[with apologies to Jeff Foxworthy]
Among other eminent bits, Karlis Podnieks has an interesting test you can use to see if you are a Platonist. As psychologists like to say, denial is more than just a river in Egypt and the first step to recovery is accepting the problem. So, take the test… its for your health! ;-)
Foundations of Mathematics. Mathematical Logic. By K.Podnieks
Read the full post and comments »Suppose, someone has proved that the twin prime conjecture is unprovable in set theory. Do you believe that, still, the twin prime conjecture possesses an “objective truth value”? Imagine, you are moving along the natural number system:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, …
And you meet twin pairs in it from time to time: (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), (71,73), … It seems there are only two possibilities:
a) We meet the last pair and after that moving forward we do not meet any twin pairs (i.e. the twin prime conjecture is false),
b) Twin pairs appear over and again (i.e. the twin prime conjecture is true).
It seems impossible to imagine a third possibility…
If you think so, you are, in fact, a Platonist.
Meta
3 Responses
The general area this is being debated is called embodiment. By that term mathematics is distinguished from Platonism. For example, math appears disembodied in the sense of ‘truths’ that are fixed over time from generation to generation. So that the sense of embodiment is hard to distinguish in math. This other wordliness of math is not true.
Godel and others of that stamp are trying to show by consistency in logic that something can’t be done mathematically. Such investigations have plagued math in terms of infinitely large and infinitely small issues in math. The key issue that Godel rasies is logical consistency which in my view is language related problem than a math related problem.
thanks,
Doyle
There is a third possibility, highlighted by the work of Brian Rotman, which delves into the embodiment issue Doyle raises. Such a perspective causes quite a bit of consternation amongst platonists. Oh darn :-)
Doyle, Autoplectic, thanks for the comments. Gödel as you may know was a thorough Platonist and the movement seems to be regaining some momentum these days (I will post in a short bit Avigad’s review of Tait’s recent book). Doyle’s second paragraph is interesting since it echoes both the sentiments of many leading “real” mathematicians (real, as opposed to logicians) as well as the philosophers who brought us the “linguistic turn” (Wittgenstein). My own opinion (tentative) is that it is both. Perhaps you (Doyle) can elaborate some more on your comment (which is very edifying for me).
Autoplectic: Have not heard of Brian Rotman. As always I learn something new from your messages. Will look it up.
I am flattered to know you guys are reading this stuff and spending time to respond!