On Epistemology
On the Nature of Truth
Premise: The truth value of an epistemic position ("is (not)") is three-dimensional:
1.1. Sequentiality: An epistemic position may be applicable/inapplicable for the point in time to which it is applied.
1.2. Certainty: An epistemic position may be secure/insecure within the range of those positions that are applicable.
1.3. Effectuality: An epistemic position may be sustainable/unsustainable due to the degree of effect it would produce.
Examples:
1. "He is an artist" is inapplicable for the child or the person who has quit the vocation.
2. "He is an artist" is unsure if "He is a mere craftsman" or "He is a mere hack" are also applicable.
3. "He is an artist" is untenable for the person who destroys all art they produce.
Note: In 2, the use of "artist" is not categorical, but rather a placement on a nominal scale within a category. For a finite range of discretely possible epistemic positions, where the range is applicable, certainty is the distribution of possibility within one position in relation to the whole. Hard (Heisenbergian) uncertainty, if I understand correctly, holds that this is objective. In a subjective sustainability problem, effectuality would be sufficient to establish applicability of the range, but not to establish applicability for a single position within it; assuming that positions are incompatible, only one is actually applicable; it's simply a failure to establish which. In an objective certainty problem, effectuality is sufficient to establish simultaneous applicability for various positions within the range; since positions are incompatible, another dimension of actuality is required to model the distribution.
It may be clearer if one considers "secure" and "insecure" as judgements of applicability in a second temporal dimension. For simplicity's sake, we'll take "artist" in its categorical sense, such that as soon as a person starts producing works of art they are an artist, and as soon as they quit the vocation they cease to be an artist. Now, consider a twenty year period in the life of a person, at the middle of which they quit their artistic vocation. For the first decade, "He is an artist" is applicable. For the second decade, it is not. Now consider that stretch of two stints--one in which "He is an artist" is applicable and one in which it is not--as a second temporal dimension running not forward and back but side to side. The idea in the notion of certainty is that any moment may have span such that "He is an artist" is both applicable and inapplicable. It thus becomes less secure, more insecure, my point in this labelling being to escape the implicit absolute of "certain"; if something is secure, that doesn't mean it couldn't be more secure.
See the Community episode in which Abed has a meltdown trying to answer the question: "Nicholas Cage: good or bad?" Why? Nicholas Cage veers wildly in performance such that over the stint of one movie he's great, but over the stint of the movie immediately after he's awful. Because the stretch in which those two stints is being collapsed down to ask if he's essentially good or bad, Abed is to all intents and purposes approaching it as an objective certainty problem: the span is such that two mutually incompatible positions are equally applicable, indeed equally actual. (The joke is partly in rejecting it as a subjective sustainability problem: effectuality is sufficient to establish that Cage is too good to be considered bad, but it is also sufficient to establish that Cage is too bad to be considered good.) Cage is being treated as existing in a superposition of two eigenstates, like Schroedinger's Cat. (The correct answer to the question is, "Yes.")
We can develop this notion of certainty to something more sophisticated if we return to the comparison with a conventional notion of time. If we take "artist" as a position on a nominal scale within a category, we can imagine a twenty year stretch in which a creator begins as a mere craftsman and develops their artistry to a peak point as a maestro, only to degenerate afterwards to a mere hack. Here, we're treating "artist" as encapsulating the quantifiable applicability of artistry, which becomes more and more applicable as it increases up to the peak, less and less so afterwards. Let's imagine it as a nice smooth bell curve. Improvement begins slow but accelerates when the creator finds their voice. It slows again as they approach the best they can be. There's a tipping point where they start to dry out, and a plunge as they surrender to hackdom. Finally it bottoms out as it becomes harder to get any worse with their basic craft skills. Over the twenty year stretch, the y position on that curve is the degree of their artistry.
An upside-down reflection of that curve would map the applicability of the two other qualities: mere-craftsmanship and mere-hackdom. We'd start at a peak of mere-craftsmanship at the same height as the zenith of creativity. This would decrease slowly then plunge as artistry rises, bottoming out as artistry peaks. From the tipping point, mere-hackdom kicks in, taking off as the creator gives up and artistry plummets. We end with mere-hackdom at the same pinnacle mere-craftsmanship occupied at the start, at the same pinnacle artistry occupied in the middle. Now all we need to understand is that there are two crunch points: where artistry surpasses mere-craftsmanship; where hackdom surpasses artistry. And in this use of the terms "mere craftsman," "artist," and "mere hack," which quality has surpassed which is written into the definitions via that "mere."
One could use "wannabe," "maestro" and "has-been" here, instead. It doesn't matter. The point is, these are nominal labels for discretely possible epistemic positions with a range. Though the qualities they encapsulate overlap, the labels define states that are mutually incompatible. "He is a mere craftsman" ceases to be applicable as soon as "He is an artist" is, and "He is an artist" ceases to be applicable as soon as "He is a mere hack" is. Across the stretch of twenty years, there are three positions applicable in three different stints.
Now, all we need do is, again, translate to our second temporal dimension, imagine that curve running side to side rather than front to back. At the single moment in which we are looking to establish whether "He is an artist" is true, what we find is a superposition of three mutually incompatible eigenstates. "He is an artist" is applicable, but so too are "He is a mere craftsman" and "He is a mere hack." We can say with absolute security (i.e. certainty) that he is a creator. And it's not a subjective sustainability problem. It's not that effectuality is inadequate to discriminate whether the threshold has been passed between mere craftsman and artist or between artist and mere hack. It's that effectuality is sufficient to establish each of these sustainably. Actuality is itself complex.
One could see it as a problem of inconsistent definitions addressing actuality in terms of discrete, encapsulated entities rather than decomposing them to variable qualities, but at the mesocosmic level we occupy, with the way we parse sensation... we can't not see the world in terms of objects. And when we unpack the stuff of actuality at the lowest level, its qualities themselves end up with this uncertainty, e.g. the very location or energy of an electron. Deal with it. We need a measure of the degree to which the actuality of an epistemic position is rendered unsound not by sequentiality, its applicability or inapplicability over time, or by effectuality, its sustainability or unsustainability by evidence, but solely by the legitimacy of alterior incompatible positions--its security or insecurity as a contender with or without competition.
On the Nature of Alterity
The idea of truth being composite like this may seem a horrifying breach of logic to some. How can it be that, in one moment, three mutually incompatible positions are all true? Even with just the two, whether it's Nicolas Cage or Schroedinger's Cat, how can we imagine that an epistemic position and its inverse are both simultaneously true? Isn't Not(A & NotA) the very foundation of logic? It's all very well pointing to the crazy counter-intuitive mindfucks of quantum physics, but how can we hope to make sense of the world applying an epistemology that rejects the very law of noncontradiction?
If one can imagine change from one moment to the next, however, that change always already requires (A & NotA) to be an actuality. It is indeed the very cornerstone of actuality itself that this premise does not apply, that there is a conjunction of alterior states which are incompatible. That this moment is no longer the previous moment, A, means that it is now NotA. That the previous moment has not been rendered a logical impossibility which could never have happened, that A retains the truth value of did happen, means that truth is contingent on location in at least one temporal dimension (hence the sequentiality written into applicability.) This is the very essence of the notion of change, and we surely have no problem whatsoever in imagining that fluidity of the change from one state to another, the role of the "&" in (A & NotA) as a transition between them. That alterity of temporally fused states we call change does not generally blow our minds with the notion of a week in which Monday and NotMonday somehow manage to both be true.
All we need do is apply the same principle to accept a different type of mutability, to say that just as Not(A & NotA) is unsound by dint of one state flowing into the next, it is unsound by dint of one state bleeding into its nearest in another temporal dimension. If we can accept that we straddle A and NotA from one moment to the next, in the shift between them, it is not really that hard, I think, to accept that we straddle A and NotA across simultaneous moments, so to speak, in the superposition of alterior states, in the span of time. What persists in the shift from one moment to the next is the stuff the (non-persistent) alterior states of which we're transitioning between. This is only to take another angle on it, arrange moments side by side, and say that across these moments stuff consists to blend the (non-consistent) alterior states we're transectioning through.
So the truth value of an epistemic position has these two dimensions, applicability and security, because it is limited in both. Part of the sharpness of wit in that "Nicholas Cage: good actor or bad actor?" joke lies in the fact that, while we don't have to deal with large-scale physical uncertainty in terms of his location, we do consistently collapse sequentiality like that and adopt epistemic positions on subjects that are irresolvable unless we accept that not only does the truth change over time but truths overlap in the same time. Epistemology must accommodate that actuality because that is the nature of actuality.
