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Redoing the Analytic of Concepts

(Published Aug. 29, 2022 by Mariven)

Introduction to an Introduction

!pstart Hi! When I started this, I wanted it to be done by the beginning of June. But it was never quite right, so I just had to keep writing and rewriting - it's still not quite right, but if I have to work on it for another day I'll throw my laptop out the window. If I could fill in the blank in the following question, I'd be done: "The only genuine problems in philosophy are problems concerning --------". I _know_ the answer, but I cannot fill in the blank with it much as I cannot stuff the ocean into a sheet of paper: it's too vast, too deep, and it'd start leaking anyway. Yet I have the obligation to provide it, for the process by which it is answered is the process by which _everything_ is answered (this being the conceptual means of _answer-formation_) and I seem to be alone in my understanding of this. !pnext To make this slightly easier to read, a lot of the less-relevant content within this essay is separated into a second endnote section, the Extra Notes section; unlike normal endnotes, links to these extraneous digressions (which are indexed A, B, C, ... instead of 1, 2, 3, ...) are not shown in the main text until a button at the top of the Extra Notes section is pressed. You can go and click it now, if five thousand more words sounds like fun. !pend


!pstart This essay is meant as a motivation of and introduction to a vast metacognitive project: the development of _an_ understanding of the entire faculty _of_ understanding. It's necessarily a _non-systematic_ project as regards not only its content but the method of its development, given that it (a) both relies on and operates through a messy product of evolution not optimized for any sort of self-legibility, and (b) improves _itself_ in a manner only seen through carrying it out; further, it is a necessarily _individual_ project, as no two faculties of understanding are quite the same in any way (let alone every way), this fractal difference ripping naive attempts at generalization apart. While these factors make it very difficult to coherently introduce such a project, it is fortunately not completely unstructured, as even though we may not proceed with rules, there are _dynamic schemata_ that, when employed with the proper mental diligence, start to bring the full edifice of the understanding to light. !pnext I don't expect that to be totally clear, since it packs too much data into too little space, but to hazily communicate the general shape and target of this project - to carve out the right sort of semantic grooves. A manner of following a self-directing path to the completion of an understanding of the understanding. The instrumental value of this project lies not just in the ability to detect and defend against latent errors in our understandings of things, but in the ability to determine where new understandings are required for a given task and then to _consciously evolve them_ in a creative, volitional manner - rather than waiting for them to slowly arise over months or years. Just to list one particular benefit: insofar as we understand the general form of our understanding, we can perform a "pure deconfusion" of concepts, or a deconfusion of all concepts that may be deconfused insofar as is possible with reference not to the _specific content_ of the concept around which confusion exists but to the cognizer themselves.
!tab The methodology behind this project I call _conceptive analytics_. Since I'm using both of these words in unconventional ways, let me break it down: !pend !parastart My goal here isn't to establish any idealist, monist, or other such philosophical positions - I intend to stay _away_ from mainstream philosophical discourse where I can help it - but to establish a means of effectively navigating this world that I must simply hope exists around me in more or less the manner I've been led to believe it does After all, this is what I was going to do _anyway_, and it's what basically all philosophers do no matter their "beliefs", so I may as well lean into it. . Unlike philosophy, there are _goals_: to chart and thereby optimize the mental faculties through which humans are capable of doing mathematics; to discover and catalogue the basic features of mentation that combine to form intelligence; to become conscious of the manners in which I already mentally represent and manipulate complex situations, so that I can do it more carefully, more clearly. I believe the methodology outlined above is the most general and efficient method of pursuing these goals. While philosophers have already Balkanized much of the territory along this pursuit, it'll generally be clear on how best to take the path that avoids their disputes (except in those cases where the dispute is basically over, e.g. my hopefully uncontroversial discussion of Kant below). !paraend


!parastart This page will elaborate on the project of understanding the understanding, which project I call the _analytic_ on a clue from Kant, going into further detail on the motivation, ends, and shape of such a project To be honest, my up-frontness with the Kant references is a sort of filter. The mathematical and scientific pictures I employ are essential for me - that's just the way I've learned how to think - but they tend to attract the sort of person whose disposition is to hum along to such tunes because they're "scientific and rigorous" rather than because of _how their actual content is being deployed in argument_. I would trade a thousand people who come away from this essay with an essentially superficial, aesthetic understanding of what I'm trying to do for a single person who _sees it themselves_, and "continental" philosophy references are a good filter in that regard; rest assured to that one person, I do not assume you have !c{prior familiarity with Kant}{I'd be stretching if I said that _I_ did...}, and you can probably just skip everything directly related to the Critique of Pure Reason. . It is merely an _introduction_ to this project, and not in any way an attempt to undergo it or even sketch out my progress along it. I'm undecided on whether I should make a second part to this essay through a holistic sketch of the conceptive framework I've built so far, or through a rigorous construction of one particular part of it; feedback will probably decide (assuming there'll be any).
!tab There are many different ways to split the project in order to make it more manageable, some such illusions being more useful than others; the division I'll be employing later in this introduction is tripartite. !paraend !parastart Division A, covering the *immediate* or *phenomenological*, asks for the form of understandings insofar as they are given through and from the inner world of experience. !pend !pstart Division B, covering the *discursive* or *metacognitive*, asks for the form of understandings insofar as they arise through cognition, or the evolution of thoughts To underscore the illusivity of this classification: I've grown uncomfortable with some aspects of this this division lately, such as the way (my concept of) it lumps together "the study of the postulated forms through which mind thinks about the world", "the study of the general long-term dynamics of mentation through its effect on thought", and "the study of the logical forms through which mind reasons about things", and I may replace it or break it down in the futue. But I also might not; who knows? . !pend !pstart Division C, covering the *transcendental* or *ideatic*, asks for the essential characteristics of objective external things through which they can be understood at all, the essential characteristics of beings such that they are capable of understanding anything, as well as the extent to which the understanding may be made to engage with those particular forms in things so as to identify and disarm its hidden sophisms. !paraend

Another way of motivating this method of division is as follows:

!parastart[important][style="margin-top:0"] The nature of conceptivity is what we must conceive of as determining the nature of everything that we think, because it is precisely _through_ conceptivity that _we_ can think of anything at all. It is _we_ who work with concepts, and these concepts are thereby determined by _our_ form of conceptivity; if we implicitly take this form to be a sort of flat, empty canvas on which we can freely build thoughts, this is because our thoughts naturally warp with it - so that if we look at it solely _through_ thoughts, which have the warping _baked in_ to their trajectories, we see no disturbance! But there is no objective, "Euclidean" concept-based coordinate system for thoughts, only a dynamic manifold at best locally charted by maps which thoughts build on and change with. !pnext[important] Yet if it's maps all the way down, we ought to become cartographers! There's clearly something about this system of concepts that, despite its thoroughgoing relativity, nevertheless enables us to accurately work with the territory - for instance, the computer I'm typing on right now works because we've developed unbelievably accurate methods of predicting and controlling electrons _en masse_ - and analyzing this link between the two will let us determine the nature of the human understanding of the world. !pnext[important] It is through examining thoughts in an at least partially _pre-conceptual_ manner that we can see the direct effects of human conceptivity, through examining the patterns that thought mysteriously but habitually ends up displaying over long periods of time that we can see its systemic effects, and through examining the ability of conceptive maps to wrap themselves into empirically verifiable pictures of the world that we can fully understand the "use" of conceptivity for us. These correspond to the phenomenological, metacognitive, and ideatic approaches to conceptive analytics, respectively. !paraend


