## Can philosophy integrate the irrational as mathematics can?

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## Can philosophy integrate the irrational as mathematics can?

Yes.
9
82%
No.
2
18%

### Re: Can philosophy integrate the irrational as mathematics c

Magnus Anderson wrote:
Prom wrote:The actual existential experience of rationing and rationalizing always involves only what information is available to the chooser at the moment of a decision in a series of contiguous steps.

That's why I say that being rational means making the best possible decision that is available to the decision maker at the time rather than making a decision that leads to the attainment of one's highest goal.

I don't think it is ever about the highest goal. It is about the goal (a sub-goal) being pursued at the moment - the next step within view. Whether that sub-goal was a rational choice is a different issue - and I agree those choices are rarely the best available - except for one issue -

Being rational means using what information is available in making choices (a rational process). That information is never truly complete - "given what I have been told -- this is my best option." The path taken might be an irrational path - but the one taking that path is being totally rational - it is not the person but the process itself that either leads to the person's actual intentions and is rational or doesn't lead him there and is irrational.

I think to call the person irrational is to say that the person's brain literally can't rationally process information - the person is psychotic (or as James put it - "broken brain").
Member of The Coalition of Truth - member #1

You have been observed.
Though often tempted to encourage a dog to distinguish color I refuse to argue with him about it
It's just same Satanism as always -
• separate the bottom from the top,
• the left from the right,
• the light from the dark, and
• blame each for the sins of the other
• - until they beg you to take charge.
• -- but "you" have been observed --
obsrvr524
Philosopher

Posts: 3138
Joined: Thu Jul 11, 2019 9:03 am

### Re: Can philosophy integrate the irrational as mathematics c

-
encode-decode -

Something that I noted about the pi = irrational issue and related to the integration of irrationality into society is the following -

It was apparent to me that the only reason pi was being called irrational was because it was not commiserate with the traditional use of "natural" counting numbers - specifically modulo 10. If you have a natural number as a diameter the circumference will be irrational - because natural numbers do not get along with circles.

But what if you choose to use the magnitude pi as your basic unit of measure (rather than 1). That would be modulo 10pi. You are choosing to make what has been called "irrational" (because it didn't fit past language) as your basic number system. Then an interesting thing happens -

With the natural based unit circle a rational diameter forms an irrational circumference. But if the diameter of a pi-unit circle is $$\pi$$ (meaning 1 unit in modulo-pi) the circumference will still be $$\pi (modulo-pi)$$ (because it will be $$1*\pi$$). The interesting thing is that $$\pi$$ (in modulo-pi = 1) is the new "rational" and the circumference of the unit circle = $$\pi (modulo-pi)$$ and is still irrational.

The social implication is that even if everyone accepted a proposed particular irrational way of thinking (such as wokism - making it the new "rational thinking") some of the same events seen as irrational before will still be seen as irrational along with formerly rational events. The new norm doesn't decrease the perceived irrationality - it just makes it more due to a deeper irrationality.

So perhaps regardless of irrational thinking there are some things that everyone is going to agree are irrational regardless of their irrational thinking. Or there are some concepts that are going to be seen as irrational no matter what mental language is common - universal irrationality.

But then if there is a universal irrationality - doesn't that imply that there might be a universal rationality?

I'm thinking that a concept like a square-circle might be seen as irrational by literally anyone (regardless of what they are willing to say out loud). And perhaps the concept that "A is A" (but spoken in their irrational language - perhaps "A is not other than not-A") will still be seen as rational. The trick is merely to be able to speak the accepted irrational language. And that is what politicians and salesmen do.

Perhaps politics IS the integration of irrationality.
Member of The Coalition of Truth - member #1

You have been observed.
Though often tempted to encourage a dog to distinguish color I refuse to argue with him about it
It's just same Satanism as always -
• separate the bottom from the top,
• the left from the right,
• the light from the dark, and
• blame each for the sins of the other
• - until they beg you to take charge.
• -- but "you" have been observed --
obsrvr524
Philosopher

Posts: 3138
Joined: Thu Jul 11, 2019 9:03 am

### Re: Can philosophy integrate the irrational as mathematics c

Great Again wrote:The two-valued logic is also not suitable for the treatment of propositions about future events, because it implies a false determinism and leaves no space for the freedom of man. If A is a proposition about future events, then the statement "A is true" can be more accurately described by the statement "There are (that is: present) causes that force the occurrence of A in the future", and the statement "A is false" can be more accurately described by the statement "There are causes that force the occurrence of non-A in the future".

A sentence like "Bill will be home tomorrow" will not usually be true or false in this sense, because there are usually no compelling causes that determine Bill's behavior. Thus, to deal with such cases, one must introduce a third truth value, which can be assigned the property "unknown" or the property "not yet" (cf. the arrows in my diagram), which a proposition A about future things takes on precisely when there are no compelling causes for A or not-A to occur.

A roughly similar argument is already found in Aristotle (the famous example of tomorrow's sea battle).
Great Again wrote:
Great Again wrote:Classical logic includes only propositional logic and predicate logic, in which the principles of forbidden contradiction (principium contradictionis) and excluded third party (principium exclusi tertii) and, related to them, the bivalence principle (see my earlier posts) are valid.

Non-classical logics are those in which at least one of the principles of classical logic is not valid. Particularly important are those systems in which the principle of the excluded third or the bivalence principle is invalid. Such logics were developed because they were motivated by developments in mathematics (cf. for example my earlier posts about antinomy).

Non-classical logics include e.g.:
- Multivalued logic (generic term for all other logics in which the bivalence principle is not valid).
- Modal logic (also: Alethian logic).
- Intuitionistic logic.
- Dialogic logic.
- Temporal logic.
- Deontic logic.
- Conditional propositional logic.
- Doxastic logic.
- Epistemic logic.
- Relevance logic.
- Non-monotonic logic.
- Fuzzy logic.

