The Map Is Indestructible (Part I)
Korzybski's (In)sanity, Gödel’s (In)consistency, Barfield’s Rainbow, Leibniz’s Monads, Žižek’s Hegelian Ideology, and Pynchon’s Mad Love
As Kurt Gödel found mathematics and seemingly any self-referential system cannot make itself axiomatic or formal, so the same goes with all of thought. With Gödel, we can consider Alfred Korzybski, the brilliant challenger of Aristotelian thinker, who we might also associate with Hegel of the Science of Logic. Korzybski’s Science and Sanity attempts to help us recognize ‘mathematics as a language similar in structure to the world in which we live.’¹ Perhaps Korzybski succeeds in this, but if so, that would perhaps help the case of making Gödel’s work part of the world itself.² ³ ⁴ And what would this mean? That we are always dealing with maps that are indestructible precisely because finding a point of incompleteness will not necessarily mean they are wrong: though the realization brings anxiety, “incompleteness” can benefit maps. If incompleteness is essentially part of every map, then finding maps incomplete will not necessarily overturn them. Far from necessarily relativizing them out of existence or into nihilism (though that can happen for some), the vulnerability can make the maps more invincible.
I
Mathematics can achieve self-consistency, but this consistency does not necessitate correspondence with reality; likewise, ideas and thought seek a similar consistency (in a network or worldview), but for thought to achieve this consistency does not mean the thought corresponds.⁵ Korzybski was fascinated by mathematics, and he saw in a study of what math “was” the possibility of understanding thinking and semantics more broadly (‘[i]t seems that mathematics […] have never gone so far as to appreciate fully that they are willy-nilly producing an ideal human relational language of structure similar to that of the world and that of the human nervous systems’); if this is right, then there would be further reason to believe what Gödel discovered could be applied to thought more broadly.⁶ Does this mean Korzybski believed thought could be objective like math? No, he believed both math and thought were semantic and symbolic creations (he asks us to ‘treat numbers as relations,’ which means ‘fractions and all operations become relations of relations, and so relations of higher order’), that in their arbitrariness were still necessary and possibly right, even if we could never make them axiomatic (“the science of subject” of Hegel and Korzybski may overlap).⁷
Thought always “worlds,” as every fact generates “a factview,” which means that ideas are always “toward” map-making; similarly, symbols and symbolics (like mathematics or language) seem to require “a greater context” to be possible or meaningful, suggesting that symbolics must generate systems like ideas must generate worlds (even a standalone smiley face symbol needs a world “beyond itself” in which people smile at one another). And as symbols are made “toward” these “greater contexts” for meaning, so in thought the object-cat is made “toward” the idea-of-cat (or vice-versa, which must be so situated in a network to be meaningful), as if this relation is axiomatic, though this particular “toward-ness” itself can never be said to be such. The thought and connection are ultimately arbitrary, as is a given map, and yet the thought could nevertheless be true. “Arbitrary” and “false” are not similes, and oddly to think we must always deal with something arbitrary (is this why “the fear of error is the fear of truth” for Hegel?), which suggests thinking might not be what we think.
If not invented, Alfred Korzybski at least popularized the common phrase “the map is not the territory,” and it is partly meant to honor him and his work with Gödel when we say, “the map is indestructible.” The map used to refer to a given location isn’t that location itself, and by extension the map isn’t “grounded in” the objective reality of the location, though it might, relative to humans (and our scope), accurately reflect that location and help us move around within it. This seems obvious enough, but this point carries for all of thought: the word “cat” isn’t the object-cat; the symbol “A” isn’t “the thing-A-symbolizes”; and so on. Unfortunately, Korzybski noted that humans are incredibly prone to come to think that “A = A” without realizing it (in the sense that humans are prone to think “the signified = the signifier,” though we realize this is absurd when asked about it directly). Like Leibniz and aligning with Alex Ebert’s work, we can see in Korzybski a critique of “the equal sign” (which perhaps is also a way to think of Gödel in the relation between correspondence and coherence; they at best are equivalent); Korzybski wrote that ‘[a]s words are not objects — and this expresses a structure fact — we see that the ‘is’ of identity is unconditionally false, and should be entirely abolished as such.’⁸ This poises a great challenge though, because ‘the general el structure of our language is such as to facilitate identification,’ which means all thought; in other words, to think and speak, we employ identification (and “an equal sign”) that are not possible.⁹ To think is to suggest an error, and yet we might be right (all maps are wrong but some are useful, to allude to George Box).
If “is” doesn’t exist (if there is no A/A or “A = A” in actuality only A/B or “A is like B”), we are left with ‘a descriptive language’ of the ‘functional, actional…’ (it is “processes” all the way down).¹⁰ And if that is what we must employ (which would have us accept Gödel), we need to employ it quickly. Why? Able to align with Hegel, Korzybski writes:
‘Someone may say, ‘Granted, but why fuss so much about it?’ My answer would be, ‘Identification is found in all known primitive peoples; in all known forms of ‘mental’ ills; and in the great majority of personal, national, and international maladjustments. It is important, therefore, to eliminate such a harmful factor from our prevailing systems.’ Certainly no one would care to contaminate his child with a dangerous germ, once it is known that the given factor is dangerous. Furthermore, the results of a complete elimination of identity are so far-reaching and beneficial for the daily life of everyone, and for science, that such ‘fussing’ is not only justified, but becomes one of the primary tasks before us.’¹¹
A/A with identification and “the equal sign” are everywhere, and Korzybski believes this leads to all kinds of ills for humanity (a people stuck in a symbolic or “way of thinking” will suffer immensely once they begin encountering in the world for which their symbolic cannot account). He writes that he attempts to ‘formulate[] a system, called non-aristotelian, which is based on the complete rejection of identity and its derivates,’ believing the consequences for not doing so will be mentally severe (which even if Korzybski doesn’t completely succeed in his effort for ‘a science of man,’ at least points to a need for Hegel and “A Modern Counter-Enlightenment”).¹² ¹³
Fair enough, but if we remove A/A (and with it the dream of addressing Global Pluralism through “the equal sign,” perhaps “the multiculturalism” which Dr. James Hunter critiques, as discussed in Belonging Again), we are left with A/B (and an ‘investigation of the mechanism of time-binding’), and that means we are dealing with maps — and maps bring with them their own problems, their own anxieties and “Pynchon Risks.”¹⁴ Zak Stein once wrote that ‘We must find ways / to undue the spellbinding trance / of the genocidal grammar / we are being forced to speak,’ and in terms of A/A, Korzybski would agree (we can think of A/B as needed ‘for ‘mental’ hygiene’), and yet to escape the “grammatical genocide” requires us to face a Pynchonian Abyss.¹⁵ ¹⁶Such is the unavoidable requirement of those, like Hegel, who realize that in a new logic like A/B we ‘must not disregard the human-natural-history structural fact of the inherent circularity of all physiological functions which in any form involve human ‘knowing.’ ’¹⁷ Otherwise, a new ‘theory of sanity’ will be out of reach; insanity, within A/A, our “rational” destiny — not that A/B guarantees anything (that could require “=”).¹⁸
II
In critiquing “is-ness,” Korzybski wasn’t arguing that “a thing wasn’t a thing” or that the world was an illusion: his concern was that we failed to see “things as networks” or realize that ‘language [was] a fundamental psychophysiological function of man’ (which is to say it required an odd use of maps as if they were territories that nevertheless couldn’t be, A/B).¹⁹ Aristotelian logic can leave out the reality that we understand and refer to things through things they are not, say “the thing-cat” through and with “the concept-of-cat,” which can be coupled with Hegel’s understanding that things are always “passing over into otherness.” Korzybski would likely agree, adding that if we didn’t take this reality seriously, our sanity would be at risk. In order to identify, we need a “layer” of language and concepts, all of which is situated in a “network” of world and “otherness,” that isn’t what we identify, and so to say, “A is A,” we require what isn’t A (B). “The blanket of language” we use over the world isn’t the world, and yet it is through that blanket that we can discuss the world as if it is “just” the world, risking sanity. This doesn’t mean Aristotle should be abandoned, but at the very least a sublation is needed (as Cadell Last has stressed in Logic for the Global Brain).
