The Law of Existence – Part 2

Law of Existence – continued

In my previous post, I promised to illustrate how the Laws of Thought, as they are used today, emerge naturally from the Law of Existence. Time to make good on my promise.

In a comment left by reader SelfAwarePatterns he mentioned that he didn’t see how the Law of the Excluded Middle (LEM) was rendered false by the Law of Existence. He’s absolutely right – it’s not false, and indeed it’s very naturally present already within the Law of Existence. What is false however, is the ‘closed’ interpretation of the LEM which says that a Thing only ever is or (exclusive or) is not. That is clearly false, and to use the example he gave:

If I am a bachelor, I’m also inevitably not a non-bachelor.

So if one were to adhere strictly to the LEM:

Either I am a bachelor, or I am not a bachelor.

So what’s the problem here then? I seem to be not only stating the obvious, but somehow re-stating the LEM? The problem is our notion of the existence of a Thing and what that implies.

Using the ‘closed’ interpretation leads us to the ‘blind spot’ perspective where one can’t say what a bachelor is because there’s no room for identifying what a non-bachelor is.

I know, it sounds pedantic and I’d be the first to agree – except that the subtlety at such a low level  has bigger ramifications of bias at higher levels of abstraction and reasoning. A few fine examples are the rash-like aversion to inconsistency in so many fields of ‘rational’ research, and yet the hypocritical usage of a highly-convenient inconsistency: the ‘complex number’ i.

Another consequence of cataphatic-only reasoning is that the current understanding of the axiomatic Set Theory (take your pick which one – they’re all blind to this) is the fallacy of the null set: the null set is not a set! I can’t emphasize this strongly enough.

The null set is usually defined in the following way:

  1. The null set has no members/elements.
  2. The null set is a subset of all sets.

[First, sets are usually defined as having members. But with the null set, now you’re talking about a set which has no members – so what exactly do we know about ‘sets’ here? That’s like saying “well, a car moves, but it also does not move” uh, OK, so what you’ve just said applies to every single thing in the universe (i.e. absurdity/principle of explosion). So what are we even talking about? Why even call these things ‘sets’? Might as well just call them “things” – I do! But that’s a little digression.]

OK, so this notion of a null set being the subset of every set is usually justified by a double-negative as follows:

For any set, A, the null set does not have any members which are not members of A.

This formulation works nicely if we are looking for a way to say it’s a subset. Replacing the ‘null’ set, rephrasing it with, say, B, we get: “For a set A, B does not have any members which are not members of A“. Duh, right? Remembering that a ‘subset’ is not the same thing as a ‘proper subset’, so A could have more members than B if we’re talking normal subsets, and couldn’t if we’re talking proper subsets (and let’s not kid ourselves: what honestly is the difference between a proper subset of a set, and the set itself?).

But often the reverse formulation is entirely neglected:

For any set, A, the null set does not have any members which are members of A.

This is obviously true if the null set has no members, period. But this second part states that the null set is forever ‘outside’ every set – and that’s a description of the “universal set” (also a fallacious set!).

So either the null set and the universal set are identical or the null set is not a “set”. If it’s not a set, that means we’re now defining that sets must ‘contain’ at least one element/member lest it not be a set proper.

Also, here’s a little question to blow your mind (and in so doing, dust away any remaining conviction that ‘sets’ are worthwhile mathematical objects): Can elements exist without being members of any set?

Of course not! Say there was one element which was not a member of any set. Well then you could define the set with one member: the element which is no member of any set! Say what? This is the famous Russell Paradox.

Now it’s all-well-and-good to stop there and admire the paradox. But something more has to be said: If elements cannot exist without also being members of at least one set then all elements are sets necessarily. So remind me again why we’re even calling them sets?

Have a break… you deserve it

Welcome back!

So if the Law of Existence (as I’ve chosen to call it for now) is indeed the full expression of the Law of Identity (i.e. A Thing is ‘what-it-is’ and is not ‘what-it-is-not’), then that’s the Law of Identity already covered.

By both being and not-being, that’s the Law of Contradiction gone (nothing can both be and not be) – except if we understand it as a permissive statement “Nothing (some stuff, especially if you understand this as ‘undifferentiated sameness’) can both be and not be at the same time.

And we’ve already visited the Law of the Excluded Middle before the break.

