tag:blogger.com,1999:blog-3891434218564545511.post7393098589643633842..comments2024-03-27T20:37:09.185-05:00Comments on Alexander Pruss's Blog: First- but not second-order vaguenessAlexander R Prusshttp://www.blogger.com/profile/05989277655934827117noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-3891434218564545511.post-63699687267465496732011-11-02T23:00:11.330-05:002011-11-02T23:00:11.330-05:00If higher order vagueness is between us and the fu...If higher order vagueness is between us and the fundamental particles, then their precise properties don't exist in any meaningful sense, as we cannot detect them. The higher-level vagueness takes the former ontological place of the fundamental properties. <br /><br /><i>"Vagueness is not probability, so it might not multiply."</i><br /><br />It can either be characterized by a number, or it can't. <br /><br />I'm open to it not so being, but I would need to know which alternative you propose. <br /><br /><i>"In any case, there is no guarantee that a sequence of numbers less than 1 multiplies to zero."</i><br /><br />It very quickly approaches arbitrarily close to stopping. <br /><br />At some near, finite point it's [1 - epsilon] and in practice you can ignore epsilon any time it is smaller than your instrument error, because by definition it is indistinguishable from a perfectly precise reality.<br /><br /><i>"But language is itself a part of the world."</i> <br /><br />I had not thought of it that way. Still, that works out to exactly my point. <br /><br />You've limited vagueness to the realm of language. More precisely, there's vague relationships between two things. Neither of the things themselves are vague beyond first order.Alrenoushttps://www.blogger.com/profile/11119846531341190283noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-68423633313250595942011-11-02T21:21:31.256-05:002011-11-02T21:21:31.256-05:00"Fundamentally, particles must be exactly wha..."Fundamentally, particles must be exactly what they are..."<br /><br />This leaves open the possibility that there is non-fundamental vagueness.<br /><br />"A vaguely bald person is either probably bald - say 70% - or partly bald. If it has meta-vagueness, then again it's either 70% probably or 70% true. If that goes on forever, it multiplies out to 0% overall."<br /><br />Vagueness is not probability, so it might not multiply.<br /><br />In any case, there is no guarantee that a sequence of numbers less than 1 multiplies to zero. For instance the product of the numbers in the following sequence is non-zero: 1, 1-1/2, 1-1/4, 1-1/8, ...<br /><br />"It's not that baldness per se is sharp or vague, just our words referring to it."<br /><br />That's a tempting move, but I am afraid it doesn't seem to cut it. Suppose that the word "bald" is vague. So it's vague whether "bald" applies to some individual x. But language is itself a part of the world. So the vagueness about whether "bald" applies to x seems to be a genuine vagueness about the world. You might say that this is just a matter of vagueness in the word "applies". But that just gives us another step in a regress: it is now vague whether "applies" applies to "bald" and x.Alexander R Prusshttps://www.blogger.com/profile/05989277655934827117noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-16007386311302925142011-10-31T16:39:01.245-05:002011-10-31T16:39:01.245-05:00I learned I need to consider second-order vaguenes...I learned I need to consider second-order vagueness...or rather, the lack thereof. <br /><br />I believe in absolute sharpness, just due to the law of identity. Fundamentally, particles must be exactly what they are, and a balding man has exactly as many hairs as he has, made of exactly as many particles as make them up. <br /><br />Moreover, even linguistic vagueness falls to the no infinities principle. <br />A vaguely bald person is either probably bald - say 70% - or partly bald. If it has meta-vagueness, then again it's either 70% probably or 70% true. If that goes on forever, it multiplies out to 0% overall. Not even slightly vague. It has to stop or very quickly approach arbitrarily close to stopping. <br /><br /><br />I think you're working harder here than you have to, though. Sharp communication is expensive, and for baldness it isn't worth it. It's not that baldness per se is sharp or vague, just our words referring to it.Alrenoushttps://www.blogger.com/profile/11119846531341190283noreply@blogger.com