By analytic of concepts I do not mean the analysis of concepts, i.e., the usual procedure in philosophical inquiries of dissecting already available concepts in terms of their content and bringing them to distinctness; rather, I mean the hitherto rarely attempted dissection of the power of understanding itself.
From Immanuel Kant's Critique of Pure Reason, B90, tr. Pluhar.
!parastart As demonstrated by his attempt at a transcendental analytic, whence the above quote, Kant was one of those few oddities who not only managed to see but _took seriously_ the necessity of the mind, if it wishes to understand the world, to understand itself first: to attempt to determine how it itself works, what its peculiar forms of reasoning are, what it is capable of properly securing for itself as knowledge. This ought not to be a purely 'philosophical' goal, to be relegated to the stagnant halls of philosophy departments Yes, the word ‘philosophy' breaks down etymologically as ‘!c{love}{philos} of !c{wisdom}{sophia}'. Just as with science, though, there is a sharp break between the behavior of the community of practitioners and the ideals they nominally hold themselves to. Philosophy qua discipline is doomed by its being a discipline, by its being a thing one does professionally within a judging community and therefore a thing one structures according to the essentially artificial terms of that community; a love of wisdom becomes a “love” “of” “wisdom”, the layers of indirection added onto each of these terms distancing the philosopher from any feeling that could actually be called love. (One of the primary pastimes of academic philosophy is its neverending dissection of the works of a small procession of large names, trying to say "this was the meaning they had in this text" instead of "this is the meaning _we_ can build _on_ this text" - a practice with the curious feature that the fact of its existence explains why it continues to exist). , but a practical one we ought to have mastered the general discipline of a long time ago The relative success of e.g. Buddhist monks in a few isolated parts of this undertaking demonstrates the utter failure of the rest of civilization. Even the most simple and physically verifiable things are lost on us - the Wikipedia page on saccadic masking has the following hilarious but exemplary !c{pair of sentences}{emphasis mine}: "The phenomenon was first described by Erdmann and Dodge in 1898, when it was noticed during unrelated experiments that an observer could never see the motion of their own eyes. *This can easily be duplicated by looking into a mirror, and looking from one eye to another*". ; now, we're piloting vehicles faster than have ever existed, but we still don't know how to drive. To secure a foundation for this mysterious faculty responsible for our success as a species ought to be one of _the_ human projects, yet it remains largely unpursued. Sure, sometimes people break off !c{small, bite-sized chunks}{influences of language, sociality, desire, sensory priming, etc. } assuming that those can be comprehended on their own, or they sometimes dream of understanding "the brain" as a sort of alienated fleshy machine that seems to compute Neuroscientific tools have not revealed the actual content and structure of cognition; if you'd like to point to this or that fMRI analysis as a counterexample, I'd encourage you to think harder. Look at the finding. Then look at the goal. Ask yourself it would look like for this goal _to_ be achieved. Neuroscience is useful, but it is not yet able to play a starring role in understanding the faculty of understanding. - but so rarely is a drive to understand _actual mentation_, *the thing that you are doing right now as you read this* , explicitly staked out and followed. (_No_, don't start conceptualizing from the outside about it like you _always_ do! You already _are_ it; all that's required is to be _mindful_ of your being it!).
!tab What is necessary is to learn how to not just see but _digest the entirety of one's own mind_. !paraend !parastart Kant clearly had the drive, intellect, and creativity required to understand those abilities of mentation he set out to understand, but he was not _mindful_ The Pali word sati might be a better fit here; while its use in the (Buddhist) suttas is often translated to mindfulness, this loses out on the connotation of _direct observation_. To quote the formidable Bhikkhu Bodhi, "_sati_ makes the objective field 'present' to awareness as an expanse of phenomena exhibiting their own distinctive phenomenal characteristics, as well as patterns and structures common to all conditioned phenomena. The net effect is to make the objective field clearly available for inspection" (source). of _actual_ mentation; thus did he employ these talents to sew for the mind a perfectly cut dress totally incompatible with its actual proportions. Measuring the shape of the mind makes clear its dizzying chaos, and the necessary amorphousness of any satisfactory conceptual dressing of itThere is a _very_ tight rope to be walked between the oversystematization that comes from not learning to get comfortable with this amorphousness - immanentizing the Idea"Transcendental unity"; to be explained later - and the incoherence that comes from being too lenient with it - transcendentalizing suchnessEnglish does not have the right word, which is tathātā.. Perhaps this would have let him avoid the clean (far too clean to be true!) divisions of mental activity underlying his analytic. Nevertheless, even where his approaches fail, his motivations offer great insight: thus are the driving ideas behind Kant's works so often useful even as his attempts at executing them remain heartbreakingly off-target. One driving idea of his that I've found to be an extremely useful conceptual wrapper for my own investigations is that of the analytic of concepts, or, as per the quote above, the exegesis of the faculty of understanding It was the Critique of Pure Reason that first clued me onto the possibility, necessity, and amazing difficulty of dissecting the general form of thought, and - perhaps in the same manner that a baby duck imprints on the first moving thing it sees - I find it very convenient to remix his established frameworks and terms. Nevertheless, I'm not a Kantian in the slightest, since I diverge from basically all of his conclusions; there's a necessary tension in this, in that using someone's terminology predisposes me towards their understanding of the general situation in which those terms were coined and gained their meanings via usage, so that I might therefore be misled into presuming at some semantic level conclusions which I simply couldn't abide by were I conscious of them. This won't _stop_ my rampant string of burglaries, but it ought to at least make me careful.
!tab We might imagine a crow who, laboriously building a nest with leaves and twigs, every so often finds a passerby wearing something it can take - a torn bracelet, a ripped fragment of cloth, a shoelace pulled loose - and, deftly stealing these things, uses them in creative ways to make its nest better. Whatever can be wrapped tight in a shoelace can probably be reinforced by twigs as well, but these stolen goods can, by virtue of some pre-existing structure within them, be used to serve some of those ends more effectively. The materials it patches in may have an effect on the larger structure, but if the crow is intuitive and learns quickly it will be able to determine and control this effect, e.g. learning that these kinds of rubbery things exert force as they try to return to their original position and using this fact to bundle stuff together; if not, it might find the nest start to contract during the next heavy rain until it collapses, and it may not even have any idea what happened.
!tab It is essentially the same with my treatment of the various words and metaphors I steal - if I am not careful and cognizant of the meanings I take them as having both intuitively and discursively, I'll be worse off in the long run. Stolen goods must be _fenced_, and in the case of concepts the method by which this is to be done is the _internal reconstruction_ of concepts for oneself, as will be explained later.
. !paraend !parastart[important] Broadly speaking, my goal is to _retry the analytic_ - to derive a new understanding of the faculty of understanding itself "Retry as in a video game or as in a courtroom?" Both - the _re-attempt_ is, upon success, a _vindication_ of the idea. . As mentioned, the _methodology_ I am approaching this with is conceptive analytics, or the abstract ecological study of conception _qua_ the form of the empirical conceptive ecology. (Try saying _that_ fast). These are merely names, though, and any one name could not fit nicely onto what is essentially a web of ideas unified in a _direction_ rather than a _topic_, but names are essential to communication, so here we are - I can only hope that we do _not_ allow the static nature of this signifier to render static that which is being signified. !paraend