It is hard to imagine using language and not referring to relations, for ‘even objects […] could be considered as relations between the sub-microscopic events and the human nervous system’ (we don’t experience atoms, for example, just atoms through our senses, hence relation).²⁰ To discuss meaning must be to ‘consider[] a multiordinal term, as it applies to all levels of abstractions, and so has no general content,’ which is to say we are always referring to a “stack” of dimensions or “network” of relations that we might say “emerge” to a meaning that cannot be generalized beyond the specific case of interpentration.²¹ This means ‘structure, and so relation, becomes the only possible content of ‘knowledge’ and of meanings,’ and so, pointing to Gödel, every “thing” must be “incomplete” in of itself, for no thing or “set” can contain its relations.²² A complete “thing” or “set” would require there to be no relations external to it which it requires for its meaning, orientation, intelligibility, etc.; the moment a “thing” needs something it isn’t to be itself, Gödel and Korzybski smile.²³ And of course, every “thing” must, for as ‘[a] map is not the territory it represents,’ so “a thing is not the relations” (‘but, if correct, it has a similar structure to the territory, which accounts for its usefulness’ — which unfortunately might not be possible for “things” to have within and under the framework of A/A, risking insanity, hence Korzybski’s work).²⁴
Korzybski suggests that a world that doesn’t believe real work can be done except where an “object,” “thing,” and/or “goal” can be clearly identified (with perhaps “certainty” in a world where certainty is mostly impossible, not “fuzzy logic” like A/B, per se) is a world (perhaps like ours) that will struggle to develop and advance, making it likely it will end up stuck in a framework and so insane (‘[t]he use of the little word ‘is’ as an identity term applied to the objective level had paralyzed most effectively a great deal of hard and prolonged work’).²⁵ Korzybski strongly emphasizes the mental and psychological toil we suffer if we identify and situated ourselves in an inadequate symbolic, and he believes this is exactly what occurs if we overly identify with “is” (and ‘once we have acquired a bad habit [it] is very difficult to eliminate’).²⁶ A/B must be “fuzzy,” but reality itself is “fuzzy,” so a world that doesn’t allow “fuzzy thinking” is a world that cannot think itself.²⁷ ‘The structure of the actual world is such that it is impossible entirely to isolate an object,’ which means a “closed structure” or “non-fuzzy world” is impossible (and yet we can often think of a “structure” as precisely that which is closed, a testament to “the equal sign”).²⁸ ²⁹ Unfortunately, the very structure of our language itself trains and habituates us to think otherwise, setting up for insanity (infected by “is-ness,” our langauge ‘is elementalistic, and so singularly inadequate to express non-elementalistic notions’ — we must surrender ‘the organism-as-a-whole principle’).³⁰ ³¹ As Hegel understand, we are in need for a new logic, a new language — a new “science of subject.”
III
Might Kurt Gödel help free us from “is,” as championed by Korzybski? Yes, but only if we are ready for that freedom and aren’t driven by it into a Pynchon novel versus Childhood (as we’ll be explained). ‘Like Moliere’s Monsieur Jourdain, who spoke prose all his life without knowing it, mathematicians have been reasoning for at least two millennia without being aware of all the principles underlying what they were doing.’³² Bertrand Russell and Alfred Whitehead took up the challenge in their Principia Mathematica to undercover these underlying principles, and then Gödel spoke up. As a starting point for understanding Gödel’s project, as explained well through Gödel’s Proof by Ernest Nagel and James R. Newman, Gödel found that ‘elliptic geometry is consistent if Euclidean geometry is consistent […] The inescapable question is: Are the axioms of the Euclidean system itself consistent?’³³ And to cut to the chase, ‘ [Gödel] proved that it is impossible to establish the internal logical consistency of a very large class of deductive systems — number theory, for example — unless one adopts principles of reasoning so complex that their internal consistency is as open to doubt as that of the systems themselves.’³⁴ In other words, Gödel found that the project of Principia Mathematica was self-refuting in its self-reference: it was not possible to ground math in axioms and make it axiomatic in of itself. ‘[Gödel’s] grand final step is […] we are forced to conclude that if [Principia Mathematica] is consistent, its consistency cannot be established by any meta-mathematical reasoning that can be mirrored within [Principia Mathematica] itself!’³⁵
To connect this with Korzybski, we might say that if a map was complex enough to plausibly claim it was the territory, it would cease being a map and became the territory itself, rendering it useless and/or unusable. Furthermore, there would be no map, and so the moment we achieved an “equal sign” the map would vanish and the effort to make “the map = the territory” would fail. Instead, a “meta-mathematical reasoning” would be needed that avoided using an equal sign that nevertheless made something axiomatic, but this would only be possible by incorporating reason which could not be found in the consistency of the original postulation (hence, a relation), thus undermining the axiomatic effort. To bring in Leibniz, as discussed throughout O.G. Rose, we might say that proving “x was similar to y” would ultimately require making “x = y,” at which point y wouldn’t exist and in fact it would be the case that “x = x.” If it was somehow true that “x = y” and yet y didn’t equal x, this couldn’t be established within “x” or “x = y”: additional “meta-mathematical reasoning” would be necessary, which couldn’t be included in “x” or “x = y.” In other words, to ground something axiomatically, an equal sign would be required, but if x = y then x would be y, and so the statement “x = y” would be meaningless.
To be clear, ‘[t]his imposing result of Gödel’s analysis should not be misunderstood: it does not exclude a meta-mathematical proof of the consistency of [Principia Mathematica]. What it excludes is a proof of consistency that can be mirrored inside [Principia Mathematica].’³⁶ To emphasize, this isn’t to say that “math isn’t true” or something, but to say that math can never be fully verified within its own system. Math can in fact be verified as true through outside systems, which suggests math cannot be true thanks to its own self-justification but only external-justification (relational, as Korzybski emphasizes). Again, ‘[Gödel] showed that it is impossible to give a meta-mathematical proof of the consistency of a system comprehensive enough to contain the whole of arithmetic […] unless the proof itself employs rules of inference different in certain essential respects from the [rules] used in deriving theorems within the system.’³⁷ Hence, what is supposedly “axiomatic” relies on the consistency of other systems and rules, the consistency of which, to be such, relies itself on the consistency of others systems and rules, and so on — an eternal regression. This doesn’t mean those systems and rules are false, but that those systems and rules cannot be determined as true or false within those systems and rules (to allude to Derrida, the systems and rules must always “defer” their justification to other systems and rules, as words must always “defer” their meaning to other words — on and on). (There cannot be A/A, only A/B.)
Gödel found that a given system cannot “ground itself” as true or false, as a given word cannot “give itself” its own meaning (again, to allude to Derrida): something external and relational is necessary. To put it simply for how Gödel backed this claim, Gödel found that mathematics could contain within it a “Liar’s Paradox” (for the technical explanation of how he found this, please see Gödel’s On Formally Undecidable Propositions of Principia Mathematica and Related Systems). “The Liar’s Paradox” is as follows:
“True or false: this statement is false.”
