most recent 30 from http://mathoverflow.net 2013-06-19T12:00:24Z http://mathoverflow.net/feeds/question/94983 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/94983/mathematical-analysis-of-lewisian-concepts-esp-natural-properties Hans Stricker 2012-04-23T21:13:41Z 2012-04-23T21:59:42Z

<p><a href="http://plato.stanford.edu/entries/david-lewis/" rel="nofollow">David Lewis</a> was one of the <a href="http://leiterreports.typepad.com/blog/2009/03/so-who-is-the-most-important-philosopher-of-the-past-200-years.html" rel="nofollow">great philosophers of our time</a>. He was a genuine philosopher, his focus was on theoretical metaphysics. And he had something to say about mathematics. His last book - he only wrote four - was <a href="http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&amp;id=pdf_1&amp;handle=euclid.ndjfl/1093635842" rel="nofollow">Parts of Classes</a> (1991). It had a strong set theoretical - and as you may guess mereological - impact.</p> <blockquote> <p>I wonder if there is a thorough mathematical analysis of - some of - Lewis' concepts and arguments, subsequently or unknowingly (see Michael's answer below).</p> </blockquote> <p>I am especially interested in his concept of <em>natural properties</em> which he introduced in <a href="http://scholar.google.com/scholar?q=New+Work+for+a+Theory+of+Universals" rel="nofollow">New Work for a Theory of Universals</a> (1983), and whether and how this concept might be applicable to mathematics. </p> <p>Very brief summary (just a teaser): To each set corresponds a property. Such properties are <em>abundant</em>. To the definable sets correspond a restricted but still very large family of properties. Natural properties in turn are very sparse, play a prominent role (at least in Lewis' metaphysics), have to be grasped somehow intuitively, and it's not clear, how they and their corresponding sets can be characterized. </p> <p>PS: I found an announcement of a <a href="http://arts.uwaterloo.ca/donotlinkto_oldarts2/documents/Tappenden-Nov192010.pdf" rel="nofollow">talk on <em>Natural Properties in Mathematics</em></a>. Does anyone have a transcript of this talk or something like that?</p> <p>PS 2: <a href="http://mathoverflow.net/questions/14281/naturally-definable-sets-of-natural-numbers-3" rel="nofollow">Here</a> is an older question of mine asking for natural properties in arithmetics.</p>

http://mathoverflow.net/questions/94983/mathematical-analysis-of-lewisian-concepts-esp-natural-properties/94985#94985 Michael Greinecker 2012-04-23T21:47:32Z 2012-04-23T21:47:32Z

<p>Lewis introduced the concept of <a href="http://plato.stanford.edu/entries/common-knowledge/" rel="nofollow">common knowledge</a> (I know that you know that I know that you know that...) in his book <a href="http://www.amazon.com/Convention-Philosophical-Study-David-Lewis/dp/0631232575/ref=sr_1_3?ie=UTF8&amp;qid=1335216403&amp;sr=8-3" rel="nofollow">Convention</a>. The concept has been formalized in a partitional model of knowledge in the simple and elegant paper <a href="http://www.ma.huji.ac.il/raumann/pdf/Agreeing%20to%20Disagree.pdf" rel="nofollow">Agreeing to Disagree</a> by Robert Aumann. Aumann wasn't aware of the prior work of Lewis. The concept of common knowledge became one of the building blocks of modern non-cooperative game theory and has been extensively studied and generalized. A survey can be found <a href="http://cowles.econ.yale.edu/~gean/art/p0882.pdf" rel="nofollow">here</a>.</p>