The Idea of an Analytic

!parastart To be clear, when I say "an understanding of the understanding" - the first being a sort of mental object and the latter a sort of mental faculty - there are a great many pairs of words that could be substituted in place of “understanding” and "understanding" while _roughly_ getting at the same end-goal: an account of knowing Not in the usual prescriptive sense of defining what constitutes knowledge, but in the descriptive sense of determining how mental states we say exhibit knowledge are formed. In general, "knowledge" is a _very_ dirty word, so we ought not to attempt to ask "why do I know this" but instead "what leads this mind to the thought 'I know this'?". , a dissection of thought, even a _Critique of_... damn it, I forgot. Nevertheless, I find that understanding is the best word to use among these, due to !c{its linguistic affordances and semantic particularities}{i.e., the particular space of uses it admits}: for instance, even at the same time that it more easily denotes a process than does the word "knowledge", so too is the word "understanding" more easily used as a count noun (such that we can say _ an_ understanding, _multiple_ understandings, etc.) - this lends it an extra dimension of freedom, making it more natural to speak of ways in which understandings can differ, and perhaps be wrong understandings each wrong in a unique way, whereas "knowledge" is more likely to be taken as singular, and "wrong knowledge" more likely to be taken as an oxymoron (or, at best, conceptually stuffed into the monolithic category of "erroneous", in which forms of wrongness are equally alike)."Understand" can also be used in many more situations where "know" wouldn't make sense, or would be too strong or overspecified a word, and yet modified with adjectives so as to gain what strength it needs to rival "know" should it need to. !paraend !parastart[important] All of this is to set up a play on words: taking Kant's use, I mean by an analy*tic*, singular, _some_ given completion of an understanding of the understanding, and by analy*tics* !c{_tout court_}{on its own, without a modifier} the process of understanding the faculty of understanding, which in my case tends to be _conceptive_ analyticsI'm sorry.. !pnext For instance, Kant's analytic - equipped with the adjective 'transcendental' due to his insistence that it is the only _possible_ one supporting understanding as it exists in us, which necessity-given-experience is more or less the meaning of the word C.f. B88: "That part, then, of transcendental logic which sets forth the elements of understanding's pure cognition, as well as the principles without which no object can be thought at all, is transcendental analytic". It's curiously similar to the Buddha's notion of !h[boldOnHover]{paṭicca}{depend/rely}!h[boldOnHover]{samuppāda}{produce/effect}, often translated as _dependent origination_, or the doctrine that all things have not merely causes but _necessary conditions_ without which they are unable to exist (see e.g. Brasington's book, pgs. 13-14). In general, there seem to be a lot of funny parallels between Kant and the Buddha - I won't elaborate here since it opens up a massive and unnecessary attack surface, but some hack could probably make a career out of a deep comparison between the two. - describes the faculty of !c{Understanding}{capitalized to indicate that Kant uses this word in his own way} as being the unifying function of apperception towards pluralities "Plurality" being my approximation of his actual term 'manifold', which I have a diferent meaning to give. of presentations (i.e., the ability to subsume pluralities under the _singular_ concepts and percepts of things as are encountered in conscious experience), the various possible strategies falling under four general functions (those of !h{quantity}{manners of unifying presentations taken as homogeneous extensive magnitudes (c.f. B201-2)}, !h{quantity}{...taken as homogeneous intensive magnitudes}, !h{relation}{...taken as presented physical objects}, and !h{modality}{...taken as empirically cognized forms}), each of which may be applied in one of three logical forms, yielding twelve pure concepts of the Understanding (or, Categories) Thus does Kant see the faculty of Understanding as having been understood _purely in and of itself_, given that the Categories make no reference to actual phenomenal experience. (At the same time, they obviously can't actually do anything _without_ experience, and must therefore be privy to it in some way; the seeming paradox in forcing something that makes no reference to experience to experience itself is salved by the introduction of a set of innately existing procedures for converting phenomenal experiences into logically tagged mental images upon which the Categories may operate, these procedures being called transcendental schemata).
!tab It's essentially this four-fold categorical structure of the Understanding that Kant continues to analyze, filling in several hundred more pages with awe-inspiring (yet unreal) demonstrations of the power of a completed analytic.
!tab For instance, four _autonomically_ performed functions of synthesis means four _blind spots_ of reasoning corresponding to the logical gaps these syntheses cross; it also means four inherent errors of reasoning, activated by the mechanical operation of the Categories even on empty presentations such as the "I think" which Kant takes to accompany all concepts. Thus do we get four _antinomies_ of pure reason, or equally rational yet contradicting theses produced by venturing past reason's blind spots I imagine this to be something like implicitly breaking a rule to 'prove' an erroneous result, as in:
Let $a = b\ne 0$. Multiplying by $a$, $a^2=ab$. Subtracting $b^2$, $a^2-b^2=ab-b^2$. Factoring, $(a+b)(a-b) = b(a-b)$, so that $a+b=b$. Substituting, $2b=b$, and dividing by $b$, which is nonzero, $2=1$.
, as well as four _paralogisms_ of pure reason, or reasonable yet erroneous theses concerning the "I". In this general way does an analytic reveal the essential limits of the understanding. !tab (Note: I am _not_ a Kant scholar or in any way an expert on anything Kantian (save perhaps for boring people to death), nor is this exposition based on or even really informed by the words of anyone who _is_; it is my own dangerously amateurish understanding of the CPR).
. !pend !parastart For now, all I intend to do is establish the foundation for analytics and to sketch the general shape of the first few advances it is to make. Insofar as it advances, the field must take the form of a _narrative progression_: the essential reason for this is that since the object of the analysis is also the means of conducting the analysis, both of these being the faculty of understanding, the carrying out of the analysis changes the form of output of the analysis in unexpected qualitative manners. Discovered properties of the object become properties of the tool, where they go on to condition the discovery of new properties - so the analytical program must necessarily march on in its own idiosyncratic way, a.k.a. its progression. !paraend !parastart Now, melodramatically speaking, one who analyzes a system _hopes_ that it is based upon only a few fundamental and discoverable principles from which all its behavior follows, and _despairs_ that it may instead be formed from a diverse, heterogeneous, and often undiscoverable array of causes interacting in arbitrarily complex ways. Thus, for instance, we may say that Kant's analytic was driven by a blind hope as regards its simplification of the entire faculty of the understanding down to a few basic principles, themselves derivable from even fewer principles, all splitting off from the transcendental unity of apperception, though it rejected the hope of a knowable external world. !pnext[important] In fact, such a blind hope can be seen driving so much of human thought - in physics, for instance, it's basically taken for granted that quantum field theory and general relativity are but parts of a single whole of which the two theories are merely edge cases (just as classical mechanics is the edge case of quantum mechanics given by taking Planck's constant, which roughly determines the quantization level of some !c{observable quantity}{e.g. measured wavelength or spin}, to zero). We may have no clue what that whole is, but we steadfastly hold on to the _existence_ of one. Given the success of past unifications of physical theory, physics may justify its hope of final unification via !c{induction}{it's happened over and over, so we can expect it to keep happening}, but in fields like sociology, linguistics, psychology, the undying hope of humanity has served just as much to _blind_ us to complex truths as to _guide_ us to the simple ones. !pnext[important] It seems to be the case in many complex systems, such as those studied by the above fields, that single reasons for things end up, when analyzed further, !c{_fraying_ into tufts of tangled reasons}{c.f. the image of frayed wires; this is a general feature of concreteness}, presenting in this manner an inherent scale conflict, a microscopic ordered chaos underlying a macroscopic chaotic order; the mind itself is the exemplar in this case, such that an analytical progression, even though it may be inspired by an initial !c{_moment_ }{In its rarer use akin to "aspect", rather than "duration".} of hope, ought then to enter a _moment of despair_ in which no unity can be sought and everything seems to operate according to essentially independent, arbitrary _happenstances_. This is not the end, though, as there are universal ways to force this seeming chaos to, like iron filings being scattered around a magnet, show us new sets of implicate orders hidden within the non-conceptualizable chaos - a second, _ideatic_ order to reality that we arrive at by steadily tearing at the first, _empirical_ order we place upon reality.
!tab Let's try to crawl before we walk, though, and work through some situations which demonstrate to us the need for and general targets of a study of the forms of the understanding. !paraend

Some Useful Words

!parastart Since we'll be jumping across multiple layers of abstraction very quickly, I'll offer some words which I find make it easier to talk about abstraction. These definitions are neither firm nor sharp, so they must be taken not as _the_ definitions but as _guiding shapes_ to interpret the words with respect to - you've done this all your life, so don't start complaining now. It's just as when we use Newtonian physics for everyday problems, or use common yet poorly defined words like "knowledge" while seeming to _know_ what we mean by them, these words may be used fruitfully so long as we are aware of their limits and the approximations and assumptions we make in using them. (To be honest, you can probably skip this section, since my use of these words generally falls within the standard use - except for 'formal', which I use in the rarer sense of 'form-ic'). !paraend !parastart So (generic, particular) and (formal, materlal) are both pairs of words I take as contrasting one another along a specific dimension of meaning; some other properties of things which I take as contrasting are: !paraend