So, as we unpack epistemic truth to its constituents, we strip away the artifice of essentialist logic which in rejecting the conjoined alterities of (A & NotA) rejects change itself. Unless we allow for change in the very underpinnings of our approach to epistemology, we cannot address actuality--that which is--only that which appears constant through the changes--that which (seemingly) must be. Which is not epistemology at all, but rather might better be termed alethology. Or simply metaphysics. Here, change is made central, axiomatic, as it must be. We must have an existential logic that allows (A & NotA) because what we are dealing with here is existence.
We might do well to abandon the very notion of truth, indeed, in favour of actuality, (or in the establishment of such for epistemic positions, sound and unsound, as I've been slipping in here,) because where truth is slathered with millennias' worth of essentialism painting it in notions like eternal and necessary, actuality bares its raw existentialism in the first syllable. The actual is, at its root, of or pertaining to the act, always already active. This is the heart of is-ness, that in so far as an epistemic position has a positive value of actuality, as long as it is sound, it is applicable to that which persists, and secure among that which consists, as an articulation sustainable upon that which resists.
Which is to say, with the final dimension of actuality, effectuality, we are dealing with that which actively asserts itself against non-is-ness, flouting the theoretical baseline state born of alethic approaches--an eternal nothingness in which nothing ever was, is, or will be--by instantiating as the stuff by which, of all possible worlds, ours marks itself out to us as actual. Substance is that which resists--has always already resisted--the absence of its necessity, defying the logic of creatio ex nihilo simply by being manifest and patently so--patently just so, versus all the other just so's, and so-and-so's, and such-and-such's, that could have been.
The degree of effect produced, the extent to which an epistemic position, if it is manifestly sustained in and of itself, instantiated in the phasespace of all possibilities, brings into being a shock wave of ramifications, of consequential manifestly sustained epistemic positions which serve as evidence for it, as the ripples on a pond serve as evidence of the splashed stone--this is a fundamental measure of the truth of that position. We can think of it as sustainability from our subjective perspective, in so far as we're often trying to reverse-engineer the cause from the effects, but that is only a pragmatic spin on effectuality as measure of how far an epistemic position sustains itself, if we only had the savvy to explicate all the consequences by which it manifestly does so. If the effectuality of any given point in, or region of, space is variable, together with applicability and security, this becomes a measure of instantiation at any such locale, and in so far as effectuality is causal impact, instantiation means the energy level therein.
On the Nature of Necessity
A ramification of this: if truth is actuality, there are no necessary truths, not if we go by the fairly standard definition of such, in which a necessary truth is not just logically necessary--a presupposition the negation of which would be an oxymoron--but therefore true: since oxymoronic presuppositions are invalid and can't be true in any possible world, so the argument goes, they can't be true in our world; the logically necessary negation of that presupposition is, therefore, a hard fact of our world, as it would be of any other.
This is not sound in this epistemology. A negation of an oxymoron would be necessarily applicable in all possible worlds, but it would only be sustainable in the subset of any actual worlds. The set of all possible worlds is a phasespace of permutations of applicability abstracted from the sustainable, the spectrum of what could be abstracted from what is. One cannot add a dimension of sustainability to expand the set such that every possible world gains a counterpart with sustainability. Creating a set of all possible worlds which are possible and a set of all possible worlds which are actual, that criteria would be redundant, as the worlds which are possible are already possible, and the worlds which are actual are also already possible. The latter remains a subset of the former. If one thinks to define the sets as mutually exclusive--worlds which are only possible versus worlds which are actual--this only renders the former a subset too, a zone within the same phasespace of all possible worlds we began with. The point is that for all the negation of an oxymoron remains necessarily applicable across all of these, it is only a hard fact in any of the possible worlds that is itself a hard fact; it is not necessarily "true" because it is not necessarily instantiated in stuff in any world other than our own. It is, at best, a necessary precondition of that which is true.
Further, in the one possible world we know to have sustainability, for all that a negation of an oxymoron is logically necessary, this does not in fact make it necessarily applicable and sustainable. That is to presuppose, by the law of noncontradiction, that an oxymoron is necessarily inapplicable and unsustainable because it is logically invalid, that in no situation of actuality will it ever be the case that two mutually incompatible epistemic positions are simultaneously applicable and indeed sustainable by dint of them both being literally in effect. Effectively, this is to deny the dimension of certainty, to assert that the actuality value of all applicable and/or sustainable positions is always absolutely secure.
Since insecurity is defined by incompatibility, to reject it as a dimension is simply to assert that a position and its negation never co-occur: Not(A & NotA). The presupposition that the law of noncontradiction applies here rests on the presupposition that the law of noncontradiction applies, an illegitimate circular argument. For any negation of an oxymoron to be not just logically necessary but a necessary truth, the law of noncontradiction must be a necessary truth, and it is arguable in both respects: its applicability and sustainability remain completely contestable, so there are zero grounds to call it true; and the circularity of logic entailed in asserting the security of an epistemic position that insecurity is not possible means there are no grounds to even call it logically necessary. It is necessary to logic, not by logic, an axiomatic stricturing conceit.
Further, in the one possible world we know to have sustainability, the law of noncontradiction is evidently inapplicable and unsustainable as a presupposition, being not wholly applicable and sustainable as a supposition in every moment. This is the case in the sense that language simply isn't strictured such that two mutually incompatible epistemic positions are never equally applicable. But it is also the case in the hardest sense of sustainability, the consequential epistemic positions manifestly sustained in actuality itself substantiating--in all senses of the term--the actuality of insecurity. We can observe (A & NotA) in effect.
So there can be no necessary truths in the standard definition. An epistemic position may have the hyper-consistency in which its negation would be an oxymoron, but with contradictory positions potentially sound anywhere but in the realm of traditional logic which deems them invalid as a preconditional constraint, we cannot speak of these as necessary. They are, for want of a less obscure term, decretory--relating to or fixed by a decree or decision. The decree here is the law of noncontradiction, by which the negation of any oxymoron is automatically fixed as a precondition in any discourse cleaving to the strictures of traditional logic.
Actually, it is no bad thing to strip this usage from the term "necessary." In its primary sense of a requisite condition or consequence--that which is necessary to an outcome, that which is necessary as an outcome--it is profoundly of the discourse of causality, of contingency. It belongs not with "truth" but with "action" and "reaction," as descriptor of the very relationship of contingency, of one actuality being contingent upon another, the necessary, which is, as another parsing of the causal chain of substantiation, itself as liable to be contingent on some other actuality. It is dangerous to obfuscate this. There is a categorical difference between that which must be in order for X or that which must be with any instance of X and that which must be. The first two are necessity. The last is precondition.
The philosophical abuse of this word which appropriates it from the domain of existential consequential dynamics to put a mask of imperative authority upon some abstracted schematics held to be the essential--which is to say, spiritual--order of preconditions predetermining all things is a travesty, and the intellectual bankruptcy of this gambit is evident in the persistent ontological shenanigans by which these wholly suppositional conceits are rigged to set a Toy God on a throne as a "necessary truth."
Even where we're dealing with the most impartially constructed and evidently applicable and sustainable alethic models, as with mathematics and physics, the presuppositions and suppositions of these abstracted schematics are necessary only as any other condition or consequence, necessary in the sense of requisite to an end, in the sense of outcomes bound to follow, in the sense of consequential dynamics. They model the apparent necessities we live through, which is to say they seek constances of patterns of change which may be presupposed as defining that dynamics, but progress in this endeavour is achieved precisely by rejecting the imperative of a presupposition, recasting it as supposition in order to make it revisable by theory and/or experiment; they remain necessarily inadequate because inadequacy must follow causally when adequacy is contingent on an answer to why that which is necessary actually is--i.e. why any of all possible worlds, of all possible alethic models, any of these should actually be instantiate; and they are only ever, at best, a model that fits the substance of the mystery.
On the Nature of Actuality
For my part, I posit that there is no necessity in the essentialist sense, that the mistake is to see the set of all logically possible worlds as a set of discrete potential universes in which some alethic model or other is written into the fabric, with one, some or all of these instantiated who knows how. I posit that the start point is a chaos of complete spatial and temporal inconsistency in which certainty and sustainability are just two of six of however many dimensions, the whole always already instantial. If one can imagine time as three dimensional, there's no need to imagine a start and end for it, no more than one must imagine a golden spiral carved over the surface of the moon beginning or ending at the inmost and utmost points it would never reach were its graving a process in time rather than a whorl around a globe.
