Using the power of analogy, a new structure-mapping engine gives computers the ability to reason like humans and even solve moral dilemmas.
Source: Making computers reason and learn by analogy: Structure-mapping engine enables computers to reason and learn like humans, including solving moral dilemmas — ScienceDaily
I’ve said it before, human thinking works on sameness and difference – key being difference!
Here, they’re taking the cataphatic approach – probably bouncing off Douglas Hofstadter’s work on analogy, but guys! don’t forget about the opposite – dissimilarity!
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?”
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”
Definition of a Thing:
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”
The human mind, I am convinced, operates in terms of sameness and difference*. From this conviction I have recently come to label two modes of thinking – ways which the mind ‘makes sense’ of the world:
Continue reading “Understanding Understanding: Two modes of mind”
If ever there was something which merited the name “God” in my eyes, it would be the Mobius Strip. But I don’t believe in a personal, let-alone sentient, god. I’d be far more inclined to call it “Tao” instead. Buddhists might call it “Om” (or “Aum”). Mathematicians should call it “i” (the square root of negative one), but there are even more examples in Mathematics (the involution, the half-rotation, inconsistency, contradiction, “not” or the symbol ¬). Electronics circuits represent it as the inverter whose ouput feeds back into its input. Philosophers might call it “contradiction” or more formally the “paradox of self-reference” epitomized in the Liar Paradox:
“This statement is False.”
Continue reading “The Deep Symbolism of the Mobius Strip”
The circle is a strange creature, and most definitely not as simple as it seems. In fact, you will see that a circle in the plane doesn’t enclose anything – that ‘inside’ and ‘outside’ are completely arbitrary and in the end, meaningless. Hold on to your seats!
Continue reading “The Circle in the Plane: How bizarre is this?”
On Infinity and Boundaries:
You have to understand that if you have an infinite “expanse” of sameness that is unchanging, and that you (I say ‘you’, but I mean ‘it’ or ‘unknown’ for the time being) cause a Thing to exist from that sameness, if it is to ‘exist’, then it must necessarily be perfectly bounded; and if it is perfectly bounded, then, reciprocally, so too is the ‘infinite’ sameness (which is now clearly not infinite).
Continue reading “Strange and relative thinking: two examples”
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.
Continue reading “Adjacent Existents – A Theory”
To my previous post, Louis Kauffman, himself, generously took the time to reply. I have included his reply in the comments section of that post. In that comment, I’d promised to continue the discussion in a new post. Here it is, with the brief continuation of the dialogue I had begun with Mr. Kauffman. I have copied the discussion here below:
Continue reading “Mathematics and the Real”