More pretty soon: galaxies with DM, etc…

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]]>Given any 2 positive numbers, m, n, there exists another number, p, such that m < np.

That was taken for granted, as you just did.

However, shortly after 1950, Model Theorists (a type of logician) realized that was an AXIOM. Can't prove it from the standard ZF axioms of arithmetic. Hence the discovery of non standard analysis.

https://en.wikipedia.org/wiki/Non-standard_analysis

In the Godel theorem an existence proof shows that one comes to choices, where two logics offer themselves, one or the other being driven by a new axiom… The choice is purely META (extraneous to the logic initially analyzed). The Godel thing is purely existential, not COMPUTATIONAL (Godel numbers exist, but can't be computed).

Before Godel, one could fear that a logic, as a closed rational system, was INTRINSICALLY TAUTOLOGICAL (Hilbert didn't understand that). Godel showed that, in the sort of logic used in arithmetic, no logic was logical: it required to go META (by forced to make axiomatic choices)

Anyway, the short of it is that "rationality" necessarily involves irrational jumps, once a situation is not fully predictable… sort of by definition…

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]]>I agree, the idea that working toward higher rationality involves embracing some irrationality is intuitively appealing, in a Godelian or meta-axiomatic sense.

But, as an economist, my hackles go up whenever “rationality” is introduced, as discussions of it tend to become sickeningly tautological and Panglossian.

cheers,

b

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]]>Oh, and, BTW, there were missing axioms in Euclid… Or even in basic arithmetic. **In the 1950s, non standard analysis pointed out that standard arithmetic used the ARCHIMEDEAN axiom (as it became known). For any positive integers, m, n there is a third one so that m < pn… That had not been noticed before. denying it gave sense to Leibnitz's infinitesimals…**

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]]>It’s absolutely not rehashed Godel. Godel demonstrated that, because of the INFINITY AXIOM, any logic L, branches off infinitely into other logics. However, Godel didn’t say when the branching occur, just that it will occur. It’s actually a variant of Georg Cantor DIAGONALIZATION PROCESS. If you want my opinion, no big deal… Although it shot down any pretense to make mathematics the end-all, be-all… (Hilbert’s program.)

My point was simply that, in any Logic, one modification of one axiom, emotional or logical (formal) makes a new logic. What do I mean by “emotional” axiom? Take Euclid for example. There was a bunch of axioms, PLUS the implicit (META) axiom that it was all there was to it. Actually the latter point, that meta axiom was fiercely debated for the parallel axiom, bringing 21 centuries of stupidity (they were trying to demonstrate something that was OBVIOUSLY false, and very well known to be false, before Euclid… It’s in… Aristotle…)

Now as far as the too long didn’t read… Well, I agree many of my essays are very long, all too long, in this five second, three word logic worlds… It takes time to chop down… I have an essay on the Me 262 jet, for example, and another on meditation. Simply leaning down the Me 262 essay will take an hour, and another hour to get it ready for publication. Personally I don’t mind reading long essays, as long as they are interesting…. It doesn’t mean I belabor every nook and cranny… If really interesting I can go back to them later…

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]]>“Everything is incomplete!” (Ponder that…).

Re: PC in Berkeley: it is funny in a schadenfreudian kind of way that Trump is sending a large number of the illegal immigrants flooding into Texas to Broward County….

cheers,

b

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]]>Yes, in all PC correct Berkeley… **People, even Politically Correct people, especially PC people, are all into being correct… as long as it doesn’t concern them, personally**

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]]>Thanks!

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