If we answer this question with “true,” we say it is true that the statement is false, and if we say “false,” we say that the statement is true. Because of how the question is poised, neither answer will work: the question is inherently “indeterminable.” In finding this possibly contained within mathematics, Gödel found that where there is math, there is that which cannot be decided upon and hence no axiomatic consistency. Not because math is true or false, but because it cannot be its own validity or falsity (relation is needed). To put it another way: a complete system such as Principia Mathematica can contain as true the proposition that “this system isn’t axiomatic.” That’s the problem: the consistency of the model entails that which suggests the model isn’t consistent “as true” (the consistency can entail inconsistency as consistent, “(in)consistent,” if you will). As Nagel and Newman write on Gödel’s proof, ‘we have just shown that G is undecidable within [Principia Mathematica], so in particular G has no proof inside [Principia Mathematica]. But that, recall, is just what G asserts! So G asserts the truth.’³⁸ Hence, ‘if [Principia Mathematica] is consistent, it is incomplete’.³⁹ In its completeness, it is that which is incomplete: [Principia Mathematica] turns out to be not just incomplete, but essentially incomplete.’⁴⁰ (As Gödel put it himself: ‘The statement ‘c is inconsistent’ is not c-provable.’)⁴¹
Do note that it can be the case that the Liar’s Paradox is both “true and false” (A/B) but not “true or false” (A/A). In this way, mathematics can be justified if it is “two things at once,” which is “a logical contradiction” — or at least until we bring in another dimension (like time or “becoming”), and then this “logical contradiction” becomes more Hegelian and like a paradox that compels entities into “becoming,” higher dimensionality, relationality, and the like (a move from Algebra to Geometry, considering Descartes and Leibniz).⁴² If this is so, following Korzybski, we require thinking (Hegelian) contradiction precisely to develop “a science of sanity” and not go insane, and yet we have historically associated “contradiction” with “madness” — is human history a story of irony? Comical like Kafka?
IV
To help us better understand all this, let us consider a paragraph from Rebecca Goldstein’s Incompleteness on Kurt Gödel:
‘A formal system […] is an axiomatic system — with its primitive givens (the axioms), its rules of interference, and its proved theorems — except that instead of being constructed of meaningful symbols — such as terms referring to the number 0 or to the successor function — it is constructed entirely of meaningless signs, marks on paper whose only significance is defined in terms of the relations of each to one another as set forth by the rules.’⁴³
A formal system is entirely self-contained, meaning it only relates to itself (and hence doesn’t entail “relations” beyond itself and so in a sense at all). ‘While pre-purged axiomatic systems were understood as being about, say, numbers (arithmetic) or sets (set theory) or space (geometry), a formal system is an axiomatic system that is not, in itself, about anything.’⁴⁴ Why is that of interest and relevance? Because if a “formal theory” can be proven as possible “in theory,” then it might be possible in reality and that mathematics could be a formal theory; however, if “formal theories” aren’t even possible theoretically, the effort is doomed. Well, Kurt Gödel disproved the possibility of “formal theories” at all, finding within all possible formal theories an essential contradiction (which could be taken as evidence that we need to “tarry with contradiction,” alluding to Hegel, that every formal theory must entail contradiction to be itself, A/B).
‘A mathematics done formally is a mathematics purged of any ‘given’ truths,’ which again is to say completely self-contained, and that is not possible even in theory.⁴⁵ Despite seeming esoteric, why was this so impactful? As Rebecca Goldstein describes it, ‘[f]or much of the history of Western thought, at least since the time of Euclid, the axiomatized system was generally deemed to represent mathematics — and thus knowledge itself — in its most perfect form.’⁴⁶ Goldstein suggests we can see in this effort a ‘drive for limiting our intuitions,’ and we could say that ‘[a] formal system is an axiomatic system divested of all appeals to intuition’ (which again is impossible, but Hegel is also right that intuition is dangerous, hence our problem).⁴⁷ If achieving this limiting was the drive of much Western thought, Gödel in a sense “ended history” (suggesting Heidegger) — but if that history was leading to insanity (in denying a “science of sanity” which required A/B), Gödel in light of Korzybski (and Hegel) did us a great service (like Viril did for Dante…). Gödel helped end the quest for “autonomous rationality” and “totalization” (A/A), as often critiqued in O.G. Rose, which also suggests he helped us end the neurotic and problematic reign of the Big Other (Lacan and Korzybski can be thought together). Or at least Gödel could have if we didn’t at scale seemingly interpret him as disproving the possibility of all truth — a terrible mistake that doesn’t help us toward “a non-aristotelian science of sanity” but poisonous nihilism.
Anyway, according to Gödel, proving the axiomatic consistency of mathematics ‘cannot be established unless rules of inference are used that cannot be represented within the calculus, so that, in proving the [consistency], rules must be employed whose own consistency may be as questionable as the consistency of the formal calculus itself.’48 This conclusion (which I believe applies to all thought and language) can be determined using the ‘remarkably ingenious form of mapping’ Gödel used to establish many of his major conclusions (“A ‘Gödel Numbering,” which might describe all maps).⁴⁹ What Gödel asks is:
‘what makes the meaningless symbol ‘0’ merit the interpretation of ‘zero,’ and the meaningless symbol ‘+’ merit the interpretation of ‘plus’ — rather than say, vice versa? And what would make us feel convinced that the tilde ‘~’, merely a squiggly line that obeys certain formal rules, genuinely represents the abstract concept ‘not’?’⁵⁰
Similarly, what makes a given “map” come to represent a certain “territory?” It’s a longer argument, but ultimately Gödel proves this cannot be the result of a “formal system” but inevitably involves something external like intuition (‘for every consistent class c, w is not c-provable, [and so] there will always be propositions which are undecidable (from c)’).⁵¹ Notions can be “grounded” in systems, but those systems themselves cannot be “grounded” in themselves (and so it goes with all language and thought). If everyone on the planet started to use the word “cat” to signify “the-phenomenon-of-a-tree,” the word “cat” would function no different than the word “tree,” and we would have no reason to think we speak falsely when we refer to a tree as a “cat.” Everything is “always already” situated, which means “the equal sign” is “always already” impossible (ever-deferred, alluding to Derrida, and as Deleuze wrote: ‘the ‘ ‘there is’ […] remains perfectly indeterminate’).⁵² If we read then that “a tree is signified by the word ‘tree,’ ” we would in fact think the writer or speaker erred: everyone knows that a tree is a “cat” (the consistency of the system itself would have “tree = phenomenon-of-cat” be part of its true consistency, even though to us, that consistency would be false if it entailed this point). So it can be said about all of language: if the word “boy” was used for the word “and,” “cow” to signify “the-phenomenon-of-person,” etc. — no matter how language and thought might be rearranged and scrambled up, if consistent (in its “scrambled” state), the system would contain no essential inconsistencies and be true relative to itself, even though to us, the system could be nonsense.⁵³ This in mind, it might be possible to head toward insanity while maintaining a consistency that suggested sanity, as might be occurring to us as we operate in consistent A/A increasingly toward A/B due to technology, Global Pluralism…suggested by the spread of “philosophical melancholia,” alluding to Hume and Berger.
If equality is impossible (only equivalence), then we cannot entirely erase “nonrationality” from our world: we must always think beyond consistency. Gödel found ‘the interpretation of a symbol hinges on how the symbol behaves inside theorems of [Principle Mathmatica] (and this, in turn, hinges on the axioms and the rules of inference of [Principle Mathmatica]).’⁵⁴ The same goes with thinking and perception: the system of “how we think about the world” hinges on thoughts not inconsistently shifting into different thoughts (of “signifier of A” not randomly becoming a “signifier of B,” for example); likewise, the system of “how we perceive the world” hinges upon what we perceive not “shape-shifting” into something different, of “signified A” not randomly becoming “signified B.” And yet how that consistency is justified cannot be through a formal system: something “other” and “outside” is always needed).
