No — jgill
we could play around with the axioms to disallow irrationals, oui? — Agent Smith
Many years ago I was watching the Academy Awards (don't ask me why I would waste my time that way). Whoopi Goldberg was at the microphone, and she said something like, "We don't need the space program. We should get rid of it. Nothing ever came out of the space program", as she was being broadcast via satellite. You gotta love it. — TonesInDeepFreeze
inconsistency — TonesInDeepFreeze
If it is consistent, it is not complete; if it is complete, it is inconsistent. — Agent Smith
all that money earmarked for space ventures could be spent on more pressing matters — Agent Smith
Gödel? If it is consistent, it is incomplete; if it is complete, it is inconsistent. — Agent Smith
What could possibly be more pressing than people getting their satellite dishes on the roof to watch reality TV shows of people eating bugs? — TonesInDeepFreeze
pi is not a ratio of two rational numbers.
pi is the ratio of the circumference of any circle and its diameter. But if the diameter is rational then the circumference is not. So still pi is not the ratio of two rational numbers.
So there is not a contradiction. — TonesInDeepFreeze
Since music is numinous in nature, it being somewhat of a bridge between us and the universe, the Pythagoreans probably extrapolated the math found therein to the universe itself. — Agent Smith
The discovery of irrationals, kind courtesy of Hippasus of Metapontum who was thrown overboard to prevent word of this getting out, threatened to overturn what was up to that point a perfect world. A simple and yet magnificent way mathematics could serve as the foundation of the universe had to be abandoned. I wonder what Max Tegmark has to say about this? — Agent Smith
I know, I know, pay no attention to the man behind the curtain. — jgill
Mathematicians come up with general formulas, involving pi and other irrational numbers. Isn't it the case that engineers make use of those general formulas, from which they can decide what specific specific values to use as close enough for the task at hand? — TonesInDeepFreeze
Yes sir! But what happens when understanding the foundation of the universe is "the task at hand"? — Metaphysician Undercover
Sadly, it seems math discussions on TPF are doomed to descend to the level of farce. — Real Gone Cat
Thus, the diagonal of the square is now commensurable with its side, which we've known to be untrue since the time of the Pythagoreans! — Real Gone Cat
Good luck with that. — jgill
Thanks, but unlike the undisciplined mathematicians who make willy nilly axioms however they please, we don't rely on luck here — Metaphysician Undercover
... unlike the undisciplined mathematicians who make willy nilly axioms however they please ... — Metaphysician Undercover
I've told you about a million times already, you can have axioms for whatever you want*, even inconsistency if that's your thing. — TonesInDeepFreeze
I reject your productivity and outcomes argument, whatever rubric it correctly falls under.
— TonesInDeepFreeze
[...] your actions fall short of moral excellence (in that indignancy fail prudence and justice) — Kuro
[...] in not acting rightly one retracts from the virtue of their character, which is less so a property of any particular fault or flaw in action rather than those habits which become second nature to them and come to form their decisions & methodology (which is what the discussion came about, the generalized implications versus the particular one, hence the relevance of the quote). — Kuro
I find myself as frequently frustrated as Mr. Tones with respect to the mathematical, logical or other formal/technical errors that are somewhat frequent on this forum. However, a rude attitude seldom yields anything productive: there is the option of politely leaving a discussion, perhaps at no fault of your own but the inadequacy of your interlocutor, or explaining their mistake at a reasonable level.
"Fanning the flame", so to speak, is unnecessary in whole. [...] — Kuro
I didn't say the axioms are wicked, I said they are wlly nilly. — Metaphysician Undercover
In the philosophy of mathematics, I am not a scholar, but I have read many books and articles. In mathematical logic and set theory, I'm not a scholar, but I have a good handle on the basics through taking courses and careful study of several textbooks — TonesInDeepFreeze
somehow the truths of math have been revealed to no one else but you. — Real Gone Cat
What, in your wisdom, is math after all? — Real Gone Cat
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