According to Neo-Platonists, mathematics exist independent of human quest, so they are in fact discovered, not invented. Even the most abstract mathematical objects are real and invariable, immaterial of course and in no way related to physical existence, space and time, but anyway they do exist in a non-objective world. For a Neo-Platonist, there is an answer to Cantor's Continuum Hypothesis, only we do not have the means to obtain it, that is, we do not understand real numbers sufficiently. For Formalists on the other, mathematical objects do not exist. Mathematics consist of symbols, axioms/sentences composed of such symbols and rules to transform sentences into others (e.g. theorems), but none of these has any particular meaning. Mathematics is therefore a humanly constructed language devised by human beings for definite ends prescribed by themselves. Formalists often speak in terms of Neo-Platonic real objects, but only for reasons of convenience. For a Formalist, the Cantor's Continuum Hypothesis is meaningless for there is no such a thing as a complete understanding of the real numbers. As long as we follow the strict rules of transforming series of symbols into other series of symbols, there is no point in asking whether we approach reality or not, because there is no reality. Constructivists take the extreme view that if something cannot be constructed in a finite number of steps it does not exist. The leader was L.E.J. Brouwer who even devised a famous counter-example to show that the trichotomy law for real numbers (every real number is either negative, zero or positive) is not true. The argument involved a strictly defined but impossible calculation with Pi the result of which would define in turn the sign of a related number. Constructivists would dispose all questions about infinity on these grounds. Source Discuss. Moderator request: is this free thoughts or philosophy?
it was proven that there several aspects of math are independent from the human perception, which mean they are true anywhere, such as logic for example. its long being thought that we will communicate with other intelligent beings using math not linguistic capabilities.
As I see it, this reality is all an elaborate illusion. Creation was never created and is always creating. I wrote this an infinite number of times by now, yet this is the first for the me that is me at this time being in this body. Later on when I go away, some other person will be in my body writing this and answering this, as time recycles events.
I already have a thread on this, started 2 weeks ago. Sam as usual, you came in second... Please Register or Log in to view the hidden image!
