I’m not rejecting math, except to the extent that it does not apply to physical reality, such as a completed infinity (ie the bounded unbounded). Your refusal define what you’re talking about is your problem if you intend to challenge my definition and the definition of every dictionary on earth.
You can’t say you reject my definition and then not offer a replacement and then continue to use the word. You also cannot offer a definition that relies on the very fact that you’re disputing (a set bijected with a subset of itself requires that the set be unbounded).
If infinity is not the unbounded, then simply tell me what it is… in plain english with good faith effort to convey meaning.
What I find weird is that you won’t even say which. You could say, “I hereby reject Cantorian infinity,”
I reject ALL infinities as nonexistent because they are just as absurd as your assertion that anything could be both bounded and unbounded, in terms of cardinality, at the same time.
How can the cardinality of the set 0 and 1 be “uncountable” and also be bounded? And not only that, but be bounded by a bigger unbounded thing? This is absurdity!
What is unbounded is without borders and cannot be said to exist. How can we have a box with no walls or a container with no confinement?
And all this strife and struggle because you so desperately want this concept of infinity to exist.
This debate is exactly the same as the atheist/theist debates I hear on youtube.
and at least I’d know what you’re talking about. But you act like you’ve never even heard of it.
I’ve heard of it, but have no interest in it because it has no practical use, at least not to me. Arithmetic, algebra, geometry, trigonometry, calculus all have uses that apply to the world I live in and I’ve never needed set theory. I’ve read that there are uses for it in computer programming to counter infinite loops, but I’m not a programmer and perhaps there could be another way which doesn’t involve set theory.
And that’s hard to do if you follow mathematical philosophy online.
I follow math from the engineering perspective as it relates to reality. The purpose of this thread is to establish if infinity exists and not if it exists in manmade constructs. I could write a play containing pink elephants and then claim pink elephants exist and that is essentially what you’re doing by appealing to math.
For the record and for anyone interested, Cantor’s theorem (linked in my earlier post) gives us a never ending upward hierarchy of infinities, one greater than the next. There’s the natural numbers, the powerset of the naturals, the powerset of the powerset of the naturals, and so forth. Each one has a larger cardinality than the one before.
For anyone interested, there is some controversy about this:
“I protest against the use of infinite magnitude as something completed, which is never permissible in mathematics. Infinity is merely a way of speaking, the true meaning being a limit which certain ratios approach indefinitely close, while others are permitted to increase without restriction.” Johann Carl Friedrich Gauss - a German mathematician and physicist who made significant contributions to many fields in mathematics and sciences. Sometimes referred to as the Princeps mathematicorum (Latin for “the foremost of mathematicians”) and “the greatest mathematician since antiquity”, Gauss had an exceptional influence in many fields of mathematics and science, and is ranked among history’s most influential mathematicians. en.wikipedia.org/wiki/Carl_Friedrich_Gauss
Who is more authoritative than Gauss? Only Euler and he existed too early to chime in.
“I don’t know what predominates in Cantor’s theory - philosophy or theology, but I am sure that there is no mathematics there.” Leopold Kronecker - a German mathematician who worked on number theory, algebra and logic. He criticized Georg Cantor’s work on set theory, and was quoted by Weber (1893) as having said, “Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk” (“God made the integers, all else is the work of man.”) en.wikipedia.org/wiki/Leopold_Kronecker
And since no infinite cardinality is the largest; any individual cardinal is bounded by all the ones above it.
Can’t you see that makes no sense? If no infinite cardinality is the largest, then there is no bound; therefore it can’t be bounded; especially by something bigger that is also unbounded. This is like saying our infinite universe is bounded by a larger infinite universe when neither have any bound.
These ideas were controversial in the 1880’s, but today mathematicians have incorporated them into standard math.
The reasons for that are pretty obvious once one takes into account the religious aspects.
When you’re a math major you learn that all of modern math is built on infinitary set theory.
I don’t see how 2+2 depends on infinite set theory. I don’t see how A=PI(r^2) depends on infinite set theory. I don’t see how ax^2 + bx +c = y depends on infinite set theory. I don’t even see how integral calculus depends on set theory.
Mathematician Solomon Feferman has referred to Cantor’s theories as “simply not relevant to everyday mathematics.” en.wikipedia.org/wiki/Controver … e_argument
NJ Wildberger published a rant proclaiming it nonsense and a religion researchgate.net/publicatio … ou_believe
And in turn, all of physical science is based on infinitary math too.
No it isn’t.
“As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.” — Albert Einstein
Even if the world isn’t finite, the math used to describe the world depends on the mathematical theory of the infinite. If one rejects the modern mathematical theory of infinity, they reject all of the formalisms of modern physics too. That’s a tough intellectual position to take.
I find the assertion that the unbounded exists in physical reality is a tough position to take, especially when it cannot be tested scientifically nor even conceived cognitively, much like god, and must be held on faith.
The notion of infinity should, in physics, always and only be understood as a place-holder for an unspecified finite boundary.