“ALL Reality is Transformation” – A Review

Reality:

It may seem absurd that I see Reality (indeed, all Reality, hence the capital ‘R’) as being ‘made of’ Transformations. I am the first to admit it because this is my view almost despite myself – “I would it weren’t so”. In fact, it’s this very discomfort, this very dismay that motivates me to review each reason, carefully, once more.

While it may seem reasonable that, in seeking something which can both be ‘Sameness’ and ‘Difference’, I choose Transformation as the definitive candidate, it nevertheless seems difficult to grasp how that might come to be, in the real physical realm.
Continue reading ““ALL Reality is Transformation” – A Review”

Look again! Law of Paradox is True…

This is my most risky post. This is one of those posts I know will peg me as mad, but will turn out to be true, if only someone were to come along later and maybe re-word it so that it is more palatable to a wider audience. So here goes…

Much of philosophy is dependent upon three laws – what are called the three laws of formal ontology:

  • The Law of Identity (ID). It states “That which is, is.”
  • The Law of the Excluded Middle (EM). It states “Everything either is or is not.”
  • The Law of Non-contradiction (NC) (also strangely called the Law of Contradiction). It states “Nothing can both be and not be.”

I will show you that the last law (NC) is a contradiction in itself, and by being so, admits the validity of paradox.

But first, some ‘ground rules’ or tools with which to break down the three laws:

  • Truth:
    • Take to be True that which is permanent, which ‘hold still’. Truth forever is True.
  • Falsity:
    • Take to be False that which is not permanent, that which does not ‘hold still’. Falsity is never (not forever) True.
  • Not:
    • The inverse of ‘is’, where ‘is’ is ‘not-not’. So, ‘not’, on its own, is of similar quality to False, because it is unstable, undeterminable, and can never ‘hold’. All odd numbers of ‘nots’ are identical to a single ‘not’.
  • Is:
    • The inverse of ‘not’, or not ‘not’. ‘Not-not’, is of similar quality to True, because it is, stable and determinable, and will forever ‘hold’. All even numbers of ‘not’s are identical to a double ‘not’ –> ‘not-not’.
  • Or:
    • This is ‘not’, in the sense of ‘one, not the other’, this is a part, a disjunction, as per above False.
  • And:
    • This is not ‘Or’, or ‘not-not’, in the sense ‘Not(one not the other)’, this is the rejection of the part, acceptance of the whole, a conjunction, as per above True.
  • All:
    • That which exists and that from which is existed, both Thing and not-Thing. “Is and is not” which is ‘not-not not-not not-not not’, which is False, forever changing and unpredictable and cannot hold still.
  • Thing:
    • A ‘thing’ is what is, that which stands-out from the All, i.e. that which is not-All. Thing evaluates to “not-All”, so one more ‘not’, and so evaluates to ‘not-not’. True.
  • Nothing:
    • That which is not-Thing, i.e. “not not-All” – where ‘not-not’ is, so “Nothing is All”. Nothing == All. Nothing has the same qualities as All and as Falsity, it is forever changing and unpredictable and cannot hold still. False.

 

Now let us look at these laws:

The Law of Identity: “That which is, is.”

  • “That which is”, is “Thing” as per above. Thing is ‘not-not’.
  • “Is”, we’ve seen, is ‘not-not’.

Rebuilding this statement, we have “Thing is”: ‘not-not not-not not-not’: ID is True.

 

The Law of the Excluded Middle: “Everything either is or is not.”

  • “Everything” is ‘every (single) thing’. We can thus consider just one ‘thing’ and consider its truth to be applicable to every one of them. Thing is ‘not-not’.
  • “Either” is superfluous to “or”, so we can rephrase it to “Everything is or is not.”
  • “Is”, we’ve seen, is ‘not-not’.
  • “Or”, above, is ‘not’.
  • “Is not”, is ‘not-not not’.

Rebuilding this statement, we have “Thing is or is not”: ‘not-not not-not not not-not not’ – eight ‘nots’, which is True. EM is True.

 

The Law of Non-Contradiction: “Nothing can both be and not be.”

  • “Nothing” is ‘No Thing’, is not Thing, is ‘not not-All’, is ‘is All’, evaluates to ‘not-not-not’.
  • “Can”, is permission, so is equivalent to “is”, ‘not-not’.
  • “Both” is superfluous to ‘and’, just as ‘either’ was superfluous to ‘or’.
  • “Be” is “is”, ‘not-not’.
  • “And”, as above, is “is”, ‘not-not’
  • “Not be” is not “Be”, is not “is”, is “is not”, ‘not-not-not’.

Rebuilding the statement, we have “Nothing is and is not”: ‘not-not-not not-not not-not not-not-not’ – ten ‘nots’, which is True.

 

But let’s look at that last one (NC) again: We’ve seen that Nothing is All. So “All can both be and not be” This is a permissive statement indicating that A=¬A, a paradox! How can the Law of Non-Contradiction contradict itself?!? Because it admits paradox! At every moment, we remain coherent, even though it sounds so strange: “Nothing is and is not” <–> ”All is and is not”<–> ”All is True and False” (which, finally, is of vital importance if we’re to even have a concept of Truth, because there can be no Truth without what is not-True). This only admits that our Reality allows for the existence of Paradox (which, when you think about it, makes sense A) because we’ve got a name for it: Paradox, and B) we’re a part of this Reality, and we can conceive of Paradox, and C) it is a truly pesky thing which keeps cropping-up whenever mathematicians try to formalize the logic of the fundamentals of mathematics – paradox doesn’t go away!).