Problem Demonstration

Like anyone over the age of, say, four, I have a highly developed, highly idiosyncraticAs in, unique to myself as an individual just like my handwriting or my genome - not shared by others except in miraculously rare coincidences of similarity (unlike particularities, which can be widely shared). toolkit of mental processes - of various key concepts, heuristics, and so on that I have internalized and to which I repeatedly return by force of habit if not necessity; I can't help but to analyze the world through this toolkit, the structure of which therefore determines the general forms through which I conceive of things by, among other things, determining how I'm inclined to ascribe formal descriptions to particular happenings and how I'm inclined to put events, objects, forms, and other mental content into relations. My mathematical training, for instance, has honed my ability to apply the concept of necessity to my various reasonings about things - I'll put more effort than most people into an attempt to outline which observed aspects of the thing seem to me to have necessarily caused other observable aspects of the thing, yet this is generally not done out of wise and intentional cognitions in that direction, but because my mind has been woven into such a pattern as to capture and dissect them in that manner, just as a spider web woven in a certain way can't help but to catch insects of a certain shape and size.

!parastart As regards the legibility of any such example of the deployment of a tool from the mental toolkit, the above regarding necessity is one of the best-case examples of an example, because a clear cause can be attributed to it (viz. mathematics - mathematical proofs are essentially exercises in determining necessity!) and a commonly understood form of cognition can be verbalized to communicate it (viz. the cognition of some first criterion as being necessary for some second one); the vast majority of Reason's toolkitI capitalize “Reason” here to mark it as a generic faculty of humans, an uncountable noun encapsulating the process of reasoning, which is distinguished from the countable noun seen in e.g. “A reason this might happen is…”, which is a particular concrete mental object. requires a much keener eye to identify in action, and a much keener tongue to communicate in terms of language. Pretty much every single person who has attempted to study the nature of Reason has failed due to this, passing over into an abstract conceptualization of Reason which the mind finds easier to hold in place without even realizing that they have abandoned the actual thing, the actual processes inside their heads. !pend !pstart Anyone familiar with meditation is familiar with this general phenomenon, which I call *conceptual drift* - just as we start focusing on e.g. a candle's flame only to find after a bit that we've degenerated into holding fast to the conceptual representation of the flame as "flame" while incidentally happening to be looking at an actual flame, we start critically examining actual Reason in action only to lose our grip. so as to end up creatively expositing on a conceptualization of Reason which is not Reason itself (and creativity is the _exact opposite_ of what we want here - we want to add as little as possible to our observations while recognizing that which we must necessarily add in order to legibilize them). Kant, for instance, studies Reason in an entirely unreflective manner, not looking at the actual process of reasoning inside his head that picks apart his concept of Reason except on rare occasions where the answer is basically predetermined. !paraend

Yet I maintain that it can be done correctly. As for _why_ we might want to do this -- there are many obvious reasons. To give my main one, though, I'll quote Feynman:

It has to do with curiosity. It has to do with people wondering what makes something do something. And then to discover, if you try to get answers, that they're related to each other – that the things that make the wind make the waves, that the motion of water is like the motion of air is like the motion of sand.
The fact that things have common features - it turns out more and more universal. What we are looking for is how everything works, and what makes everything work.
Richard Feynman (Source video)

The simple fact is that I need to know. I'd be lying if I said I was doing this for this or that practical reason, as the practical reasons were never really what kept me up at night - only the pain of, upon having glimpsed the vague outlines of grander conceptions of thought and reality, knowing just how terrible it is to not have _captured_ them.

Yet, of course, there are practical reasons - extremely important ones. All intellectual endeavors - at least, those that bother to be of any service to humanity - benefit from clarity, and therefore from that proper systematization of clarity that offers us general tools to understand what exactly we are talking about and what mental motions we are performing in our cognitions of things. there's a set of common issues with human understanding that the vast majority of confusion and catchable error seem to stem from We can picture the general distribution of error-causation among systemic issues with the understanding as being a Pareto distribution, with a vast majority of the caused errors stemming from a small minority of issues, so long as we don't mean this too literally. , and which cannot be solved without first understanding what's going on with understanding in general. Furthermore, understanding the understanding, when taken far enough, shows itself as allowing in a natural way the artificial reconstruction of the process of understanding, so as to implement it e.g. computationally in line with one's own thought patterns and values.

Concepts Are Semifictional

To take one of the understanding-issues way up along the (again, metaphorical) Pareto distribution, consider the following narrative, the _fiction of the unified concept_: when humans agree via language to let a word X hold some particular semantic significance Really, there's nothing to this clause besides the speaking of a common language: this agreement is implicit in speaking the language, and the semantic significance is to be found in the actuality of its use. , people will tend in any given use of the word X to immediately yet mistakenly take the concept that stimulates that particular use of X as being given in the word itself, as being the _meaning_ of the word, and therefore as existing inside the minds of anyone else who uses it. Thus do we fictionally represent the word as referring in itself to a static concept, forgetting not only various other ways in which we may use it for entirely different arrangements of concepts _Not_ in the easy homonymous sense, where the different employments may as well be different words, e.g. "I killed the fly"/"I wonder how airplanes fly", but in the harder sense where we have a whole continuous range of conceptual arrangements to which a common word is applied. For instance, as concerns the word "see", there's both an absolutely conceptual way to use it and an absolutely visual way to use it, but also a continuous interpolation between them which vibrates with various other connotations the word can take on. Look: "now I see what you mean by 'conceptual'", "now I see Picasso's painting style", "now I see how this stain could be tomato sauce", "now I see the tessellated pattern of the wallpaper", "now I see you pulling up so I'll hang up the phone", "now I see a bottle of shampoo on the counter", "now I see more clearly with these new glasses", "now I see nothing since I lost both my eyes". but the essential subjectivity we insert into whatever we read as a consequence of the variance in the conceptual aspect that is taken to correspond to any particular use of a word with respect to the taker. This particular kind of error will be discussed in much greater detail later, but since it's such low-hanging fruit, let's demonstrate the fictional conceptuality of the word 'reality' I'll take this to include other forms of the word insofar as they can be interchanged in any given sentence without the alteration of semantic or conceptual content in that sentence. (For instance, sentences containing "reality" can usually be rewritten to contain "real" instead without really changing them, but it's rarer that we can write "realistic" instead without really changing them - thus the former is one of the forms the fictionality of whose conceptuality is tied very closely with that of 'reality', the latter somewhat less so). Anyway, when I say that the word 'reality' is fictional in its conceptuality, I don't mean by that phrase that "reality is conceptual" or "reality is fictional" or "the conceptuality of reality [itself] is a fiction". (Note that neither do I _reject_ any of these in saying that, nor do I _accept_ them via this parenthetical; they're just not relevant). I am saying that there is no singular and universal conceptual form - no one "thing that is meant" by those who speak the word (yes, in plain English - we don't need to reference particular dialects). !tab Really, there isn't even really a patchwork of meanings, as the existence of such a patchwork would imply the existence of individual meanings, as though generated by some unifying, transcendental structure of conceptions from which the whole of the patchwork's operation, and in particular its generation of singular things called "meanings", could be deduced; but no such structure exists - it is an analytical problem to exposit the means of understanding the forms of such non-singular things (the hope lying in the very possibility of despair), the processs by which we think these strange illusory thoughts concerning "meaning", and those aspects of their nature through which meanings really are to _some_ extent genuinely coherent and communicable. After all, if there were no such thing, it would be pointless to write this essay, as I couldn't expect anyone to get what I mean - not just because I'm a terrible writer, but because there wouldn't be any "what I mean" deducible from an essay in the first place. This theme repeats itself over and over throughout this essay - there _is_ something real and true in the vague abstractions we employ, but we have to meet this truth on its own alien terms, as our attempts to build it artificially (see _any_ book on linguistics, sociology, psychology, analytic philosophy, etc., etc.) are nothing more than ridiculous simulacra. as a means of demonstrating the utility of understanding the understanding.