Fuzzy logicians say that most concepts are factually fuzzy in the sense that they can apply to different objects to different degrees. The fuzzy logicians are right. Whether or not a particular term applies to an object is often not a matter of a simple yes or no, but often a matter of degree. In fuzzy logic, one specifies the degree to which a term applies to a particular object by a number from the continuum between 0 and 1: If an object does not fall under a certain term at all, the term in degree 0 applies to it; if it falls completely under it, the term in degree1 applies to it; and if it falls only more or less under it, the term in degree g with 0<g<1 applies to it. For a term one has to specify a function which determines under which circumstances it applies to an object and in which degree. (This function determines a fuzzy set.) For example, one can specify that the predicate "x is a tall man" applies to men up to 1.60m in degree 0, to men from 1.90m in degree 1, and to men between 1.60m and 1.90m in certain (with height increasing) degrees between 0 and 1; a 1.75m tall man may be tall in degree 0.5, for example.

Since the 1980s, fuzzy logic has increasingly found its way into technical applications under the keyword "fuzzy control", especially where exact mathematical calculations of the processes to be controlled are complicated, lengthy or hardly possible due to the many and unmanageable influencing variables. In this case, precise measured variables are first translated into fuzzy terms such as "quite fast", "quite close to the target", etc. ("fuzzification" is the word for this), which then form the basis for simple rules that are easily accessible to human intuition: "If the car is quite fast and quite close to the target, then brake quite hard". The "outputs" of these rules are then transformed back into precise control instructions according to specific procedures. This procedure allows control on an "intuitive" basis without the availability of an exact mathematical model of the process to be controlled. Fuzzy control has found its way, for example, into the control of video cameras, washing machines, elevators and even subways.

Multi-valued logics have been around for a long time, and they all have one thing in common: statements that are either true or false according to the bivalence principle are not valid.

According to Gödel's results, one must presuppose an infinite number of truth values.

Ulrich Blau has given a number of reasons why the logic underlying everyday language is three-valued. I would say it is multi-valued.

If X is rational and irrational, and in addition something that is itself rational or irrational, but without precise assignment, i.e. not yet known, but with high probability assignable in the future, then the possibility can be kept open that this still undetermined will turn out to be something determined in the future. For this purpose, a truth value in terms of the future and a truth value in degrees are given by numbers from the continuum between 0 and 1, where 0 or e.g. 0-0.2 stands for "still undetermined" or "rational and irrational (because in each case determinable only in the future)".

Great Again

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### Re: Can philosophy integrate the irrational as mathematics c

the analysis of probability on the a-priori assumption that the fuzzy logic has more sense in supposing that it's more certain probable future determination could designate less 'fuzzy' math than that analysis could tend to suggest, may be more likely then not.
Meno_
breathless

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### Re: Can philosophy integrate the irrational as mathematics c

Great Again wrote:
Great Again wrote:The two-valued logic is also not suitable for the treatment of propositions about future events, because it implies a false determinism and leaves no space for the freedom of man. If A is a proposition about future events, then the statement "A is true" can be more accurately described by the statement "There are (that is: present) causes that force the occurrence of A in the future", and the statement "A is false" can be more accurately described by the statement "There are causes that force the occurrence of non-A in the future".

A sentence like "Bill will be home tomorrow" will not usually be true or false in this sense, because there are usually no compelling causes that determine Bill's behavior. Thus, to deal with such cases, one must introduce a third truth value, which can be assigned the property "unknown" or the property "not yet" (cf. the arrows in my diagram), which a proposition A about future things takes on precisely when there are no compelling causes for A or not-A to occur.

A roughly similar argument is already found in Aristotle (the famous example of tomorrow's sea battle).
Great Again wrote:
Great Again wrote:Classical logic includes only propositional logic and predicate logic, in which the principles of forbidden contradiction (principium contradictionis) and excluded third party (principium exclusi tertii) and, related to them, the bivalence principle (see my earlier posts) are valid.

Non-classical logics are those in which at least one of the principles of classical logic is not valid. Particularly important are those systems in which the principle of the excluded third or the bivalence principle is invalid. Such logics were developed because they were motivated by developments in mathematics (cf. for example my earlier posts about antinomy).

Non-classical logics include e.g.:
- Multivalued logic (generic term for all other logics in which the bivalence principle is not valid).
- Modal logic (also: Alethian logic).
- Intuitionistic logic.
- Dialogic logic.
- Temporal logic.
- Deontic logic.
- Conditional propositional logic.
- Doxastic logic.
- Epistemic logic.
- Relevance logic.
- Non-monotonic logic.
- Fuzzy logic.

Fuzzy logicians say that most concepts are factually fuzzy in the sense that they can apply to different objects to different degrees. The fuzzy logicians are right. Whether or not a particular term applies to an object is often not a matter of a simple yes or no, but often a matter of degree. In fuzzy logic, one specifies the degree to which a term applies to a particular object by a number from the continuum between 0 and 1: If an object does not fall under a certain term at all, the term in degree 0 applies to it; if it falls completely under it, the term in degree1 applies to it; and if it falls only more or less under it, the term in degree g with 0<g<1 applies to it. For a term one has to specify a function which determines under which circumstances it applies to an object and in which degree. (This function determines a fuzzy set.) For example, one can specify that the predicate "x is a tall man" applies to men up to 1.60m in degree 0, to men from 1.90m in degree 1, and to men between 1.60m and 1.90m in certain (with height increasing) degrees between 0 and 1; a 1.75m tall man may be tall in degree 0.5, for example.

Since the 1980s, fuzzy logic has increasingly found its way into technical applications under the keyword "fuzzy control", especially where exact mathematical calculations of the processes to be controlled are complicated, lengthy or hardly possible due to the many and unmanageable influencing variables. In this case, precise measured variables are first translated into fuzzy terms such as "quite fast", "quite close to the target", etc. ("fuzzification" is the word for this), which then form the basis for simple rules that are easily accessible to human intuition: "If the car is quite fast and quite close to the target, then brake quite hard". The "outputs" of these rules are then transformed back into precise control instructions according to specific procedures. This procedure allows control on an "intuitive" basis without the availability of an exact mathematical model of the process to be controlled. Fuzzy control has found its way, for example, into the control of video cameras, washing machines, elevators and even subways.

Multi-valued logics have been around for a long time, and they all have one thing in common: statements that are either true or false according to the bivalence principle are not valid.

According to Gödel's results, one must presuppose an infinite number of truth values.

Ulrich Blau has given a number of reasons why the logic underlying everyday language is three-valued. I would say it is multi-valued.

