A triangle with interior angles of 180/0/0 would be a degenerate triangle. It allows you to say that any three points in a plane determine a triangle instead of saying that any three non-colinear points do. Mathematicians are generally pleased when they don't have to make special rules to cover edge cases. — Srap Tasmaner
In that case, my difficulty with the OP is that we are trying to get degrees out of the substance/mode binary. Maybe that can be done, but at face value it is implausible. Unless there are only two degrees — Leontiskos
is it moral to get with a teacher versus an actual professor? — Zolenskify
I do really like the idea of trying to come up with a continuous graduation reality concept, which isn't an accuracy of a representation, or a way of counting things that already apply, or a way of saying how individuated an entity is. But I don't think it's possible, honestly. — fdrake
If you say that logic is not merely symbol manipulation, then what do you say it is? — Leontiskos
the paradox of your notes is that whereas the figure collapses uniformly, the surface areas of the 3D figures are limitless. — javi2541997
I think this recent move by the US to allow Ukraine to use US arms to strike targets deep inside Russia blatantly shows their escalatory intentions. — Tzeentch
For example, I am not an expert on mathematics, but some paradoxes are interesting, and I want to expand my knowledge of that — javi2541997
. . . or that contemporary philosophers in general are not interested in mankind’s search for meaning? — Joshs
What I mean about the difficulty of contemporary analytic philosophy, is that it's often extremely dense, written by and for those who can draw on a great deal of specialised scholarship — Wayfarer
If I were a professor, I would evaluate more the grammar than the content itself. Maybe a student is great in math, but if his grammar is terrible, I think he should not be able to promote. Simple. — javi2541997
because on many philosophical views the goal of a philosophy teacher is not going to be publication, but teaching (really more mentoring), which of course certainly happens, but in academia there is the whole "publish or perish" thing that can often backload this. — Count Timothy von Icarus
I don't see why it needs such a presupposition. Humans have found that nature is intelligible. — Janus
Interesting. Does nature include quantum mechanics and consciousness? — Tom Storm
Elementary calculus does not require "actual" infinities. — jgill
Calculus uses infinite sets on day one. Even before a student gets to calculus, with analytical geometry we're using infinite sets. The real line and the real plane are infinite sets.
But it seems you mean that calculus doesn't usually mention transfinite ordinals (though the set of natural numbers is a transfinite ordinal), which is true. — TonesInDeepFreeze
I have used R, but not a transfinite number. Unless I occasionally use the "point at infinity" in complex analysis. — jgill
Points at infinity are not required to be transfinite numbers. — TonesInDeepFreeze
If there is an air of insubstantiality about this thread, it is because it is concerned with the philosophy of philosophy. This makes it particularly liable to disappear up its own fundament.
Accordingly, I propose, firstly, that philosophy is always parasitic; one might try a 'philosophy of nothing', but it wouldn't get very far. Rather, one first starts to talk or write about something and at some later stage, one starts to examine the verbiage philosophically. as philosophy of religion, or knowledge, or psychology or whatever. — unenlightened
If possible, (ideally sic) the best foundation is bedrock, If one has reached bedrock, as Wittgenstein would have it, one has reached the end of that portion of philosophy, the questions are resolved or dissolved, and the superstructure is as sound as it can be.
By contrast, spiritual talk is untethered, lighter than air and floats higher and higher until it reaches such height that it attains outer space, where there is no longer any up or down, and no one can hear you pontificate. — unenlightened
:roll:Modern philosophy is philosophy developed in the modern era and associated with modernity
I was thinking that the tradition of the "top-level" idea casts philosophy as specifically "the queen of the sciences" — Srap Tasmaner
Set theory is needed for the rest of math and so is logic — Srap Tasmaner
But here I would question whether the notion of cause adds anything that is not already given in the mechanistic description. — SophistiCat
You seem to want to dilute the concept so as to include just about any kind of mechanistic analysis, which is tantamount to eliminating causation — SophistiCat
But how is that "checking the validity of one argument using another"? — TonesInDeepFreeze
I don't know what you mean. Example? — TonesInDeepFreeze
https://en.wikipedia.org/wiki/Proof_by_contradiction — Hanover
Regarding knowledge of the curriculum - the kind of student that satisfies all benchmarks in a subject has already been discouraged from pursuing their insights and skills due to herding them through the curriculum at a required pace. It is not uncommon to see an allegedly failing student have a profound insight, which you nevertheless cannot spend time developing with them — fdrake
But since my big post from 6 days ago was opaque to you I'm quite discouraged from continuing on. — keystone
Not sure. But a lot of potential PhDs seem to wash out just from the long dreariness and uncertain job prospects after completion, — BC
When you mention "the Lounge," are you referring to an actual place, or do you mean taking a pause in the conversation until others join in? — keystone
Overall, I think you have started down a path that is far too complicated for the desired result. — jgill
Someone could say the same thing about the epsilon-delta formulation of a limit, which was introduced to give calculus a more rigorous foundation. — keystone
I think there's also a difference between "memory" or memorizing something and the knowledge (and the understanding) of something. — ssu
I would like to ask the reader about how does the reader suppose that knowledge can influence one's identity? — Shawn
A real number corresponds to a specific subgraph within a potential structure. In the 1D case, this is represented by a potential curve and the two potential points that are directly connected to it. — keystone
It's a philosophical question which most philosophers are not equipped to even begin to answer — flannel jesus
But what's that got to do with the topic of the thread? — Clearbury
DKE is accurately characterized as 'the stupider a person is, the less likely they are to realize how stupid they are' — Clearbury
the main point is that the DKE is accurately characterized as 'the stupider a person is, the less likely they are to realize how stupid they are' — Clearbury
i wouldn't have thought an expert would write a wikipedia page - they're too busy being experts — Clearbury
However, in 2D and higher dimensions, a curve is determined not only by its endpoints but also by an equation. Perhaps incorporating that equation into the vertex might make the concept more digestible — keystone