If one can imagine that moon turned inside out to a bubble of the instantial, indeed, all imaginable curves of relationships between sequentiality, certainty and effectuality wrought in the inner face of a hollow sphere, intersecting in all permutations to form a phasespace of all possible states, in which all epistemic positions are applicable and none secure, sustainability can be understood as simply that which one expects of chaos. Absolute inconsistency must be inconsistently inconsistent. It must be granular across all scales. Maybe, contrary to Hassan i Sabbah, everything is true and nothing is permitted--in the sense of absence of substance being just as unforbidden, negative space being a facet of chaos defining finities of form, beautiful intricacies of contingent truth.
Toy Gods or Cosmic Order--I have never seen the appeal of looking to conceits of sterile "necessary truths" for the source of actuality. Or the necessity, indeed. Within chaos, what should we expect but zones of the instantial that cohere as instants, any one of them unbeginning and unending as a golden spiral but, in their intricate convolution of dimensions, a phenomena of substance manifest as a sustainable and secure instant in the infinity of the applicable? An actuality--any actuality--might, I mean, seem to that which is composed of its substance--i.e. us--a course of sustainability through applicability with insecurity to either side, in a lateral dimension we are largely oblivious to except for where, in stretching the limits of our observation to the quantum level, the limits of that security become evident.
This notion of actuality is in itself something of a fanciful alethic conceit, of course, but beneath the grand cosmological suppositions, it is an attempt at least to ground our approach to knowledge, our epistemology, in a recognition of change as a fundamental feature, a recognition that the law of noncontradiction, (A & NotA), is the very opposite of lived experience. Change is the bedrock of our experience, the stuff of which it's made, and if we would reconcile the fluidity of time with the fixedness of truth, I think experience points the way to a fusion of the two as different perspectives on each other--literally.
We are aware of that flow between states because we are aware of the aspects of actuality for which the values vary from one moment to the next. We are aware, in each moment, of the state of that multi-dimensional phasespace we call sensation, with its qualia of red and green, yellow and blue, the scent of honeysuckle, warmth, birdsong. We have a subjective sense of the passing of time as part of that phasespace, as a peculiarly distinct dimension of this model, a dimension we're ever slipping onward through. Where most other dimensions of that phasespace are ultimately making sense of stuff which is, at the other end, measured by the degree to which it has effect, simply energy, (albeit sometimes taking the form of matter, having gotten all tangled up with itself,) it doesn't seem so left-field a supposition to me to fancy our forward motion from state to state as a scan, taking in the volume of actuality-as-time, time-as-actuality, in slice by slice encapsulations of 2D state, with security and substantiality as x and y axes, with the z axis simply our vector of travel.
Time's arrow is a puzzle if we imagine the straight line of a single dimension in which either direction is equally legitimate. Introduce another dimension or two, and one can introduce the chirality of a logarithmic spiral, the essential outwardness of one direction versus the inwardness of the other. There is nothing to choose between left and right. Forward is only whichever way we face. Up is only an artefact of gravity. But outward... outward is the fundamental direction of an expanding universe.
On the Nature of Existence
What would it mean to exist in such a 3D time? With no presupposition of essential arrow-like linear progress, of a flow from a start point that could only have some atemporal First Cause, can we reconstruct anything like the existential experience of not just stepping into the Heraclitean river but being carried along through it? Maybe we can, I think, if we return to that golden spiral on the silvery surface of an inside-out moon. It might even be easier to make sense of than the arbitrary onwardness of a cosmos of largely time-symmetric processes, where the increase of entropy in a closed system over time is only an index of the directionality, requiring the directionality in its definition, and where we might wonder why one dimension in that four-dimensional spacetime has a wavefront effect to us, rather than simply the whole 4D cosmos standing in a steady state.
That's to say, if we imagine Edwin Abbott Abbott's Flatlanders living in their two dimensional space, experiencing their third dimension of time as an ongoing progression, couldn't we equally imagine each moment on that plane snapshotted and placed atop the previous, such that the third dimension is constructed as height rather than time? Imagine a Big Bang / Big Crunch like cosmic history for Flatland, starting as a dot, expanding in a circle of ever increasing radius, slowing its expansion, starting to contract again, and ultimately ending at another dot. Take each momentary state of Flatland and set them atop one another from Big Bang to Big Crunch and you end up with these strata constructing a nice regular sphere, the size of an orange, say, the beings in our pocket universe microscopic.
Once you have this 3D object, even presupposing there's an inherent upwards grain to it--a slow entropic dimming of colour from Big Bang to Big Crunch, say--where do we get the weird effect of flux in this stable, static form? Why should that little thread of a being deep in the heart of the ball, caught like a fly in amber, have a sense of being born Master Circular O. Circle, Esquire in an ever-changing Flatland, living through the dynamics of days and decades until his eventual death, at the end of that microscopic thread, a millimeter up from where it began? If we're treating time as a singular dimension like this, I mean, change is only vertical structure. We can't insist that such a structure must be constructed from the ground up, in a temporal process. To do so is only to add another dimension of time, to cast the vertical temporal construction of this 3D object as playing out sequentially in a fourth temporal dimension, as if we watched it grow before our eyes. How then do we get the flow of change?
Let's return to our bubble of complete chaos, our inside out moon and the spiral etched into its inner surface. This spiral being a structure, we can't insist that it takes time to construct, no more than we can do so for the sphere of Flatland's history. We can't presuppose time for the process of inscribing it, or we're simply bootstrapping our conceit, applying time as linear dimension again to explain time as a linearity. If we're to tackle the nature of existence here, it must take no linear time at all to construct this spiral, and yet the spiral must manifest something that looks and acts like the flow we know, something with sequentiality, with consequentiality.
If it's a Fibonacci Spiral then, there's sequentiality written into it: its definition constructs it sequentially--as opposed to applying a polar co-ordinate equation, say, where any and all angles concurrently define a radius for that angle. In so far as each number in the Fibonacci Sequence (1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144...) is the sum of the previous two, there's not just sequentiality but consequentiality. There's even a parsing into overlapped states of a sort, if we view it that way, where the second number in one state (13 & 21) becomes the first number in the consequential state (21 & 34). I cannot help but see here a hint of that (A & NotA) which is the paradox of change, the combination of alterities, the persistence between the shift, an ambit of applicability straddling past moment and current moment, creating the future moment in the combination thereof, transitioning to the new state, and leaving a trail of the past behind it, curled away within it, as it moves ever onward.
It's a pattern of growth, the Fibonacci Sequence, and that's what we're dealing with in time's arrow, surely, not the transition between states but the accretion of states. With movement in a temporal dimension, we have only transition, implicitly reversible and implicitly requiring time in its own definition. Accretion requires something more complex. But, one might quibble, that sequence is still just a sequence of numbers, still just one-dimensional. But, I might respond, the bracketing of (13 & 21) that produces 34 implies circumscription of state via another dimension.
As our Flatlander, Master Circular O. Circle, Esquire, once in another figurative fancy, might have met twin circles that were really one 3D being--a torus--intersecting the plane, so we might imagine him now intersecting with the Lineland of a single dimension, bisected horizontally by the plane, circumscribing (13 & 21) within his 2D unity. It is this shifting frame we're looking for, the circumscription of (A & NotA,) and it seems to me we require something beyond mere linearity to achieve it. That if we suppose something beyond mere linearity, we start to see something with the paradox of unified alterior states we're looking for, the paradox of flow.
Here there might be a temporal flux of sorts then, but it is not as simple as traveling in a straight line along a one-dimensional axis. If we might suppose in this figurative conceit a frame of consequential flow, (and it's a fair-sized if, I freely admit,) the self-similarity of such a spiral at any scale is going to make any moment indistinguishable from the last or the next. If we imagine a being somewhat similar to our Flatlander carried steadily forward in this flow, for all that there's the consequentiality, and the outwardness, and the chirality, it's going to be a dull life for... Fred, let's call him, as changeless as if he lay in a sensory deprivation chamber, in a train travelling at a constant speed in one spatial dimension. If nothing varies beyond position along that curve, all points along the journey will be equivalent states, and our Fred will appear to himself to be static.
