Temporality and ‘Difference’/Derrida. (Language and Logic IV)
Meaning is notoriously temporal; context dependency includes difference in time – the passage of time carries with it the passage of meaning. Past meanings may be listed (but how many have we lost…); the present is ever-renewed (and meaning with it). As for the future - ‘deferral’ is of course imminently temporal (and nothing defers itself like ‘the future’).
Temporalising logic as… temporalising difference? Temporalised difference as three: past, present and future – but not necessarily in that order…
And temporally speaking A is never (still) A… (the river that passes). Although we may, of course, choose to define it as such – or not; according to use and point of view.
Indeed, if we take our cue from meaning (our understanding of things) then we find it is irredeemably temporal (unless time is foreclosed, axiomed out; then we have, putatively, eternal meaning, universals, a-historicals, a prioris…unmoved movers, etc…). Our interaction in the world, as part of the world (including our understanding, or interaction with ourselves) is profoundly temporal; perhaps unsurprisingly, as this way of relating, collating, presenting and understanding information that we call temporality (our experience of it as past, present and future) would appear to be hard-wired; the forum for our incoming data and for ’ourselves’ as such, a ‘report’ on ourselves given by our sensorium and compared to our memory. A forum perhaps made by ourselves; but as objects. So a given. A present. Presenting information; what we are…
‘Hard-wired’ too, is, or appears to be, our desire for the ‘other-than-temporality’; the foreclosure that permits universals, axioms, a priori, foundations and heavens alike… But although used as such - as if outside of time – in practice ‘it’ (and its culturally, and historically specific avatars) are not. Just another moment in the eternal present. (Albeit a rather useful one).
So, if we rule out the attempt to make an ‘originary difference’, or putting the concept of ‘difference’ outside as foundation, in effect making of it an extra-temporal entity, then, perhaps the nearest thing to an originary meta-set, or ‘originary difference’ would have to be contentless, the thin (white) line in between (a thin white line on a white page): or… presenting a plenitude of contents, ever-changing, differing, such that only the ‘frame’, which we delight in calling the self (etc.), remains (well…. in each particular case… for a time anyway…).
Or perhaps a better name for this meta-set, this ‘final frame’, etc, would be… the Eternal Present. (Our experience of the eternal present: our experience as the eternal present).On which, in which, or through which, ‘difference’ draws its distinctions…
And character…. Individual traits (of which we are so proud). Individual, indeed idiosyncratic, ways of presenting that information. Of ordering, and presenting, repeating patterns of what we have understood, of the meanings we have made. Repetition so constituting identity. Whence the importance of ritual to identity (collective as well as ‘individual’).
To reprise an argument from the previous article, on logical categories and time (L&LIII). (Or to paraphrase Levinas…) Otherwise (than) a-temporal… in logic, for example, if p then q; q, (>) p, is false, not all q signify p (~q, (>) ~p, is OK), meaning, if q then sometimes p, or E(Some)q,(>) p; the latter being the correct inference. However, note that ‘sometimes’ reminds us that the ‘some’ is not a-temporal (nor tautological, as in fact the content shows), we exist in time and so, realistically, by ‘sometimes’, we also mean concretely in time; which occasion, today but maybe not tomorrow…today an effect may be caused by one thing, tomorrow by another (crop failure).
The fact that Popper makes the reliance of science on this proof of the consequent, of effect, q, to infer the correctness of the hypothesis, p, is not proof of the insufficiency of the empirical method, but rather the reliance on logic alone, on ‘reason alone’, in this otherwise rather successful human activity… So showing that everyday logic is sufficient when allied to the empirical method – it also shows that our hypotheses are language-bound, and so modifiable, not due to ‘falsify-ability’ or logical precision, but the next most cohesive and referential, so explanative and testable hypothesis; if representation is not taken for objects, but as the symbol system which mediates our (relation to the) world, then we expect to alter it with observation and not to stand eternally (as with the tautologies of formal logic or other artificial languages).
In short, the eternal realm, finally, if it exists anywhere, is the realm of formal languages (‘Heaven’ has returned by the back door), the ‘outside’ of (historical) contingency is the place of our universals and ‘eternal verities’ - however this outside ‘is nowhere’ (Xunzi). Or rather conjured out of our heads. We may assert it ‘outside’, as a-historical, but it is we who produce it (it is an important aspect of our experience and basis for much thinking), historically, in time…’inside’… And so in this way re-finding time, returning time, the sign of the ‘times’ to ‘some’, rendering it ‘sometimes’, so counter-posing the provisionalities of actual temporal contingency to the eternity of ALL, abstract and tautological, but untrue, as nothing is ‘always’ true (outside of pure tautology, even quantity, number, is the product of probability… or desire, where it is that we actually ‘round off’ the decimal point…). Nothing is always true, for all time, all times (if it is real)… so rescuing, ‘Some’, for temporality, from the a-temporal ‘All’ (‘actually existing’ ‘all’s are used as ‘some’s (are provisional), as in ‘given the stability of other factors’, or ‘if we disregard xyz’ etc; these also are ‘if… then…’ assertions, but used in their natural linguistic richness and contextual complexity).