If X is rational and irrational, and in addition something that is itself rational or irrational, but without precise assignment, i.e. not yet known, but with high probability assignable in the future, then the possibility can be kept open that this still undetermined will turn out to be something determined in the future. For this purpose, a truth value in terms of the future and a truth value in degrees are given by numbers from the continuum between 0 and 1, where 0 or e.g. 0-0.2 stands for "still undetermined" or "rational and irrational (because in each case determinable only in the future)".

A not entirely serious suggestion: We could declare everything irrational to be taboo.

An example from mathematics:

The idea of irrational numbers, in our notation therefore infinite decimal fractions, should remain incomprehensible to the mind, never be told in school about irrational numbers.

Euclid said - and one should have understood him better - that incommensurable distances behaved "not like numbers". In fact, in the accomplished concept of the irrational number lies the complete separation of the concept of number from the concept of magnitude, and this because such a number - pi, for example - can never be delimited or represented exactly by a distance. But it follows that in the conception of the ratio of the square side to the diagonal, for example, the number as a sensual limit, a closed quantity, suddenly touches a completely different kind of number, which remains foreign in the deepest inside and therefore uncanny, as if one were close to uncovering a dangerous secret of one's own existence. This is revealed by a strange late Greek myth, according to which the one who first brought the contemplation of the irrational out of the hidden to the public, perished by a shipwreck, "because the inexpressible and imageless should always remain hidden".

An expression like e^ix, which constantly appears in our formulas, is supposed to seem absurd to us, to be a taboo.

Only calculate with finite fractions, examine the integer ratio of two distances. Great!

Even the idea of a number zero must not even arise, because it has no sense in terms of drawing.

If one would do all that - and only all that -, such a mathematics would be already perfect, only differently perfect.

Sleyor Wellhuxwell

Posts: 77
Joined: Sun Jan 24, 2021 2:35 pm

### Re: Can philosophy integrate the irrational as mathematics c

Sleyor Wellhuxwell wrote:If one would do all that - and only all that -, such a mathematics would be already perfect, only differently perfect.

- And inexplicable.
Member of The Coalition of Truth - member #1

You have been observed.
Though often tempted to encourage a dog to distinguish color I refuse to argue with him about it
It's just same Satanism as always -
• separate the bottom from the top,
• the left from the right,
• the light from the dark, and
• blame each for the sins of the other
• - until they beg you to take charge.
• -- but "you" have been observed --
obsrvr524
Philosopher

Posts: 3138
Joined: Thu Jul 11, 2019 9:03 am

### Re: Can philosophy integrate the irrational as mathematics c

-
"Male and female he created them" - the strong and the meek - the rational and the irrational.
The East and the West.
Member of The Coalition of Truth - member #1

You have been observed.
Though often tempted to encourage a dog to distinguish color I refuse to argue with him about it
It's just same Satanism as always -
• separate the bottom from the top,
• the left from the right,
• the light from the dark, and
• blame each for the sins of the other
• - until they beg you to take charge.
• -- but "you" have been observed --
obsrvr524
Philosopher

Posts: 3138
Joined: Thu Jul 11, 2019 9:03 am

### Re: Can philosophy integrate the irrational as mathematics c

Great Again wrote:Can the irrational be dealt with in philosophy in the same way as in mathematics?

The irrational is that which cannot be grasped by reason, which is considered "superrational", "subrational", "unreasonable", but not "counterrational", "counterreasonable", "anti-rational", "anti-reasonable".

N. Hartmann speaks of the "transintelligible" and means that which is beyond the reach of human understanding.

Friedrich Wilhelm J. Schelling calls the irrational "in things the incomprehensible basis of reality, that which cannot be dissolved into understanding with the greatest effort, but remains eternally at the bottom. Out of this incomprehensible, in the proper sense, understanding is born". Schelling teaches that all rule-like, all form arises from the rule- and formless.

Irrational numbers.

If one is to be able to perform exponentiation or root extraction with any rational numbers (in the exponent), it is necessary to introduce new numbers: the irrational numbers. There are algebraically irrational and transcendentally irrational numbers.

The totality of all irrational numbers (algebraic and transcendental) and all rational numbers gives the set of real numbers: "|R".

R.png

Refer to all my posts and book excerpts ever posted on this forum. Keywords are 'per privationem', 'pure negation', 'multivocity', the 'abomenon'.
Qui non intelligit, aut taceat, aut discat.

BTHYS TOU ANAHAT KHYA-PANDEMAI.
-- Hermaedion, in: the Liber Endumiaskia.

ΑΝΤΗΡΟΠΑΡΙΟΝ,
in formis perisseia mutilata in omnia perisarkos mutilatum;
omniformis protosseia immutilatum in protosarkos immutilata.

Measure the breaking of the Flesh in the flesh that is broken.
[ The Ecstasies of Zosimos, Tablet
the First.]

Parodites
Thinker

Posts: 765
Joined: Wed Jan 08, 2020 12:03 pm

### Re: Can philosophy integrate the irrational as mathematics c

" Ulrich Blau has given a number of reasons why the logic underlying everyday language is three-valued. I would say it is multi-valued."

Three-valued is Pierce's semiotics. In truth, it is tetrapolar; four-valued, the four components being what I call the four vocities or four epistemes. I have found tetrapolar logic at work all through history's philosophy, but it came into semiotics pretty recently. Namely in Harman's four-fold epistemological withdraw. https://richardcoyne.com/2018/02/17/four-fold-reality/

I go into the irrational in general and many variations on three-part, four-part, and five-part logics, etc. in the following text out of one of my books:

Parodites wrote:A theory of theory,- a philosophy of philosophy,- a 'theory of everything', cannot formally exist,
because Theory [Philosophy] cannot account for its own Negativity, that is, for its own negation,
which would be 'pure negation'- that Negativity which cannot be accounted for through Theory or
'absorbed' by the strictures of System, in Bataille's formula,- or the 'secret of consciousness' as
appercepted by the appropriate schema through transcendental synthesis, which Kant claimed
existed only in the depths of the soul, rent fatally beyond the veil of the Dialectic. This is the
nature of Bataillean violence: the fundamental scissure of Discourse. Thus when we point the
dialectic against itself,- when we work out a dialectic of the dialectic,- as Kierkegaard ironically
recapitulated the Hegelian philosophy, we achieve what Kierkegaard called the 'paradox' (what
Plato called the 'aporia') as an engine of thought, while similarly, when we invert the dialectic, as
Marx did, we initiate a process of de-construction by which all concepts are dissolved into
elementary fragments of material-history and reduced to a singular quanta of Force a la. the Will
to Power. As the Hegelian thought builds up, within the movement of Geist, the Babel-tower of
positive knowledge toward the Absolute, so the Marxist dialectic deconstructs System and
descends toward a bare materiality, within whose conflux of elementary forces the image of
Utopia has been hopelessly distorted. A reductio ad absurdum of the categorical Negation occurs
as well, when we attempt to circumscribe a dialectic of the dialectic, leading to Baidou's 'bad
infinity' 1 and Bataille's un-absorbed Negative as an accumulation of those entropic stresses upon
the system of Capital produced by the flow of material-history, to again return to the Marxist
formula. This reduction was precisely the meaning of 'Death' in Heidegger's account of Being.
Heidegger sought in fact to fully explicate Dasein's opening toward Death by bearing the
Negative to its implicated reductio ad absurdum, (this titanic struggle was his project of
de-struktion) peering beyond the veil of History through a kind of ontological black-hole
compressed within the folds of Aryan race-memory, whose event-horizon had trapped the
European soul within the inescapable orbit of Capital, Modernity, the image of Techne(ology) and
the merely ontic,- that is, the metaphysical Presence of ousia's Absence, toward which the human
dimension is properly enfolded by Death,- by Death as a kind of noetic 'escape route' out of the
'phenomenal bind' of correlationist philosophy, [Or, in other words, an escape route out of the
confused nebula, bereft of political or 'emancipatory' potential, found in the purely intermediate or
initiatory role of Dasein, which rests on a movement from its own horizon of possibilities
(Moglichkeit) to the disclosure of an actual futurity, (Wirklichkeit) to be later grasped by a pure
ontology of time in which the movement from potentiality to actuality, in terms of the Aristotelian
categories, becomes a movement from the non-ego to ego,- that is, a kind of cosmic awakening of
insensate matter to Geist reenacted on the part of Dasein. "Hoher als die Wirklichkeit steht die
Moglichkeit." Ernest Joos, 1983: "Lukacs' last autocriticism, the Ontology; On the Usefulness of
Ontology." On the inter-mediation of Heidggerian disclosure, see Raymond E. Gogel, "Quest for
Measure; the Phenomenological Problem of Truth."] in Meillassoux's reconceptualization of
'finitude', which we must also pair with our conceptualization of Dasein. [See: Anamnesis;
Aesthetics After Finitude. When the post-Kantian correlationist doxa is dispensed with, we are
left with an 'un-territorialized' domain of the human Subject formerly rejected by the three modes
of Kant's critique,- criticism, skepticism, and dogmatism, a la. 'philosophy',- an uninhabited
subjectivity awaiting a new 'terraforming aesthetics', just as we are provided with the converse,
that is, a hyperrealist or 'inhuman' vision of the cosmos in which the distinction between primary
and secondary, or 'subjective' and 'external' qualities has been extinguished. In "The Existence of
the Divine", Meillassoux calls this radically contingent separation of the human subject and the
'arche fossil' of the Real simply, "the impossibility of the whole", for whose assertion
object-oriented ontology and speculative realists, like Harman, have been accused, to some extent
justifiably,- and to a greater extent, unsurprisingly, given the fact that we find here an oblique
continuance of the Heideggerian strain,- of disavowing the philosophic vocity of the Subject,-
much as the assertion of Dasein disavows the vocity of the 'human' subject. The chiasmus torn in
this absent Whole, or the 'disjunction of exteriority and immanence',- in order to be brought out of
the theoretical depth of the impossible and so made philosophically readable,- must be
conceptualized through a new, properly ontological thinking-through of Time, which Heidegger
had promised in the third division of Being and Time, but had not achieved, and Badiou simply
ignored. While I find great intellectual sympathy in OOO and speculative realism, most especially
with regard to their implicit rejection of the pre-Socratics as well as the respective modern
equivalents in the cult of popular science, (A thinking which undermines philosophy, like the
pre-Socratics and the sophists equally accomplished, as though philosophy were simply an
outdated mode of science,- as opposed to a fundamentally different human project entirely. See
Harman's book "Object-Oriented Ontology" for a great account of the Pre-Socratics in their
undermining of the Western philosophical project.) or likewise an assumed faith in the tenability
of a Theory of Everything, it should be clear from my own conceptualization of the episteme that
an alternative to their theorizations of a pure ontology of time is pursued in these books. In the
third dialectical triad, the logoic chiasmus noted here is intellectually supplanted by the 'lepsis',
such that the pure ontology of temporality is then left to trace the movement of a
super-transcendent methexis (toward ektheosis) through the super-immanent lepsis (using
Eriugena's notions of supra-immanence and supra-transcendence) and its resulting perichoreia,-
an 'Image' of Time which cannot be reduced to the merely intramundane or 'encosmic' (See
Joshua Ramey, in "The Hermetic Deleuze: Philosophy and Spiritual Ordeal." Thus: "The
cosmological and metaphysical problem for orthodox Christian thinkers was that, if in creation
the same divine being is both the expressor and the expressed of a world, how it is possible to
avoid the unwanted consequence that God's nature might be limited to the expression of
intramundane or merely encosmic possibilities? Some kind of process theology seems to loom,
whereby God's essence would be seen as restricted by time, or even that God might be forced to
discover God's own essence through time.") movement from potentiality to actuality within the
'tritogenos' like that at the basis of a causal or correlationist theorization of temporality,- namely
as a distinctive vocity: the vocity of the Subject as a kind of "hepatic inscription of the chora"
capable of confronting the "choraic motility of the semiotic" and infiltrating the symbolic order,
as divine perichoresis, with an intrusion of jousissance (beyond the threshold of structured and
socially reinforced libido) that embodies the inherent lacuna 2 or instability of the body, that is,
the Negativity of the mortal Subject, whose unstable forces, as graphe or traces of more elemental
universal forces, therefor draw the subject upward into the visionary ekstasis of the eidos,- into
the mantic presence of the Symbolic.] * The inability of Theory to account for its own Negation
leads to what I have named 'mimetic hyperinflation', while the subversion of mimesis appears as a
consequence of the perfection of techne as a hypermnemata, in whose image the direction of
human history has been deterministically bent, rendering impossible, through any hopeful
'bridging of the gap' between independent semioses, what Ji Hwan Lee calls, in "Integration
mechanism and transcendental semiosis", trans-interpretance, upon which basis the stability of
'belief' can be maintained and those excesses driven up by multilinear semiosic processes properly
sublimated. ** We take the hypermnemata as a potential theory of the 'Spectacle',- meaning, a
conceptualization of the Spectacle amenable to philosophical analysis, namely through the use of