Suppose now, however, we add a vertical dimension. This is a spiral on the surface of the moon, after all, and for all that the moon is turned inside-out, its surface remains a rugged rockscape of crag and crater. And if the spiral is sequentially scribing itself over it, from state to state, it's not digging deep, gouging through, simply tracing its way lightly over the terrain. So, now the flow is angling up here and down there, now different points along the journey have different gradients, and any being that is a part of it, bound into the sequentiality might be aware of gradients and thereby aware of their change, acquiring this strange new sense of temporal progression. Afloat in his dark watery upright cocoon, Fred would remain quite unaware that he's moving forward spatially, (figuratively spatially, at least.) With only gradient defining state change, he would appear to himself to be simply varying in terms of angle, pitching up and down. Since we're dealing with a line already curving, the third dimension comes into play immediately too--the side-to-side at right angles to the forward direction, with this too varying up or down, a sideways gradient introducing roll as well as pitch, wherever the flow traces a path not up but along some slope in the mountains of the moon.
Born into this flow, Fred would have a sense of temporal progression and of ever-changing angular orientation. Both would be entirely products of a three dimensional timescape, but to him forward would be a straight-shooting time's arrow, and his own state the stable thing that changes in it, angular orientation the substance of his reality. We should, I think, be imagining his sense of temporal progression unmoored from any imaginary "rate" of flow, to be clear: to Fred, locked into the cascade of consequentiality, it's simply that the more radically the pitch and roll shift, weaving up and down, the more he senses that shift, the more stint seems to pass, the longer it takes to travel, say, a mile forward; meanwhile, on a clear stretch, as things flatten out, travelling a mile seems to take a fraction of the time. (Or vice versa, stint expanding as shift decreases, the boredom of inactivity tending to stretch our subjective sense of stint while, as they say, time flies when you're having fun.) In fact, the flow is covering both miles in no time at all by any exterior measure. In fact, his sense of a one-dimensional flow is already actually 2D, the ratio of stint and shift.
We need not imagine that sense of angular orientation as anything remotely comparable to the kinaesthetic sense of pitch and roll we would experience travelling in such a manner. Imagine instead that Fred, being as alien to us as Master Circular O. Circle, Esquire senses gradient as colour, with upwards and downwards pitch signified by red and green respectively, roll to the left and to the right signified by yellow and blue. These being the two basic opponent processes from which, along with the light-dark opponent process, our perceptual colourspace is constructed, Fred essentially experiences his cosmos as an all-encompassing glow ever-shifting from one hue to another. He could even construct a world from the dimensional relationships between the opponent processes, red and green as his north and south, yellow and blue as his west and east, imagining himself adrift over his own little Flatland, something like a slice of our L*a*b* colourspace.
Fred would have no idea that his motion is in fact over a three-dimensional surface, that what he experiences as random drift around an ocean of colour is in fact a product of that complexity: where he seems to be drifting far north (i.e. redward,) it's actually that the steady forward flow of consequentiality is carrying him up a steep gradient; where he seems to be drifting to the greenish-yellow, he's actually traversing a steep downslope sideways and rolled to the left because of it. If you told him that the forward direction of the flow was actually a curve around the inner surface of a whole hollow sphere of time, this polychromatic Flatlander would simply have no reason to place any credence in this. No, no, no, he'd say. He lives in a Flatland of oceanic light--violet and scarlet and umber. Look! That way is redward, and this direction is greenways.
So he's carried along through this existence malarkey, finding that an epistemic position, "I'm moving redward," is applicable one moment, inapplicable the next, finding his alethic supposition that "One can only go so far redward," sustainable by the evidence of his senses, while, for the most part, the basic linearity of the curve means that the sideways dimension of security is of little impact. Since time and truth are three dimensional, there's a little span to Fred's flow, but it's about as slim as a path can get.
Still, since we're imagining his qualia of pitch and roll quite other than our proprioception, we'll imagine the exterior mechanism quite other too. No inner ear for Fred, rather he gleans his raw data via sensors extended out into the flow, his qualia translations of readings of how high the ground is rising to the right and how low it's falling to the left, or vice versa. And over time Fred's senses attune, develop. He's able to reach out further across the span of the flow, narrow as it is.
The further out he reaches, the more accurate a reading he gets for the general gradient of the slope he's travelling along--or, as Fred in his Flatland of oceanic light thinks of it, the harder he looks, the clearer the colour becomes, so he knows exactly how far west of the centre of the world he is--or wherever. This being good to know for a curious being, he tries all the harder, gets better and better at it. Only, one day, when he reaches out really far, an unfathomably strange thing happens. Because the flow does sometimes pass over humps and dips in its journey, so when Fred's senses become able to reach out insanely far, what he gets back are readings of the flow falling on both sides where it passes over a hump, or rising on both sides as it moves through a dip. Or, as Fred perceives it, he finds himself dealing with an impossible colour that's somehow yellow and blue together. I mean, he's in two places in his Flatland at once, simultaneously west and east. And that's just not, as far he's concerned, even possible.
This is the very substance of his actuality behaving in a way that defies sense. Location has a single value. You're either here or you're there. You can't be here and there simultaneously. Fred has long since abstracted the law of noncontradiction from his experience of the opponent processes of red and green, yellow and blue. As simple as that sensory system is, the relationships of mutual incompatibility written into it have been enough for him to formulate the rule: Not(A & NotA). And this... this is the very fabric of his Flatland breaching that logic, flouting its own evident physics. It's utterly counter-intuitive, if not downright incomprehensible.
If we suggested to him then that this was due to the substance of time itself extending not just forward but side-to-side, in a dimension of certainty, I dare say, it would still seem a wild fancy, as it would if we told him the stuff of his world, that oceanic light, was all the effectuality of time, the rising and falling of actuality in its third dimension warping his path from the featureless nullity of a flat plain to a rough ride over the wilds of stuff. He would think of space as a plane, and time as a dimension, and energy as stuff within that continuum. He would, like us, have a notion of truth that was quite distinct from time and energy, one with little need to accommodate insecurity--with little capacity to accommodate this notion of a sideways temporal dimension to each moment he passes through. But he would, as we are, I think, be dealing with an actuality in which, to all intents and purposes, truth is time, with energy as a dimension. Truth is time is instance is substance. And existence is to be of that actuality.
Sequentiality, certainty and effectuality. Applicability, security and sustainability. Stint, span and shift. I see these as being as fundamental to our existence as length, breadth and height--or upwise angle, sidewise angle and distance outwards, if one prefers polar co-ordinates to define location in space. In so far as any dimension is removed from the measure of actuality, we are no longer speaking of existence. Some of the more vapid "problems" of philosophy become quickly dismissible if we take this as foundation--the existence of universals, the truth of a proposition about a fictional character, the necessary existence of a Toy God.
In this existentialist epistemology, if we accept (A & NotA), we leave it perfectly legitimate to construct a subset of logical systems which, as a constraint, reject it, but we open logic out to a system of suppositions rather than propositions, (one which I would contend--and no doubt will at some point--may become more powerful by exploring the transitions where (A1 & NotA1 [i.e. A2]) becomes (A2 & NotA2 [i.e. A3]) and by making explicit the modalities that come into play when the absolute is-ness of a law of identity resting on that law of noncontradiction is abolished--for then we must start to talk also of what was or will be, what would and could be, what might or may or must or should be. Which is to say, we can begin to make a logic in which epistemic, alethic, boulomaic and deontic positions are structurally self-evident, a formal logic which fits the actual logic of actual reason and renders the dynamics less easily disguised--a distinct necessity where the conflation of epistemic and alethic positions is a demonstrably persistent problem.
In sum, I see this as essential, necessary--in the good old-fashioned sense of requisite. Our notion of truth is inadequate to the task. It is a time for a revision. Being far from au fait on the current state of academic philosophy, I may of course be simply reinventing the wheel here, or performing the philosophical equivalent of outsider art, but so it goes. If one throws oneself into a seven thousand word essay on epistemology, one does it as much as anything simply to work through one's own ideas. If nothing else, some of the core ideas here are the underpinnings of a conceit in a novella I've been working on for a while, set on a future Mars where notions of the soul or the sign have been rendered obsolete by the notion of stance, where every moment in time is to be considered in terms of stint, span and shift. When one sets out to invent a workable fictional future philosophy, it seems, one rather ends up committing philosophy. So, I appear to be calling for a wholesale reconstruction of our notions of time and truth.
Well, I suppose I'm never one to do things by halves.