Leaving us… where? In one direction the path leads to the sciences, providing the picture, and the patterns, that underlie, that lie beyond our experiential ken, the other side of our subjectivity (the stored cultural knowledge of humanity updated by experiment and theory); in the other direction, well there is none… none, that is, that we are not already traveling, in time – our temporality and its irreversible direction. No clearing, no lost path, no authentic trail; only our perpetual finishing point … and starting point…
The Eternal Present.
‘Difference’ (Derrida) and temporal logic. One or two. Or in-between. Or both… (all three).
Binaries and Difference: Antitheses and (their) Difference (in place of a Synthesis). (Extremely speculative).
Key point: When we see all philosophies oscillating between monism and dualism, (‘materialism’ or ’idealism’, mind and matter, nature and culture, etc…), between a binary as opposed to a unitary manifold model of the world, then perhaps we should take note: this is the given state of affairs (not having to choose between them). Holding two positions in tension, this appears to be one way our minds cope with reality; the two positions taking turns, depending on the balance of strength and weakness, appositeness and unsuitability of application. In short, ‘both …and …’, is the position to take, descriptively speaking (so learning from the history of philosophy). With the difference between them as one way of ‘having it both ways’ (as we do in Quantum physics with the alternation of particle and wavelength as basic descriptive unit). Clearly the fields that ‘both’ types of philosophy ‘range’ over is the key issue; with both ‘starting points’ exhibiting aporia or blind spots with regard to the material at hand… that they are two (broadly speaking, that all such divisions are ‘two’) are contained within the frame of human experience and perception, this observation, or method of thinking, is transgressive of logical axioms (‘metaphysics’) - so making two, as one, in their difference would seem the way to go (Hegel maybe tried this, in his own way, as did Kant’s mapping of the antinomies).
The implication is that the methodology suggested here offers a way of having both: firstly through the frame of the Eternal Present where all other frames then fit-in as sub-frames with no right to absolute priority… so ‘existing’ as moments, not last words. In a thought experiment, in mathematics or logic, or in computer languages, we may ride ‘up’ or ‘down’ a layer, but the Eternal Present is the experiential final frame in which all others, up or down, meta-set or self reference, may be found to ‘nestle’ - finally because we only have one, ours, or more precisely, mine, or me… which we must return to… - or, even more precisely, that we ‘take with us’ when we ‘move levels’ – the present is always the present level we are in). So, meta-frames, of course, are all transgressive (and in infinite sequence constitute a ‘bad infinity’; finally the mirror image of the infinite rewind, or dance of self-reference). So, if necessary, both (terms of opposing sides or valencies) can be treated as we would treat a meta-set and self-reference. As meta-frames they must axiomatise out inconsistent matters (leaving behind putative ‘universals’ or even a kind of negative grounding outside); which then (as in any relation of natural to artificial language) come back to haunt them. Insofar as they are self-grounding they must succumb to self-reference. Can we treat these opposite sides as two windows in the Eternal Present? Sitting either side of ‘difference‘ ’itself’, as more present than the binary, just like the relation of past and future to the Eternal Present. So treating of all binary philosophies as meta-set, or as self-reference (if mirror images, or as either or both together if simply opposites; such that the meta-set offers a unitary manifold, or a monism, but self-reference as contradiction offers a binary relation or dualism)? The Eternal Present, here appears to act like Derrida’s ‘difference’ as the term in between, which steps into one or the other (the others, layers, or sides) as necessary; but finally returns or remains as it is – in between (such that the moving ‘up’ or ‘down’ a level in turn suggests yet another level, just difference must have two sides, and the Eternal Present two semi-presents…). Can we posit a relation of irreversibility, such that past and future (and so, meta-set and self-reference) are isomorphic? What happens if we do? Materialism/idealism; out and in? Past as matter, as happened, was actual (past thoughts also are matter, past matter was and is present as idea). Future as idea only (ideas also are matter, matter is present to us as idea) but do not -yet- have material equivalents, we can point, but not to an event or its record)! An issue to be resolved is that of polarity and non-exchangeability. Of the degree of isomorphism to past and future (like or not like the past and future in their relation of irreversibility) and of past and future (their commonality apart from this irreversibility – which difference appears to require the presence of the present in between, precisely, their difference… around which, from which, their ordering is drawn).
