Gödel's Incompleteness Theorem

[wolven7]

Today's topic, thinking about it, while driving: Gödel's Incompleteness Theorem as applied to the entirety of human knowledge, and the incomplete understanding of mathematical variables, specifically related to our belief that "Mathematics is the Universal Language." Cf. The idea that we are not able to truly understand each other, without stipulative definitions and designations, therefore, another species may have a conceptual apparatus completely unlike our own.

E.g. What is Mathematical computation, to us, may, in fact, be food, to them. Blue may=fish.

This calls into question the very existence of "a priori truth," as all concepts must be conceived and then propigated. Taught. Teh designators by which we teach and learn these will dictate what we teach and learn.

In short: Mathematics is not a universal language, and what we hear as radio noise may, in fact, be radio signal to someone or something else.

Discuss.

Comments

[rainydaymary.livejournal.com]

Godel's Incompleteness Theorem demonstrates the incompleteness of our mathematical system: precisely, that not everything within that system can be proved using the components of that system. It has nothing whatsoever to say about any other modes of understanding.

[wolven.livejournal.com]

The point of the Exercise, or Thought Experiment if you will, is to Use that Theorem as a Model for other modes of Thought.

Good Morning. And You are...?

[wolven.livejournal.com]

See also the Writings of (if not myself, at other points in this journal), J.R. Lucas, who also believes that the application of the over-arching Theory of incompleteness can be made to cognitive science, and many other areas of philosophy.

[raidingparty.livejournal.com]

Simple bit, here; when investigating computer architecture here, I came upon the clue I could encode 0=umbrella, 1=orange, 2=g major chord, and so on, and someone else could encode a computer with numerical values defining entirely different concepts, but they'd both be equally valid.

There's also one of my favorite ideas, that it's possible that everyone else sees everything in negative from you, and you'd never know. They point to a dark red apple and say, "red", but if you were to get inside their mind's eye you'd see light green dappled with dark purple spots.

[wolven.livejournal.com]

Right. The inverted spectrum hypothesis. It means, ultimately, that while we will be Able to communicate, eventually, we must first agree upon a linguistic and conceptual model, by which we frame it.