Premise: The truth value of an epistemic position ("is (not)") is three-dimensional:
1.1. Sequentiality: An epistemic position may be applicable/inapplicable for the point in time to which it is applied.
1.2. Certainty: An epistemic position may be secure/insecure within the range of those positions that are applicable.
1.3. Effectuality: An epistemic position may be sustainable/unsustainable due to the degree of effect it would produce.
Examples:
1. "He is an artist" is inapplicable for the child or the person who has quit the vocation.
2. "He is an artist" is unsure if "He is a mere craftsman" or "He is a mere hack" are also applicable.
3. "He is an artist" is untenable for the person who destroys all art they produce.
Note: In 2, the use of "artist" is not categorical, but rather a placement on a nominal scale within a category. For a finite range of discretely possible epistemic positions, where the range is applicable, certainty is the distribution of possibility within one position in relation to the whole. Hard (Heisenbergian) uncertainty, if I understand correctly, holds that this is objective. In a subjective sustainability problem, effectuality would be sufficient to establish applicability of the range, but not to establish applicability for a single position within it; assuming that positions are incompatible, only one is actually applicable; it's simply a failure to establish which. In an objective certainty problem, effectuality is sufficient to establish simultaneous applicability for various positions within the range; since positions are incompatible, another dimension of actuality is required to model the distribution.
It may be clearer if one considers "secure" and "insecure" as judgements of applicability in a second temporal dimension. For simplicity's sake, we'll take "artist" in its categorical sense, such that as soon as a person starts producing works of art they are an artist, and as soon as they quit the vocation they cease to be an artist. Now, consider a twenty year period in the life of a person, at the middle of which they quit their artistic vocation. For the first decade, "He is an artist" is applicable. For the second decade, it is not. Now consider that stretch of two stints--one in which "He is an artist" is applicable and one in which it is not--as a second temporal dimension running not forward and back but side to side. The idea in the notion of certainty is that any moment may have span such that "He is an artist" is both applicable and inapplicable. It thus becomes less secure, more insecure, my point in this labelling being to escape the implicit absolute of "certain"; if something is secure, that doesn't mean it couldn't be more secure.
See the Community episode in which Abed has a meltdown trying to answer the question: "Nicholas Cage: good or bad?" Why? Nicholas Cage veers wildly in performance such that over the stint of one movie he's great, but over the stint of the movie immediately after he's awful. Because the stretch in which those two stints is being collapsed down to ask if he's essentially good or bad, Abed is to all intents and purposes approaching it as an objective certainty problem: the span is such that two mutually incompatible positions are equally applicable, indeed equally actual. (The joke is partly in rejecting it as a subjective sustainability problem: effectuality is sufficient to establish that Cage is too good to be considered bad, but it is also sufficient to establish that Cage is too bad to be considered good.) Cage is being treated as existing in a superposition of two eigenstates, like Schroedinger's Cat. (The correct answer to the question is, "Yes.")
We can develop this notion of certainty to something more sophisticated if we return to the comparison with a conventional notion of time. If we take "artist" as a position on a nominal scale within a category, we can imagine a twenty year stretch in which a creator begins as a mere craftsman and develops their artistry to a peak point as a maestro, only to degenerate afterwards to a mere hack. Here, we're treating "artist" as encapsulating the quantifiable applicability of artistry, which becomes more and more applicable as it increases up to the peak, less and less so afterwards. Let's imagine it as a nice smooth bell curve. Improvement begins slow but accelerates when the creator finds their voice. It slows again as they approach the best they can be. There's a tipping point where they start to dry out, and a plunge as they surrender to hackdom. Finally it bottoms out as it becomes harder to get any worse with their basic craft skills. Over the twenty year stretch, the y position on that curve is the degree of their artistry.
An upside-down reflection of that curve would map the applicability of the two other qualities: mere-craftsmanship and mere-hackdom. We'd start at a peak of mere-craftsmanship at the same height as the zenith of creativity. This would decrease slowly then plunge as artistry rises, bottoming out as artistry peaks. From the tipping point, mere-hackdom kicks in, taking off as the creator gives up and artistry plummets. We end with mere-hackdom at the same pinnacle mere-craftsmanship occupied at the start, at the same pinnacle artistry occupied in the middle. Now all we need to understand is that there are two crunch points: where artistry surpasses mere-craftsmanship; where hackdom surpasses artistry. And in this use of the terms "mere craftsman," "artist," and "mere hack," which quality has surpassed which is written into the definitions via that "mere."
One could use "wannabe," "maestro" and "has-been" here, instead. It doesn't matter. The point is, these are nominal labels for discretely possible epistemic positions with a range. Though the qualities they encapsulate overlap, the labels define states that are mutually incompatible. "He is a mere craftsman" ceases to be applicable as soon as "He is an artist" is, and "He is an artist" ceases to be applicable as soon as "He is a mere hack" is. Across the stretch of twenty years, there are three positions applicable in three different stints.
Now, all we need do is, again, translate to our second temporal dimension, imagine that curve running side to side rather than front to back. At the single moment in which we are looking to establish whether "He is an artist" is true, what we find is a superposition of three mutually incompatible eigenstates. "He is an artist" is applicable, but so too are "He is a mere craftsman" and "He is a mere hack." We can say with absolute security (i.e. certainty) that he is a creator. And it's not a subjective sustainability problem. It's not that effectuality is inadequate to discriminate whether the threshold has been passed between mere craftsman and artist or between artist and mere hack. It's that effectuality is sufficient to establish each of these sustainably. Actuality is itself complex.
One could see it as a problem of inconsistent definitions addressing actuality in terms of discrete, encapsulated entities rather than decomposing them to variable qualities, but at the mesocosmic level we occupy, with the way we parse sensation... we can't not see the world in terms of objects. And when we unpack the stuff of actuality at the lowest level, its qualities themselves end up with this uncertainty, e.g. the very location or energy of an electron. Deal with it. We need a measure of the degree to which the actuality of an epistemic position is rendered unsound not by sequentiality, its applicability or inapplicability over time, or by effectuality, its sustainability or unsustainability by evidence, but solely by the legitimacy of alterior incompatible positions--its security or insecurity as a contender with or without competition.
*
On the Nature of Alterity
The idea of truth being composite like this may seem a horrifying breach of logic to some. How can it be that, in one moment, three mutually incompatible positions are all true? Even with just the two, whether it's Nicolas Cage or Schroedinger's Cat, how can we imagine that an epistemic position and its inverse are both simultaneously true? Isn't Not(A & NotA) the very foundation of logic? It's all very well pointing to the crazy counter-intuitive mindfucks of quantum physics, but how can we hope to make sense of the world applying an epistemology that rejects the very law of noncontradiction?
If one can imagine change from one moment to the next, however, that change always already requires (A & NotA) to be an actuality. It is indeed the very cornerstone of actuality itself that this premise does not apply, that there is a conjunction of alterior states which are incompatible. That this moment is no longer the previous moment, A, means that it is now NotA. That the previous moment has not been rendered a logical impossibility which could never have happened, that A retains the truth value of did happen, means that truth is contingent on location in at least one temporal dimension (hence the sequentiality written into applicability.) This is the very essence of the notion of change, and we surely have no problem whatsoever in imagining that fluidity of the change from one state to another, the role of the "&" in (A & NotA) as a transition between them. That alterity of temporally fused states we call change does not generally blow our minds with the notion of a week in which Monday and NotMonday somehow manage to both be true.
All we need do is apply the same principle to accept a different type of mutability, to say that just as Not(A & NotA) is unsound by dint of one state flowing into the next, it is unsound by dint of one state bleeding into its nearest in another temporal dimension. If we can accept that we straddle A and NotA from one moment to the next, in the shift between them, it is not really that hard, I think, to accept that we straddle A and NotA across simultaneous moments, so to speak, in the superposition of alterior states, in the span of time. What persists in the shift from one moment to the next is the stuff the (non-persistent) alterior states of which we're transitioning between. This is only to take another angle on it, arrange moments side by side, and say that across these moments stuff consists to blend the (non-consistent) alterior states we're transectioning through.
So the truth value of an epistemic position has these two dimensions, applicability and security, because it is limited in both. Part of the sharpness of wit in that "Nicholas Cage: good actor or bad actor?" joke lies in the fact that, while we don't have to deal with large-scale physical uncertainty in terms of his location, we do consistently collapse sequentiality like that and adopt epistemic positions on subjects that are irresolvable unless we accept that not only does the truth change over time but truths overlap in the same time. Epistemology must accommodate that actuality because that is the nature of actuality.
