideas (internal) about ideas (noumenal) are again ‘about noumenality’.

[23] I’m a bit wary of introducing levels into metaphysics but as Robert Pirsig observed, in Lila, analysing mystical reality into comprehensible structure is an inevitable consequence of creating a mataphysics at all. His four-level metaphysics, developed in that book, consists of material, biological, social, and intellectual quality, but is still overarched by a metaphysical master term, dynamic quality. In the same way I am going to keep emergence as a central term in this metaphysics; indeed, I think one can see dynamic quality and emergence as very much the same thing, under slightly different aspects, and with rather different metaphysical unfoldings and consequences – as my next chapters should make clear.

[24] ‘When you say words a lot, they don’t mean anything. Or maybe they don’t mean anything anyway, and we just think they do,’ as Delirium says in Neil Gaiman’s Brief Lives. Behind this apparent non- or anti-sense can be found any number of rich ideas, such as Wittgenstein’s suggestion that words take their meaning from their shared, practical uses, or Derrida’s contention that texts can have other meanings, radically different from the interpretation the author wrote into them. And they can, however disrespectful to the author that might be.

[25] The idea is perhaps natural to me, since as a mathematician I have encountered the unifying programme of category theory, which builds a metastructure out of the fundamental likenesses of existing algebraic structures. Er, what are those, then? An algebriac struccture, in higher mathematics, is rather far removed from the x’s and y’s from high school. Actually, you can still have x’s and y’s but they may or may not stand for recognisable numbers, and the rules for combining them become the object of study in itself. For example, you can have an analogue for mulitplication by itself, or an analogue for addition by itself; you can have both of them together (this happens in an algebrac structure called a ring, which is the nearest thing to our conventional counting numbers although it’s capable of being much, much more); you might or might not have in place the inverses (think division or subtraction) of these operations (if you do, you might have an algebra called a group, which is critical for analysing systems with symmetry, geometric or otherwise); if you call x and y vectors and also throw in simpler things called scalars, you could build yourself a vector space, an algebraic generalisation of the ordinary two- and three-dimensional vectors sometimes used in high-school physics (think of the scalars as pure magnitudes that can scale up the vectors); and around or beyond the point where I checked out of algebraic mathematics you get things like number fields, Banach spaces, Clifford algebras, spaces of knot polynomials (very useful in superstring theory)… Category theory exploits the fairly evident fact that all these entities start from a set of objects, a few (usually a very few) rules, and some standard ways of morphing one example of an algebraic structure into another example. Given that commonality, especially with the morphisms, one can explore in potentially powerful ways the senses in which these different algebraic areas for mathematics look alike. Whether category theory has actually opened things up all that much, or whether it is simply beautiful but irrelevant, is still an open question: it has both adherents and opponents among research mathematicians.

[26] I shall start in on this in Chapter 4, where I use Proposition 12 to develop dynamic entities or structures I call truth-value resonators or TVRs. Basically, Proposition 9 gives a structural basis in internal reality for TVRs, and Proposition 12 says that, vis-a-vis external reality, TVRs actually work. The TVR concept is also key to my attempt to explore the richness of the reality boundary, to which I drew attention back in Proposition 1. Since I said there that the boundary is wholly inside internal reality, there is agreat opportunity to build the TVR concept on the foundations of direct experience. In fact any valid epistemological structure can be so built, starting as it were from both ends of the propositional arc.

[27] Some mathematical symbol meanings: = ‘boundary of’, = ‘is contained in’,
= ‘empty’ or more literally ‘the empty set’, ‘A\B’ = ‘what’s in A but not in B’,
= ‘logically implies’, = ‘union or joining of’, = ‘m is a mapping from A to B’,
= ‘structural product under the aspect A’, = ‘there exists’, ! = ‘unique (there’s only one)’, ~ = ‘equivalence relation’, f^–1 = ‘inverse map of map f’. So everthing’s clear now?

[28] Zen and the Art of Motorcycle Maintenance, Chapters 11, 25, and 30.

Chapter 2

Why am I, if not for this?

Knowledge and scepticism

Being, acting, and meaning

An arc of propositions