Brian, my only issue with finitists (as it seems I have still failed to make clear) is one of logical consistency. If one rejects “actual infinities” then one should similarly reject “actual circles”, “actual square roots”, “actual probability fields”, actual anything that relies upon or implies continuity in any form.
If you do that, then you simply hold a philosophical position which I think is unproductive. No skin off my nose, certainly. So long as you do not attempt to use that philosophical position to restrict the math, of course.
Well, I see no reason to make those assumptions, actually. Though it might depend upon how you are defining perfect. Usually, when we say something is not perfect we mean that the actualization does not match the ideal conception. If infinity is an ideal conception, then the assumption that nothing is perfect is false. If infinity is not an ideal conception, then the assumption that infinity is perfect is false. In short, it appears your axioms are contradictory. That has nothing explicitely to do with infinity; it applies equally to any abstraction.
I am afraid I do not understand what you mean in “math purveying it as perfect from logic”. I assume the precusror of it is “infinity”, but I do not know what you mean by the phrase as a whole.
arl
If I visualize any continuity, I have visualized infinity. When I imagine a circle, I do not imagine it with a nea-infinite number of “gaps” too small to see. What I visualize is continuous.
I simply noted that said equation strongly implies that a negative value for E is allowed. It is neither more nor less sensible than speaking of negative mass. In fact, the equation by itself leaves the possibility of c as a compound value open, too. This simply illustrates the danger of taking the form of an equation and arguing that it carries an implication for what reality must be.
I wouldn’t presume to limit anything in math, I think the concept only needs limiting in theosophy as it relates to cosmology. However, I am more than curious as to how one holds theosophic concepts apart from math. This is another thread, or course.
As an aside, I was left wondering through all of this why anything divided by zero is not infinity (why can’t something un-de-fined also be in-finited). I know, it wouldn’t work mathematically by category, but…nevermind. Thanks as per usual.
In a line (segment), between any two points are contained an infinite number of points.
There’s an infinite number of points in a meter.
There’s an infinite number of points in a light-year.
Some infinities are bigger than others?
Yep.
Lets say you start at zero, and count to infinity, using all numbers.
0,1,2,3,4,5,6,7,8,9,10,11,12…
Then do the same, using only even numbers.
0,2,4,6,8,10,12,14,16,18,20,22…
the “all” infinity is twice as big as the “even” infinity.
Don’t think of infinity as a quantity, but as a direction.
Some infinites are bigger than others, but what you have shown is that the set of integers can be paired one-to-one with the set of even integers. So the set of integers is the same size as the set of even integers. A set is infinite if and only if it can be put into a one-to-one correspondence with a proper subset of itself.
The set of reals is too large to be put into a one-to-one correspondence with the set of integers.
