I don't know why I'm participating in this. — Srap Tasmaner
But it does match it, as I've already noted. Your mere assertions are getting old. — Leontiskos
Either you consider the sphere as embedded in 3-space, and the cross section plane isn't "flat" in some sense - it's at an incline. Or you consider the surface as a 2-dimensional object, in which case there's not even a plane to think about. Pick your poison. The latter is the original counter example and is much stronger, the former is easier to remedy. — fdrake
But clearly that's not true, as the definition you provided doesn't match something you clearly recognised as a circle! — fdrake
How will you parry my counterexample? — fdrake
If it makes you uncomfortable, stop tromping on my bridge. — Banno
And you are ignoring the fact that I used it twice. — Srap Tasmaner
He doesn't need to. The sphere is a 2-manifold, and his great circle is a set of points on that manifold. There are no planes here, nothing else, only the points on the surface of the ball.
You are imagining the sphere embedded in the usual 3d Euclidean space. Now, imagine it isn't. There is no point the points on this great circle are equidistant from. — Srap Tasmaner
What do you think a plane figure is? — fdrake
that circle instead would be a closed curve inside a subset of R3 — fdrake
but it does not satisfy Euclid's definition of one verbatim — fdrake
You could also have ardently insisted that indeed, the great circle was not a great circle because it was not a plane figure. — fdrake
Well who said anything about cross sections? — fdrake
You'll now need to tell me in what circumstances can you take a cross section of a volume and have it work to produce a circle. Let's assume that you can take any volume and any cross section and that will produce a circle... — fdrake
The cross-section of a sphere is a circle. — Leontiskos
The great circle is the circle I've highlighted on the surface of the sphere. Since the circle is confined to the surface of the sphere, it is not a plane figure. — fdrake
Euclid says: not a circle. The great circle is not a plane figure. — fdrake
Let's change track. You tell me exactly what you mean by a circle with an intensional definition, and we'll go with that. Then do the same for roundness and pointy! — fdrake
A circle is a plane figure bounded by one curved line, and such that all straight lines drawn from a certain point within it to the bounding line, are equal. The bounding line is called its circumference and the point, its centre. — Circle | Wikipedia
If the presupposition is that all systems are equal, our preferences for them arbitrary, then of course logical impossibility is pretty much meaningless.
But we don't pick systems arbitrarily. — Count Timothy von Icarus
Imagine you start at a point, and you go 1 step north and 1 step northeast
The taxicab metric says you've travelled 2 total units - you add the steps.
The euclidean metric says you've travelled sqrt(2) total units - you measure the line. — fdrake
A circle in taxicab geometry, a set of points defined as equidistant from a single point, looks a lot like a square in euclidean space. — fdrake
I could also insist that it is a circle, and how are we to decide between your preference and my preference? — fdrake
The derivative of a curve... — fdrake
A circle is, by definition, a set of points Euclidean equidistant from one central point.
And thus we've revealed what sneaky hidden presumption you had through lemma incorporation. — fdrake
Take all the points Euclidean distance 1 from the point (0,0) in the Euclidean plane. Then delete the point (0,0) from the plane. Is that set still a circle? Looks like it, but they're no longer equidistant from a point in the space. Since the point they were equidistant from has been deleted. — fdrake
If we go by Leontiskos intuition that round things cannot be pointy in any context, well the Earth is in trouble. — fdrake
I just wouldn't call them circles to my students learning shapes. — fdrake
That's the nub of the issue - methodological naturalism is taken to be a metaphysics, which it actually is not. — Wayfarer
Basically I see the appeal of Aristotle and common sense as a mistaken appeal -- it makes sense of the world, but need not hold for all empirical cases: There are times when a person is in contradiction with themself, or an organism has a contradictory cancer, or a social organism is composed of two opposite poles (hence Hegel's use of contradiction in attempting to understand a social body or mind). — Moliere
And I, for one, take up the liar's paradox as a good example of an undeniable dialetheia: A true contradiction. — Moliere
logical impossibility isn't all it's cracked up to be — fdrake
Material logic — Count Timothy von Icarus
Historically logic is the thing by which (discursive) knowledge is produced. When I combine two or more pieces of knowledge to arrive at new knowledge I am by definition utilizing logic. — Leontiskos