So, now what? You may be feeling a bit cheated. At least that’s how I feel – like I’ve just spent all this time writing about these ‘laws’ which do nothing more than to say the same thing in different ways…

Well, in a way, that’s my point. This is a case for perspective. I’ve never claimed that my ideas were going to destroy anything we already knew about the world – what I want you to do is see the world as it is, not as you want it to be. Understanding that you can’t have a Thing without also necessarily having its non-Thing is the essence of understanding existence as it is. Consider it like being a fish who finally notices its swimming in water. That the ‘nothing’ around it is actually ‘something’ – that it’s all something in fact – only that all somethings are separated by and share boundaries (all extant things are conterminous with all others). That there are no ‘gaps’ in existence, ever. But, as I’d mentioned in my previous post, inconsistency is the very nature of those boundaries – they are what make things both be and not be at the same time. These boundaries are the negation – the involutory transformation by which all things exist. I want you to notice the boundaries, not the things which they define. Once you see that it’s the boundaries that define all things, and you take a deep look (and think) around you at anything, you will see that ‘really’ the only thing which exists is the boundary itself – as you move away from the boundary you move in ‘sameness’ (whichever kind of sameness that ends up being – ‘whiteness’ of the fridge door, ‘woodness’ of the table, ‘atomness’ of an atom, and on and on) until you reach the other side of the boundary. Crossing that moves you into another, different sameness.

Seeing the thing as the thing itself is a very Western (cataphatic) perspective. The Eastern (apophatic) perspective sees the form of the thing as the thing itself, to put it awkwardly. The key is to see using both perspectives.

So to get a deeper understanding of these Laws of Thought as they might have been correctly understood (especially within the context of Logic, which is, after all, what I’m after here), one must see that a statement is a Thing subject to the same Law of Existence as any other Thing. Being unique (because ‘not’ all other possible statements) it is True (hold on now, bear with me a second – this is uncomfortable, I know!). From the perspective of that statement all other statements are False (i.e. not-True). But, remembering this, now realize that any other statement, from its perspective is also True, and it’s all other statements that are False.

What you’re seeing here is a system of logic where every statement is à priori True (wait! gimme a sec!), but being uniquely existent statements, they are all different from each other (so this isn’t full-on trivialism! Have courage, tough it out!). So then how and where does ‘Falsity’ come into the picture? Well, I’ve shown you how each statement ‘thinks’ (to personify here a little bit) every other statement is False – but how do we, speaking/reasoning humans determine a False statement?

A real False statement is a ‘True’ (in that it is uniquely existent and has been spoken/thought) statement which does not match experienced reality. So you have True-True statements which ‘attach to reality’ 1-to-1. And from there, other adjacent statements either attach to reality also, or they do not – and that’s the ‘real’ Law of the Excluded Middle.

So what do I mean by ‘attach to reality’? When the truth of the statement is identical to the truth of reality. That is, when the statement is not un-real (see the double-negation?). So a discussion about unicorns can attach to reality in some places, but not in others: a unicorn is a horse (attach to reality) with one horn (does not attach to reality). One can carry-on a ‘logical’ conversation for all that pertains to the horseness of a unicorn, but that’s as far as it goes. This may seem very messy, but I think (humble opinion) that this is what allows us humans to talk about abstract things as though they were real.

Well, again, I’m exhausted, and if you’ve gotten this far, you might be also. This is really tricky stuff to be able to talk about, so reading about it must be even trickier. I can only recommend that you take from all this one simple rule: A Thing cannot exist without its complement which is also a Thing. Then explore and test it for yourself in your own language. You’ll see what I mean eventually. I wish you the flash of insight.

Thanks for reading!

Taomath

One thought on “The Law of Existence – Part 2

  1. Hi Tom,
    Mind bending stuff, as always.

    “A Thing cannot exist without its complement which is also a Thing. Then explore and test it for yourself in your own language. You’ll see what I mean eventually. I wish you the flash of insight.”

    I fear the core insight you’re trying to impart isn’t coming to me. (Or maybe it is but I’m missing its significance.) It may simply be a blind-spot on my part.

    I wonder if you could note one or more of what you see as the implications of the insight. That might allow me, along with anyone else who isn’t getting it, to backtrace our way to it.

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