Overall, we might say that ‘Gödel’s conclusion […] has something to say about the feasibility (or lack therefore) of eliminating all intuitions from mathematics’ (or “nonrationality” from “rationality” in general, alluding to O.G. Rose), a move which ‘might also have a thing or two to say about the actual existence of mathematical objects, like numbers and sets.’⁵⁵ After this point, Goldstein notes that:
‘the adequacy of formal systems — their consistency and their completeness — is linked with the question of the ultimate eliminability of intuitions, which is linked with the question of the ultimate eliminability of a mathematical reality, which is the defining question of mathematical realism, or Platonism.’⁵⁶
Ah, and Gödel was a Platonist, which isn’t eliminated by his work but actually defended. To use my language, Gödel defends a distinction between “the true and the rational” and helps make it clear that no “formal system” (in philosophy, economics, mathematics, etc.) can ever avoid needing to incorporate “nonrationality” (or that “outside” it — “other,” A/B). For Korzybski, that means we are always dealing with relations and “non-identification,” which means not only that no map is the territory, but also that no map can be meaningfully written or constructed without reference to a territory (it is not possible even in theory for a map to be constructed that was “a perfect map” without reference to a territory outside of it, for even if it was “perfect,” we could not meaningfully identify such from within the consistency of the map itself, rendering its “perfection” indeterminable — “indeterminacy” is the best for which we could hope.
‘[Gödel] showed that it is impossible to give a meta-mathematical proof of the consistency of a system comprehensive enough to contain the whole of arithmetic […] unless the proof itself employs rules of inference different in certain essential respects from the [rules] used in deriving theorems within the system.’⁵⁷ So it goes with thinking (and language by extension), and it is perception that is “the system outside the system” that supplies ‘rules of inference different in certain essential respects’ to the rules of thinking. And so it goes vice-versa: thinking supplies to perception ‘rules of inference different in certain essential respects’ from the rules of perception. Thinking keeps it the case that the word “cat” signifies the-phenomenon-of- cat and that “ ‘cat’ = ‘cat,’ ” while perception keeps it the case that “ ‘the-phenomenon-of-cat’ exists as ‘the-phenomenon-of-cat’ ” (is known/perceived) and that “ ‘the-phenomenon-of-cat’ stays ‘the-phenomenon-of-cat’ ” (rather than us see a whale one time and a dog the next whenever we look at a cat — phenomena don’t shape-shift). Both thinking and perception, unto themselves, maintain a consistency that justifies the other system: by a cat staying as a cat and “cat” staying as “cat,” “cat” can successfully “point to” cat and hence legitimize thought/language, as cat can “point to” “cat” and hence legitimize perception. And when they justify one another, thinking and perception accurately orientate us in the world, even though they cannot fully justify themselves (as mathematics is invaluable even though un-axiomatic).
Even if consistent, thinking cannot “ground itself”: thinking “grounds” itself in reality “as true” through perceived phenomenon (which thoughts can be “toward”). The thought “cat” “grounds itself” in the world through and/or “thanks to” the perceived “phenomenon-of-cat,” as the number “2” “grounds itself” through the perceived multiplicity of phenomena. Like thought, perception too cannot “ground itself”: perception “grounds itself” in reality because thought provides for perception ways by which to understand reality meaningfully (and failure to realize this risks sanity). To perceive a cat without the word “cat” is to perceive that which we cannot know “as a thing” to know that what us perceive is “a thing” as opposed to (a) “no-thing,” hence giving us reason to believe we actually do perceive (“what is”) (well). Overall, this means thinking and perceiving can justify one another, but they cannot fully justify themselves. What Gödel found about mathematics applies to the ways by which we know the world. Thinking and perception require one another to be (meaningfully) “grounded,” but that means neither is self-justifying (intelligibility is fundamentally dialectical and A/B).
Without thought, a given cat cannot be “pulled out from” its place in the world as “a thing” independent of that word: without thought, “all is one” (we might say), and though it is true that “all is one” in perception, this truth is meaningless without thought (and so unknowable as a reality and/or truth, which is perceived).⁵⁸ At the same time, what thought “thinks” about perception isn’t necessarily “what is the case,” even though “what is perceived” requires thought to be meaningful.⁵⁹ A fallible act of thinking is needed for intelligibility that at the same time runs the risk of helping us believe in the “non-relation” and “identification” Korzybski warns against. Oddly, if an act of “pulling out” is needed for intelligibility and yet Korzybski is right, this would mean that what puts sanity at risk is precisely thinking itself. Thinking naturally identifies, and identification risks sanity (comical). Thinking threatens sanity.
In showing that A/A and “formal systems” are not even theoretically possible, Gödel seems to have doomed us to madness and relativism, but he has actually made possible a realization of A/B as Absolute and hence “a science of sanity” that Korzybski believed we desperately needed. We seem to have often thought that sanity was a matter of removing paradox and contradiction, but Korzybski helps us see that contradiction is an invitation to consider higher and more complex dimensionality, mainly relations (and suggests we would see this need if we really took mathematics seriously, for in doing this we might realize Gödel). Gödel and Korzybski together suggest a continuation of Hegel’s project in the Science of Logic, and a quotation that might frame Korzybski’s work:
‘In dealing with ourselves and the world around us, we must take into account the structural fact that everything in this world is strictly interrelated with everything else, and so we must make efforts to discard primitive el terms, which imply structurally a non-existing isolation.’⁶⁰
Gödel helps justify this effort (this “purging” of the mind virus by Korzybski of “is-ness” wherever it lurks), and he doesn’t keep us from but opens the way to “a science of sanity” (based on “confidence” instead of “certainty,” as discussed in The Conflict of Mind with Karl Popper).⁶¹ Everything must relate; no “formal system” (or “self-forming system”) is possible. Korzybski repeatedly emphasizes ‘the ‘organism-as-a-whole’ principle,’ which is anti-reductionist (which perhaps is “the science of sanity,” as many on the Liminal Web seem to realize), and we might think of this as “the map-territory relation,” as justified by “the incompleteness theorem.”⁶² Like Hegel’s contradiction, far from making us insane, Gödel is a key to sanity in a world that we must think about through thinking which constantly tempts us with and habituates us to “insane identification.” The “groundlessness” Gödel presents us with is only a terror to those stuck in the symbolic of A/A without A/B, hence why Gödel compliments Korzybski and Hegel. Korzybski eliminates all efforts of identification as acts of madness, whether in science, philosophical, economics, politics, selfhood…as we should expect given Gödel (‘[t]he young student [who] found a proof for a theorem, the first incompleteness theorem, that had the rigor of mathematics and the reach of philosophy’), as we can hope in given Hegel (whose role in this we will elaborate on in The Absolute Choice).⁶³
.
.
.
Notes
¹Korzybski, Alfred. Science and Sanity. Fifth Edition (Second Printing). Brooklyn, NY: Institute of General Semantics, 2000: 247.
²In Chapter 18, Korzybski discusses quantum theories, and I’m curious what Korzybski might say to making “Non-Locality fundamental” as does Stuart Kauffman, which may or may not be reconcilable with Lee Smolin’s effort to make time fundamental. For Non-Locality to be fundamental seems to require something “like time” or Bergson’s Duration, but I’m not sure. As Zizek writes that ‘the claim that in quantum measurement the observed phenomena and the measurement itself are part of some globally interconnected reality remains a philosophical intervention, a revenge of classical ontology on quantum physics.’⁰¹ In other words, is only philosophy capable of approaching the Duration and/or Nonlocality we might now require?
⁰¹Žižek, Slavoj. Freedom: A Disease Without Cure. New York, NY: Bloomsbury Academic, 2023: 111.