word searches are neither good arguments nor good ways of informing yourself about philosophy. — Count Timothy von Icarus
I disagree you can disregard the "not S" step, because the statement in its entirety must be false. If I say "if I pray then my prayers are answered", stating "I don't pray" says nothing about the consequent of that statement so we don't know what it means. Q is merely implied because if there are no prayers, they cannot be answered. — Benkei
Q is merely implied because if there are no prayers, they cannot be answered. — Benkei
So I agree this is valid — Benkei
But the logical structure and the argument are not necessarily the same. — Benkei
At what point though is it incumbent upon the person with the "bad (cultural) habit" to change them, ethically? When it leads to harm? When should a cultural habit that leads to possible harm be excused? — schopenhauer1
Physicalism in relation to methodological naturalism seems to me like an empty suitcase taken on a plane. — Baden
3. Physicalism’s close association with methodological naturalism and the confusion there engendered risks denigrating the latter. — Baden
[Methodological naturalism's] justification as a method rests on its results rather than any metaphysical presumptions. — Baden
Of course, this might have less to do with culture than political arrangements — schopenhauer1
Now, the more complex question though, is when does it become incumbent upon people of a certain culture to evaluate a possible negative cultural trait/feature to see if it needs to change?
...
At what point might one take the new cultural feature and change the previous culture, if at all? — schopenhauer1
If not P, then not Q (if R, then S)
Q equals if R, then S
Not R
Therefore, not S
Therefore, Q (through double negation)
Therefore, P — Benkei
Edit 2: To continue the line of thought that ↪Leontiskos, if let's say a culture simply had built-in (extremely) violent responses to injustices, and then someone was not from that culture but promoted (extremely) violent responses to injustices, but advocated it out of philosophical regard, if we determined the extreme violence was "bad", would the philosophical regard agent be worse than the cultural agent? — schopenhauer1
You deny entry when the immigrant does not meet the countries established laws for entry. — Philosophim
However, what about ¬(A→B)? What can we say about this in English? — Lionino
However, I wouldn't take it as a badge of honor to be entirely ignorant of the basics of logic prior to the 20th century on account of this fact. — Count Timothy von Icarus
The idea that there is "nothing but formalism" is the problem. — Count Timothy von Icarus
Not having experienced it so far doesn't rule it out, though. — frank
The framing in the OP seems to lean towards the idea that "logic" is "formal logic." Thus, we speak of "languages," "systems," and "games" and difficulties within or between formalisms as problems for "logic." — Count Timothy von Icarus
Formal logic is about "ways of speaking," but logic is not about "ways of speaking" tout court. — Count Timothy von Icarus
Anyhow, to the extent that logical nihilism will tend to imply that things have no causes, that there is no metaphysical truth, etc. I think it's open to the criticism that:
A. This seems demonstrably false on all the evidence of sense experience, the natural sciences, etc.;
B. No one actually has the courage of their convictions on this matter and really acts as if causes and truth are "just games," and;
C. This makes the world inherently unintelligible and philosophy pointless. — Count Timothy von Icarus
Plus, to the extent that someone still tries to justify logic on "pragmatic" grounds it seems to be the case that any "pragmatic" standards bottom out in arbitrariness, there being no truth about what is truly a better standard or what truly ranks higher on any given standard. Hence appeals to the "usefulness of certain games," are unsupportable. — Count Timothy von Icarus
How do we determine which logic is appropriate for a given situation/problem? Sorry if this is a banal quesion. — Tom Storm
↪Leontiskos ↪Banno To what extent does your disagreement on this involve, perhaps, one being a conservative and the other liberal? — Tom Storm
And that is where we stand. Presuming that there is one true logic is no longer viable. — Banno
Logical pluralists seem to argue that different contexts require different logics and this seems to be determined by the kinds of reasoning or the goals of inquiry involved. — Tom Storm
Logical pluralism takes many forms, but the most philosophically interesting and controversial versions hold that more than one logic can be correct, that is: logics L1 and L2 can disagree about which arguments are valid, and both can be getting things right. — SEP | Logical Pluralism