Which of the nine pictures below depicts something _real_? For convenience, let's assume for now that there is a physical world that can _by fiat_ be called real, and that it is more or less as the sciences describe it to be - thereby do we furnish ourselves not only with the various particles and forces discovered by physics, but also with the various manners through which neuropsychology (biology more generally) sees this real matter and energy as conditioning subjective forms of mind. Given this, which of these pictures may we take to be a depiction of something real?

In the usual reading order: (i) the hierarchy of computational complexity classes (symbolized here just by the most common ones), (ii) the Earth's moon, (iii) a mapping onto the human somatosensory cortex of its representation of the body (the "cortical homunculus"), (iv) a computer rendering of an RNA polymerase II protein transcribing some DNA, (v) a honey bee, (vi) some orbitals of the hydrogen atom, (vii) a sentence diagram, (viii) a trajectory following the Lorenz attractor, and (ix) a one-to-one correspondence between the set $\mathbb N^+$ of positive naturals and the set $\mathbb N^+ \times \mathbb N^+$ (the pair at the start of the path being the first/corresponding to 1, the next pair corresponding to 2, ...)

Most people, I suspect, would answer that (ii), (iv), (v), and (vi) are real, maybe (iii) as well, while (i), (ix), and maybe (vii) are _true_ rather than _real_. Ignoring "!h[no-bg]{ceci n'est pas une ___}{}"-type problems, it at least seems clear that (ii) canonically points out a certain clump of actual matter, namely the actual moonIt is because there is an unambiguously singular actual thing, and because I asked "which things _depicted_ below are real" rather than "which things below are real", that we even have the capability here to ignore the treachery of images, identifying a picture of the moon as depicting _that_ particular physical object that appears in the sky.. This much is certainly real, right? Well, "thing" may be debated - we might say that the identification of a single entity from all that matter is merely conceptual, does not actually mark out a feature of physical reality, and that when we say "the moon" we are employing a concept that is not real due to a sort of !c{_artificiality defect_}{I'm not actually going to use this terminology, don't worry} - but regardless of whether we accept this argument, the matter in which we see "the moon" is physically real and basically unchanging matter being more or less veridically perceived through the depiction. (Unless, of course, something has gone terribly wrong - perhaps the moon disappeared in 2018 and has since been replaced by a complex system of satellite mirrors and hypnotic effects - though while we can't rule this out, we have no reason to believe any such thing has happened. Please remain unsuspicious until a general advisory has been posted to the contrary).

!parastart One step down the ladder, (v) points out a thing that at some point physically existed - some actual bee which probably died a long time ago. Yet, on the supposition that the bee has died and decomposed, being transmuted into various bacteria and fungi, is the photo still a photo of something real? Is this different from the criterion on which the it is a real photo? If that bee is somehow still alive, then, given that it like most living organisms has likely shuffled through all of its component atoms, the photograph is not one of any existent arrangement of physically existing things, so - if we bite the artificiality bullet and claim that "the moon" is real, is "the bee" then real or not? We might call this a _permanence defect_. !pnext This doesn't seem to be that pressing of a concern - first because we think of a single reality subject to a flow of continuous change, rather than a continuous flow of single realities (notice how I referred to the _same_ bee above), and second because we often think of a reality as including its past: most people will feel fine calling a photo of e.g. Thomas Edison a real depiction of a real person A painting of Edison and a painting of a photo of Edison might both be a "fake depiction of a real person", though the painting itself wouldn't be fake as an _object_, just as a _depiction_. . For those who do accept the reality of Edison, myself included, consider the following: if I take a lightbulb and blow it to bits with twenty megatons of TNT, can I then continue to say that the lightbulb is real? I want to deny this, but it's not immediately clear to me how I can both think to deny reality to the dynamite while at the same time bestowing it upon the lightbulb. After all, if they are "real", and reality means a single thing, they ought to be real in the same sense; but even though they've both gone through the same process of being created and destroyed, I feel like I should judge them differently.
!tab The problem exists between the intuitive judgements I make concerning the application of attribute ("reality") to two different objects ("Thomas Edison", "vaporized lightbulb") and the !h{dianoetic}{discursively reasoning, as opposed to intuiting} comparison of these two judgements - namely, it seems to me that the attribute named 'reality' should be applicable to a given object based on cognizable criteria concerning that object, but here are two different objects for which those criteria I'm conscious of existing in "reality" are the same and yet for which I have different judgements. !pnext The issue is that 'reality' does not actually name a singular attribute with such-and-such cognizable criteria; in fact, the existence of such criteria themselves is an illusion, as the mental processing that leads to such-and-such a judgement is represented neither _fully_ nor _faithfully_ by my consciousness of mental processing. Not that I can't expand my consciousness of what's going on through introspection - if I do so, I find that when I say "Thomas Edison is real" I'm activating a dichotomy in my mind between fictional and non-fictional people, whereas when I say "the lightbulb is no longer real", I'm activating a dichotomy in my mind between physically existent objects _at a certain moment_ and physically non-existent objects at a certain moment. Congruently, my first interpretation of the sentence "Thomas Edison is no longer real" as meaning something like "he was real, but then he became fictional", which doesn't make sense to me; but if someone were to say this to me, I'd almost instantly cut this first interpretation loose to form one which matches with my account of the situation, "he was alive, but then he died", perhaps noting the strange use of the word 'real'. There is no singular concept that the word 'reality' evokes for me, as I'm using a slightly different concept in each judgement. (Alternatively, consider: the words 'fake', 'fictional', 'imaginary', and 'non-existent' might all be taken as antonyms to 'real', but do not all mean the same thing). !pnext If someone thinks "no, neither Thomas Edison nor the lightbulb are real, though they _were_ real", this paradox doesn't exist for them. The intensity and precise form of the paradox will vary from person to person; certainly some people take reality generally to consist exactly in physical reality and to _explicitly_ take as an argument a given _moment_, and this solves the paradox (save for the sub-problem of the reality of structured things accidentally included in it). Thus is there an essentially personal aspect: a correct answer to this paradox can only be a correct answer for a particular person. !paraend

Continuing with the picture: (iv) is not an actual photo of any actual protein, being computer-generated, so it really does fall prey to the Magritte attack - there is no physically existing thing that the photo depicts. Yet we may say that the photo _represents_, in a looser sense, every RNA polymerase II protein, and in this particular sense the picture is "_of_" a real thing, even if it does not _depict_ a real thing. (In this sense, would a _painting_ of the actual bee - posing on an actual couch, holding an actual pollinated flower in its mandibles - _depict_ a real thing?). Call the failure of an image to be a "real image" of something (which is necessarily real, if it has a real image), as with the bee painting, a representational defect; call the failure of an image to be an image of a single real thing, as with the protein image, its multiplicity defect.

