And as I tried to impress on you, a curve is not even close to a multitude of straight lines. — Metaphysician Undercover
Now you're getting the idea. Yes, I agree, that anyone who scrapped that stuff would be greatly handicapped at this time of scrapping the stuff. But necessity is the mother of invention, and what would develop out of the scrapping, making a fresh start, knowing what we know now, would be a great improvement. — Metaphysician Undercover
jas0n
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So, if we're to avoid the pitfall of talking past each other, we must come to an agreement as to what the words we use mean,
— Agent Smith
To do so would require that we use words, yes? Hence the hopelessness of starting from scratch. And what works in math won't work in philosophy. 'Language is received like the law,' and meaning evolves historically. — jas0n
Well, there are lots of ambiguities in mathematical symbolism. The equal symbol for example, then the idea of transforms and transformations, etc. In advanced math one has to consider context to interpret accurately. — jgill
"The Old Shadow" (Freddy N.) – Erdős was merely projecting. :wink: — 180 Proof
The issue is that this type of approximation produces the illusion that we understand what a curve is, when we really do not. There's a fundamental incommensurability between two dimensions of space, which makes things like pi and the square root of two irrational ratios. What it indicates is that we lack a proper understanding of space.
The fact that we are in the habit of reducing straight lines at angles to each other to curved lines through the application of infinity, Is evidence that we simply ignore this deep misunderstanding, and proceed as if we think that we understand. I would argue that the "damage control" which you claim, is basically non-existent, because those employing the principles actually believe themselves to have an adequate understand, when infinity proves useful, therefore wouldn't even seek damage control. The problem is prevalent all through modern physics, with vectors and spins, etc. — Metaphysician Undercover
Le meglio è l'inimico del bene — Voltaire
Actually "infinite-sided polygon", to me, can only be interpreted as an incoherent object — Metaphysician Undercover
The vacuum cannot not reveal "Himself". — 180 Proof
No. That's like a fish giving up water. We think metaphorically, maybe only metaphorically. The point is to not be trapped unwittingly in a metaphor — jas0n
Philosophers (and regular folks) still don't agree what 'God' means, what 'exist' means, what 'intervene' means (at least in this context), and of course what 'mean' 'means.' Meaning is social and therefore ambiguous. We mostly ignore this, because we mostly stick to practical talk. Start talking religion and politics and things get ugly. Somehow the other fellow just doesn't 'see' it (the folly of his ways, his bad logic, etc.) — jas0n
think you underestimate their force and prevalence. Lakoff, Hofstadter, Wittgenstein. Folks have been trying to tell us that we think in pictures, often without realizing it. See what I mean? (With your inner eye.) Do you grasp what I'm saying? (With your intellectual hand?).
How can abstract thoughts get themselves established in the first place? — jas0n
over simplification — apokrisis
Too much money and too many generational careers have been dedicated to this mission for it be a "random shot in the dark". Like gravity waves, Higgs bosons, black hole imagery, thousands of exo-planets (Hubble, Kepler, etc), acceleration of cosmic expansion, etc – just in the last quarter century alone, my man, like "The Killer" himself sang, "there's a whole lotta shakin' going on" in so-called "Big Science". — 180 Proof
Some have claimed that our technical/abstract terms are just dead metaphors, their blood having been drained till they are imageless. — jas0n
(∀x)(DOGx→(∃y)(y=x)) — MLP
Most language is too meaningful, too suggestive, explosively untamed. It needs context, context, context. Philosophy still doesn't know what it means by 'meaning.' But (practical) math requires much less context and yet delivers far more clarity. Math is 'hard' because...most people find it too boring for the necessary concentration ? Or they drag in too much meaning and can't just see it as a calculus? I think it's harder to understand Hegel or Derrida or Wittgenstein than to learn calculus. I don't claim to have mastered any of those thinkers. The dialogue is endless. — jas0n
If I tell you that a tower of infinities actually exists in something like a Platonic realm, what does that mean for you and me? If you tell me that you do believe in but not , what am I to make of that? Does it mean you therefore aren't interested in it? But perhaps a skeptic studies the system to debunk it. On the level of math, it's dry logic, something like a symbol game. This tower exists within that 'fiction,' just as the bishop exists in the rules of Chess. It's not clear what is being denied or asserted when we are talking about the outside of this game. Does the denier mean to indicate that his intuition has peeked into Platonic heaven and only found infinity classic? Or is it a matter of taste? Utility? Maybe a mix of things. In any case, ambiguity — jas0n
Math is brilliantly stupid — jas0n
That's math, though, a game of symbols, a generalization of chess, one might say. One can be ultra-precise in this limited domain. — jas0n
Yes. And for me the issue of whether there are 'really' various infinities leads inexorably what we could mean if we say so. All roads seem to lead to the 'problem' of the meaning of 'meaning. — jas0n
It all depends on how you define "circle-like". — Metaphysician Undercover
IMO, there would be no difference at all. The phrase 'infinite-sided polygon' is typically interpreted as a circle. (Nonstandard interpretations are possible, of course.) — jas0n
Even having been a prof of mathematics I learn something about the subject on this forum. Never came across this. — jgill
What motivates panpyschism? — OP
Looked it up, and it's a big part of math. 'We'll transform this into a quadratic equation, which we covered last week...' — jas0n
As you probably know, the old timers of math tended to feel that way...that only 'potential' infinity was respectable. But beyond what is accepted formally (say you embrace the symbol game of an infinite tower of differing infinities), an ancient problem remains. What does it all mean? To what does it all refer? How does it hook up with the rest of life? — jas0n
circle-like — Metaphysician Undercover
What if your die had an infinite number of sides, do you think it would be circular? — Metaphysician Undercover
arbitrarily close — jas0n
Well it makes for a lovely myth (sort of like Nietzsche going mad from his denial of God). He moved on from the lemniscate to the Hebrew alphabet before going mad, btw — jas0n