the episteme-model of vocity and Truth, (and its respective counter-Hegelian epistemology and
aporetic metaphysics) by which the underlying 'mnema' of the technomimetic substrate might be
excavated from its own autopoietically generated materials without encouraging further viral
transmission of those materials. The first task of such a project would be the deployment of a kind
of buffer-zone in which the mnematic core of 'System' might be unloaded, with a secondary
protocol focused on a re-engagement of the symbolic-exchange function and thus, eventually, a
reconstruction of philosophy out of its at that point inert materials. The episteme, as a model of
the subject's unique vocity as well as that of the variable thresholds to the Real which the Subject
can access, promises a theoretical explication of the category of 'experience', that is, an
explication of the experiential subject's vocity, recalling one of Walter Benjamin's most urgent
tasks,- (for he felt that it was this,- a conceptualization of the nature of experience in its totality,-
which the Kantian framework most urgently lacked, with the 'secret' of the appercepted subject
being said to reside unutterably in the soul, by Kant himself) a task which, given the limitations of
critical-theory as merely a mimetically inverted Hegelian dialectic, was fated to remain
unfulfilled. Such a model of human experience,- one of experience in its totality, in its vocity,-
would, in its praxis, give rise to a theory of creativity, not merely an aesthetics- and therefor,
would materialize the very creative techniques and strategies as served for its subject precisely as
what I have before called "a mode of aisthesis capable of conforming the very effects whose
techne it informs and so inverting the series of causes",- that linear series whose ultimate telos is
self-fulfilled in the image of Capital. (ie. inverting the structure of temporal co-relation, to use the
terms utilized in the present text.) It is with these techniques that the reconstructive task hinted at
here would be initially surmounted. *** In so many words, instead of representing the text as a
symbolic act (a dramatic tension dialectically stabilized by either the Peircean triad or the
Burkean pentad) by which the value-exchange function is converted into symbolic-exchange,-
stabilizing the boundary of the Other metonymically, following Lacan's discourses,- the text
might be conceived of as an index of operations conducted as value-exchange or Robinsonian
transfer-protocols. (somato-mimeses) The text then, instead of passively representing the
speaker's experience in words as per classical structuralist critique, manifests a signal that, in
combination with the signal 'acousmatically generated' by the reader, produces an endonomon
regulating, through mimesis, a model (an index) of the extrinsic,- the extrinsic, which is therefor
the object of the text, not the object either of the speaker or reader, as it is in the typical
hermeneutics schools. ****
1. The 'bad infinity' of the Hegelian dialectic can be traced all the way back to the Aristotelian deconstruction of the Eleatic and Pythagorean
monads. See Luigi Borzacchini, "Incommensurability , Music, and Continuum: a cognitive approach.", on the artificial construction of the
mathematical continuum and the evolution of its more philosophic underpinnings: "To outline this evolution, I must first and foremost remind ...
that the Pythagorean monad could not be divided. However, Aristotelian empiricism could not remain insensitive to the idea of the 'one' as a
measure unit, and Aristotle's philosophy had to remove the antinomy inherent in the idea of 'One', both indivisible- the 'Being' in the Eleatic
framework, and the monad, both unit and point, in Pythagoream Mathematics- and divisible, the measure unit of the 'magnitude'. The solution
required that the idea of continuity based on the divisibility-of-the-magnitude had to be connected to the idea of continuity based on the
singleness-of-the-separating-extremes through the idea of sign/point. A sign/point can always and everywhere, potentially but not actually,
distinguish/divide the continuum, whereas a unity actually is an already distinguished and well defined object to be considered as a whole." (He
calls this 'apeironic' treatment of the concept of continuous magnitude the hidden evolutive principle of Greek-descended models of the
mathematical continuum. He goes on elsewhere, describing it in "The Sophist: Genesis of Formal Thinking in Philosophy and Mathematics", as
"the source of never ending paradoxes well recognizable ever since the beginning of formal thinking. Negation, truth and being ground an
antinomical argument, from the “negative judgement paradox” (impossibility of asserting falsity), through the “liar paradox” (contradictory nature
of self-asserting falsity), to set-theoretical paradoxes and to Gödel's and Tarski's limitative theorems.") In fact, this incommensurability of the two
formulations of the monad, the 0-dimensional substrate for all higher abstraction, and the consequent duplicity of the Pre-Aristotelian and
Aristotelian models of the continuum, can be observed by us in the modern crisis concerning the incompatibility of quantum mechanics and
relativity, for, as Bohm states, concerning his notion of an Implicate Order, this is in reality simply an incompatibility between the continuum
modelled in relativity, which represents indiscrete continuous motion, and that in quantum mechanics, which concerns discrete transformations and
phase-spaces, spin-systems and discontinuous motion,- that is, 'quantized' motion: "...in relativity, movement is continuous, causally determinate
and well defined, while in quantum mechanics it is discontinuous, not causally determinate and not well-defined. Each theory is committed to its
own notions of essentially static and fragmentary modes of existence (relativity to that of separate events connectible by signals, and quantum
mechanics to a well-defined quantum state). One thus sees that a new kind of theory is needed which drops these basic commitments and at most
recovers some essential features of the older theories as abstract forms derived from a deeper reality in which what prevails is unbroken wholeness."
This inherent antinomy appears elsewhere in modern research, as in the relationship between parallel D-branes and muti-sheet spacetime, citing
Pei-Ming Ho and Yong-Shi Wu, in "Noncummutative Geometry and D-Branes": "Indeed, there are striking similarities between the D-brane
dynamics and the non-commutative geometric construction of the standard model: the parallel D-branes versus the multi-sheet space-time, the
inter-brane connections versus the Higgs fields, and so on." The continuous and discontinuous models of the continuum and their integral paradox
thus go all the way back to the very foundations of Western logic and, just as Aristotle failed to unite them by way of categorical reasoning and
dialectical synthesis, so any further attempts at a constructed synthesis on the part of modern physics is equally unlikely to bear much fruit.
2. The lacuna serves, when 'digitally modulated' by the binary logic of the chiasmus, as a 'site of exception' or Kunzean metalepsis, that is, as an
ambient signal through which the 'stochastic resonance' itself becomes an extravalence and trans-apparition, a steganographic liquidity and
non-representation "to be mapped in a flux of encryptions",- [See Cabrales and Carruthers on 'Poetry as Cosmic War'.] a feedback-loop for the
Landian abomena of the 'Outside' within an abiding-between conceptuality and matter, recalling the manner in which Irigaray and Plant define the
female symbolic lacuna as a kind of binary zero,- not a lack of signification, not simply an 'exception' from the system of positive male exchanges
and the driven metonymy of libidinous becomings, not an absence at the missing center of gravity,- but a zone of multiplicities which, like the
Cantorian aleph, enables that proliferating digital continua to exist from which it itself springs forth as a 'ghost in the machine',- a phantasmal
extroprojection, the technological excruciation of self-sublimed capital making way for the anastrophe, that is, an anthropocentric de-conditioning.
However, the hypermnematic conversion of the productive forces of the Market ensures that these forces cannot exceed capitalist control,- which is,
was, or never-was, the fundamental hope of accelerationist doxa and the aesthetic praxis of its xenopoetics, or the essential feature of an anastrophic
reorganization of market-forces. [Benjamin Noys, Cybernetic Phuturism: The Politics of Acceleration.]

