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.

4 thoughts on “Look again! Law of Paradox is True…

    1. Ha! I guess so. To add to the above:

      If the Law of NC is True – “Nothing can both be and not be”, and the Law of EM is True – “Every Thing either Is or Is Not”, then Everything (the set of all Things) can both be and not be – therefore Everything is Nothing… ;D

  1. Very insightful. This is the same paradox that arises in naive set theory. If we treat the set of all things as an object itself, then NC fails. This is why set theory does not consider sets to be objects or “things”. In this case, I think there is a subtle distinction: nothing and non-thing are different. A non-thing is simply a different class of “things” in that they can be the object of our consideration, but they do not exist. A better word for a non-thing would be a non-existing thing. All is not nothing, it is a non-thing. It is not in the class of existing things but it is not nothing either, it is a non-thing.

    1. Hi Oliver, thanks for visiting, and extra-thanks for commenting!
      I see your point, but I still think it’s a ‘cheat’ to avoid personal discomfort of accepting the validity of ‘paradox’.
      While I wouldn’t use your words in that order (I would say All and Nothing are the same, and from the first ‘not’ you get Thing and ‘non-Thing’) it is true (kind-of) that Nothing/All and ‘non-Thing’ are not the same. But it can be argued that they are: Thing is ‘removed’ from All/Nothing via the ‘not’, but All/Nothing is the ‘remainder’ from which ‘Thing’ was partitioned, so is, arguably, ‘non-Thing’. So Nothing and ‘non-Thing’ are still the same… A real head-scratcher though 🙂

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