³We should note that Korzybski argues ‘[f]rom the point of view of general semantics [that] mathematics […] must be considered as a language,’ so Korzybski is possibly suggesting that a “pure structure” of language is “like” the world (Korzybski does not think mathematics is ‘co-extensive with all language,’ so there are nuances to be considered).⁰¹ ⁰² Korzybski writes that ‘[a] semantic definition of mathematics may run somehow as follows: Mathematics consists of limited linguistic schemes of multiordinal relations capable of exact treatment at a given date.’⁰³ What does this mean? Well, ultimately it suggests to me that mathematics is Geometric, which suggests ‘that the content of all knowledge is structural, and so ultimately relational.’⁰⁴ Where mathematics goes, so might go the world, for mathematics has a claim to be “the most fundamental of all possible ways/languages of knowing,” and if we necessarily find relations even in mathematics, then there is reason to think we will find relations everywhere else. And this poises a problem, which might bring us to Gödel (in light of Leibniz, as discussed throughout O.G. Rose), for if the axiomatic is only possible in the Algebraic (where the “equal sign” is possible, “A = B”), but the Algebraic can’t include relations as fundamental and real without becoming Geometric (where only “equivalence” is possible, “A ≡ B”), then achieving the axiomatic is impossible. This doesn’t mean “truth” is impossible, only “certainty” and “nonconditional and/or non-relational truth” (we must be Geometric, which invites Complexity, Emergence, perhaps even Non-Locality…).
Perhaps we could say that a reason why “self-reference is always incomplete” (and we are always dealing with self-reference) is precisely because the relation itself is real through which the self-reference occurs, which could itself cannot be included in the self-reference; thus, (in)completeness. Furthermore, if relations are real, then certainty is impossible as is any axiomatic grounding, because we could say that we are always dealing with a “three body problem” (Point A, Point B, and the Relation A-B), which makes exact calculation impossible. ‘Psycho-logically, the emphasis [must be] on difference.’⁰⁵
⁰¹Korzybski, Alfred. Science and Sanity. Fifth Edition (Second Printing). Brooklyn, NY: Institute of General Semantics, 2000: 250.
⁰²Korzybski, Alfred. Science and Sanity. Fifth Edition (Second Printing). Brooklyn, NY: Institute of General Semantics, 2000: 251.
⁰³Korzybski, Alfred. Science and Sanity. Fifth Edition (Second Printing). Brooklyn, NY: Institute of General Semantics, 2000: 253.
⁰⁴However, as a critical note from Korzybski: ‘[I]f we enquire into the meaning of the word ‘exact,’ we find from experience that this meaning is not constant, but that it varies with the date, and so only a statement ‘exact at a given date’ can have a definite meaning.’⁰⁰¹ Well, if time is somehow fundamental, then this very quandary is fundamental, which might suggest a temporal way that Godel is fundamental (for “self-reference” is only valid at a given date, which is fundamentally never constant).
⁰⁰¹Korzybski, Alfred. Science and Sanity. Fifth Edition (Second Printing). Brooklyn, NY: Institute of General Semantics, 2000: 253.
⁰⁵Korzybski, Alfred. Science and Sanity. Fifth Edition (Second Printing). Brooklyn, NY: Institute of General Semantics, 2000: 253.
⁰⁶Korzybski, Alfred. Science and Sanity. Fifth Edition (Second Printing). Brooklyn, NY: Institute of General Semantics, 2000: 254.
⁴Furthermore, Korzybski believed there were limitations to mathematics, as there were with Aristotelian logic, and yet nevertheless mathematics and logic were still necessary in being “like” the structure of the world (we might say a “sublation” was needed, suggesting a need to transition into Hegel). Where did this leave us? The need not just for a mathematical or logical advancement, but a symbolic and semantic evolution as well, for otherwise we would just advance “within” the semantics of math and logic already present (which wouldn’t be enough and could lead to self-effacement), and furthermore with the wrong symbolic humans can only think but so much (if we were still using Roman Numerals, for example, we couldn’t do modern mathematics, to use an example from Korzybski). Does this suggest Korzybski understood a need for us to develop “a science of subject” like Hegel and Cadell Last discuss, a new psychoanalysis like what arises in Lacan, and perhaps ultimately a new “narrative?” Maybe, and if there is something about “metaphysics” and “symbolics” which are connected, then Korzybski is perhaps suggesting to us that we require a new “metaphysics” today or else we will go mad. “A Metaphysics of Relations,” as popular on the Liminal Web? Perhaps, but relations are Real.
⁵In fact, the very consistency of mathematics can be precisely why correspondence cannot be determined, which makes sense if reality is “open” or perhaps if Nonlocality is fundamental.
⁶Korzybski, Alfred. Science and Sanity. Fifth Edition (Second Printing). Brooklyn, NY: Institute of General Semantics, 2000: 259.
⁷Korzybski, Alfred. Science and Sanity. Fifth Edition (Second Printing). Brooklyn, NY: Institute of General Semantics, 2000: 260.
⁸Korzybski, Alfred. Science and Sanity. Fifth Edition (Second Printing). Brooklyn, NY: Institute of General Semantics, 2000: 263.
⁹Korzybski, Alfred. Science and Sanity. Fifth Edition (Second Printing). Brooklyn, NY: Institute of General Semantics, 2000: 263.
¹⁰Korzybski, Alfred. Science and Sanity. Fifth Edition (Second Printing). Brooklyn, NY: Institute of General Semantics, 2000: 264.
¹¹Korzybski, Alfred. Science and Sanity. Fifth Edition (Second Printing). Brooklyn, NY: Institute of General Semantics, 2000: xcvi-xcvii.
¹²Korzybski, Alfred. Science and Sanity. Fifth Edition (Second Printing). Brooklyn, NY: Institute of General Semantics, 2000: xcvii.
¹³Korzybski, Alfred. Science and Sanity. Fifth Edition (Second Printing). Brooklyn, NY: Institute of General Semantics, 2000: 7.
¹⁴Korzybski, Alfred. Science and Sanity. Fifth Edition (Second Printing). Brooklyn, NY: Institute of General Semantics, 2000: 7.
¹⁵Korzybski, Alfred. Science and Sanity. Fifth Edition (Second Printing). Brooklyn, NY: Institute of General Semantics, 2000: 9.
¹⁶Korzybski though is confident that it is undeniable we must take this Pynchon Risk, writing: ‘The present non-aristotelian system is based on fundamental negative premises; namely, the complete denial of ’identity,’ which denial cannot be denied without imposing the burden of impossible proof on the person who denies the denial’ (mainly, producing an object which is what signifies it).⁰¹
⁰¹Korzybski, Alfred. Science and Sanity. Fifth Edition (Second Printing). Brooklyn, NY: Institute of General Semantics, 2000: 10.
¹⁷Korzybski, Alfred. Science and Sanity. Fifth Edition (Second Printing). Brooklyn, NY: Institute of General Semantics, 2000: 12.
¹⁸Korzybski, Alfred. Science and Sanity. Fifth Edition (Second Printing). Brooklyn, NY: Institute of General Semantics, 2000: 14.
¹⁹Korzybski, Alfred. Science and Sanity. Fifth Edition (Second Printing). Brooklyn, NY: Institute of General Semantics, 2000: 18.
²⁰Korzybski, Alfred. Science and Sanity. Fifth Edition (Second Printing). Brooklyn, NY: Institute of General Semantics, 2000: 20.
²¹Korzybski, Alfred. Science and Sanity. Fifth Edition (Second Printing). Brooklyn, NY: Institute of General Semantics, 2000: 22.
²²Korzybski, Alfred. Science and Sanity. Fifth Edition (Second Printing). Brooklyn, NY: Institute of General Semantics, 2000: 23.
²³Korzybski writes: ‘[T]he inherent structure of the world, life, and the human nervous systems, [suggest why] human relations are so enormously complex and difficult […] In mathematics we find the only model in which we can study the invariance of relations under transformations, and hence the need for future psycho-logicians to study mathematics.’⁰¹ In this, it’s as if Korzybski wants us to study mathematics to study the kind of being which can think mathematics (where perhaps at the point of “total saturation,” alluding to Ebert, lacking any subjectivity, we still see subjectivity and relations, thus providing strong proof for the essentialness of relations). Its almost phenomenological, where from experience we inquire into the “conditions of possibility” necessary for such an experience to occur; likewise, from the existence of mathematics, Korzybski would have us ask, “What kinds of structures and conditions must be present in reality and humanity for mathematics to be possible?” To put this another way, “What are the conditions of reality like so that mathematics, which tries to move beyond subjectivity, still entail it and relations?”