All, some may argue is not Nothing. But when you take Everything, and remove all boundaries between every Thing, you are left with a masse whole with no Thing – which is the apeiron – the All with out limit.

Set theory, Mereology, boundaries and continuity

With this notion of wuji, or apeiron, or continuum, or whatever, the whole idea of set theory never sat well with me. The null set (the set which has no members) doesn’t quite make the cut. Consider the continuum – perfect homogeneous Everything – and you realize, like the definition of apeiron, it is limitless, or has no boundaries. Thus it cannot be contained and so cannot be a member of a Set – ‘the set of Everything’ for example. Then I thought about the boundaries. These boundaries are the only way to distinguish something within the apeiron. So instead of thinking of sets, I thought of boundaries within a limitless whole. Being infinite, the first boundary is actually a bisection, splitting everything in the middle. without actually ‘cutting’ anything.

Think of it like a strip of paper with black on the reverse side, white on the other side facing you. If you give that paper a half-twist, you are now differentiating the strip into half-white, half-black. The first thing in a continuum would be a Point which, in 1D, requires two boundaries So a second half-twist (I would opt for an un-twist actually but I’ll get to that) is needed. Sure enough, you now have a ‘segment’ of the strip-continuum which is clearly black in the middle and white on either side. So what we know about a Point’s position in a line is that it is not the point to its left and not the point to its right. The twist and un-twist is so that you have the truth value ‘within’ the boundaries:

---|>0---0<|---   (my crude graphic of two NOT gates facing each other)

This got me thinking further: What is the smallest number of boundaries required to enclose a 2D region? I realized that three line segments joined as an equilateral triangle was the most basic enclosable region. So a 2D region is enclosed by three 1D regions. Then a 3D region is enclosed by four 2D regions. This was a trend that allowed me to reaffirm my earlier concept: a 0D ‘region’ is ‘enclosed’ by one transformation – the zero-D Reflection, Not.

Let nB = the minimal set of boundaries required to enclose a region in the nth dimension. |nB| is the number of boundaries within that set. nBm where m is the index of nB sets

0B={Not}, |0B|=1

1B={0B1, 0B2}, |1B|=2

2B={1B1, 1B2, 1B3}, |2B|=3

3B={2B1, 2B2, 2B3, 2B4}, |3B|=4

nB={n-1B1, n-1B2, n-1B3, …, n-1Bn+1}, |nB|=n+1

So the smallest 3D region is delimited by four 2D regions. This is, of course, the tetrahedron, which can be made by four planar ‘cuts’. A triangle can be ‘cut’ out of paper using three cuts. A segment of string can be made with two ‘cuts’.

So, also, I discovered another field of study in mathematics called Mereology – the study of wholes and their parts. There is mention of Alfred North Whitehead – a strong proponent of Process Philosophy, which is very strongly similar to the rationale that I’m using on this site. Everything is a process, or act of transformation.

Well, once again, this is a short entry, but more to think about… Hope you enjoyed it!

Substance vs. Space

It is important to distinguish the apeiron, or wu, from the space which emerges from it. They are not the same thing – or if they are, I need to be careful.

Just because the Dynamic and the Static define Points and then 1D Rotations etc., that does not mean that every Point is the Dynamic or whatever. Instead it means there is a Point wherever a zero-dimensional Reflection occurs. Wu is the substance, and the Point is the space which emerges from it. Transformations are the substance of Reality, at least I maintain. But transformations do not ‘occupy’ space, they define it.

This is the slipperiness of the notions we’re working with. Wu (apeiron) is not the null set, no matter how tempting it is to define it that way. Yes, the null set has no members, and Wu is the uniform unchanging substance of Everything and consequently has no relations, but it is not a set precisely because it has no boundaries, and so cannot be delimited by the concept of a set (remembering that null is “The set containing no members”). Wu cannot be contained but is the container. So the first ‘element’ of Wu is the null set, i.e. a delimited portion of Everything, which is not Wu. The null set is defined by the zero-dimensional Reflection ‘not.’

Maybe Wu can be defined by x ∉ ∅, without {}, thereby making it not-a-set, i.e. an element – but an element that cannot be an element of any set!

Even the ‘finesse’ available in set-theory which is the proper subset, where every element of a subset is identical to the set (from which it is ‘subbed’) yet this is not the same set, doesn’t fit the bill. This is why the null set is its own subset but not its own proper subset. Apeiron still doesn’t fit, because you still can’t say it is a proper subset of the null set, since it’s not a set!

There is another tack available to my reasoning though – because I said initially that Wu is transformations, it doesn’t mean that all transformations are identical. Yes, they are all inter-dependent (transformations transforming other transformations), but the first Static is sufficient for the emergence of Space, and the first Dynamic is sufficient for the emergence of Time, but is that to say that all of space is an infiny of points? I don’t think so. Yes, we use Points to refer to the position of something, so yes, this creates the possibility of reference.

Unfortunately I know far too little of Topology to begin to understand the various configurations available for a collection of Points. Yes, they certainly could be spherically arranged. They can also be flat (Euclidean). But an infinite expanse of an infinity of Points renders the ‘curvature’ of space a moot point, since an infinity of points allows for any shape imaginable – the concept of curvature ceases to hold any meaning.

Bah! I’m losing steam here. Running out of ways to move forward. Could my reasoning have gone down a dead-end path? Could I have thought myself into a corner? It looks like it, but I’m not giving up. I may have to start from Nothing again.