tag:blogger.com,1999:blog-5275657281509261156.post800868645903411352..comments2024-03-28T04:04:55.806-07:00Comments on Faculty of Language: Explaining CamelsNorberthttp://www.blogger.com/profile/15701059232144474269noreply@blogger.comBlogger18125tag:blogger.com,1999:blog-5275657281509261156.post-19543217102954407132013-08-17T21:58:08.169-07:002013-08-17T21:58:08.169-07:00Someone could argue that both 1-humped and 2-humpe...Someone could argue that both 1-humped and 2-humped camels, when very thirsty, may become totally flat. Of course, in such a case, the 2-humped one becomes convex so it seems that being concave is not inherent to him, that he can switch easily from convex over to concave and vice versa (whatever uneasy he may feel when convex). But, as a matter of fact, this metamorphosis is quite uninteresting from the theoretical point of view for it is concerned solely with the camel's performance. Competence-wise, he's, no doubt, inherently concave.<br /><br />Now, what about some more linguistic issues?VilemKodytekhttps://www.blogger.com/profile/13161547663393188912noreply@blogger.comtag:blogger.com,1999:blog-5275657281509261156.post-70988622162266443912013-08-17T07:28:12.736-07:002013-08-17T07:28:12.736-07:00>>>Aren't both concave and convex cur...>>>Aren't both concave and convex curves convex sets? <br /><br />In general, convex/concave functions are not convex sets, i.e. it is not generally the case that for any two points of f, any point on the line segment joining those two points is also in f. <br /><br />I have no issue with the function interpretation (it's a joke after all), but the same point applies since any linear function is both a convex and a concave function; hence, flat-backed camels would still be predicted. It seems from your last reply to me that you really had in mind **strictly** convex/concave functions SCX/SCV. If that is what you meant, then yes, of course, flat-backed camels would be excluded by definition. <br /><br />The linear functions/flat backed camel case is just one example of the general problem with the claimed superiority of SCX/SCV over {1,2} as argued by Andy Farmer. Even under the SCX/SCV theory, the objection originally raised by Andy remains: Is SCX/SCV really superior to the {1,2} theory? In the SCX/SCV case, the relevant space was stipulated by you to be just the set S={SCX,SCV}, which does not exhaust the 'naturally' available space F of, say, all continuous functions (including e.g., linear functions and "wavy" functions). In the {1,2} case, you assumed without argument that the relevant space is N. But this stacks the deck against the {1,2} theory; the {1,2} theorist could just as well stipulate that the relevant space is B={1,2}. Put differently, the relevant correspondence would seem to be between F and N, or between S and B, but not between S and N. <br /><br />From this perspective, it looks like S={SCX,SCV} is nothing more than a cute relabelling of B={1,2}. To make your case would require a principled argument, which as far as I could see, you did not provide (and which cannot be legitimately obtained from the joke :-). <br /><br />OK this surely really is overkill since I doubt anyone would disagree with your general point. It's been an entertaining discussion. <br />Gengogakushahttps://www.blogger.com/profile/07717812091719853637noreply@blogger.comtag:blogger.com,1999:blog-5275657281509261156.post-88924139680787911352013-08-15T09:05:01.209-07:002013-08-15T09:05:01.209-07:00A little bit more overkill :) From my rusty memory...A little bit more overkill :) From my rusty memory, convex sets are those objects in which every point can be joined to another point by a straight line that never strays outside the object. In other words, convex sets are path-connected. A straight line trivially fits that definition. Concave objects don't, since they have a hollow through which you can run a straight line between two points.Andy Farmerhttps://www.blogger.com/profile/16968137307258749074noreply@blogger.comtag:blogger.com,1999:blog-5275657281509261156.post-83938328328607022282013-08-15T08:52:16.843-07:002013-08-15T08:52:16.843-07:00Aren't both concave and convex curves convex s...Aren't both concave and convex curves convex sets? If so doesn't that suggest that this is not a useful definition? That said, I take the point. I was thinking of convexity in terms of minima and maxima of curves. A convex curve having a minimum value, concave having a maximum. This way of thinking of things leaves straight lines out, I believe. But all of this, interesting as it is, and I am not being facetious, might be a bit of overkill. The joke/riddle was useful to indicate the main point: that which predicates you use is important in defining the range of alternatives and this is an important, nay critical, part of the theoretical game.Norberthttps://www.blogger.com/profile/15701059232144474269noreply@blogger.comtag:blogger.com,1999:blog-5275657281509261156.post-29671956071789303552013-08-15T05:42:21.128-07:002013-08-15T05:42:21.128-07:00>>>flat lines being those that are neithe...