For example, such binaries have the form; more matter versus less matter; putatively, more real versus less real (action/symbol; event/language; thing/sign; nature versus culture, etc. etc.) in which case the balance of past and future as material and immaterial (actual in the past, versus the future as idea only), works; with the present as both material (our corporeality, our situatedness) and idea (thought experience, representation). A synthesis of sorts, but perhaps not quite as Hegel imagined (leading to a ‘higher’ as opposed to historically-following conception), nor simply (!) a logical antinomy after Kant, rather their possibility as foreshadowed by ‘the shape of our pocket’, by the relation of conceptualization to temporal experience as a kind of basic template – logic following the paths already outlined (perhaps one day being amenable to explanation in terms of psychology and physiology).
(We have seen this ’mapping out’ in the many appropriation of the ‘Semiotic Square’; a temporal version would offer present (A), future, past (both B, or ~A), as three corners with eternity in the corner opposite A ( ~~A); the first three would co-imply each other such that the present was present and the other two were semi-present, leaving ‘eternity’ as non-present; the diagonal linking past and future would indicate both opposition and non-reversibility or uni-directionality (their difference); the implications between past, future and eternity would signal the sliding of the former two potentially to infinity (albeit in opposite directions) so in turn suggesting eternity.)
So: if difference is made present/prior (and not secondary) then the other two (terms) come second, are less present, are like past and future; so Derrida’s difference can be made to join the temporal conception, or more interestingly, to occupy the place of the Eternal Present.
It is in this way that the temporal structure of the self may be read as modeling, forming, and influencing logical structures, and philosophical speculation, so offering itself (its own set of interrelations) as Ur-form, conceptual topology, or skiamorph - even as the determining limit of other models or philosophies (see also the previous article in this series, L&L III). This suggestion of an original landscape based upon our sense of temporality, our configuration as in the place of the Eternal Present, also appears to serve as the model for our alternating (and some times downright schizophrenic) reliance upon monist and dualist philosophical genres (as observed in the section above). This interrelation works out as follows:
(i) In the case of the Eternal Present as ALL (the case in every case) we have a monism which implies ‘up’ and ‘down’ as opposites (contained by it) as binaries, in this the Eternal Present is the last word, the meta-set, and outside limit. However no outside proper is possible to a monism, so no external view, or viewpoint, that would offer the vision of the whole, because it is a effect of (imagined in, or even echo of) the Eternal Present, but now ‘returned’ to the Eternal Present, as home/origin (both in and out, as self-reference and as contradictory…). Therefore the sense of unity is normally recognised as necessary, but fictional… the central contradiction of a monism (how can we know that it is such without transgressing its borders, standing outside the monism implies a dualism…). But perhaps this argument rests upon the visual senses too much; a sense of proximity or conceptualization based upon the sense of touch could not offer the illusion of a whole (so avoiding the central contradiction), but only ‘contact’, points of contact and apprehension of (degrees of) proximity. The touch of the surfaces that feel as of the past or future, or the sense of the sublime that attends the withheldness (whence the term Absolute Other, or Outside for this genre of notions) that we find characterising Eternity or the extra-temporal (whence our sense of the silliness of the variety of concrete images given to Heaven, God, etc – and utility of a taboo, iconoclastic, in this respect). With the sense of touch, or other form of de-visualising a monism, we are naturally nudged away from the sense of a ‘one’ to a pre-unified, ‘zero’. Also the movement from a closed to an open sense of presence.
(ii) In the case of the Eternal Present as SOME (as not–all, the case in some cases, or some of the time, not always the case) we have the model for a binary, a dualism, a divided manifold. What is present is conceived as in opposition to, as opposite and complementary to, other times – so as basis for a radically divided topology. In the ‘Future’ and the ‘Past’, we have an opposition offering a time which is never ‘there’ (was, or, will, better, might, be there); never here. The Eternal Present alone, or together with the other temporalities (past, future) as in opposition to ‘Eternity’ offers an even more ‘radical alterity’; an absolute Beyond or unreachable realm (albeit in religions one policed by Death and Myth). This sense of alterity remains true regardless of if we conceive of ‘Eternity’ as the quantitative infinite extension of the past and the future that leads to a qualitative Other (the route via infinity, the mathematical sublime) or just qualitatively Other as such, as ‘outside of time’; an intuitive extrapolation of the Eternal Present from ‘now’ to ‘always and forever’ – so creating, ex-nihlo, the site of gods and universals. This ‘now and then’ dualism may be considered as offering the model for the ‘mind and its other’ genre of philosophies. Yet this overview (of them both, of both irreducibles or incommensurables) also implies an external point of view - implies an encompassing meta-set…! The central contradiction being the envisagement (vision again) of a binary so implying an external position – so the possibility of a unifying monism… Logic, it begins to ‘appear’ is visual in at least a part of its foundations, its claim to solid standing (even if axioms try to chivy out the unavoidable extra-meanings carried by any natural language description) - the showing that underlines, or is in excess, of telling is visual in its ground. In a conceptual economy based upon touch however (and so also avoiding the metaphor of solids and co-occurring use of gravity), we would have the touching of something different, once, twice, many times – the perception of difference, then differences… so perhaps offering a potential plenitude, or pluralism).