Korzybski discuses ‘mathematics considered as a form of human behavior,’ and so he is not interested in mathematics to avoid subjectivity but precisely to understand it (it is useful for “a science of subject, oddly).⁰² ‘We must realize that structure, and structure alone, is the only link between languages and the empirical world,’ and it is in mathematics that this structure can be best approached.⁰³ It’s admittedly an odd approach (as perhaps any and every “science of subject” must be), but Korzybski believes that understanding reality is not about avoiding subjectivity but on inquiring into what kind of being humans must be to be capable of mathematics (an inquiry that might also help us move beyond asking if math is created or realized: even if its digits are created, its structure might be realized, but that structure might not be “in” mathematics itself).
A way to consider Korzybski’s project: ‘As words are not the objects which they represent, structure, and structure alone, becomes the only link which connects our verbal processes with the empirical data. To achieve adjustment and sanity and the conditions which follow from them, we must study structural characteristics of this world first, and, then only, build language of similar structure, instead of habitually ascribing to the world the primitive structure of our language’ (emphasis added).⁰⁴ Korzybski believes we let our language shape the world versus the world shape our language, and as a result we suffer psychologically. His aim is to aid us and help us stop making this mistake.
Doesn’t Gödel counter Korzybski though, seeing as Korzybski writes that ‘the structure of human knowledge precludes any serious study of ‘mental’ problems without a thorough mathematical training’ — doesn’t that sound like a notion Gödel would threaten?⁰⁵ It sounds that way, but for me Korzybski’s belief is that we need to study mathematics precisely to deeply “get’ what Gödel is saying. ‘Considered as a language, mathematics appears as a language of the highest perfection, but at its lowest development,’ Korzybski writes. ‘Perfect, because the structure of mathematics makes it possible to be so (all characteristics, and no physical content), and because it is a language of relations which are also found in this world.’⁰⁶ In the language of mathematics, unlike other languages, it is much more difficult to avoid what Gödel is discussing,
⁰¹Korzybski, Alfred. Science and Sanity. Fifth Edition (Second Printing). Brooklyn, NY: Institute of General Semantics, 2000: 23.
⁰²Korzybski, Alfred. Science and Sanity. Fifth Edition (Second Printing). Brooklyn, NY: Institute of General Semantics, 2000: 50.
⁰³Korzybski, Alfred. Science and Sanity. Fifth Edition (Second Printing). Brooklyn, NY: Institute of General Semantics, 2000: 50.
⁰⁴Korzybski, Alfred. Science and Sanity. Fifth Edition (Second Printing). Brooklyn, NY: Institute of General Semantics, 2000: 59.
⁰⁵Korzybski, Alfred. Science and Sanity. Fifth Edition (Second Printing). Brooklyn, NY: Institute of General Semantics, 2000: 74.
⁰⁶Korzybski, Alfred. Science and Sanity. Fifth Edition (Second Printing). Brooklyn, NY: Institute of General Semantics, 2000: 69.
²⁴Korzybski, Alfred. Science and Sanity. Fifth Edition (Second Printing). Brooklyn, NY: Institute of General Semantics, 2000: 58.
²⁵Korzybski, Alfred. Science and Sanity. Fifth Edition (Second Printing). Brooklyn, NY: Institute of General Semantics, 2000: 35.
²⁶Korzybski, Alfred. Science and Sanity. Fifth Edition (Second Printing). Brooklyn, NY: Institute of General Semantics, 2000: 46.
²⁷‘The subject of this work,’ Korzybski tells us, ‘is ultimately ‘speaking about speaking.’ As all human institutions depend upon speaking — even the World War could not have been staged without speaking — and as all science is ultimately verbal, such an analysis must cover a large field.’⁰¹ Is it possible to imagine such a topic not being “fuzzy” or “meta?” I don’t believe so, and yet if Korzybski is right the only way to avoid madness is through “fuzzy logic,” which we might now allow ourselves to think, stuck under the tyranny of “is-ness.”
‘A word is not the object it represents; and languages exhibit also this peculiar self-reflexiveness [which] introduces serious complexities […] The disregard of these complexities is tragically disastrous in daily life and science.’⁰² Indeed, but we suffer disaster profoundly, for we avoid “fuzzy logic” — a tremendous accomplishment, yes?
⁰¹Korzybski, Alfred. Science and Sanity. Fifth Edition (Second Printing). Brooklyn, NY: Institute of General Semantics, 2000: 46.
⁰²Korzybski, Alfred. Science and Sanity. Fifth Edition (Second Printing). Brooklyn, NY: Institute of General Semantics, 2000: 58.
²⁸Korzybski, Alfred. Science and Sanity. Fifth Edition (Second Printing). Brooklyn, NY: Institute of General Semantics, 2000: 57.
²⁹Structures in the world are relational, and in language being clearly relational (arguably “the purest language” for Korzybski), studying language could uniquely help us arrive at “a science of man” (A/B). ‘Our only possible procedure in advancing our knowledge is to match our verbal structures, often called theories, with empirical structures, and see if our verbal predictions are fulfilled empirically or not, thus indicating that the two structures are either similar or dissimilar’ — or so Korzybski claims, and for him this isn’t simply done by matching particular formulas and conclusions of mathematics with the world but in matching structures.⁰¹ Mathematics is relational like the world, and so it is by observing relations in the world that we can advance our knowledge through theories. We might say that for Korzybski we’ve paid too much attention to the definitions of words, and not enough attention to how words structurally require relations (meaning we haven’t considered ideas-as-relations with experience-as-relations, contributing to insanity).
⁰¹Korzybski, Alfred. Science and Sanity. Fifth Edition (Second Printing). Brooklyn, NY: Institute of General Semantics, 2000: 63.
³⁰Korzybski, Alfred. Science and Sanity. Fifth Edition (Second Printing). Brooklyn, NY: Institute of General Semantics, 2000: 64.
³¹Korzybski, Alfred. Science and Sanity. Fifth Edition (Second Printing). Brooklyn, NY: Institute of General Semantics, 2000: 65.
³²Gödel’s Proof by Ernest Nagel and James R. Newman. New York University Press, 2001: 39.
³³Gödel’s Proof by Ernest Nagel and James R. Newman. New York University Press, 2001: 17.
³⁴Gödel’s Proof by Ernest Nagel and James R. Newman. New York University Press, 2001: 5.
³⁵Gödel’s Proof by Ernest Nagel and James R. Newman. New York University Press, 2001: 106–107.
³⁶Gödel’s Proof by Ernest Nagel and James R. Newman. New York University Press, 2001: 107.
³⁷Gödel’s Proof by Ernest Nagel and James R. Newman. New York University Press, 2001: 58.
³⁸Gödel’s Proof by Ernest Nagel and James R. Newman. New York University Press, 2001: 102.
³⁹Gödel’s Proof by Ernest Nagel and James R. Newman. New York University Press, 2001: 104.
⁴⁰Gödel’s Proof by Ernest Nagel and James R. Newman. New York University Press, 2001: 103.
⁴¹Gödel, Kurt. On Formally Undecidable Propositions of Principia Mathematica and Related Systems, Dover Publications, 1992: 72.
⁴²To justify itself, mathematics requires contradiction, but contradiction is that which cannot be true without bringing in another dimension, relation, scope, etc. (contradiction forces an effacement or sublation of consistency). As explored in “A Is A” by O.G. Rose, contradiction is part of being but with non-contradiction. “A thing” is a “(non)contradiction,” if you will, as a complete mathematical system is “(in)consistent.” If I say, “A cat is a cat,” I say, “A cat isn’t atoms,” and yet a cat is made out of atoms, and so is atoms at the same time it is a cat. Hence, a cat is “that which isn’t a cat” while it simultaneously that which “is a cat” (“A/(A-isn’t-A)” is “A/(A-isn’t-A)”), and we can know what a cat is relative and thanks to that which “a cat is without” (“without B”). And all this brings us to inquire into how what Gödel found about mathematics applies to all of thought, which will equipped us to explore Korzybski, and then to tackle how both thinkers can help us from being “thoughtless” within ideology.
