Nicholas Knisely has an interesting post up today that plays off two recent articles that discuss the nature of mathematics. The real issue here is whether there is an underlying order in the world that we discover or do we invent that order ourselves? In other words was Plato right:
A post on Slashdot (h/t) points to an article in Science News about an ongoing debate about the connection between mathematics and the nature of reality. (We were just discussing that question here earlier this week.)
The article in Science News begins:"[A]re new mathematical truths discovered or invented? Seems like a simple enough question, but for millennia, it has provided fodder for arguments among mathematicians and philosophers.
Those who espouse discovery note that mathematical statements are true or false regardless of personal beliefs, suggesting that they have some external reality. But this leads to some odd notions. Where, exactly, do these mathematical truths exist? Can a mathematical truth really exist before anyone has ever imagined it?
On the other hand, if math is invented, then why can’t a mathematician legitimately invent that 2 + 2 = 5?
...Plato is the standard-bearer for the believers in discovery. The Platonic notion is that mathematics is the imperturbable structure that underlies the very architecture of the universe. By following the internal logic of mathematics, a mathematician discovers timeless truths independent of human observation and free of the transient nature of physical reality. ‘The abstract realm in which a mathematician works is by dint of prolonged intimacy more concrete to him than the chair he happens to sit on,’ says Ulf Persson of Chalmers University of Technology in Sweden, a self-described Platonist.
The Platonic perspective fits well with an aspect of the experience of doing mathematics, says Barry Mazur, a mathematician at Harvard University, though he doesn’t go so far as to describe himself as a Platonist. The sensation of working on a theorem, he says, can be like being ‘a hunter and gatherer of mathematical concepts.’"
Read the rest here.
The article on Slashdot about the piece above also includes a link to a paper recently published entitled "Let Platonism Die" which includes a claim that Platonism "has more in common with mystical religions than with modern science".
The point of which seems to be that there's a fundamental question about reality. Does it reflect a designers intent, and is that intent mirrored at all levels of reality, or is creation essentially a result of random processes and any attempt to find an purpose or meaning is simply a human desire for order projected onto the Cosmos.
Father Knisely, who was a theoretical physicist and astronomer before becoming a priest comes down on the side of a ordered reality:
I'm such a thoroughgoing Platonist (neo actually) that it seems obvious to me that mathematics (and science) is about uncovering the underlying order. But I'm also religious and believe I've encountered in one way or another the orderer, so perhaps my sense that mathematics is discovered isn't all that surprising.
Read it all here.