To take a step back. the discussion is about mathematical Platonism, a theory of mathematical truth which is apparently motivated by the Correspondence theory of truth. That is being rivaled by another theory, also motivated by CToT, wherein the truth-makers of mathematical statements are physical facts, not some special realm of immaterial entities. The relevance of my claim that there are unphysical mathematical truths is that is an argument against the second claim.
Lakoff and Nunez give an account of the origins and nature of mathematical thought that while firmly anti-Platonic doesn't back a rival theory of mathematical truth, because that is not in fact their area of interest..their interest is in mathematical thinking.
That is being rivaled by another theory, also motivated by CToT, wherein the truth-makers of mathematical statements are physical facts
Who said that? Actual formal systems run on a coherence theory of truth: if the theory is consistent (and I do mean consistent according to a meta-system, so Goedel and Loeb aren't involved right now), then it's a theory. It may also be a totally uninteresting theory, or a very interesting theory. The truth-maker for a mathematical statement is just whether it has a model (and if you really wanted to, you could probab...
Among my friends interested in rationality, effective altruism, and existential risk reduction, I often hear: "If you want to have a real positive impact on the world, grad school is a waste of time. It's better to use deliberate practice to learn whatever you need instead of working within the confines of an institution."
While I'd agree that grad school will not make you do good for the world, if you're a self-driven person who can spend time in a PhD program deliberately acquiring skills and connections for making a positive difference, I think you can make grad school a highly productive path, perhaps more so than many alternatives. In this post, I want to share some advice that I've been repeating a lot lately for how to do this:
That's all I have for now. The main sentiment behind most of this, I think, is that you have to be deliberate to get the most out of a PhD program, rather than passively expecting it to make you into anything in particular. Grad school still isn't for everyone, and far from it. But if you were seriously considering it at some point, and "do something more useful" felt like a compelling reason not to go, be sure to first consider the most useful version of grad that you could reliably make for yourself... and then decide whether or not to do it.
Please email me (lastname@thisdomain.com) if you have more ideas for getting the most out of grad school!