* For more on this term, as it relates to the Platonic theory of Presence, see Nicolet., Isar, "Chora: Tracing the Presence"; Review of European
Studies, 2009. The perichoreia defines the final manifestation of the chora's impossible presence. The aporia of metaphysical Presence is one of
Plato's most significant, reaching its most energetic pitch of course, in the Timaeus. Presence is here encoded by the unstable logic of the 'chora',- a
kind of hypnagogic or transitional phase (tritogenos) between the immaterial eidos, on the one hand, and the material eidolon on the other, that is,
the world of Being and that of the Image, the world of the actual and the potential. The 'impossible presence' of the choreia, (like that of the
Aristotelian monadology noted above) which is absent from itself, only instantiates the distorted logic of 'pure difference' for which it has been so
often attacked by critical theorists with the mistaking of absence for presence, with the conflation of negativity and knowledge,- for such a
misconstrual of the eidos for eidolon,- arising out of the reduction of this 'Image of Time' (the perichoreia) to its ontological minima, that is, the
chora or 'Being of Time',- (as stated concerning the correlationalist dynamis) gives rise to an illegible graphe of the Platonic choreia,- and thus, to
the loss of its hepatic inscription in the choreia of the body, which replicates the 'Form' of the higher universe in the lower one as a 'participation',
according to Plato's account and the cosmology of the Timaeus. Recapitulating what we have said regarding Stellardi and thought's own
impossibility, or negativity, as the very engine of thought, we find Sallis reaching the nearly identical conclusion, specifically with regard to his
delineation of certain aporias within the Platonic corpus. He tells us: "What is it that thus withholds the Platonic text from metaphysics at the very
moment when metaphysics is founded? What is it that holds the Platonic text at the threshold of metaphysics?" Heidegger understands the lethe to
be a kind of choraic counter to phusis,- one which performs the basic phenomenological closure and counters all emergence into presence, thus
imposing a 'phenomenological withdraw' which, at a lower level of abstraction, echoes that withdrawal we have already discussed at the
epistemological level. Sallis indicates that it is precisely this belonging of the lethe to aletheia that renders the impossible presence of the choreia as
Thought's very arche: "Then it would be a matter of tracing in the dialogue the lines- or, rather, the shadows- of archaic closure, of the closure
belonging to the arche, belonging within the origin at the origin, at the threshold of metaphysics." Thus, we draw the main insight from Sallis'
"Phenomenology and the End of Metaphysics", as succinctly given in Bernard Freydberg's interpretation, citing "The Thought of John Sallis;
Phenomenology, Plato, Imagination; Delimitations": "The end of metaphysics has been, is always, prefigured in its beginning. The drive to
presence constitutive of metaphysics reaches its limit- is delimited- at its outset by that which makes it possible at all: aletheia, to which lethe
essentially belongs. "Beginning" and "End" no longer constitute an opposition and most surely do not constitute a temporal order of any kind." Of
course, the perichoreia is just this "image of Time", which cannot be absorbed by any temporal order.
** Working from the Peircean model and ternary logic, we have: "Cognition consists of multiple layers. Each neuron group in layers processes
information and transmits it to other layers. The more information is integrated, the more obvious and usable signs become. Horizontally, signs in
semiosis are associated and mediated with each other. Vertically, they collaborate beyond the horizon; from sensory neuron to reflective
consciousness. Semiosis involves trying to reach a final interpretant through following a possible interpretation-course by the force of a guiding
principle. Whereas, in trans-semiosis, we attempt to integrate two semioses despite their conceptual gap. In that situation, transcendence occurs. If
integration is impossible, semiosis would rev up excessively. Accordingly, intense neural stimulations are generated. Once probable routes of
interpretation have rapidly accumulated in quantity, they cross a threshold where restrictions are broken or do not exist. Then, we jump to a stable
belief, attaining trans-interpretance that has competence for casually suturing a conceptual gap without any adequate foundation."
*** I would clarify several terms in relation to what has been said here. The interaction of the primary and secondary processes, (the inorganic and
organic, the inhuman and human, cosmic and egoic, social and individual; the 'anorganic' and 'aorgic', to recall Schelling's distinction) borrowing
the terms used in Simondon's socio-psychology, has thus far occurred on great scales of time,- giving rise to what Land and the CCRU referred to as
long-range feedback cycles,- the kind of cycles we find ourselves unable to statistically model, much like the massive data-sets related to weather
patterns and their computer-driven prediction, which had inspired the concept of the hyperobject. This unpredictable feedback-cycle has produced
an epistemological blind-spot (this blind-spot is, simply "critical-theory".) within which one such hyperobject (A 'dragon'; see Consolandi, in: "I
Saw a Dragon! - Envisioning Hyperobjects: culture, collaboration and madness in the Anthropocene." Note also J. Sheu, in: "Conceiving the
Hyperobject in Stanisław Lem’s Solaris". ) has been generated, namely through the process I refer to as mimetic hyperinflation: Capital. Capital
represents a final submission of the secondary or human, individuating process, to the primary one. The hypermnemata is the auto-poetically
generated form in which the secondary process, ie. human history, has been re-encoded on the higher-dimensional surface of the unreadable
hyperobject. This sociological trajectory, because it is the eventuality of an inertial telos suspended within the image of Capital itself, constitutes the
self-fulfilling prophecy par excellence,- inevitable, perhaps, though only from within its own ontological horizon. The question is one of first
reaching an ontological ground-zero, or what I have called the skhisma,- an ontological-minima of differentiation,- and then finally escaping that
horizon. In the past, man possessed a metaphysics, and not merely a statistics-driven, scientifically derived model of himself and the world, as that
reified by critical-theory, such that a revitalization of metaphysics is required in order to excavate the human mnema from the process of
material-history. The 'episteme' is posited as just such a metaphysics.
**** Combining the suggestions made here with the philosophy of the episteme, we might sketch a cursory model of the new communicative
network: 1) Episteme: The Authorial Signal. 2) Ontic: The Acousmatic, or the signal produced by the reader. 3) Immanent: the Index; the
metaleptic plane; the horizontal. At this level of analysis, we explore the mimetic sublation of the Other via semiosic (Girardian) excesses generated
by value-exchange, (the endonomon as an index of tyche or potential) that is, 'non-representational' conducts unamenable to Husserlian analysis'
programmatic action-sense equivalence in the fulfillment of sign-structures as purely representational. (See Siegfried Mathelet, "Atypical Habits:
An Addendum to Schutz's Typology of Conducts Part II Non Representational Meaning in Action".) 4) Transcendent: The Extrinsic; the vertical.
Here we explore transcendental semiosis of the Other via symbolic exchange, circumventing the problem of 'non-representational' contents in
Husserl's pre-predicative consciousness and Schulz's typology or phenomenological 'sociology of concepts'. Here, different texts index "parallel
worlds", such that the Shakespearean corpus, for example, cannot be made to say anything about any world other than the one it indexes, unless
another text is produced to index it. Passive representation is entirely dispensed with, and the noematic is replaced by the endonomic.

