George Spencer-Brown (GSB) did some wonderful work for a system of logic that has us consistently painting ourselves into a corner. That’s the problem. His work contributes to a system of reasoning that is consistent but incomplete.
What he doesn’t see (and few who I’ve encountered who understand his work) is that he is stuck within a cataphatic mode of thought. When he says “Let us take the form of distinction for the form.” he effectively merges the boundary between things with one of the spaces that boundary ‘encloses’.
So he takes ‘the mark’ as being indicative of what it encloses. This is wrong – or maybe it’s better that I say it’s ‘too eager’. Continue reading “Spencer-Brown: Cataphatist”→
To say that the Universe ‘exploded’ from a ‘thing smaller than an electron’ in what’s commonly called “The Big Bang” could be a complete misunderstanding of the data we’ve gathered from our observations of the galaxies and ‘stuff out there around us’. Let me show you the ‘other side’: Continue reading “Honey, I Shrunk the Universe…”→
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: Continue reading “The Law of Existence – Part 2”→
George Boole’s “Laws of Thought” have been extremely useful in many disciplines, but I contend that they are nevertheless incomplete. In their dominance over most of Logic and Philosophy, they have caused a conceptual ‘blind spot’ in the many fields of research which use or emanate from such reasoning – including the Foundations of Mathematics. It’s time we set the records straight. I propose one law, which for now I call “The Law of Existence”, and show how the Laws of Thought emerge naturally from its consequences. Continue reading “The Law of Existence – a better logic?”→
If a Thing is to exist, it must be, by necessity, at the very least ‘not’ that-from-which-it-exists. This ‘not’ is what enables it to exist, and as such is the transformation by which it exists. This transformation is the defining boundary of a Thing; the Thing is fully-bounded by “not”. But the existence of a boundary gives rise to there being two sides. And so we understand that for a bounded Thing to exist, there must exist that Thing’s complement – that is, the that-from-which-it-exists. “not” is an involutory transformation in that a second “not” cancels both. However, in normal speech, this cancellation is referred to as “is” – where “is” is “not not”. So we understand that by being defined by ‘not’, an extant Thing is absolutely unique. If it was not, then it would not exist – because it would not not-be something else (it is not-not something else – thus it ‘is’ something else). Continue reading “Set Theory 2.0 – a first attempt”→