So, as we unpack epistemic truth to its constituents, we strip away the artifice of essentialist logic which in rejecting the conjoined alterities of (A & NotA) rejects change itself. Unless we allow for change in the very underpinnings of our approach to epistemology, we cannot address actuality--that which is--only that which appears constant through the changes--that which (seemingly) must be. Which is not epistemology at all, but rather might better be termed alethology. Or simply metaphysics. Here, change is made central, axiomatic, as it must be. We must have an existential logic that allows (A & NotA) because what we are dealing with here is existence.
We might do well to abandon the very notion of truth, indeed, in favour of actuality, (or in the establishment of such for epistemic positions, sound and unsound, as I've been slipping in here,) because where truth is slathered with millennias' worth of essentialism painting it in notions like eternal and necessary, actuality bares its raw existentialism in the first syllable. The actual is, at its root, of or pertaining to the act, always already active. This is the heart of is-ness, that in so far as an epistemic position has a positive value of actuality, as long as it is sound, it is applicable to that which persists, and secure among that which consists, as an articulation sustainable upon that which resists.
Which is to say, with the final dimension of actuality, effectuality, we are dealing with that which actively asserts itself against non-is-ness, flouting the theoretical baseline state born of alethic approaches--an eternal nothingness in which nothing ever was, is, or will be--by instantiating as the stuff by which, of all possible worlds, ours marks itself out to us as actual. Substance is that which resists--has always already resisted--the absence of its necessity, defying the logic of creatio ex nihilo simply by being manifest and patently so--patently just so, versus all the other just so's, and so-and-so's, and such-and-such's, that could have been.
The degree of effect produced, the extent to which an epistemic position, if it is manifestly sustained in and of itself, instantiated in the phasespace of all possibilities, brings into being a shock wave of ramifications, of consequential manifestly sustained epistemic positions which serve as evidence for it, as the ripples on a pond serve as evidence of the splashed stone--this is a fundamental measure of the truth of that position. We can think of it as sustainability from our subjective perspective, in so far as we're often trying to reverse-engineer the cause from the effects, but that is only a pragmatic spin on effectuality as measure of how far an epistemic position sustains itself, if we only had the savvy to explicate all the consequences by which it manifestly does so. If the effectuality of any given point in, or region of, space is variable, together with applicability and security, this becomes a measure of instantiation at any such locale, and in so far as effectuality is causal impact, instantiation means the energy level therein.
*
On the Nature of Necessity
A ramification of this: if truth is actuality, there are no necessary truths, not if we go by the fairly standard definition of such, in which a necessary truth is not just logically necessary--a presupposition the negation of which would be an oxymoron--but therefore true: since oxymoronic presuppositions are invalid and can't be true in any possible world, so the argument goes, they can't be true in our world; the logically necessary negation of that presupposition is, therefore, a hard fact of our world, as it would be of any other.
This is not sound in this epistemology. A negation of an oxymoron would be necessarily applicable in all possible worlds, but it would only be sustainable in the subset of any actual worlds. The set of all possible worlds is a phasespace of permutations of applicability abstracted from the sustainable, the spectrum of what could be abstracted from what is. One cannot add a dimension of sustainability to expand the set such that every possible world gains a counterpart with sustainability. Creating a set of all possible worlds which are possible and a set of all possible worlds which are actual, that criteria would be redundant, as the worlds which are possible are already possible, and the worlds which are actual are also already possible. The latter remains a subset of the former. If one thinks to define the sets as mutually exclusive--worlds which are only possible versus worlds which are actual--this only renders the former a subset too, a zone within the same phasespace of all possible worlds we began with. The point is that for all the negation of an oxymoron remains necessarily applicable across all of these, it is only a hard fact in any of the possible worlds that is itself a hard fact; it is not necessarily "true" because it is not necessarily instantiated in stuff in any world other than our own. It is, at best, a necessary precondition of that which is true.
Further, in the one possible world we know to have sustainability, for all that a negation of an oxymoron is logically necessary, this does not in fact make it necessarily applicable and sustainable. That is to presuppose, by the law of noncontradiction, that an oxymoron is necessarily inapplicable and unsustainable because it is logically invalid, that in no situation of actuality will it ever be the case that two mutually incompatible epistemic positions are simultaneously applicable and indeed sustainable by dint of them both being literally in effect. Effectively, this is to deny the dimension of certainty, to assert that the actuality value of all applicable and/or sustainable positions is always absolutely secure.
Since insecurity is defined by incompatibility, to reject it as a dimension is simply to assert that a position and its negation never co-occur: Not(A & NotA). The presupposition that the law of noncontradiction applies here rests on the presupposition that the law of noncontradiction applies, an illegitimate circular argument. For any negation of an oxymoron to be not just logically necessary but a necessary truth, the law of noncontradiction must be a necessary truth, and it is arguable in both respects: its applicability and sustainability remain completely contestable, so there are zero grounds to call it true; and the circularity of logic entailed in asserting the security of an epistemic position that insecurity is not possible means there are no grounds to even call it logically necessary. It is necessary to logic, not by logic, an axiomatic stricturing conceit.
Further, in the one possible world we know to have sustainability, the law of noncontradiction is evidently inapplicable and unsustainable as a presupposition, being not wholly applicable and sustainable as a supposition in every moment. This is the case in the sense that language simply isn't strictured such that two mutually incompatible epistemic positions are never equally applicable. But it is also the case in the hardest sense of sustainability, the consequential epistemic positions manifestly sustained in actuality itself substantiating--in all senses of the term--the actuality of insecurity. We can observe (A & NotA) in effect.
So there can be no necessary truths in the standard definition. An epistemic position may have the hyper-consistency in which its negation would be an oxymoron, but with contradictory positions potentially sound anywhere but in the realm of traditional logic which deems them invalid as a preconditional constraint, we cannot speak of these as necessary. They are, for want of a less obscure term, decretory--relating to or fixed by a decree or decision. The decree here is the law of noncontradiction, by which the negation of any oxymoron is automatically fixed as a precondition in any discourse cleaving to the strictures of traditional logic.
Actually, it is no bad thing to strip this usage from the term "necessary." In its primary sense of a requisite condition or consequence--that which is necessary to an outcome, that which is necessary as an outcome--it is profoundly of the discourse of causality, of contingency. It belongs not with "truth" but with "action" and "reaction," as descriptor of the very relationship of contingency, of one actuality being contingent upon another, the necessary, which is, as another parsing of the causal chain of substantiation, itself as liable to be contingent on some other actuality. It is dangerous to obfuscate this. There is a categorical difference between that which must be in order for X or that which must be with any instance of X and that which must be. The first two are necessity. The last is precondition.
The philosophical abuse of this word which appropriates it from the domain of existential consequential dynamics to put a mask of imperative authority upon some abstracted schematics held to be the essential--which is to say, spiritual--order of preconditions predetermining all things is a travesty, and the intellectual bankruptcy of this gambit is evident in the persistent ontological shenanigans by which these wholly suppositional conceits are rigged to set a Toy God on a throne as a "necessary truth."
Even where we're dealing with the most impartially constructed and evidently applicable and sustainable alethic models, as with mathematics and physics, the presuppositions and suppositions of these abstracted schematics are necessary only as any other condition or consequence, necessary in the sense of requisite to an end, in the sense of outcomes bound to follow, in the sense of consequential dynamics. They model the apparent necessities we live through, which is to say they seek constances of patterns of change which may be presupposed as defining that dynamics, but progress in this endeavour is achieved precisely by rejecting the imperative of a presupposition, recasting it as supposition in order to make it revisable by theory and/or experiment; they remain necessarily inadequate because inadequacy must follow causally when adequacy is contingent on an answer to why that which is necessary actually is--i.e. why any of all possible worlds, of all possible alethic models, any of these should actually be instantiate; and they are only ever, at best, a model that fits the substance of the mystery.
*
On the Nature of Actuality
For my part, I posit that there is no necessity in the essentialist sense, that the mistake is to see the set of all logically possible worlds as a set of discrete potential universes in which some alethic model or other is written into the fabric, with one, some or all of these instantiated who knows how. I posit that the start point is a chaos of complete spatial and temporal inconsistency in which certainty and sustainability are just two of six of however many dimensions, the whole always already instantial. If one can imagine time as three dimensional, there's no need to imagine a start and end for it, no more than one must imagine a golden spiral carved over the surface of the moon beginning or ending at the inmost and utmost points it would never reach were its graving a process in time rather than a whorl around a globe.
