Do straight lines exist? And even if you traveled the earth forever you will see the same places more than once. — TiredThinker
You just went right past what I wrote. — TonesInDeepFreeze
I merely stated the needed corrections to your uninformed argument — TonesInDeepFreeze
I'm just puzzled/intrigued by the fact that you can't do math with nihilism and also with . — Agent Smith
AFAIK, there are "straight lines" only in the abstract Euclidean space. However, the shortest path between any two points is a geodesic ...Do straight lines exist? — TiredThinker
The circumferential path does not end (i.e. it's in-finite); no point ("place") on the path is a boundary, therefore the path is unbounded.And even if you traveled the earth forever you will see the same places more than once.
'infinity' as a noun does not ordinarily have a mathematical definition, though 'is infinite' does. A mathematical definition is never circular nor a tautology. — TonesInDeepFreeze
* The notion of 'potentially infinite' is of course central to important alternatives to classical mathematics. However, as far as I know, formalization of the notion is not nearly as simple as the classical formalization of 'infinite'. Therefore, if one is concerned with truly rigorous foundations, when one asserts that the notion of 'potentially infinite' does better than that of 'infinite' one should be prepared to accept the greater complexities and offer a particular formalization without taking it on faith that such formalizations are heuristically desirable, as we keep in mind that ordinary mathematical application to science and engineering uses the simplicity of classical mathematics as one first witnesses in Calculus 1. — TonesInDeepFreeze
* What writings by intuitionists are fairly rendered as describing potentially infinite sets or sequences as "finite entities of a priori indefinite size" or as "finite entities" of any kind? — TonesInDeepFreeze
Science and engineering continues to work with classical mathematics , as well as classical logic, due to their vagueness, simplicity and brevity as a junk logic for crudely expressing ideas . . . — sime
Unless infinity is formally identified with a finite piece of syntax, whereupon becoming a circularly defined and empirically meaningless tautology, infinity cannot even be said to exist inside mathematics, let alone outside — sime
I'm willing to concede that my colleagues and I have produced mathematical contributions that are worthless, but calling classical mathematics "junk logic" and "crudely expressing ideas" is a ridiculous accusation. On the other hand, that may not be what you are saying. It's hard to work through some of your lengthy paragraphs. Probably just me. — jgill
:chin: Such as unknown unknowns which necessarily encompass "knowns":I am asking about and infinite landscape. Only new information all the time. — TiredThinker
The more we learn about the world, and the deeper our learning, the more conscious, specific, and articulate will be our knowledge of what we do not know; our knowledge of our ignorance. For this indeed, is the main source of our ignorance - the fact that our knowledge can be only finite, while our ignorance must necessarily be infinite. — Karl Popper
* What writings by intuitionists are fairly rendered as describing potentially infinite sets or sequences as "finite entities of a priori indefinite size" or as "finite entities" of any kind?
— TonesInDeepFreeze
SEP's article on intuitionism is a useful introduction for understanding the notion of Brouwer's tensed conception of mathematics — sime
absolute infinity isn't a semantically meaningful assignment to a mathematical entity — sime
* 'infinity' as a noun does not ordinarily have a mathematical definition, though 'is infinite' does. A mathematical definition is never circular nor a tautology. — TonesInDeepFreeze
The semantic notion of absolute infinity (whatever that is supposed to mean) — sime
existence of non-standard models that satisfy the same axioms and equations without committing to the existence of extensionally infinite objects. — sime
Science and engineering continues to work with classical mathematics , as well as classical logic, due to their vagueness, simplicity and brevity — sime
outdated formal traditions that still remain dominant in the education system. — sime
Infinite sets come into play in Calculus 1. What pedagogy would you propose for people to find derivatives without infinite sets? — TonesInDeepFreeze
. . . directly measuring the quotient of two arbitrarily small intervals Dy and Dx with respect to some observed function — sime
the classical definition of df/dx with respect to the (ε, δ)-definition of a limit, can be practically interpreted by interpreting ε to be a potential infinitesimal, and δ as representing a random position on the x axis given the value of ε , which when applied to the function yield df and dx as potential infinitesimals, i.e. finite rational numbers, whose smallness is a priori unbounded. — sime
Get involved in philosophical discussions about knowledge, truth, language, consciousness, science, politics, religion, logic and mathematics, art, history, and lots more. No ads, no clutter, and very little agreement — just fascinating conversations.