(iii) However, in life, in our lived actuality, the Eternal Present is not opposite to ‘no Eternal Present’; because ‘its’ particular ‘Future’, ‘Past’ and ‘Eternity’, are always contained by it, contained in it, whence their enclosure within citation marks, ’…’. Contained, but not limited, contained by a sense, unlimited, or so it ‘feels’, as we touch the different textures of other temporalities without being able to posit their end… conscious only of their presence. So no ‘out there’: always ‘there’, as ‘in here’… in here and now (a memory must be present now to be a memory), and always particular, a person, a lifetime… radically particular, situated, embodied, my or ‘your’, I. Here the suggestion is that many problems of philosophy can be seen as coming from generalizations (actually provisional ‘eternalisations’ present ‘only’ in thought). As ironing-out particular contextual, situated, differences… (so creating contradictions, A^~A).
Dualism versus Monism (Reprise). An ‘in’ and ‘out’ topology versus ‘all in’; already we have the contradiction of positing a state other than the same (the Eternal Present), as ‘we’ take up a position on either side (even if we posit our selves as made from both, whence in fact the necessity for the division in the first place) versus a monism which denies ontological division; so already introducing the infinite regresses of self-reference (self/same as prior) or an infinity of meta-sets (other as prior) in a binary, and of meta-set (positing an ‘outside’) or self-reference (positing internal divisions, a divided self or identity) in a monism. It only takes one self-reference (say to an element as a set) or one meta-set step taken (the step to a ‘larger’ set), to imply the rest of the infinite regress or extension. The contradictions of a would-be monism or dualism show the same oscillation, indeterminacy or aporetic undecidability. Perhaps we should regard this as natural. (Part of our constitution as human).
‘Difference’ read as positive (back to one, or the only way we can have three?). After Derrida. ‘Difference’ as the middle term between two opposites, but now read as more ‘positive’ than its parent binary. For deconstructive philosophy this constitutes the limit position of its operations… any further movement must come from reality itself, as creating new hierarchies, new dominant cultural binaries - or just catching up with the implications of equality of representations, of communities, genders etc, in practice, in institutions in the public (as in the private) sphere. So ‘difference’ is taken at the end of the deconstructive process as the positive, or (most) present term between two, less or semi-present, layers (A, B, opposites). Like the Eternal Present in its relation to its (semi-present) others. Not like the Eternal Present as the Eternal Present does not require making present… it is always present, and difference (as the third term) usually does… usually as the result of a deliberate strategy designed to subvert received hierarchies and move the argument on (through inversion to equalization). But dig deep enough and the ‘ground’ of their difference is the Eternal Present (where they are, and what shape inspires their relation). The place of presence is the present; any inversion of presence (not necessarily the same as hierarchy, for equalisation operates through the mutual de-presencing of the binary in question elevated their difference to the position of presence, that which is foremost in the present…) must follow its rules.
So the reversal of the opposites from present to semi-presence and the difference as from inferred semi-presence to presence suggests the contours of the Eternal Present in relation to its others, the opposites of past and future.
Difference as one: reducing two to a single difference? (Again, after Derrida). Another attempt at a monism? Or a holding in tension of the two? Perhaps held by a third (often referred to as the ‘middle voice’)? So holding in tension a monism and a binary; their overlap, or ‘third thing’? And it is possible to show, of course that their commonality is much greater than their difference… that which has been made the source of key to their ‘difference’, another strategy in equalization, before the law at least, for the elements that make up the difference remain to be made positive, render both sides positive, from A(+)/~A(-) to A(+)/B(+). Also to be borne in mind is that the difference, if it is culturally significant, will have become constitutive, whence the strategy of not shifting the focus to commonality, but to positivity – but here we are entering the world… of cultural politics, of ‘culture wars’. Another point of view (which does not wish to be such); is this the only way to make a ‘third’; a new irreducible…). Or does the implication lead (in theory at least) to refusing the step to a ‘single‘ difference as ‘one’; and in so doing holding open the stage of a ‘pre-one’, a ‘zero’ – a ‘fuzzy set’ or a form without a fixed content… or a fixed boundary (remember we are talking experientially not physiologically). Again this sense of ‘difference’ and its staged strategy appears a little like the relation of the Eternal Present and its others… present, ‘originary’, but impossible to pin down… never ‘one’.
Or the (Hegelian) synthesis of the two positions, such that a new holding together in tension, a ‘new constellation’, emerges. A new starting point… calling forth its very own polemically, and structurally, necessary opposite… (as we have seen, the structure of the Eternal Present itself to its others would demand such a calling forth… always more than difference, but as the sum, or possibility of all difference… (the ‘place’ or ‘position’ that allows difference presence) the ‘place’ or ‘position’ which allows difference to occur)?