⁴³Goldstein, Rebecca. Incompleteness. New York, NY: W.W. Norton & Company, 2005: 131.
⁴⁴Goldstein, Rebecca. Incompleteness. New York, NY: W.W. Norton & Company, 2005: 131.
⁴⁵Goldstein, Rebecca. Incompleteness. New York, NY: W.W. Norton & Company, 2005: 133.
⁴⁶Goldstein, Rebecca. Incompleteness. New York, NY: W.W. Norton & Company, 2005: 128.
⁴⁷Goldstein, Rebecca. Incompleteness. New York, NY: W.W. Norton & Company, 2005: 129.
⁴⁸Gödel’s Proof by Ernest Nagel and James R. Newman. New York University Press, 2001: 67.
⁴⁹Gödel’s Proof by Ernest Nagel and James R. Newman. New York University Press, 2001: 67.
⁵⁰Gödel’s Proof by Ernest Nagel and James R. Newman. New York University Press, 2001: 71.
⁵¹Gödel, Kurt. On Formally Undecidable Propositions of Principia Mathematica and Related Systems, Dover Publications, 1992: 71–72.
⁵²Deleuze, Giles. Difference and Repetition. Translated by Paul Patton. New York, NY: Columbia University Press, 1994: 119.
⁵³If “cat was used to refer to the-phenomenon-of-tree,” it would be true that “ ‘cat’ = tree” (perhaps risking sanity). If everyone thought “Russia” signified China and vice-versa, it would be false to say, “Napoleon invaded Russia,” and true to say, “Napoleon invaded China.” If I were to look at a sunset and think “that sunset is ugly,” if I never encountered the idea of beauty, I would have little reason to think I thought wrongly (and in fact perhaps I thought rightly, using “ugly” to signify beauty). If tomorrow everyone on the planet forgot everything they knew and all traces and evidence of civilization as we knew it vanished, the people could be “objectively right,” relative to themselves, to believe they stood at the beginning of history. If everyone on the planet was taught “8” instead of “A,” then it would be correct to sing “8, B, C, D, E…,” and to spell “Anna” as “8nna.” If I was to read a book and misread the word “blonde” as “brown” in regard to the protagonist’s hair-color, as long as no description forces me to reexamine my mental image, I would form a movie in my head of a protagonist with brown hair, and relative to that movie, all evidence would lead to believe that I am correct to envision my protagonist this way. The science-fiction writer knows that whatever is consistent about his or her world is true, and so it goes with our world as well (authored or not). Being is (in)consistent. (“ ‘A/(A-isn’t-A)’ is ‘A/(A-isn’t-A)’ (without B)”).
⁵⁴Gödel’s Proof by Ernest Nagel and James R. Newman. New York University Press, 2001: 72.
⁵⁵Goldstein, Rebecca. Incompleteness. New York, NY: W.W. Norton & Company, 2005: 134–135.
⁵⁶Goldstein, Rebecca. Incompleteness. New York, NY: W.W. Norton & Company, 2005: 135.
⁵⁷Gödel’s Proof by Ernest Nagel and James R. Newman. New York University Press, 2001: 58.
⁵⁸On the other hand, discussed in II.2, without thought, we are risk of the “oneness” of dream-equality. “The oneness of identification” or “oneness of dream-equality” — is this what we’re ever-oscillating between, waiting for sublation?
⁵⁹To allude to “Ironically” by O.G. Rose, if we decide two things are separate because they don’t touch, we decide that “existence” isn’t a valid “unifier” compared to say “physicality” (touching), a decision which entails thought that we have no “grounding” in perception to determine. Perception requires thought to be meaningful, but what is thought about perception cannot necessarily be found in perception, as what is perceived cannot always be found in thought (like numbers).
⁶⁰Korzybski, Alfred. Science and Sanity. Fifth Edition (Second Printing). Brooklyn, NY: Institute of General Semantics, 2000: 108.
⁶¹David Hume argued that no matter how many times we see a ball drop when released in the air, we can never say for sure that “the ball will fall every time”; hence, we can never establish “natural law,” only “constant conjunction.” Hume made it clear that verification (which we can associate with “identification” in Korzybski) was impossible, and it wasn’t until Karl Popper that humanity was in a way “shielded” from this revelation. Popper argued that the basis for establishing something “as true” wasn’t based so much on verification as it was on falsification, with a given premise being true primarily because it hadn’t been falsified versus confirmed. Falsification entails verification in a sense, but verification doesn’t necessarily entail falsification. By changing the focus to falsification, Popper established a way by which verification could establish itself as true, despite Hume’s profound objection.
Likewise, we can know what we think and perceive are “there” (“in some way”) because they aren’t falsified, even though we lack the capacity to “ground” or verify what we think and perceive, and please note that “falsification” would better align with “equivalence” that Korzybski suggests we need for sanity. Until a tree turns into a dog, we have no reason to think that our perception of a tree isn’t “actual enough.” Perhaps the whole world is a simulation inside of a computer, but until we experience that in reality which falsifies the claim “reality isn’t a simulation,” we have no reason to believe “reality is a simulation,” even if it is somehow. Likewise, we have no reason to believe “how I perceive and think about reality isn’t reliable enough,” until that which falsifies the claim occurs. Until then, asking questions like, “Do I think what actually is true?” and/or “Do I perceive the actual world?” are meaningless.⁰⁰¹ ⁰⁰²
Popper gives us a tool by which we can live our lives with a sense of confidence, but does it follow that what isn’t falsified is axiomatic? No, but what isn’t falsified is that which we can live as if it is axiomatic and objective (even though perhaps it is not, though perhaps it is). But the point still holds: we cannot say what we think and perceive are axiomatically such as we think and perceive of them: we can only say, “It is as if x is axiomatically x” (in experience). Gödel found the same about mathematics: we can only say, “It is as if ‘2 = 2’ is axiomatic.” Even when it comes to what hasn’t been falsified, there is uncertainty: the best we can achieve is an “un-falsified/uncertain premise,” per se. Even what we perceive cannot be made axiomatic, but considering Popper, we have grounds to believe x = y (in perception) (x perhaps being “tree” and y being “the definition of tree” and/or “how we perceive tree”) until falsified (as we have reason to believe word “x” works for x until the word ceases to accurately signify x). Perhaps we can achieve “x is y” (now), but not “x is y” (always). For both what we perceive and think, the best we can achieve is an “as if,” not an “is,” per se, which for Korzybski is a slight difference upon which “a science of sanity” can hinge.
The longer something isn’t falsified, the more confidence we can have over what isn’t falsified. The longer a tree doesn’t turn into a dog, the more we can feel confident that trees don’t turn into dogs. The certainty formulates naturally: it happens without us even willing it, more subconscious than conscious.⁰⁰³ And the confidence emerges as a result of the “consistency” of (the) thought and/or perception, in the same way our certainty about math stems from its consistency. This is why it was so stunning when Gödel found that the consistency of mathematics essentially included its inability to be axiomatic, as it is probably troubling to accept that uncertainty is essentially part of certainty (the not-falsified).⁰⁰⁴
After Gödel, at best we might say things are “upheld” from the side like a web. The more consistent the system and the longer that consistency remains consistent, the more confidence we can be about it. People through schooling, experimentation, trial and error…come to be confident that the word “cat” signifies the-phenomenon-cat (relative to their given language, though not relative to language itself), for the word “cat” consistently and successfully refers to that phenomenon (as we are prone to create a “natural law” of a consistent event, say of a ball falling from a hand). The certainty comes from the experiences, not from anything “under” the experiences, and furthermore we are confident about that which, if not true, collapses the system. The more vital the fact, the more “certain” (from anxiety) we can be about it, not because it is necessarily any more true, but because, if it isn’t true, everything falls apart. To use the comparison in “Certainty Deterrence and Ideology Preservation” by O.G. Rose, as during the Cold War nukes were used to “deter” people from using them lest the whole world end, so we are “certain” about that which if not true, causes our whole worldview to collapse. If we aren’t certain that trees don’t turn into dogs, we must call into question everything we perceive (for beliefs are always “situated” and “networked,” as Korzybski understood), and if nothing is stable, nothing we think or believe can withstand being shaken.