If one can imagine that moon turned inside out to a bubble of the instantial, indeed, all imaginable curves of relationships between sequentiality, certainty and effectuality wrought in the inner face of a hollow sphere, intersecting in all permutations to form a phasespace of all possible states, in which all epistemic positions are applicable and none secure, sustainability can be understood as simply that which one expects of chaos. Absolute inconsistency must be inconsistently inconsistent. It must be granular across all scales. Maybe, contrary to Hassan i Sabbah, everything is true and nothing is permitted--in the sense of absence of substance being just as unforbidden, negative space being a facet of chaos defining finities of form, beautiful intricacies of contingent truth.
Toy Gods or Cosmic Order--I have never seen the appeal of looking to conceits of sterile "necessary truths" for the source of actuality. Or the necessity, indeed. Within chaos, what should we expect but zones of the instantial that cohere as instants, any one of them unbeginning and unending as a golden spiral but, in their intricate convolution of dimensions, a phenomena of substance manifest as a sustainable and secure instant in the infinity of the applicable? An actuality--any actuality--might, I mean, seem to that which is composed of its substance--i.e. us--a course of sustainability through applicability with insecurity to either side, in a lateral dimension we are largely oblivious to except for where, in stretching the limits of our observation to the quantum level, the limits of that security become evident.
This notion of actuality is in itself something of a fanciful alethic conceit, of course, but beneath the grand cosmological suppositions, it is an attempt at least to ground our approach to knowledge, our epistemology, in a recognition of change as a fundamental feature, a recognition that the law of noncontradiction, (A & NotA), is the very opposite of lived experience. Change is the bedrock of our experience, the stuff of which it's made, and if we would reconcile the fluidity of time with the fixedness of truth, I think experience points the way to a fusion of the two as different perspectives on each other--literally.
We are aware of that flow between states because we are aware of the aspects of actuality for which the values vary from one moment to the next. We are aware, in each moment, of the state of that multi-dimensional phasespace we call sensation, with its qualia of red and green, yellow and blue, the scent of honeysuckle, warmth, birdsong. We have a subjective sense of the passing of time as part of that phasespace, as a peculiarly distinct dimension of this model, a dimension we're ever slipping onward through. Where most other dimensions of that phasespace are ultimately making sense of stuff which is, at the other end, measured by the degree to which it has effect, simply energy, (albeit sometimes taking the form of matter, having gotten all tangled up with itself,) it doesn't seem so left-field a supposition to me to fancy our forward motion from state to state as a scan, taking in the volume of actuality-as-time, time-as-actuality, in slice by slice encapsulations of 2D state, with security and substantiality as x and y axes, with the z axis simply our vector of travel.
Time's arrow is a puzzle if we imagine the straight line of a single dimension in which either direction is equally legitimate. Introduce another dimension or two, and one can introduce the chirality of a logarithmic spiral, the essential outwardness of one direction versus the inwardness of the other. There is nothing to choose between left and right. Forward is only whichever way we face. Up is only an artefact of gravity. But outward... outward is the fundamental direction of an expanding universe.
*
On the Nature of Existence
What would it mean to exist in such a 3D time? With no presupposition of essential arrow-like linear progress, of a flow from a start point that could only have some atemporal First Cause, can we reconstruct anything like the existential experience of not just stepping into the Heraclitean river but being carried along through it? Maybe we can, I think, if we return to that golden spiral on the silvery surface of an inside-out moon. It might even be easier to make sense of than the arbitrary onwardness of a cosmos of largely time-symmetric processes, where the increase of entropy in a closed system over time is only an index of the directionality, requiring the directionality in its definition, and where we might wonder why one dimension in that four-dimensional spacetime has a wavefront effect to us, rather than simply the whole 4D cosmos standing in a steady state.
That's to say, if we imagine Edwin Abbott Abbott's Flatlanders living in their two dimensional space, experiencing their third dimension of time as an ongoing progression, couldn't we equally imagine each moment on that plane snapshotted and placed atop the previous, such that the third dimension is constructed as height rather than time? Imagine a Big Bang / Big Crunch like cosmic history for Flatland, starting as a dot, expanding in a circle of ever increasing radius, slowing its expansion, starting to contract again, and ultimately ending at another dot. Take each momentary state of Flatland and set them atop one another from Big Bang to Big Crunch and you end up with these strata constructing a nice regular sphere, the size of an orange, say, the beings in our pocket universe microscopic.
Once you have this 3D object, even presupposing there's an inherent upwards grain to it--a slow entropic dimming of colour from Big Bang to Big Crunch, say--where do we get the weird effect of flux in this stable, static form? Why should that little thread of a being deep in the heart of the ball, caught like a fly in amber, have a sense of being born Master Circular O. Circle, Esquire in an ever-changing Flatland, living through the dynamics of days and decades until his eventual death, at the end of that microscopic thread, a millimeter up from where it began? If we're treating time as a singular dimension like this, I mean, change is only vertical structure. We can't insist that such a structure must be constructed from the ground up, in a temporal process. To do so is only to add another dimension of time, to cast the vertical temporal construction of this 3D object as playing out sequentially in a fourth temporal dimension, as if we watched it grow before our eyes. How then do we get the flow of change?
Let's return to our bubble of complete chaos, our inside out moon and the spiral etched into its inner surface. This spiral being a structure, we can't insist that it takes time to construct, no more than we can do so for the sphere of Flatland's history. We can't presuppose time for the process of inscribing it, or we're simply bootstrapping our conceit, applying time as linear dimension again to explain time as a linearity. If we're to tackle the nature of existence here, it must take no linear time at all to construct this spiral, and yet the spiral must manifest something that looks and acts like the flow we know, something with sequentiality, with consequentiality.
If it's a Fibonacci Spiral then, there's sequentiality written into it: its definition constructs it sequentially--as opposed to applying a polar co-ordinate equation, say, where any and all angles concurrently define a radius for that angle. In so far as each number in the Fibonacci Sequence (1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144...) is the sum of the previous two, there's not just sequentiality but consequentiality. There's even a parsing into overlapped states of a sort, if we view it that way, where the second number in one state (13 & 21) becomes the first number in the consequential state (21 & 34). I cannot help but see here a hint of that (A & NotA) which is the paradox of change, the combination of alterities, the persistence between the shift, an ambit of applicability straddling past moment and current moment, creating the future moment in the combination thereof, transitioning to the new state, and leaving a trail of the past behind it, curled away within it, as it moves ever onward.
It's a pattern of growth, the Fibonacci Sequence, and that's what we're dealing with in time's arrow, surely, not the transition between states but the accretion of states. With movement in a temporal dimension, we have only transition, implicitly reversible and implicitly requiring time in its own definition. Accretion requires something more complex. But, one might quibble, that sequence is still just a sequence of numbers, still just one-dimensional. But, I might respond, the bracketing of (13 & 21) that produces 34 implies circumscription of state via another dimension.
As our Flatlander, Master Circular O. Circle, Esquire, once in another figurative fancy, might have met twin circles that were really one 3D being--a torus--intersecting the plane, so we might imagine him now intersecting with the Lineland of a single dimension, bisected horizontally by the plane, circumscribing (13 & 21) within his 2D unity. It is this shifting frame we're looking for, the circumscription of (A & NotA,) and it seems to me we require something beyond mere linearity to achieve it. That if we suppose something beyond mere linearity, we start to see something with the paradox of unified alterior states we're looking for, the paradox of flow.
Here there might be a temporal flux of sorts then, but it is not as simple as traveling in a straight line along a one-dimensional axis. If we might suppose in this figurative conceit a frame of consequential flow, (and it's a fair-sized if, I freely admit,) the self-similarity of such a spiral at any scale is going to make any moment indistinguishable from the last or the next. If we imagine a being somewhat similar to our Flatlander carried steadily forward in this flow, for all that there's the consequentiality, and the outwardness, and the chirality, it's going to be a dull life for... Fred, let's call him, as changeless as if he lay in a sensory deprivation chamber, in a train travelling at a constant speed in one spatial dimension. If nothing varies beyond position along that curve, all points along the journey will be equivalent states, and our Fred will appear to himself to be static.