Yet envisagement (as if) from outside: impossible. What is this other ‘God’ position (beyond difference, that can ‘look down’ upon the generation of difference, ‘envisage’ the summoning of a new difference to oppose the one newly arrived at, so ‘overseeing’ the arrival of a new culturally significant binary structure of understanding…)? The best we can say is that it is a thought experiment, in its own way as fictional and as necessary as the grounding granted to/by ‘the outside’ or ‘eternity’ (or to mathematics through formalisation)… This envisioning or picturing of things (see also Wittgenstein, Tractatus, for this as a starting point… the showing that supports saying, but can not be said logically) begins to seem hard-wired, unavoidable, a gift to the imagination and its open-ended creativity; but carrying the curse of the meta-set type of contradiction in its every use. A curse modifiable, if not entirely revocable, by stepping away from the reliance on the visual ‘economy’ (the appropriation of the visual as means of presentation, means of expression, privileged coin of the realm of the conceptual) the ‘showing’ of the ‘picture’. The final point of view; seeing as seeing ‘All’. (If we try another ‘economy’ of expression, that of the sense of touch, then we have no ‘All’, but only ‘a beginning’, a sense of contact, with what lies beyond as to be intuited or explored… open, not closed, like the picture of ‘All’ of something, already thing rather than process). Or both: human thought caught in the tension between ‘picture’ and tactile sensation, or feeling. The visual field and tactile apprehension; or the field or form and the feeling or emotion it may contain…
Or perhaps by or in its performance… where if the visual sense may be said to dominate, as it does in much human activity, although normally paralleled by sound, our aural sense, then whenever significance is present, evoked, or renewed, then the ritual element is also present – and this consists of the evocation of an eternal reference (guarantor of the sense of the repetition or continuity, its identity) in the frame given by the performance in space and time (so conjured up within them, their particular confines, the (re)framing of space and time, but from a ‘place’ outside of them…).The place/time/event in which a kind of ‘knowing’ is to occur. Evoked (a paronomasia or prosopopioea). True of the handshake, the nod of recognition, as of the other end of the scale of ritual repetition, the festival (or in its destructive aspect, in sacrifice or scapegoating). The renewing of an identity, its force of recognition, its memory, its viability, as made present by its contact with the eternal as conjured by the ritual act. This contact, this ‘touching’ (it is invisible, unless symbolized by effigies or mummery) beyond touching, as there is nothing to touch, a route or conduit then, but to … nowhere, never… the end of representation, of representability, the ends of representation to survive as an entity, an experience, a community, a species. The Eternal Present in its reliance on its greatest fiction, ‘eternity’. Evoked in ritual. (As axioms too are a form of ritual, guaranteeing ‘universality’).
Yet the opposite beginning point, or point-of-view (to global envisagement as meta-set), implies the opposite contradiction; self-reference. With the view from within, the ‘immanent’ as opposed to the ‘transcendent’ viewpoint, as the one that offers the paradoxes of self-reference, of the confusion of element and set… as we enter into the endless circle of hermeneutics (opposite paradox to the infinite series of meta-set frames or boxes or layers…). A good model for the process of getting to know, or ‘in medias res’, everything is already… in progress, no beginnings, no axioms, only continuity… a plane or layer without end…
What is the difference between the two key (p)layers? (‘players’ because points of view… or better, personifications, embodiments; as all layers involve or imply a player… an actual person who takes up the position that differentiates the layers, whose presence decides which is present and which other…). The actual positions belong to actors, different points of view: otherwise two positions held in one head imply… one final position? (Key=Significance, as use, as play.) Two sides, or two sides of one difference… either side as (alternately, depending on ’side’ taken, in/out, plus/minus, right/wrong, true/false, first/second, self/other, subject/object…). Can we define the ‘one’ that is the difference of the two? (Or does this imply a return to zero, as only unconscious self-awareness is left; not capable of imagining a position outside of itself, so not ‘two’, as we count from 0 to 2: ‘…as only unconscious self-awareness is left’; a true ‘materialism’, one that can not think! - but as an ideology (a metaphysics based upon a binary), ‘materialism’ can only be another kind of idealism, one which contradicts its own position, its condition of enunciation). We have no choice but to inhabit the Eternal Present; but we may chose to move the plane or layer we regard as foremost, most present, prior (etc.) to this position, taking up this ‘point of view’, so as the ‘inside’ position, leaving the others, ‘up’ or ‘down’, ‘prior’ or ‘to come’ as semi-present, not forgotten, but not now in full presence, as ‘full screen’ or ‘main sensation’ (a move we may make, and our creativity rests upon it, always providing we remember this starting point – otherwise empty formalisation or fantasy results). We do not ‘move’ to occupy this position, so much as it moves, is moved, to occupy us… (as our now-moment). Whence the ‘last word’ given to contextualization or particular embodiment, which because a moving target, is deferred…
0 or 2; or (0 (2)); is the law of identity sidelined (no ‘one’); and is restate-able in terms of 0 and 2… in effect suggesting, nothing (0) or our given, the Eternal Present, as mutable, so both everything and open-ended: or a binary (2), the mapping of the field by opposites; the state of play of the semantic or logical mind… (out of the semi-present opposites of past and future, as with their ordinality, as all points of view have an order, a priority, a uni-directionality, a ‘what comes, or came, first’… ‘and what comes, or will come, after’, like the relation of past and future, their difference…). The law of identity sidelined; contradictory: in the sense that our constitution is so…
Again: What is the difference of past and future? Their ordinality; their difference (made… more) present in the Eternal Present.
