These ideas are a work in progress.
Axiom 1: A Thing “exists” if and only if it also defines what it is “not”, which is also a Thing.
Axiom 2: A Thing “does not exist” if it is “not not” what it is not – i.e. if it is also its ‘not-Thing’ – this is identical to ‘All’/’Nothing’/’void’/’sameness’:
From Ax. 1 & Ax. 2: An “adjacency map” is a Thing. It is a ‘Thing-of-Things’ such that each Thing of a map is ‘adjacent’ to every other Thing.
If the boundary between two Things disappears (ax. 2), then this reveals a new adjacency map.
2) A Thing can “be composed of” any number of adjacency maps simultaneously
A note about Things:
It is important to understand that each ‘cell’ or ‘space’ of an adjacency map is not a ‘space of points’ like in current Set Theory unless we are specifically talking of the adjacency map of points, which itself is a ‘space’ of the adjacency map of adjacency maps.
No, every ‘cell’ or ‘space’ is a unique, whole Thing in that particular adjacency map.
One can create an adjacency map for the physical Things. This, by axiom 1 also defines non-physical Things.
If we were to then distinguish Things which are physical, then that distinct adjacency map would ‘kiss’ or ‘touch’ our physical space (i.e. be bounded by, be identified to) of our earlier adjacency map.
Two physical Things would thus define our “physicality” adjacency map but those two physical Things would at the same time ‘touch’ the non-physical ‘space’ by their “two-ness” adjacency map because “two-ness” is both physical and non-physical.
Liar’s Paradox: is perfectly acceptable: “Infinity” is sameness, so is not a Thing (ax. 1) and yet it can be the continuous sameness (self-sameness) of a Thing (ax. 2). The key is our human voluntary choice of not distinguishing (choosing not to apply ax. 1)
Truth is Nothing, if without a distinction (ax. 2), so Truth is only True while it is not False (ax.1)
Infinity, Truth, Nothingness, void, sameness are all the same.
Now, consider the ‘adjacency map’ of adjacency maps:
Yes, So what? It is an adjacency map of all adjacency maps. This continues “infinitely” such that the adjacency map of all adjacency maps becomes a non-map: it is ‘indistinguishable infinity’ where infinity is ALL/NOTHING vs. THINGNESS -> again, another adjacency map. The Liar’s Paradox is perfectly acceptable: it is “change exemplified”. i.e. it is a recursive self-inversion.
A Thing, alone, “behaves with oneness” and so is a Thing in the ‘numbers’ adjacency map.
Two Things “behave with two-ness” and so is a space in the ‘numbers’ adjacency map – but each is also ‘oneness’ otherwise ‘they’ would not be ‘two’.
So there exists a “oneness” adjacency map, and a “twoness” adjacency map etc.
These maps are all Things which “behave” ‘one-ly’ or ‘two-ly’ or ‘three-ly’ etc.
And let’s not forget that all these adjacency maps are each their own ‘space’ (or Thing) in a “numberness” adjacency map.
Points and Space.
“Space” is an adjacency map of unique points. Each point exists as “not all other points”. As such, all points of space are ‘adjacent’ in that they are ‘not’ every single one of their neighbours – otherwise they would not be ‘unique’.
Temporality arises from the very fact of existence. That a Thing exists means it must be different from the sameness out of which it stands. That means it must not ‘be’ same, and so must change, immediately.
Historicity arises from the very fact of existence. That a Thing exists means it did not exist so its Past is “not” its Future and vice versa – so it must be different to itself continuously (see temporality, above).
And yet every iteration (instant of its existence) is added to its Past – it is continuously “not” itself: This is an adjacency map being ‘fed’ into itself:
This can also be seen to be the successor function.
These are all ‘dumped’ from my brain this Sunday afternoon, so are very rough-draft. But I would like to see where this system goes.
Key things: Paradox is allowed. Indeed, it is essential, as the ‘distinction’ is paradoxical and gives rise to change.
Ok, thanks to help from the Philosophy Forums:
I’ve since discovered that what I’m working on is a System of Paraconsistent Logic – one that specifically denies the ‘Principle of Explosion’: ex contradictione quodlibet – “from contradiction anything follows”:
If a statement P is discovered to be both True and False (which doesn’t work in my system – but could be described by my Axiom 1), then this, by Axiom 2, means nothing (principle of explosion or ‘triviality’) until we find the distinction in which it is no longer trivial – in which case we have ‘discovered’ the new statement P’, via Lemma 1, and thus define a new adjacency map.
More on this as I learn.
(later) For example, I’ve realized that one could see this system as a form of Trivialism – where in ‘ignorance’ everything is a priori True – and it is as we ‘make distinctions’ (the “not”), we define ‘falsity’ as just another kind of ‘truth’…
(2016-04-25 Updated: Here, all statements are True, but being ‘statements’, are Things, and thus unique and adjacent – thus ‘not’ every other statement. Falsity emerges self-evidently from this, and so this is not utter triviality – utter triviality is Truth without distinction and thus no statement can be made)