This sentence is false

One of the supposed paradoxes of logic - if

"This sentence is false" is true - then it is false - which presents a contradiction. But if it is false, then it is true, which also presents a contradiction.
"BUT WHICH ONE IS IT?"
There are thousands of other examples of the same structure - some which involve combinations of sentences, some of which refer to others. Etc.

I have a problem with their logic...
What exactly, the fuck, does the above sentence refer to? To the SENTENCE? A sentence is a string of words, and if it doesn't make reference to something real or representative of something real - like a tree - or a concept - then it may just be a MEANINGLESS sentence. Does a meaningless sentence need to be true or false? I don't think so.
In any case, the sentence doesn't make sense, because the statement which it attempts to say is FALSE is...empty. No logical statement is by itself a contradiction - false and true simultaneously. We need to work with premises and statements of fact and then test whether other sentences are validly implied by the above, or not.

Chaos Theory of Axioms

I was writing the other day about how strange it is when you start out from slightly different axioms you may end up with entirely different theories, ethical philosophies etc...a sort of "chaos theory of axioms", for a sensitive dependence on the initial axiom

A guy on edge.org writes (and I love the clarity);
"...What we discovered was fascinating: Each major philosopher seems to take a small number of metaphors as eternal and self-evident truths and then, with rigorous logic and total systematicity, follows out the entailments of those metaphors to their conclusions wherever they lead. They lead to some pretty strange places. Plato's metaphors entail that philosophers should govern the state. Aristotle's metaphors entail that there are four causes and that there cannot be a vacuum. Descartes' metaphors entail that the mind is completely disembodied and that all thought is conscious. Kant's metaphors lead to the conclusions that there is a universal reason and that it dictates universal moral laws. These and other positions taken by those philosophers are not random opinions. They are consequences of taking commonplace metaphors as truths and systematically working out the consequences"

Pleasantly surprised

As expected, my MATH3201 Dynamical Systems and Chaos course is challenging, seriously interesting, rigorous and philosophically inspiring. Unexpectedly, the young lecturer for this course communicates with exceptional confidence, ability and did not have a fucked up, friendless childhood. High fives to Maths kids who have enough energy and balance to also have great social lives, and who know it. People, no matter what they are, convey your passions intelligently and with humour, and others cannot help but respect and admire you.

I'll now ignore this advice and rant passionlessly about why I've always loved Maths, right from the days when I attempted to introduce Pythagoras' theorem to my schoolmates (They still call me!).

I have been captivated by Cantor's maddening inquiries on Infinity which produced his monumental work on set theory, yet to appear in any syllabus of mine. In an Ivory tower, I have suffered by understanding Godel's Incompleteness Theorem. I have shared Lorentz' excitement at discovering the sensitivity to initial conditions of his computerised weather models. I can become energised by de Moivre's postulates about imaginary numbers and yet I know exactly how to treat and how to touch a girl.
I have never been an escapist. Hmph, my old nemesis Religion again. Sorry to relegate you people to the ranks of Harry Potter readers. Somebody was going to do it soon anyway

I still marvel at Von Neumann's childhood antics, the young Friedrich Gauss' outsmarting his Maths teacher and then assuming her role, and Fischer's noted stubbornness and promiscuity. The various forms of probability have not escaped my attention, irrationals fascinate and metaphysical questions about randomness intrigue me. Don't even get me started on higher order logical loops, and the great paradoxes and antimonies.

Maths is collectively hallucinated, and yet fits in with reality, and is necessary for critical thinking and sophisitcated argument on things ranging from biodiversity to politics to morality to architecture. The incremental logical skills it provides can even facilitate self awareness. We should all have been thinking about superstition when we were taught about induction.
Mathematicians may be poor at other things, but they carry society on their backs

"Cannibals don't eat clowns as they taste funny"

Evolution of abilities

Logical, mathematical and verbal skills augment a person’s other abilities...They don't detract from one's creativity...which, by the way, is about thinking repeatedly about something [NOT lightbulb moments]. The regions of the brain responsible for our higher-order logical and verbal capacities evolved after our amygdala did. So, if there is any behaviour that is likely to be unevenly distributed amongst the population...it is the capacity for structured, logical thought.
This is not to say that logical skills are only found in Maths, the sciences, Philosophy, or essay and speech writing!! One can take a logical approach to studying history, to analysing the law, to baking a cake, to understanding another person, or to the architect’s process of design. But mathematicians have their own aesthetic ideals, and could ultimately create artworks that other mathematicians think are beautiful, but which attract critical scorn from artsy types. But the artsy type couldn’t necessarily solve equations, with any amount of practise.

The reason why we can’t get computers to do certain things is that we don't EXACTLY know how we ourselves get the ‘inspiration’ to produce music, to write poetry or to paint vividly and creatively. I think its a numbers game, about risk-taking, and coming up with thousands of ideas, many of them bad. And rhuminating on them - as in when you wake up, and things are clear. Or in those experiments where, although you have no idea how you work out which word compliments each word from a list, you eventually blurt it out as your brain has been processing it all along. Sharing ideas with others like you but also getting input from very different brains has got to help too.