What would it be made of? — tim wood
Is it reasonable (however defined) for philosophers who have not studied mathematics to argue basic principles of the subject? — John Gill
Though you cannot measure how long a point is (since it has no length, as per definition) you can identify a point. And we do so through a complex process that involves the movement of our bodies (if we're talking about identifying points in physical space, that is.) — Magnus Anderson
There are many things that have no size but that nonetheless exist (and are not logically contradictory, illogical or otherwise irrational.) The word "existence" does not imply size. For example, colors and feelings exist, and yet, they have no size. A typical counter-argument is that colors are light waves and that light waves have size (their wavelength.) But light waves are not colors. Rather, light waves are things that cause colors. (This is evident in the fact that light waves can exist without conscious beings whereas colors can't.) — Magnus Anderson
It's just a line. It signifies a spatial dimension. Why does it have to be "made of" something? You may as well be asking me what a dimension is made of. It's an idea. — Metaphysician Undercover
(Imo) egg-zackly! That is, everything in and of math is an idea. Being ideas, they're subject to definitions, not reality in any sense at all. You wanna talk my ideas, then you have to know my definitions, and vice versa. As such, there is no "how it is." But there is, however, "how I say it is." — tim wood
But maths are useful in the world. As a consequence, it is necessary - and certainly useful - to not confuse the theoretical/idea side with the practical/reality side. There are "points" and there are "lines" and what either means, or any of a lot of other terms found in both theoretical and practical applications mean, is simply a matter of the application and the relevant understandings, without which nonsense reigns. — tim wood
...then they'd be making excellent arguments - excepting that with the qualification they might be trivial and not worth making. — tim wood
"A point in geometry is a location. It has no size i.e. no width, no length and no depth. A point is shown by a dot. A line is defined as a line of points that extends infinitely in two directions. It has one dimension, length." From online.A "line" has dimension, yet the "line" was said to be "made up" of points. Do you see the inconsistency? No matter how many dimensionless things you add together you will not produce a thing with dimension. — Metaphysician Undercover
I do not know how you got that! Maybe you read again? My point is that where definitions matter, in the contexts in which they matter, then they do matter. If the definition is context dependent, then outside of that context, while it may be interesting in itself, it is irrelevant.So what are you saying? We ought to just get rid of definitions altogether, — Metaphysician Undercover
You really are having problems with language. You are a) in my opinion deliberately conflating usages of "trivial" in a context where a reasonable person would not, or be in any way confused, and b) in extension, if " What is trivial to one person is important to another," then it would follow that we'd have a ready test for determining what is important. Or, that is, everything would be important, either because it is important, or, someone thinks it unimportant, thereby trivial and therefore, important! But we have no such confusion about unimportant and trivial arguments because the proper qualifiersWhat is trivial to one person is important to another. — Metaphysician Undercover
Well here's an example of confusion in your thinking. We agree that points and lines are ideas, therefore the proper objects of definitions. The which having nothing to do with true. But you mention consistency of definitions. What definitions? Your definitions? But you want to "add" points. How, exactly, do you add points?Now, I'll ask you how is it possible that the "true" nature of the "point", and the "line", — Metaphysician Undercover
Points don't exist in physical space. According to the description they are non-spatial. — Metaphysician Undercover
Irrational numbers are not only irrational, but they go on forever ... — Gregory
The same applies to pi and the circumference in the sense of infinite fintude. — Gregory
Maybe math proves that something can come from nothing since spatially finite comes directly with spatial infinity. — Gregory
Nothingness is not dark, but white and shining says the Tibetan Book of the dead — Gregory
Point taken. Nice exposition. Ignorant as I am, I actually know what you're talking about, but forget and need to be reminded. Thank you!No, this is not true. But it's such a common misunderstanding that a bit of exposition is in order. — fishfry
A point in geometry is a location. It has no size i.e. no width, no length and no depth. — tim wood
Well here's an example of confusion in your thinking. We agree that points and lines are ideas, therefore the proper objects of definitions. The which having nothing to do with true. But you mention consistency of definitions. What definitions? Your definitions? But you want to "add" points. How, exactly, do you add points? — tim wood
am not sure why you think so, Points do exist (both in time and space.) Consider that at any point in time, you occupy certain point in space. So there exist at least some of the points that we can imagine. Points that do not exist cannot be occupied by anything under any set of circumstances. — Magnus Anderson
A point in geometry is a location. It has no size i.e. no width, no length and no depth.
— tim wood
Think about what you're saying tim, "a location" without any size is nonsensical. — Metaphysician Undercover
Sure. If I'm directing you to Luigi's Pizza Barn, you may reasonably expect that location to have at least discernible size. But we're talking about mathematical points, if they have any size at all the everything is very, very large - and exploding because what's large clearly comprises many points.If there is a dot, to show the location, there is something there with size. If there is no dot, then there is no identified location. But "location" implies particularity and particularity is identifiable. — Metaphysician Undercover
Maybe I should pay more attention to what you've written here. There is no issue between us. There is an attempt to come to an understanding of how a mathematical point is defined. Maybe you could cut and paste your definition here. And resolve the difficulty of uncountable infinities of infinite size created when points have any size at all.So if you want me to agree with you on any definition of "point", — Metaphysician Undercover
Question: on a ruler one can mark units, then divide the units in half, thirds ( I think), quarters, & etc. But there is no way to mark an exact irrational length on the ruler - unless a line representing an irrational distance is constructed (like the square root of two) and marked on the ruler by direct measurement. Correct? — tim wood
I don't see why Zeno's paradox is not a paradox but Banach-Tarski is. The latter flows directly from the former, and there is no BT without Zeno — Gregory
So mock me as you like, but you're actually mocking the rest of the world.. — tim wood
Are you prepared to argue that an idea has a size? — tim wood
Now, it seems you cannot keep track of the distinction between theoretical math and the math of the world. In the world, most locations have size, for lots of reasons that have almost zero to do with size. — tim wood
Maybe I should pay more attention to what you've written here. — tim wood
There is no issue between us. — tim wood
Maybe you could cut and paste your definition here. And resolve the difficulty of uncountable infinities of infinite size created when points have any size at all. — tim wood
You're just being ridiculous. — tim wood
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