No self is one: if in a polemical move, one sex, is not one… (but two, Irigaray, always attempting to move the dominant metaphor from vision to touch); then both sexes, all selves, are not one in the sense of being inside themselves (but capable of imagining seeing them selves as ‘others’ might see them, a fantasy, often, structurally (Lacan) widely inaccurate), we may put ourselves beside ourselves, but this beside is always (already) inside. So (again) no – one. Only Zero (0). (Perhaps Sartre had this insight when he suggested that Being was Nothingness). Zero the ‘ground’ of difference. Or (in another economy of rhetoric) difference, the touching of the two others. (Those interested might like to see my writings on architecture for the uses of this formulation in comprehending visual culture and the built environment). From within, as an effect of the within, we can not talk of One, only Zero (containing Two).
So we count (continue counting) zero to two; (0) 2. Although in terms of presence of priority this should be written: 0 (2).
Is there a solution with a return to ‘one’ as the difference of the two? As containing the two sides or levels - or does this always imply another (third) position that then introduces a new dualism… if infinite regress follows. But if the three are irreducible… as with two terms on either side of a difference, then.... Always (again) positing a position outside, the view from without, then an infinite meta-set sequence follows…
‘Two terms on either side of a difference’, does this not sound like the Eternal Present, and its two others… in time (and an absolute other for both ways of thinking…)? But the Eternal Present is not ‘one’, the ‘one’ in between; it is open-ended, evolving, contingent, changing (just like its offspring and mediator with the world, natural language) infinite. So Zero is a better number for it (as the container for one (1) with its additions and subtractions, assertions and negations, its infinite subdivisions and arbitrary limitations - and, not least, its impossibility, its being one that can see itself as ‘one’, ‘Objective Spirit’, no less…).
Or is it that there is not a dualism, 2 (unavoidable with
difference, but that there is not a one…). Thus 2 implies that all levels are
dividable… are already divided… into two (if 2, then all are already two (at
least); except ‘
Do we need to entertain the possibility that the middle term is the overlap of both sets such that it contains their difference as bi-directional, adding or subtracting the difference, or changing the differentiating quality according to whether we move from set A (inside) to set B, or set B to set A (outside)? This bi-directionality may be taken as an axiom; so coping with the irreducibility of the two levels (and the irreducibility of the meta-set (reference or step ‘up’) and self-reference (reference or step ‘down’) to an element of a set, (their contradictory circling as A implies ~A to infinity). Or is it rather a question of the relation of an element, statement or value to axiom, matter to instruction, stuff to rule, description to prescription?
Or maybe the imagined outside set (meta-view or total self-image) as A1 to inside’s A (which if this step is repeated, yields, A2, A3….Ax, so to infinity, eternity as eternally deferred, or present as the mathematical sublime…). So eternity as a present of the Eternal Present (as a present in, as only present in, as an extrapolation of…, so gift of, present of, the Eternal Present, eternally given…). Imagined as ‘more than ALL’; but in fact contained within our experiential ALL (the Eternal Present).
Yet as meta-view or self-image, self and context, self and all, the imagined meta-set also yields self-contradiction as the self/part or element of the set envisages itself and its context, or set, from outside…
Again we find parallels with the irreversibility of time in experience (human temporality). As also manifested in thermodynamics (and, finally, in Chaos Theory as bringing ‘order’ (sic) to physics (‘strange attractors’)); physics being, otherwise, strangely, reversible). Irreversibility, such that: if one level is said to support another level it must be prior… (= past): implying something must be the next stage means it must follow… (= future).
Yet both ‘up’ and ‘down’ directions can include layers that are prior; it depends on how the metaphor is used ‘foundations’ suggest bottom up; ‘heaven’ or eternity usually suggest a meta-set and a causality that is heading downwards (as in the history of Chinese thought and language).