!parastart Going further, (iii) and (vi), in addition to suffering the above representational defect, share a further defect of reality -- they're merely organizational patterns of real things. In the latter case, this is because an orbital represents the probability distribution (absolute value of the quantum wavefunction) of an electron in the corresponding quantum state, rather than the electron itself (electrons with different spins can occupy the same orbitals, for instance). In the former case, this is because the sensory (resp. motor) cortical homunculus is merely a pattern according to which various neurons form !h{afferent}{afferent connections arrive (at the CNS)} (resp. !h{efferent}{efferent connections exit}) connections with various parts of the body. We might call this an indirection defect. !pnext Note also that while both images share a multiplicity defect, they suffer it to different degrees: we can expect cortical homunculi to vary more or less like snowflakes or fingerprints, whereas, say, the 1s orbital of the (non-bonded, non-ionic) hydrogen atom, is nearly identical in all such atoms Not perfectly identical, as minute fields from stray particles will always disturb them in unique ways, but _almost_ identical. . Hence we may speak of the _qualitative distribution_ of the multiplicity defect, which accounts for both the number of things that an image may be taken to represent and the diversity among those things, saying that (vi) has a much _larger_ but nevertheless _tighter_ distribution. !paraend !pstart In any given case each defect may show up to affect our judgement of the reality of whatever is presented to us. But each of us as individuals will have learned our own idiosyncratic manner of representing these defects, a manner which is also unique to the particular presentation of the _concept_ of reality activated by the question. For instance, if I ask "is society real?", it might be answered no on the basis that it does not pick out a unique thing, having instead a very wide multiplicity defect, or instead on the basis of its indirection defect, should we take it to be an epiphenomenal organizational pattern of humans If indeed there's an implicit understanding that "society" refers to a _singular_, _human_ society, discluding e.g. mole-rat societies and not splitting up into e.g. French, Russian, Indonesian society. Or does it refer instead to a _condition_ of sociality we experience? . It might be answered yes on the grounds that society is a state of things, and states can be real too, or on the grounds that collections of real things are real themselves. But the claims each of us make regarding the reality of society, as well as our judgements of such claims, will be dependent on our _idiosyncratic conceptual construction_ of 'reality' insofar as it is activated by such !c[top]{mentation}{Any mental activity, e.g. cognizing, intuiting, emoting, and so on.} Trying to say "all languages are private" or "all languages are public" is foolish - it's no surprise, then, that it's such a popular activity among philosophers. Rather, we ought to say _in what manners_ they relate to _being_ public and private - and what concepts we have in mind here, in terms of the representations and metaphors we find natural to the concepts. That we can learn languages at all as children just by looking at them in use - or that something like GPT-3 can use words in a coherent manner after training on the internet - suggests that languages have a public _drive_, and this is in fact generally the ends towards which languages are formed and used, but it is not how they _directly interface_ with us, their ability to do so being given via a private _drive_. This will be discussed in a future essay; for now, I have to say that the use of the word 'reality' is, despite its looseness, not _fruitless_. But you already knew that. . !pnext I could go on using these images to break down the fractal confusion in "our" "concept" of reality for perhaps a hundred thousand more words, but since this section is starting to drag on, I'll leave it to you to continue this method of critique using the bottom three examples, using them to evince the fractionation of the concept of reality. It's an essentially mechanical process of which I'm getting tired, so I won't do it for free. The essential point is that there is no unified concept corresponding to the word "reality" - not even in an individual, let alone in general - but instead a loose mass of desiderata, exemplars, schemata, alignments, and so on through which any given thing is determined in its particular _qualitative_ state of reality So, can we even really speak of a "concept" of reality? Not really - the fictional unity of the concept is the fictionality of the concept itself, insofar we take concepts in general to have _unity_ as a prototypical property. This is one reason why I find it important to stress conceptivity, or the 'mesoscopic' view over which fabrications like "reality" can comfortably extend themselves, over conceptuality, or the 'microscopic' view in which fabrications like "reality" cannot fit. . !pnext If we are to achieve clarity in not just discussing "reality" but in simply representing it _to ourselves_ in a manner we can coherently represent and control, we have to make clear the space of ways in which we _understand_ the word such that we are capable of endowing it with meaning at all, which requires a keen analysis of the faculty of understanding in general - an analytical understanding of the understanding. !pend

Concepts Are Misleading

Cease from practice based on intellectual understanding, pursuing words and following after speech, and learn the backward step that turns your light inwardly to illuminate your self.
!tab -Dōgen, Fukan Zazengi (Universal Recommendation for Zazen)
!parastart The same goes for truth, goodness, freedom, life, space, intelligence, intuition, concept, image, and so on - all fractally confused in ways that we rub up against as soon as we attempt to specify what exactly is meant by them, what exactly they apply to, in a manner that agrees with our intuitive understanding (intuition and understanding being two more of these words). All fabrications! Despite this, we constantly use them in daily life as though nothing were wrong, and people just keep on attempting to come up with binding definitions for these concepts Given the fictionality of the concept, you must understand my persisting use of the word "concept" here to mean the loose bundles of tools for mentation which each of these are, i.e. the non-unity which is in the same place we thought we'd find a unity. with the expectation of finally getting it right, even though they're doing nothing fundamentally different from the previous trillion failed attempts. !pnext To be sure, definitions often _are_ extremely fruitful, but primarily when they're given towards a specific end and with a specific sense - the psychologist would find a definition of intelligence as "an agent's average performance in all possible environments, each weighted by its Kolmogorov complexity", as useful as the AI researcher would find a definition of intelligence as "the ability to adapt quickly to and begin to adjust arbitrary situations" - both may complain that one word outside of their domain has merely been replaced by several other words outside of their domain. Yet in both definitions there is clearly a similar _sense_ - which is to be expected given that it's not an accident that they're both definitions of the same word - and it is this sense that the mind works with at a level far more fundamental than it could ever work with definitions. We must resolutely insist, though, that there not necessarily be anything in reality corresponding to this sense - that singular concepts have no obligation to end up being coherent simply because we think them! !pnext In this sense, we're like a crowd of blind men climbing a volcano from all sides, thinking it to be a mountain - we get to the rim, and, feeling the height leveling off, rush towards the center; but what we were feeling was merely the _outline_ of a peak which, fatally, turns out to be empty on the inside. We so often do not, cannot know whether our concepts will turn out to have anything stable at the center or whether they'll just totally let us down. !pend !pstart My own intuitive (but neither explicit nor actual) stance on the reality of the various images above follows from a general intuition: there is a physical reality in which we can only locate particles and fields, and on top of this physical reality a sort of _continuum_ of increasingly abstract, non-real structures lying on top of physical reality, with what is above _structuring_ that which is below. According to this intuition, an individual human body such as mine isn't a _perfectly_ real thing, for instance - the actual particles that make me up constantly change, so that no physical grouping corresponding to my body may be strictly identified; nevertheless, the individuality of my body seems to be a basically _biological_ phenomenon, shaped presumably by evolution, and I'd place it just barely above physical reality in terms of abstraction, making me _pretty much_ real. !pnext My purpose here isn't to endorse this intuition, but to describe it as an example. Though it's been shaping my worldview for a long time, it's only recently that I've been able to notice it, verbalize it, look into how it affects my thought, and thereby _critique_ it. That I ought to critique it is clear - I never came to it through my own explicit reasoning, instead just sort of _finding_ it there, and there are a lot of questions to be demanded of it if I'm to be convinced of its validity: !paraend !pstart And so on and so on - if I can't answer these questions, then I can't put on a firm foundation this intuition I have, and I can't trust that anything built from it will not unravel when it encounters one of these questions itself Humans in general are drawn to ideas that their intuition gives a certain preconscious appeal to, collecting such ideas like a bird might collect shiny things - there is no conscious self-interrogation by means of which a filter might be imposed, just _shiny_. "Non-duality", "systems thinking", and so on are some of the more explicit (i.e., easily verbalized) victims of this phenomenon - it's *not* that they're meaningless or useless; but that failure to be critical of, or even aware of, the effect of one's own intuition - an animal fortune-teller with no actual sight - is a general human ailment which so often renders these ideas little more than _decorations_, when they deserve better. Yet this form of decoration is largely unconscious in the same way that the halo effect is, and I ought therefore to guard myself against it, formulating ways to tell when I'm falling - or have already fallen - into it. . This unraveling is in my experience an extremely common phenomenon, making its prevention, or, at least, the illumination of its causes and nature, important to me. Now, I can't simply get all my intuitions in a list and interrogate them one by one (as if they were separable and enumerable!): they come haphazardly, indirectly, and covertly over the course of thought, and they keep growing all the time, as their formation is inevitable in the thinking through of a new problem such as, well, how to find and analyze intuitions. Therefore, we must strike at the root, seeking to understand the _general form_ of intuition and deducing from there how to bring intuition qua _faculty_ to account insofar as it contributes to clarity or confusion when thinking through things, i.e. insofar as it plays a role in _understanding_. !pend !pstart Of course, intuition cannot be understood without understanding the entire operation of the mind, as the intuitive faculty integrates itself so deeply into other faculties (volition, emotion, perception, and so on) that it cannot be pried back out and analyzed on its own. (A basic inspection of the phenomenology of mentation should make this obvious, but I'll evince it more thoroughly in a later essay). For now, I'll indicate the general idea behind this, which is that intuition gets tangled up in processes of _mutual conditioning_ with other faculties of the mind in an essential way that dianoesis is more often capable of avoiding. In any case, the result is that our project reveals itself to require a reflection of the entirety of _mind_ into itself (again, a _taking up_ of the entirety of the mind by itself). !pend !pstart Analytically speaking, what is to be done as regards _reality_ is *not* to figure out which of these objects are truly 'real', or more generally to figure out what relation they have to reality; instead, it is to examine how we actually cognize the notion of 'reality' in relation to these objects such that we may give _any answer to the question at all_. For we have individual understandings of each of these concepts which we habitually take for granted; not thinking to make our understandings clear, nor to understand the general rules on which they are formed and on which they influence thought, nor even to imagine others as having their own independent understandings, we get into endless conflicts in messy, unclear ways that render them irresolvable from the very beginning. Not only is this conflict with others - it is within ourselves as well. For, the less intensity and depth we confront this problem with, the greater is the disconnect between our more intuitive forms of thought and our more dianoetic forms of thought; this latter form being the primary means through which we solidify and communicate our thoughts, such a disconnect is tantamount to not only an involuntary illegibility to and of the outside world, but an increase to the level of disorganization in one's own thoughts as well. !pend !pstart As such, if we desire to get better at forming and communicating understandings of things, or if we desire to make progress in those fields of thought that essentially rely on fractally confused concepts of the understanding such as 'intelligence' and 'truth', it is essential that we dissect the faculty of understanding itself - that we _understand the understanding_. The conditions in the understood and the understander that make understanding possible at all, the patterns by which understandings are generally or must necessarily be formed, the manners of formation which various epistemic desiderata (e.g. coherence, agreement with reality, communicability, non-superfluity, etc.) compel the understanding to take or avoid, the manners by which the validity of understanding may be improved in practice, and many other things besides - to the extent that these are unclear to us, we are lost _as thinkers_. In our capacity as thinkers, it is precisely the faculty of understanding that we wield as a tool to forge new doctrines, disciplines, theories, models. If we're unfamiliar with our tools - not so much as regards their appearance and feeling but as regards their inner workings - we can do little with them when they fail to do what we want, e.g. to solve a certain seemingly-soluble problem. On the other hand, if we are familiar with them, we can figure out how to adapt them for the task at hand; it seems to be a general rule that slight quantitative increases in the fitness of the architecture of one's understanding of a given problem translate to large qualitative increases in one's ability to effectively attack that problem, making a study which allows us to understand and thereby customize the architectures of our understandings to given ends an _instrumental_ tool of incomparable value. !pend

