Incoming: Open game table volume 2

17 December, 2009 at 9:05 pm (roleplaying) (, , )

It is time for second volume of the rpg blog anthology.

Previously the content was quite fine, though there were some very 4e-focused articles of little use to those who don’t enjoy that game.

Now is the time to influence what the next OGT will be like. You can apply for a position as a peer reviewer and nominate blog posts. Please nominate lots of blog posts. I’ve done my share of that and there are a few theory and such posts that will almost certainly be weeded out in the peer review, as well as some that might even be accepted.

The blog post nomination works as follows: Enter up to five complete urls, press submit, find the page again, repeat as many times as you are willing to. This is not entirely ideal from usability perspective, but functional none the less.

You can read slightly more at the newly reawakened Core mechanic.

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Mathematics is and is not formalistic

2 December, 2009 at 8:33 pm (mathematics, philosophy) (, )

Some philosophy of mathematics. And of philosophy.

The question I will cover is: Is mathematics purely formal manipulation of strings of symbols?

First, the trivial answers: Yes, since all results, definitions and theorems could in principle be reduced to such. No, because doings mathematics takes imagination, creativity, and whatever other positive-sounding things I would like to mention. (It also requires manipulation of formal systems, occasionally known as abstract nonsense or computation or calculation.)

There was this philosopher named Immanuel Kant. He proved (by very nonrigorous standards and with many hidden assumptions) a number of seemingly contradictory results called antinomies (of pure reason), such that the world is infinite and finite both. I stated something similar above, but it is fairly easy to see that I cheated, since my two statements are actually about different things.

Mathematics is formalistic in that the mathematical results: theorems, definitions and proofs – can be stated formalistically. Mathematics as in the activity that mathematicians do is not so, as it involves building and understanding (often complicated) arguments, seeing analogies, seeing past analogies, and other quite non-formalistic activities.

There is more to the question. Namely, is mathematics something discovered by or created by people? (One could ask this of natural sciences, I think.) Mathematics is discovered in that all the theorems and results are fixed, given a particular set of axioms (which means assumptions): Given proposition is true or false (or undeterminable due to Gödel’s incompleteness or even meaningless in the same sense that not every string of letters is a word or has meaning) based on the axioms in use.

Mathematics is created in that the particular results achieved, axiomatics considered, and so on, are determined by the questions mathematicians ask and answer. Physics, statistics, and various other fields of inquiry motivate plenty of mathematics, for example.

What is our conclusion? It is that the answer one finds is not important, but what philosophy does is highlight concepts that are hard to separate otherwise. This is what I find useful in philosophy. This is what I wish more philosophers recognised.

(Post inspired by this one.)

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