What is our point for elaborating on all this, considering Popper, Korzybski, and Gödel together? Well, it is to help us understand the means by which “consistency” is established for us (as distinct from “correspondence”), which is not through proving. In my opinion, consistency isn’t really “proved” so much as it just “is,” meaning we don’t experience a lack of consistency (it isn’t falsified), and thus gain reason to be confident in the consistency (even without verification). For consistency to be proved it would have to entail correspondence, and if correspondence ultimately can’t be made axiomatic, so it follows for consistency. On this point, John von Neumann realized from Gödel that ‘it is impossible to formally prove the consistency of a system of arithmetic within the system of arithmetic,’ suggesting that even valid consistency cannot be a proof.⁰⁰⁵ It might be completed, yes, but “competition” and “correspondence” are not similes. Unfortunately, a “complete map” can feel like “a map which corresponds,” hence our vulnerability.
⁰⁰¹But we lack reason to think we aren’t in a computer simulation, don’t we? No, we have reason to think reality isn’t a simulation because there is nothing in experience that gives us reason to believe such is the case. Our reason for thinking we aren’t in a computer simulation isn’t that we have seen that we aren’t in a computer simulation, but because what we see doesn’t give us reason to think we are (we do not have to prove a negative). Perhaps it is true, but at this moment, we have no reason to think it is true, and hence it is meaningless to explore (though not necessarily wrong).
Also, even if I were to experience a tree turning into a dog, though this would confirm that my perception of the tree isn’t “always the same” and susceptible to change, this wouldn’t necessarily mean it is inaccurate. I would still have reason to believe that my perception of “the tree turning into the dog” itself was accurate, and I would likewise have no reason to think that all my other moments of perceiving “the tree as a tree” were false. “What I perceive” may change in a manner that suggest what I perceive won’t always be the case, but from this truth, I don’t have reason to think that what I perceive is unreliable. I accurately perceived the unexpected, and hence have reason to believe how I perceive is accurate. Perhaps it isn’t — I’d have to ask others if they saw the tree change into a dog too — but relative to myself, I have no reason to think I perceive inaccurately: I only have reason to think that the world I perceive isn’t as simple and predicable as I once thought.
Please note, at the same time, that what I experience doesn’t prove that “all trees can turn into dogs”: all I can say is that tree turned into a dog. From my experience, I cannot necessarily redefine what constitutes all trees: all I can say is that trees can turn into dogs (but that assumes that the tree I perceived was actually a tree and not a “tree-dog,” if you will). But what if, when I ask, everyone lies about not seeing the tree turn into a dog? (Perhaps that’s what you could tell yourself to protect your ideology?) What if you’re an alien and don’t know it? What if…What if…?
Additionally, from the experience of a tree turning into a dog, it doesn’t necessarily follow that “we are in a computer simulation”: perhaps rather “magic is real”? What absurd experience would prove we are in a computer simulation? If the sky filled with 1s and 0s, perhaps they are there because a magician wants me to think I’m in a computer simulation so that I don’t suspect magic is real? It doesn’t seem to me that any experience could prove the premise “we are in a computer simulation”; hence, what would be required is a falsification of the premise “we aren’t in a computer simulation,” but how could that be falsified (though do note that even if this premise was falsifiable, it wouldn’t necessarily follow that we are in one)? It doesn’t seem to me that the premise can be falsified, but is it the case that only that which can be falsified is that which is true? We’d have to know all truth to know if that was the case, which doesn’t seem to me as if we can know, at least not yet. Hence, we must use falsification with an open hand, using it as our tool, but always willing to put it aside if the tool won’t fit the job. But we must be very slow to put the tool aside and quick to pick it up again…
⁰⁰²But wait, though perhaps this insight is helpful for avoiding long rabbit trails about “Is what I perceive the actual world?” (though perhaps Popper’s insight is valuable for matters of perception), if I have no reason to think what I think is false until I experience otherwise, can’t I, if I’m a Republican (for example), just make sure I never encounter that which forces me to question all of Republicanism, and hence believe “what I believe has never been falsified” and so is possibly true? Indeed, this bring us to ideology, of which Popper’s “falsification” can actually help us preserve, problematically
As argued when we discussed “Situation Creation,” humans are “situation creators,” and we create situations (often via “sensualization”) in a manner that preserves our ideologies and “ways of seeing the world.” Conservatives can make sure to avoid Liberals in such a manner that they never have to admit to themselves “for sure” that they are avoiding those who could make them call into question Conservatism, and vice-versa: we can be masters at preserving our ideologies without letting ourselves know “for sure” that we are preserving our ideologies from threats. For if we were “certainly” aware of this fact, we would have to admit we were acting like “ideologues” rather than just “being right,” and that would hurt our ideology…
Popper’s falsification can help legitimize us in preserving our ideology, not because it is necessarily false, but because no human likes to risk finding out if their ideology is false. If I don’t have to verify my ideology because it can’t be verified, I can tell myself it is true even if I never verify it because it has never been falsified (a useful tool for maps). Hence, I can avoid ever “going out” and searching for verification and/or “evidence,” knowing the evidence will never ultimately verify what I believe, and keep assenting to my ideology, it never being falsified.
In science, falsification works as a strong test because a given person cannot keep science from moving forward: there will be tests, regardless. But seemingly no one can force a given person and ideology to “move forward” and be tested, for individuals and ideologies can “keep out” all information, evidence, situations, etc. that call ideology into question, and hence avoid falsification. I can “situation create” in a manner that not only avoids the possibility of falsification, but that also gives me a sense of “verification,” when really such evidence may not actually be present. Considering this, Popper’s “falsification” can actually be used to preserve ideology, just as much as it can help us avoid Hume’s critique. As they illuminate, insights can create shadows.
But how then do we determine what is true and what is false? That’s a great question: we have to “open ourselves up” to that which causes “existential angst,” which is to say we have to truly “critically think” (as expanded on in “On Critical Thinking” by O.G. Rose). We must face our fears, rather than only convince ourselves we are “facing our fears” without actually facing them. But how do we know when we actually do that? Will we know?
⁰⁰³As it is when it comes to certainty over our ideology and the ways by which we protect it: we can formulate and protect it without knowing we formulate and protect it, subconsciously. Ideology creeps into our lives, and then seems to appear suddenly and all at once, like a stranger in the door.
⁰⁰⁴But why does this surprise us so much? Don’t thought and perception also entail an inability to be axiomatic (being “verifiable” only insomuch as they aren’t falsifiable and we being unable to determine all that is true is that which can’t be falsified)? Since the methods by which humans perceive and think cannot be axiomatic, why should we think math would be any different? I think we want mathematics to be transcendent of us (not simply created by us), for then math provides a way to transcend ourselves and our subjectivity. But there is “no exit”: (un)certainty is life — but for Korzybski this can be our hope for sanity.
.
.
.
For more, please visit O.G. Rose.com. Also, please subscribe to our YouTube channel and follow us on Instagram and Facebook.
Good lord. You took a long time to say, *Don't be a dick with formal logic.*