Concepts Are Everywhere

!pstart To clarify the subject, I want to give a few more examples of the kinds of questions to be classed under analytics. I'll generally be using simplifications of real-life examples which initially prompted these questions in my own mind, and want to explicitly note the _mundanity_ of these examples. Recourse to convoluted thought experiments is, while fun, so often unnecessary The fact that even trained philosophers fail to grasp the conceptual-teleological logic of thought experiments - and there is a logic of teleology, or at least something approximating it - thereby making critiques without even having the cognition that these critiques may be irrelevant to the _direction_ of the thought experiment, trivially solvable with some rearranging of parts, and so on, is a good sign that we should be very careful in the not just our judgements of but our own _deployments_ of thought experiments due to the great possibility of both failure to communicate and the opening up of additional illusory attack surfaces through which it is impossible to coherently communicate that misunderstandings of such experiments often render.
!tab I haven't worked out the full picture of thought-experiment logic, or rather the structure of schemata according to which a thought experiment may be associated with its own tailored logic through its conceptual structure, but I've played around with enough thought experiments that I can see the massive edifice of this structure outlined in the wake of my conceptual movements To explain what I mean by this:
!tab Part of the importance of recording one's own thought process is that it's only when looking back at the development of thoughts over long periods of time that large-scale patterns become clear. For a visual metaphor, picture a red line on a map that tracks the location of a particular beetle, constantly being drawn but never erased so as to simultaneously be a history of the bug's location. If after three days you should notice that (1) the red line always acts strange in a certain region of the map, bending as to strictly avoid or go through a particular region and thereby outlining the _shape_ of that region when the red line is resampled into a _density map_, or you should instead notice that (2) the random fluctuations of the red line actually seem to obey a fixed distribution, or perhaps you notice (3) a constant spatial pattern to the bug's path which nevertheless doesn't determine its _position_, e.g. moving in zig-zags or circles of near-constant radius; in such cases, it is only via tracking the long-term movement of the beetle that the patterns guiding or forming or shaping its movement can become clear. On the other side of the metaphor (the beetle representing thought, the red line the path of the thought process A hypothetical thought-space is also postulated as the representand of the metaphorical map; but if you are going to imagine this space - well, you probably already have, but anyway - *do not* imagine it as two-dimensional. Force yourself to imagine it as having far more than three dimensions, intentionally hurting your visualization of it; for a hypothetical thought can vary in so many ways while not varying in others, e.g. level of abstraction of the subject, intensity/tone/kind of sensuous recreation, and this is _essential_ to properly conceptualizing movement through thought-space. ), we might think of these three observations - I've introduced enough strange terminology in this essay, so let's just phone it in and say type 1, 2, and 3, respectively - as revealing structures, whether extensive (type 1, which has extension in thought-space, yet does not _intrinsically_ alter the shape of the process), intensive (type 2, which is intrinsic to the shape of the process, yet does not have any extension, being infinitesimal), or both (type 3, a shape of the movement which shape itself has extension in thought-space), which are structures _of_ thought and are yet, as structures, _beyond_ thought. The teleological logic (teleo-logic) of thought experiments is one such structure, being in particular a type 1 structure (which may not make sense if you did not take my visualization advice).
, as so many truly interesting, mysterious things reveal themselves have been _right in front of us for our entire lives_ once we figure out how to stop taking any given form of reality _for granted_. Just a single weird wording of a phrase, a subtle peculiarity of visual processing, a small physical behavior or tendency - these are loose threads which, if pulled, each unravel so much more than one who treats them as things that just tend to happen could ever realize.

!pstart It should be clear, then, that !c{what I'm looking at}{there's that visual metaphor again!} is an impractically massive, incredibly difficult project. However, the fact that the subject of the study is the same as the means of study implies that analytics may at the same time be meta-analytics Take care to distinguish between the "horizontal" kind of meta-analytics, or the study of understandings that themselves pertain to understandings (e.g., studies of "what do I mean when I speak of a 'representation'" and "how do I currently model my deployment of concepts?"), and "vertical" meta-analytics, or the study of the forms and processes according to which the understanding is or may be understood (e.g., studies of "how does my conceptual division of the faculties of mind affect my analysis of it?" and "to what extent does the form of my memory warp the past thoughts my current thoughts build upon?"). In other words, horizontal meta-analytics is the understanding of the {understanding of the understanding}, while vertical meta-analytics is the understanding of the {understanding of the understanding}. It's the latter approach that I'm pointing towards in this paragraph. ; not all analytical questions are alike in this regard, but by tackling those more meta-analytical questions we may _build speed_ as we !c{move across}{visual metaphor again} the field, since answers to such questions (a) by virtue of their being understandings of the general forms of understandings of the understanding, allow us in the doing of analytics in general to work more efficiently with the architectures of the understandings we are trying to build of such-and-such particular properties of the faculty of understanding, and (b) by virtue of their being understandings of mental states, serve as excellent _practice_, not only for further analytical studies but for the careful and self-conscious employment of the faculty of understanding to _any_ field. Some may look down on mundanity because they find it immature or unserious - they have it precisely the wrong way around, as it is _avoiding_ connections to the real world which betrays a fundamentally immature, unserious approach to questioning; any approach to understanding the world must as a point of the highest obligation commit itself to _veridicality_, or the accurate representation of reality. If reality has to be "!c{shoved in}{and again, with a bit of kinesthesia this time}" to the approach, as it usually does with philosophy, it's likely just not a useful approach, save for insofar as it is formal or an idea-introducing prelude to a more careful approach. !pend