Causality versus implication and interpretation? Causality (the arrow of time, represented as from left to right, ->, now globalised, previously represented as flowing in the opposite direction in the cultures of the Far East, from right to left, <-). As opposed to interpretation as reading back, into things (<- whilst observing the arrow of time (in the EP ->). Inference, as working back, if ‘this’ is the case then ‘that’ must have been the case… if the EP (0) then the Past (P): (if 0, and only if 0, then P).
The present may be thought of as an event horizon with all as past, with all of itself becoming the past (including images of the future becoming past, ‘I thought, then, that this would have happened’; the future as thought in the present must become (recollected) in the past…). A frame with everything perceivable within it as rushing away, like Walter Benjamin’s Angel (and given the momentary hiatus between the reception of stimuli and the arrival of conscious perception we may say the content is all in the past…). What is rushing in is what will constitute our ‘room’ in the world. The present self. The Eternal Present.
Janus-faced, logical implication points back to causes or forwards to effects (at least that’s what we often like to call them, the linking of events or the description of a process does not require logical implication). In both cases, the logical relations are tautologically present in the present, so, yet again, like the past or the future in which their being is implied, semi-present, waiting to be found… or to be made… (whence the possibility of a wholly imagined, meaning wholly imaginary, past). Inference played forwards often involves the dependency or origin of the relation in a prior event (as when involving real events and not quantitative measure); the past projected as repetition or variation is the future. Even causality (‘if p then q’, used of events, of history) is not allowable (fruit of a pattern, imposed, too abstract), certainly not from the point of view of the Eternal Present as such, from where only the semi-presence (of the ‘place’ of the putative cause or effect) is significant. So the future, when not supposing brute repetition, offers the imagination (variation). Projection is what we finally have left, not logical inference (nor cause and effect… even though we want to use this…).
And what of the ‘higher causality’? The prescriptions or commandments of civilization? Of civilized behaviour… The proscription that is inscribed on the sacred tablets of morality, of the non-relation of ‘is’ to ‘ought’, in effect denies morality, consigning it to the same place as eternity: as only from this ‘place’ can we find its justification. Morality; precisely as impossible as eternity (as situated… nowhere), with precisely the same function, as impossible, but necessary, to human thinking, to human life… to civilized human life. But not present (not presentable) quantitatively, or in terms of cause and effect, nor logical implication (at least not without the ‘a-priori’ inclusion of moral axioms, their status, as ‘given’, as ‘read’, as universals). What is significant here is the isomorphism of eternity (et al.) and value-giving, value bestowing (both are performative in force - if we say such is the case, then so it is - both are capable only of being performed by humans, our gift to the world, as to each-other, our gift of value, so our protection, to both, if we would give it…).
Do performatives remain as ‘beyond ritual’, or what is left when the props of ritually enframing time and space (to call up the eternity which will guarantee or renew the identity propositions or identity values of the community in question) are removed? Yet as performatives require ‘felicity conditions’ so these may be read as ritual context... Ascribing value would certainly appear to combine ritual (a gathering of people in a time and space felt as event) and performative (linguistic utterance) elements…
Is there a ‘future’ attainable, such that we remember it as something we thought some time ago (as, in, the future we speculated upon, previously, now become past (actually this means the frame of the Eternal Present in which we opened a window onto the future, has past))? In which case the ‘future to return’, will be in the past, the projected future of the past… ‘the future as (once) projected in the past’. Or in the thought experiment of (a) time (line) as (if) seen from outside (like the literary convention of the omniscient narrator, like all ‘external’ points of view, a generalization of the eternal aspect of the Eternal Present. Otherwise once in the past (once happened) always in the past… (that is to say always (potentially retrievable, or remade, only in the present). Only as the frame (the semi-presence) of the future in the present does the future actually exist for us (as shown by time tense in verb endings when vocalised). And as such, as oft-noted, it ‘never comes…’ Its (full) presence is endlessly deferred.
By insisting on something which is not, but appears to be essential, or unavoidable, the sense of eternity, etc., we are having it both ways (it is and it is not), so A and ~A, or if p then q, as required as a strategy (not a logical truth alone but a part of situated discourse) when we see both paths, meta-set and self-reference as (in and out) as contradiction producing. Contradiction producing: when not purely formal, tautologous (contentless or referenceless) contradiction, then representing difference. As the content differentiates the contradiction into matter or mind in conflict… (as real social agon, or its representation, as in tragedy, completed or avoided, as the felt division of the self, division of loyalties, within…).
So the law of identity, no (A and/^ ~A), and the propositional calculus, based upon p>q, along with a predicate calculus where the Some/All relations have not been temporally restricted or specified, may be as necessary fictions, just like the positing of eternity and its avatars (among which they might be counted). Their function, their functional utility, (usually) outweighs their fictionality.