As Theory cannot circumscribe its own Negation, so neither can Theory circumscribe its own
Essence,- it's positivity or Affirmation. Harman's account of hyperobjects lies in the notion of
epistemological withdrawal. The contingent sensual qualities of an object, as available to our
senses, do not modulate the essence of the object, such that objects can only enter into
relationship with one another on the level of the sensual, whose ontological gaps can therefor
never be reconstructed within the fabric of the symbolic. Objects thus contain a haunting core
unavailable to the absorptive grasp of System, by which relationships are capacitated and
governed. The problem is that, through the formation of perceptive relationships between objects,
new objects are created, which in turn telescope hidden essences of their own, further miring
System in the kind of entropic stresses about which Bataille was so concerned. Here we also find
negation as a driving force in the 'engine of thought', though one potentially destructive in its
'unrestrained mimesis' of essences. Theory, when attempting to fathom its own hidden essence
through the fabric of relationships available to it on the part of whichever System theory has
chosen to operate under, cannot help but effloresce from out of its own confabulations ever new
multiplicities of impossible essences, whose veil (the 'confused nebula' noted above) renders
Theory's own essence progressively more and more unreadable,- that is, more and more
inaccessible to the vertical element of the philosopher's 'symplokeides'. * All such networks of
explosive essences exceed the limits of the singular human ego, such that, when perceived as
relational complexes undulating or 'phasing' in and out of our own local Real from a
higher-dimensional vantage, we might regard them as hyperobjects.
* The symplokeides, as "the active-passive becoming of ideas", [Deleuze and the Passions, P. 10.] is embedded in a world for which, due to its
finitude, no logoi, vocity, or distinctive mode can enjoy a purely active role in the governance of the field of discourse, the principle of whose
activity must be recovered, in the vertical or noetic sense, as a special unity [Concerning the symploke-eidea, see: Charles H. Kahn, "Why is the
Sophist a Sequel to the Theatetus?", Michael Morris, "Parmenides, Plato and the Semantics of Not-Being.", and Kenneth Sacks, in "Polybius on the
Writing of History", P. 118: "... the symploke directly relates to the special unity in history which demands illumination by the historian ..."]
available to the conception of the philosopher alone, who posits that 'interweaving of Forms' by which the nature of the active One and the passive
Many,- of the active Many and the passive One,- are discovered within their 'transconsistent discourse', [Graham Priest, In Contradiction: A Study
of the Transconsistent. In this book it is adequately explained, that neither the Hegelian inconsistency nor the arguments Kant used to produce the
antinomies are true dialetheic specifications, to whose class there belongs only the logical paradoxes of self-reference. Recall the distinction
active-passive combination,- the basic dialetheia or double-truth. [Socrates, in the Philebus: "The combination of the One and Man is an unaging
and immortal attribute of discourse."]

