{"id":237,"date":"2012-08-10T08:58:29","date_gmt":"2012-08-10T15:58:29","guid":{"rendered":"http:\/\/zackmdavis.net\/blog\/?p=237"},"modified":"2012-08-10T11:24:02","modified_gmt":"2012-08-10T18:24:02","slug":"mathematics-is-the-subfield-of-philosophy-that-humans-are-good-at","status":"publish","type":"post","link":"http:\/\/zackmdavis.net\/blog\/2012\/08\/mathematics-is-the-subfield-of-philosophy-that-humans-are-good-at\/","title":{"rendered":"Mathematics Is the Subfield of Philosophy That Humans Are Good At"},"content":{"rendered":"<p>By <em>philosophy<\/em> I understand the discipline of discovering truths about reality by means of thinking very carefully. Contrast to science, where we try to come up with theories that predict our observations. Philosophers of number <a href=\"http:\/\/www.maa.org\/editorial\/mathgames\/mathgames_10_18_04.html\">have observed<\/a> that the first ten trillion nontrivial zeros of the Riemann zeta function are on the critical line, but people don't speak of the <a href=\"http:\/\/en.wikipedia.org\/wiki\/Riemann_hypothesis\">Riemann hypothesis<\/a> as being almost certainly true, not necessarily because they anticipate a counterexample lurking somewhere above \u00bd + 10<sup>26<\/sup><em>i<\/em> (although &quot;large&quot; counterexamples <a href=\"http:\/\/en.wikipedia.org\/wiki\/Skewes%27_number\">are not unheard-of<\/a> in the philosophy of numbers), but rather because while empirical examination is certainly <em>helpful<\/em>, it's not really <em>what we do<\/em>. Mere empiricism is usually sufficient for knowing (with high probability) <em>what<\/em> is true, but as philosophers, we want to explain <em>why<\/em>, and moreover, <em>why it could not have been otherwise<\/em>.<\/p>\n<p>When we try this on topics like <em>numbers<\/em> or <em>shapes<\/em>, it works really, really well: our philosophers quickly reach ironclad consensuses about matters far removed from human intuition. When we try it on topics like <em>justice<\/em> or <em>existence<\/em> ... it doesn't work so well. I think it's sad.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>By philosophy I understand the discipline of discovering truths about reality by means of thinking very carefully. Contrast to science, where we try to come up with theories that predict our observations. Philosophers of number have observed that the first &hellip; <a href=\"http:\/\/zackmdavis.net\/blog\/2012\/08\/mathematics-is-the-subfield-of-philosophy-that-humans-are-good-at\/\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[10],"tags":[31],"_links":{"self":[{"href":"http:\/\/zackmdavis.net\/blog\/wp-json\/wp\/v2\/posts\/237"}],"collection":[{"href":"http:\/\/zackmdavis.net\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/zackmdavis.net\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/zackmdavis.net\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/zackmdavis.net\/blog\/wp-json\/wp\/v2\/comments?post=237"}],"version-history":[{"count":9,"href":"http:\/\/zackmdavis.net\/blog\/wp-json\/wp\/v2\/posts\/237\/revisions"}],"predecessor-version":[{"id":246,"href":"http:\/\/zackmdavis.net\/blog\/wp-json\/wp\/v2\/posts\/237\/revisions\/246"}],"wp:attachment":[{"href":"http:\/\/zackmdavis.net\/blog\/wp-json\/wp\/v2\/media?parent=237"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/zackmdavis.net\/blog\/wp-json\/wp\/v2\/categories?post=237"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/zackmdavis.net\/blog\/wp-json\/wp\/v2\/tags?post=237"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}