Suppose now, however, we add a vertical dimension. This is a spiral on the surface of the moon, after all, and for all that the moon is turned inside-out, its surface remains a rugged rockscape of crag and crater. And if the spiral is sequentially scribing itself over it, from state to state, it's not digging deep, gouging through, simply tracing its way lightly over the terrain. So, now the flow is angling up here and down there, now different points along the journey have different gradients, and any being that is a part of it, bound into the sequentiality might be aware of gradients and thereby aware of their change, acquiring this strange new sense of temporal progression. Afloat in his dark watery upright cocoon, Fred would remain quite unaware that he's moving forward spatially, (figuratively spatially, at least.) With only gradient defining state change, he would appear to himself to be simply varying in terms of angle, pitching up and down. Since we're dealing with a line already curving, the third dimension comes into play immediately too--the side-to-side at right angles to the forward direction, with this too varying up or down, a sideways gradient introducing roll as well as pitch, wherever the flow traces a path not up but along some slope in the mountains of the moon.
Born into this flow, Fred would have a sense of temporal progression and of ever-changing angular orientation. Both would be entirely products of a three dimensional timescape, but to him forward would be a straight-shooting time's arrow, and his own state the stable thing that changes in it, angular orientation the substance of his reality. We should, I think, be imagining his sense of temporal progression unmoored from any imaginary "rate" of flow, to be clear: to Fred, locked into the cascade of consequentiality, it's simply that the more radically the pitch and roll shift, weaving up and down, the more he senses that shift, the more stint seems to pass, the longer it takes to travel, say, a mile forward; meanwhile, on a clear stretch, as things flatten out, travelling a mile seems to take a fraction of the time. (Or vice versa, stint expanding as shift decreases, the boredom of inactivity tending to stretch our subjective sense of stint while, as they say, time flies when you're having fun.) In fact, the flow is covering both miles in no time at all by any exterior measure. In fact, his sense of a one-dimensional flow is already actually 2D, the ratio of stint and shift.
We need not imagine that sense of angular orientation as anything remotely comparable to the kinaesthetic sense of pitch and roll we would experience travelling in such a manner. Imagine instead that Fred, being as alien to us as Master Circular O. Circle, Esquire senses gradient as colour, with upwards and downwards pitch signified by red and green respectively, roll to the left and to the right signified by yellow and blue. These being the two basic opponent processes from which, along with the light-dark opponent process, our perceptual colourspace is constructed, Fred essentially experiences his cosmos as an all-encompassing glow ever-shifting from one hue to another. He could even construct a world from the dimensional relationships between the opponent processes, red and green as his north and south, yellow and blue as his west and east, imagining himself adrift over his own little Flatland, something like a slice of our L*a*b* colourspace.
Fred would have no idea that his motion is in fact over a three-dimensional surface, that what he experiences as random drift around an ocean of colour is in fact a product of that complexity: where he seems to be drifting far north (i.e. redward,) it's actually that the steady forward flow of consequentiality is carrying him up a steep gradient; where he seems to be drifting to the greenish-yellow, he's actually traversing a steep downslope sideways and rolled to the left because of it. If you told him that the forward direction of the flow was actually a curve around the inner surface of a whole hollow sphere of time, this polychromatic Flatlander would simply have no reason to place any credence in this. No, no, no, he'd say. He lives in a Flatland of oceanic light--violet and scarlet and umber. Look! That way is redward, and this direction is greenways.
So he's carried along through this existence malarkey, finding that an epistemic position, "I'm moving redward," is applicable one moment, inapplicable the next, finding his alethic supposition that "One can only go so far redward," sustainable by the evidence of his senses, while, for the most part, the basic linearity of the curve means that the sideways dimension of security is of little impact. Since time and truth are three dimensional, there's a little span to Fred's flow, but it's about as slim as a path can get.
Still, since we're imagining his qualia of pitch and roll quite other than our proprioception, we'll imagine the exterior mechanism quite other too. No inner ear for Fred, rather he gleans his raw data via sensors extended out into the flow, his qualia translations of readings of how high the ground is rising to the right and how low it's falling to the left, or vice versa. And over time Fred's senses attune, develop. He's able to reach out further across the span of the flow, narrow as it is.
The further out he reaches, the more accurate a reading he gets for the general gradient of the slope he's travelling along--or, as Fred in his Flatland of oceanic light thinks of it, the harder he looks, the clearer the colour becomes, so he knows exactly how far west of the centre of the world he is--or wherever. This being good to know for a curious being, he tries all the harder, gets better and better at it. Only, one day, when he reaches out really far, an unfathomably strange thing happens. Because the flow does sometimes pass over humps and dips in its journey, so when Fred's senses become able to reach out insanely far, what he gets back are readings of the flow falling on both sides where it passes over a hump, or rising on both sides as it moves through a dip. Or, as Fred perceives it, he finds himself dealing with an impossible colour that's somehow yellow and blue together. I mean, he's in two places in his Flatland at once, simultaneously west and east. And that's just not, as far he's concerned, even possible.
This is the very substance of his actuality behaving in a way that defies sense. Location has a single value. You're either here or you're there. You can't be here and there simultaneously. Fred has long since abstracted the law of noncontradiction from his experience of the opponent processes of red and green, yellow and blue. As simple as that sensory system is, the relationships of mutual incompatibility written into it have been enough for him to formulate the rule: Not(A & NotA). And this... this is the very fabric of his Flatland breaching that logic, flouting its own evident physics. It's utterly counter-intuitive, if not downright incomprehensible.
If we suggested to him then that this was due to the substance of time itself extending not just forward but side-to-side, in a dimension of certainty, I dare say, it would still seem a wild fancy, as it would if we told him the stuff of his world, that oceanic light, was all the effectuality of time, the rising and falling of actuality in its third dimension warping his path from the featureless nullity of a flat plain to a rough ride over the wilds of stuff. He would think of space as a plane, and time as a dimension, and energy as stuff within that continuum. He would, like us, have a notion of truth that was quite distinct from time and energy, one with little need to accommodate insecurity--with little capacity to accommodate this notion of a sideways temporal dimension to each moment he passes through. But he would, as we are, I think, be dealing with an actuality in which, to all intents and purposes, truth is time, with energy as a dimension. Truth is time is instance is substance. And existence is to be of that actuality.
Sequentiality, certainty and effectuality. Applicability, security and sustainability. Stint, span and shift. I see these as being as fundamental to our existence as length, breadth and height--or upwise angle, sidewise angle and distance outwards, if one prefers polar co-ordinates to define location in space. In so far as any dimension is removed from the measure of actuality, we are no longer speaking of existence. Some of the more vapid "problems" of philosophy become quickly dismissible if we take this as foundation--the existence of universals, the truth of a proposition about a fictional character, the necessary existence of a Toy God.
In this existentialist epistemology, if we accept (A & NotA), we leave it perfectly legitimate to construct a subset of logical systems which, as a constraint, reject it, but we open logic out to a system of suppositions rather than propositions, (one which I would contend--and no doubt will at some point--may become more powerful by exploring the transitions where (A1 & NotA1 [i.e. A2]) becomes (A2 & NotA2 [i.e. A3]) and by making explicit the modalities that come into play when the absolute is-ness of a law of identity resting on that law of noncontradiction is abolished--for then we must start to talk also of what was or will be, what would and could be, what might or may or must or should be. Which is to say, we can begin to make a logic in which epistemic, alethic, boulomaic and deontic positions are structurally self-evident, a formal logic which fits the actual logic of actual reason and renders the dynamics less easily disguised--a distinct necessity where the conflation of epistemic and alethic positions is a demonstrably persistent problem.
In sum, I see this as essential, necessary--in the good old-fashioned sense of requisite. Our notion of truth is inadequate to the task. It is a time for a revision. Being far from au fait on the current state of academic philosophy, I may of course be simply reinventing the wheel here, or performing the philosophical equivalent of outsider art, but so it goes. If one throws oneself into a seven thousand word essay on epistemology, one does it as much as anything simply to work through one's own ideas. If nothing else, some of the core ideas here are the underpinnings of a conceit in a novella I've been working on for a while, set on a future Mars where notions of the soul or the sign have been rendered obsolete by the notion of stance, where every moment in time is to be considered in terms of stint, span and shift. When one sets out to invent a workable fictional future philosophy, it seems, one rather ends up committing philosophy. So, I appear to be calling for a wholesale reconstruction of our notions of time and truth.
Well, I suppose I'm never one to do things by halves.
posted by Hal Duncan | 9:53 pm
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