most recent 30 from http://mathoverflow.net 2013-06-20T00:26:37Z http://mathoverflow.net/feeds/question/55572 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/55572/is-there-a-conjunction-bias Jérôme JEAN-CHARLES 2011-02-16T02:10:02Z 2011-02-18T01:00:20Z

<p>This is slightly related to question <a href="http://mathoverflow.net/questions/33366/the-unprecedented-success-of-the-intersection-operator" rel="nofollow">http://mathoverflow.net/questions/33366/the-unprecedented-success-of-the-intersection-operator</a> . </p> <p>Apart from a set of maths books of null measure, most have the following property: </p> <p><strong>Objects definitions are presented as a conjunction of properties.</strong></p> <p>Most axiomatic are also clearly conjunctive in their presentation.<br> It is uncommon to have say "<em>By definition a Zorglub is a red zorg <strong>or</strong> a white zorg</em>". </p> <p><strong>Q1</strong> : Do you agree with the bias (if not, give enough examples)?. </p> <p><strong>Q2</strong>: Is this bias mainly a discourse convention or does it lie deeper (where?) ? </p>

http://mathoverflow.net/questions/55572/is-there-a-conjunction-bias/55584#55584 Mike Shulman 2011-02-16T05:27:59Z 2011-02-16T05:27:59Z

<p>A slightly tongue-in-cheek answer: definitions are the hypotheses of theorems. If the hypothesis of a theorem is a disjunction, you can always split the theorem up into two theorems with separate hypotheses, and doing so will often clarify the statement and proof anyway. So it's natural that single definitions are not usually disjunctive.</p> <p>(Dually, if the conclusion of a theorem is a conjunction, then you can split it up into two theorems with separate conclusions. But I think we don't as often give names to the conclusions of theorems, unless they happen to coincide with a definition we gave for some other reason elsewhere.)</p>