!pstart As the source and goal of this field of study are one and the same, one may, looking at it as a circle, consider that there is no beginning and decide to give up the entire enterprise forthwith. It is true that it is circular, and that there is no point at which we can start tracing out the complete form. This does not make it impossible. For, we already have an embryonic conception of our faculty of understanding, the shape of a circle so faint as to be nearly invisible - this much follows from having a sense of how to use the word "understand". We may fill this in: starting at some arbitrary spot, we use our understanding to build on our conception of itself, darkening the outline of the field with each pass along the circle, until, we hope, we have traversed the path long enough that it is perfectly opaque, with nothing left to fill in. Represented through time, we may conceive of our position as a steady _ascent_ into a future which contains and yet improves upon its past. In this way, the circularity of analytics is actually the primary determinant of the shape it must take: not a !c{snake wrapping around to eat its own tail}{look, i'm only making the reference so nobody else can do it for me}, but the trace of a ring which steadily fills itself in. Not a _loop_, but a _helix_. !pend !pstart As mentioned in the opening, I prefer to split analytics into three divisions: one concerning the nature of the understander, one concerning the dynamics of understandings By "the world" I mean anything, real or not, that may be cognized and thereby taken as an object to be understood. held by the mind, and one concerning the nature of the relation by means of which the understander can and does come to hold some particular understanding of the understood, a.k.a. the transcendental legibility of the world. Phenomenological, metacognitive, and transcendental - for now, let's call them A, B, and C, respectively. In the _recapitulation_ of an analytic, they must as a matter of pedagogy be presented in a linear fashion, A-B-C To employ another insufferable metaphor: If I were on a keyboard and thought of a chord I wanted to play, say an E minor chord, all its notes would be inseparable to me in that chord as I heard it in my mind, but if I were telling you how to play it on a keyboard, I'd tell you to - assuming you knew the language, i.e. the notes and their positions - "play the notes E, G, and B simultaneously", verbally saying the notes _one at a time_ and then including "simultaneously" at the end as instructions for using _your_ keyboard-playing ability to recreate the same sound in which the notes E, G, and B are indeed inseparable (I may not even say "simultaneously", since pretty much everyone who knows about chords knows this instinctively, but I'd say the letters representing the notes one by one). In an analogous way, I can only present the divisions A, B, and C one at a time, and that's the order in which they must be given _if they are to be given one at a time_; further, I can only give the instructions to comprehend the divisions as being inseparable _separately_ from my naming of the divisions, with the hope that you'd combine them in your mind as I have in mine. (If after saying "E, G, B" you play the notes _consecutively_ and ask if that was the chord, we'll clearly have bigger problems than E minor). This is simply what happens when one tries to use a linear, limited representational system, such as speech or writing, to communicate things that can neither be formatted in a linear series without being changed nor represented within a single symbol of the system, such as the symbol "Em" (which, note, does not teach you "E, G, B"). , but in the _undergoing_ of its progression from an initial conception of the understanding, they must as a matter of diligence be presented as inseparable from one another, for they are in fact inseparable. This difference may seem contradictory, but the recapitulation, a series of snapshots of the helix from various angles, is very different from the undergoing, the actual drawing of the helix along a continuously overlapping arc: it's a dry, dead husk which one may use only to transmit the final form of a mental image (ecology), that the receiver may hopefully form the same image by re-expositing it themselves now that they have a rough idea of what figure it should cut. Note that I say "can be roughly split... as a matter of pedagogy... as a matter of diligence" - I cannot pretend that any sort of ultimate division can be made here, that this division is in some fundamental sense inherent to analytics itself; it is merely a simplification loosely akin to a mean-field approximation In mean-field approximation - at least, one particular kind - an intractable function $K(x, y, z)$ is replaced with a function like $K_{mf}(x, y, z) := k_A(x)k_B(y)k_C(z)$, where $k$ is a parametrized family of _tractable_ functions such that we can set the parameters $A, B, C$ so as to make their tractable product function $K_{mf}(x, y, z)$ as _close_ to the original function $K(x, y, z)$ as possible Generally with methods from the _variational calculus_, such as in the mean-field approximation used in the statistical inference/machine learning algorithm thereby known as _variational_ Bayesian inference. .
!tab Disrobing the metaphor: we approximate the multivariate, complicated field $K$, the true nature of the understanding, with members of the univariate function family $k_-$, things we can comprehend, these parameters $A, B, C$ being chosen so as to render their combination in an analytic $K_{mf}$ as close to $K$ as possible. (Of course, in an actual approximation problem we have the explicit form of $K$ and can therefore actually optimize $A, B, C$... not having $K$ here, we just have to guess off our shallow experiences of it).
. !pend

!pstart Due to their overwhelming circular recurrence and mutual interdependencies, the ideas I will present are simply not that fit for presentation via language, and as such necessarily come _batteries not included_ - requiring significant effort on the part of the reader to reconstruct the understanding I am trying to establish. It will be difficult to understand, and necessarily It's often said that "one does not understand any idea which they can't explain to a six-year old" Einstein never said this, by the way. He _did_ say that "all physical theories, their mathematical expressions apart ought to lend themselves to so simple a description 'that even a child could understand them" - the use of "describe" instead of "explain", the hopeful "ought" instead of the certain "can", and the strict focus on physics' sensory metaphor make this statement more or less reasonable as an ideal to strive for, rather than be controlled by. It is not a certainty - indeed, Einstein made this statement to explain his issue with the statistical nature of QM, which is possibly the _simplest_ view... . The grammatical structure of this sentence puts the emphasis on the "one" who "does not understand", distracting us from the other ambiguous word in the sentence by postulating a bombastic fault with the target of the quote. But if we flip the sentence to emphasize the "six-year old" who is the object of the this other word, the verb "explain", we get the equivalent but clearly ridiculous "any idea which the !c{generic}{obviously "_a_ six-year old" doesn't refer to literally _all_ of them but only a _supermajority_} six-year old cannot comprehend explanations of is not understandable by !c{any human mind}{but "you" can be any person}". To more directly point out the fault: concepts are generally not, like eyes, present at birth, needing only to be developed. Maybe this holds partially for a small few - but certainly not for the vast majority. They are _carved_ into their elaborate shapes through great amounts of repetition or directed attention, and on the backs of so many other concepts through which these repetitions or moments of attention are understood or cognized. Now, if you mean by the ambiguous word "explanation" the kind of _lie_ which takes the truth and beats it to a bloody pulp with invalid oversimplifications while attempting to keep the general shape - and indeed this is what most believers in this quote give when they attempt to demonstrate it - then, while this does bear _some_ validity (familiarity with the shape helps you hide the damage you're doing), it's more a measure of _brutality_ than understanding.
!tab It's true*r* that you don't really understand an idea if you can't explain it to a peer, and very often true that _trying_ to explain it to a child helps you understand it better. But if the only ideas you can understand are the ones you can explain to children, that just makes you a moron.
so. For those who find themselves put off by this - Kant and I are of like mind, though I'll defer to his four additional decades of tact: !pend
Many minds will succeed very well in the exact and even in deep sciences more closely allied to intuition while they cannot succeed in investigations dealing exclusively with abstract concepts. In such cases men should apply their talents to other subjects.
Kant's Prolegomena to Any Future Metaphysics, Hackett ed. pg. 8

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