The Stoics were the first to seriously reckon with the aporias of the early metaphysics, having
thought-through the challenges given to them by Parmenides and his ecstatic vision of the Ontos.
For the stoics, a four-fold category of incorporeals was elaborated, of which language, that is, the
logos,- or what they preferred to call the lekta, [See Sellars, "An Ethics of the Event"; Angelaki,
Vol. 11.] was included. Parmenides, having perfected the circularity of thought-thinking-thinking,
asserted that nothing untrue can be thought, since, if it could, it would not be part of the All of
Being or Ontos, and therefor would not be able to exist as a thought within any human mind,
since all thought is contained within the Ontos as part of the All, and,- should such an untruth
exist outside of it,- the All would in that case, paradoxically, no longer be the All, which is of
course impossible. Human thought, for the Stoics,- as one of their incorporeals,- is irreducible to
the pure abstraction of the Ontos, and exists outside of it as a material remainder, like the free
multiplicities that Deleuze (note the "Logic of Sense") utilized to ground his own rhizomatics or
'reversed Platonism'. Thus the untrue, that is, something outside the merely ontic, (the ontological
minima of differentiation at the level of Being) can in fact be thought. The possibility of the
untrue, of self-deception, of philosophizing oneself into madness and fantasy, thus demanded, for
the Stoics, a turn to empiricism over Platonic metaphysics, while for Deleuze it demanded a
similar empiricism, though one creative in purpose,- one designed to carry reason into madness,
into the radical creativity of the schizophreniac. While the Stoics lacked the technical language to
fully explain their theory of incorporeals, philosophers of the medieval period returned to it and
dedicated new resources to the elaboration of a theory of eidesis more internally consistent than
the pure abstractions of Parmenides, namely the 'potentia dei' on account of which man can access
a 'visio intuitiva' or intuitive knowledge of a non-existing object, that is, an object beyond the
'material remainder' or ontic minima of differentiation demanded ('per privationem') by the
Parmenidean ontos, upon whose basis the privilege of the abstract category might be reinstated.
This use of the 'potentia dei' is further refined over time, eventually giving us the 'transcendental
auton' and the leptic interdependency of immanence-transcendence, or thought's basic 'symploke,'-
were it only the Flesh redeemed ex anastasin nekron [saved from death] or a Soul ex anastasin
sarcos, [saved from the flesh. We find the first, traditional phrase replaced by the later, indicating
no slight Gnostic influence in the opinion of Celsus, in one of the Greek variations of the Nicene
Creed, namely that found in the Symbolum Codex Sangallensis: sarcos anastasin zoin aeonion.]
that contemplates its object, in accordance with the German mystic Matthias Scheeben, sub
creatura intellectualis,-- in visio intuitiva der Gottlichkeit, in creatura intellectualis ab
Mitteilbarkeit. [P. Norbert Hoffmann, Natur und Gnade; die Theologie der gottesschau als
vollendeter Vergottlichung des Geistgeshopfes bei Scheeben. Analecta Greogriana edita Vol. 160:
die Gottanschauung, aufweist als etwas an sich nur Gott als Gott Zustehendes und die Kreatur als
Kreatur Ubersteigendes. ... Die konkre Struktur aber des gennanten Spannungsfeldes im Zu- und
Gegeninader von Natur und Gnade entwirft Scheeben dann- und hier liegt sein weiteres
Verdienst- auf dem Grundriss des Begriffs geistige Kreatur. Auf ihn projiziert er den Inhalt
unmittelbar Gott schauen und leitet dann einerseits die Transzcendenz (Gottlichkeit, der visio
intuitiva creatura intellectualis) der visio andererseits ihre Immanenz. (Mitteilbarkeit ab visio
intuitiva-creatura intellectualis.)
On the distinction of the 'visio intuitiva' and 'creatura
intellectualis
', see Danus Slangendorpius, in: Theses Theologicae de Tribus capitibus Christianae
Religionis nempe Arbitrio Hominis. Liberum arbitrium in homine, est facultas naturalium virium,
quae obiecta naturalia quodammodo eligit aut repudiat. Facultas naturalium virium, partim ex
obiectis, in quae fertur hoc arbitrium, partim adiunctis, hominis deprehenditur.
Frantz, in
Institutiones Theologicae De Deo Uno, Et Trino Usui; P. 185: Dissertatio III, de Visibilitate Dei.
Nihil hic de visione abstractiva quaerimus, aliunde jam in manibus est, Deum naturali lumine ex
effectis agnosci; subit igitur unice sciscitari: an visio intuitiva creaturae intelligenti concedenda,
sive facultas naturalium virium, sive peculiare Dei adjutorium spectetur
? Gonettus, in Cursus:
Visio intuitiva, quae intuitive videret essentiam divinam non visis relationibus, videret Deum ut
est in se unus, licet non videret Deum, ut est in se triuus; sed ex eo, quod videret Deum, ut est in
se unus, licet illum non videret, ut est in se trinus, videret illum secundum id, quod est obiectum
essentiale beatificum. Ripaldus, de Ente Supernaturali Disputationes Theologiae. At per te visio
intuitiva Dei, prout intuitiva est, et differens a non intuitiva repugnat apprehendi absque
cognitione perfectionum consequentium naturam tanquam objecti secundarii. ... Potest admitti
beari hominem formaliter visione creaturarum in Deo, si visio Dei beans hominem repraesentat
essentialiter creaturas in Deo
. Franzelin, Tractatus de Deo Uno Secundum Naturam: Nulli
creaturae immediata visio divinae essentiae naturalis est.
]
* Alfredo Gatto, in "William of Ockham and the Odium Dei", explains this medieval development of the Stoa: "According to the Venerabilis
Inceptor, each single individuality is an atomic fact. Objects are therefore released from any archetypal structure which threatens their individuality,
since they are exclusively bound to the will of divine liberty. God’s omnipotence could then subtract any entity from its system of common
relations. Now, if there is a difference between the intuitive knowledge of an object and the object intuited, and if God, in addiction, could subtract
each res from the set of its current relations, the homo viator cannot exclude that the absolute fact [res absoluta] represented by the intuitive
knowledge of a non-existing object could not exist without the presence of the object- since, for instance, the sensible representation of a color
[visio coloris sensitiva] could be preserved by God even if the color does not exist (the two things, in fact, are wholly distinct) We have to focus our
attention on the possibility that God, de potentia absoluta, allows man to have an intuitive knowledge of a non-existing object. In spite of
appearances, this possibility does not overturn the system of human knowledge."
Qui non intelligit, aut taceat, aut discat.

BTHYS TOU ANAHAT KHYA-PANDEMAI.
-- Hermaedion, in: the Liber Endumiaskia.

ΑΝΤΗΡΟΠΑΡΙΟΝ,
in formis perisseia mutilata in omnia perisarkos mutilatum;
omniformis protosseia immutilatum in protosarkos immutilata.

Measure the breaking of the Flesh in the flesh that is broken.
[ The Ecstasies of Zosimos, Tablet
the First.]

Parodites
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