A, ~A as temporal. ‘Not’ read as ‘not-now’ (as in ‘Language & Logic III’); yet as thought, as thinkable (only the thought is now, now the event or referent has gone), as semi-present, just like the past and the future. In fact the past is precisely defined by the fact that it was once present (or as if such) but not now, not anymore, thus rendering it a memory or (if never, not yet, present) a projection (future). A, and ~ A too, depend or may be explained by reference to the Eternal Present and its contents, its ‘less-present’ others, the semi-present Past and Future, and the absent (as place, entity, event) but present (as function, phantom topography) as the ‘outside’ category of Eternity. Like all ‘outsides’, what we have here is the ‘outside’ inside… category or Ur-form of generalisations and universals (a-historical truths), gift of language as detachable from things, and of time (human temporality) as the key extrapolation of the Eternal Present (extrapolated, then contained). The law of identity as also a product of presence and semi-presence – and a referent-less reference, not absence, because we can think it, represent it (even eternity, infinity, heaven, the Absolute Other, the unrepresentable, sublimity, etc, are representable by words, even if we can not point to where they are - unless we point at our heads (where they are … contained)). For semi-presences, like the past and future can be pointed to, not as existing now, but as posited in the Eternal Present, as directionalities, differentiated only by this very difference of directionality, of pointing, in opposite directions. ‘A’ and ‘not-A’ and ‘not-not-A’. Otherwise: presence/the present, past and future (no more or not yet; ‘was’ or ‘might have been’ and ‘will be’ or ‘might be’) and nowhere, never (not ever (more)) – but representable as such, so offering a set of useful functions for thought. So in an interesting isomorphism, the logical fundamentals parallel the temporal ‘parts’ of the self which in turn parallel ‘difference’ and its others (all echoing the pattern: same, others, Other). The difference of temporality; difference(s) made out of temporality. Whose middle term (constituting difference) is not the ‘mean’ of the semi-present, nor the supporting absence of eternity (again, a very old insight, ‘heaven completes everything’, Xunzi) but the experiential meta-set, or ‘last word’ of the (eternal) present which frames all the others (between the opposites of time and not-time; the impossible ‘now’ moment in which we are forever to live out our lives - a very finite infinity indeed).
A further example: ‘and’, of course, may not only indicate a logical relation (^), but also indicate temporal order, ‘first he… and then he’, or with the sequential, or temporal ordinal indicator, ‘then’, implied, ‘he cooked the food and served it’.
Language meets temporality to give sign (the word, written and
spoken… and the habits of thought) to our other (pre-)dispositions, from
identity and its implications in life (self) and in logic (‘A’ and other
categories as also the paradoxes) to eternity and all that lives there… Except
that this ‘there’ is here. The two are not only ‘pulled apart’ here, but formed
here (the moment you are conscious of ‘one’ there must be ‘two’). Wherever
‘here’ is… (‘…from 0 to
Logic as translation (as all ‘difference’, as all crossing a given situated difference, is a form of translation). A=A; read as ‘All A=A’; is ‘outside’, universal, etc (but there are none such in actuality; or true only for a-historical formalisms). So better: Some A=A as the apposite axiom (its truth is always dependant on other concrete factors); so offering the status of A=A as axiomatic… but only if limited by ‘Some’; a provisional ‘a priori’ (inside). Or, we might say that ‘axioming-out’ time (making A universal) works in some but not all, situations; again giving ‘some’ (A) as the accurate condition. So: p>q (if p then q, as axiom) is out (because out, ‘outside’), because abstract, so a-temporal, universal but formal; for ‘all time’: but it might be argued that as all terms are limited or take their meaning from their context then ‘all’ too may be read as ‘in’. So context bound, temporal propositions are different - cast in language, cast in situated utterance. And so we have a kind of implicit translation which is sensitive to local conditions and the contextual conditions which may need to be spelt out.
Yet all A (statements of identity as propositions) must be, if p then q (if a then a(x)); so p>q = ((as if)for) All time, is nevertheless used as a kind of ‘must be’, must use, a priori structure, against which other statements or states of reality can be checked - indeed this is its strength. Now if something is prescribed then all will try to master its use… in short, with a little skill, all manner of propositions can be made to fit the formula… indeed pretty much all statements and sentences are recastable or translatable into the propositional form, (if) p>q… (but this formula is not, we remember, necessarily reversible). The skill then is not in the logic, but in the translation… in the construction, in the making them fit (and so a form of sophistry...): and conversely, to disprove the case is to make the two terms (p,q) not fit… not follow (also a form of sophistry). As we broaden, or restrict, the field of A to eliminate ~A. The connections, or contents, of A are what you want them to be.
Logicians, when they explain matters, do not usually use formal logic… but ordinary language - and often colourful and inexact language at that (Quine et al). Otherwise we would not read them.
If logicians were to speak -logically- how would we understand them.
Copyright Peter Nesteruk, 2013