Non-Well-Founded Identity Principle

Non-Well-Founded Identity Principle

In an effort to clarify this concept, I wanted to add an update:

Edit 11/02/2018

The point of the Non-Well-Founded Identity principle is to characterize identity in a way which I propose is more accurate and less presumptive. Rather than following our scientific impulses to define all things in single, final ways,  we can step back and instead integrate the full spectrum of epistemological and ontological nuances into our description of math, logic, and science. What I propose here with the Non-Well-Founded Identity Principle is a redefinition of the identity principle to one which factors in the reality of perception, which I propose is not only a bottom up construction, but a diffraction from the totality down. Unlike artificial intelligence, natural intelligence is kind of prism which opens up the ‘light’ of consciousness to its deeper nature, using both analytical steps and intuitive synthesis.

Rather than saying A=A (that everything is itself), I suggest that every phenomenon is:

  • A spectrum of presentations/qualities/properties which can be said to be bounded on on two ends.
  • On one end, all things are bounded by a conserved identity. They are simply what they appear to be in whatever perspective and context they appear.
  • On the other end, all things are a spectrum of resemblances/similarities/associations/dissimilarities that can be navigated poetically and reveal profound dimensions that echo the totality of experience.

In other words, rather than A=A, I propose instead that A equals a spectrum that runs from self equivalence (A=A) to a second spectrum of similarities that ultimately include diametric dissimilarity, i.e. running from A=A to A~!=A.

A= {the spectrum of identity running from A to (a nested spectrum of identity running from almost totally A to almost totally not A)}

This idea is extended further below so that “A” as a unit of identity is replaced by sense itself, so that any sense experience is a spectrum that runs from experience of a purely particular experience to the nested spectrum that runs from all particular experiences to all experiences to the particular experiences that define the sense spectrum itself.

End of update.

Beginning of previous article:

Here’s a crazy little number that I like to call the Non-Well-Founded Identity Principle. It woke my boiling brain up a few times last night, so I present it now in its raw state of lunacy.

The idea here is “For All A, A equals the integral between A and (the integral between A and not A)”.

This represents a refinement of trivial identity, A=A, to reflect the grounding of all propositions in the Absolute inertial frame of pansensitivity. The nested integral specifies that all integrations are themselves defined as that which is not disintegrated. Any object, subject, or sensory presentation or representation (A) is itself, and it is also the range of all possible relations, literal, figurative, and otherwise, between itself and all that is not itself (≠A).

This comes out of the idea that sense is the Explanatory Gap, i.e. the gap between private experience and public bodies is a non-well-founded set (non-well-founded sets contain themselves as members) in which primordial pansensitivity*defines its nested child sense experiences in a terms which are both unique, generic, and everything in between, depending on how the local perceptual inertia frames it.

*pansensitivity is plain old feeling, sensing, being and doing, but extended and universalized beyond Homo sapiens, as well as physics and arithmetic truth. Ontology itself – being; the is-ness and it-ness of all phenomena can be reduced further through the Non-Well-Founded Identity Principle, under which ontology becomes the nested gap between phenomenology and the sense of its own absence. This is a very tricky shell game, but it is not intended as a trick or a game. Said another way, ‘privacy is the difference between privacy and the difference between private and public experience.’

Applied to philosophy of mind, we would get: Naive realism equals the difference between naive realism and (the difference between naive realism and reductionism). Another one would be Sense equals the sense of the difference between the sense and (the difference between sense and logic). It could be said that X=/(=/≠) X, so that any number is a straight isomorphism with itself, but it is also a superposition of any potential combinations with or relativity upon any and all X that it is not.

The reductio ad absurdum can be seen in this second expression:


in which integration itself is the integral between integration and disintegration. Every set or process is defined by its own self-same initiation and termination.

Is this all insipid tautology? Is it another way of catching a glimpse of Heisenberg uncertainty or Gödel incompleteness through a fun house mirror? I don’t know much about calculus, so there may be a more conventional way of expressing these kinds of relations, but in the mean time, to me, it’s an absolutely interesting way of modeling the absolute: A universal capacity to simultaneously universalize and de-univeralize (proprietize) the universal experience.

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