Key thinkers: Kurt Gödel and the Limits of Mathematics. Mark Colyvan (p1)

[@vitakyo982]

" This sentence is false " : is self-referential , so it doesn't mean much ... It's like saying : " This set of axioms are proven by themselves " . Anyway it's possible to say absolutely anything , so we must consider the fact that some assumptions are beyond all kind of logics .

[@NzoDK]

One of the most blatant Limits of Mathematics is the inability to explain why coughing is audible from the most subtle cues of uncomfortability,

[@timneish936]

Brilliant, this made my day!

[@vitakyo982]

" In some sense " : It's the sense that in some sense gives you the sense ...

[@vitakyo982]

Is it right to call natural numbers a 'set' ? A set would be the object that contains ALL natural numbers . How is this possible ? Mathematicians often play with infinity as if it was something accomplished , & some other times consider it as an open field ... & they arrange their demonstrations bouncing from a way to the other .

[@vitakyo982]

Give me an example of a set that contains itself ... Mathematicians deal with normal & abnormal sets as if they were the same objects with ease ... Consider for example the empty set , what would be the full set ? The red set ? The set that contains minus one element ? The set of abnormal sets ? The set that made you laugh ?

[@anow2]

Curious - 4 years later, were you ever able to cognize the idea of a set containing itself?

[@davidwilkie9551]

The phrase "in some sense" gets used a lot by Mathematicians, and it's frustrating not to have an actual sense of the applied intention in context. If it's interpretable as " that which exists and it is possible to sense", ...all good, because it's an equivalent to "observable" and "perceptible"? Otherwise it is an iteration of the theme of the talk and it's "incomplete" like an excuse for rigor or not, in uncertainty. (we are doing such and such,.. no particular reason, but it has worked before if you've been paying attention) The argument should start as the Uncertainty Principle does, with number identity in a precise place or algebraic approximation? ..And is therefore an independent abstraction apart from the senses? (just an amateur observation) So the "Natural Numbers" are human invention, in which infinite combinations of infinity are defined, because "real" discrete identities are abstractions only correlated with the actively shaped continuity of algebraic (quantized) states. As a "discipline" that removes fantasy and unfounded guesswork from objective measurement, Mathematics can begin with speculative values, discover abstract operations, and then apply possibilities to theoretical situations in a quantized manner that reduces purely empirical research to focused measurement. At least, it's what is effectively observable?

[@naimulhaq9626]

Godel proved the limit of linguistic logic with the liar paradox involving infinite axioms. Mathematical logic is different, it involves finite axioms, and Godel never proved limits or undecidable /incompleteness of mathematical algorithm.