>>>flat lines being those that are neither convex or concave<br /><br />If you are using the mathematical definitions, which one would assume given how the discussion was introduced, then note that flat lines are convex sets. So humpless camels are to be expected without any other statement beyond concave/convex.Gengogakushahttps://www.blogger.com/profile/07717812091719853637noreply@blogger.comtag:blogger.com,1999:blog-5275657281509261156.post-30469472724936008182013-08-14T17:50:49.898-07:002013-08-14T17:50:49.898-07:00I think wavy would be both +convex and -convex. I ...I think wavy would be both +convex and -convex. I was assuming +/- values on the same feature were not ok. Point taken. Norberthttps://www.blogger.com/profile/15701059232144474269noreply@blogger.comtag:blogger.com,1999:blog-5275657281509261156.post-10709184739341999002013-08-14T16:57:01.561-07:002013-08-14T16:57:01.561-07:00This comment has been removed by the author.Gengogakushahttps://www.blogger.com/profile/07717812091719853637noreply@blogger.comtag:blogger.com,1999:blog-5275657281509261156.post-89120334516506678982013-08-14T11:33:52.872-07:002013-08-14T11:33:52.872-07:00Thanks for the longer reply. I understand the poin...Thanks for the longer reply. I understand the point you're making, I just don't think the example works as well as you'd like. My point about -convex is that (unless you stipulate that it means +concave) it could also mean "wavy" (i.e., any number of humps), so it's not the case that either +/-convex or +/-concave (but not both) predict 1 or 2 humps, but no more.<br /><br />Anyway, your point is taken.Andy Farmerhttps://www.blogger.com/profile/16968137307258749074noreply@blogger.comtag:blogger.com,1999:blog-5275657281509261156.post-29014241379000704562013-08-14T11:22:58.654-07:002013-08-14T11:22:58.654-07:00Sorry if I sounded short, unintentional. I guess I...Sorry if I sounded short, unintentional. I guess I have been presupposing that different concepts cut up the conceptual space differently. Theory then aims to find these and get the ones that divide the space "naturally," this meaning into cells that exhaust the conceptual possibilities exhaustively. If one is asking about curves, convex/concave do this, flat lines being those that are neither convex or concave. If one thinks of the space as defined by 'concavity', I.e. +/- concave then I guess one can think of flat camels and convex camels as both -concave or flat camels and concave camels as +concave. That would be fine with me. Then one might expect 0-humped camels as well. The general point, I hope still holds: the space is exhausted by these three options, unlike what happens when one conceives of it in terms on numerically distinguished humps. We can, of course, stipulate that N=0, 1, or 2 and no more, but it is just this stipulation that fails to provide explanatory traction. How? By inviting the obvious question; why 0-2 but no more? Pre-emptying the question lends the other conceptualization explanatory heft. Indeed one might say that it explains why 0-2 were the only correct values for N and in this way it explains what was otherwise stipulated.<br /><br />Hope this helps.Norberthttps://www.blogger.com/profile/15701059232144474269noreply@blogger.comtag:blogger.com,1999:blog-5275657281509261156.post-11286947745469450782013-08-14T10:24:51.294-07:002013-08-14T10:24:51.294-07:001 or 2 humps exhaust the possibilities, in the sam...1 or 2 humps exhaust the possibilities, in the same way as convex or concave, since you're positing two possibilities in both case, rather than somehow deriving those possibilities. Each "explanation" is as stipulative as the other, until you can explain *why* humps are either convex or concave. As David hints at, [-concave] = [+convex] only if you stipulate that concave and convex are the only possible values (i.e., it could also be flat, wavy, and so on), but then we're back where we started. We might as well stipulate that 1 or 2 humps are the only possible values, and have the convex/concave facts fall out of that.<br /><br />Sorry if this comes across as obtuse (I get the feeling it does from the annoyance your reply exudes), it's not meant to be :)Andy Farmerhttps://www.blogger.com/profile/16968137307258749074noreply@blogger.comtag:blogger.com,1999:blog-5275657281509261156.post-52569895894908592182013-08-13T18:32:03.125-07:002013-08-13T18:32:03.125-07:00Why assume one can be +/- concave? At any rate, th...Why assume one can be +/- concave? At any rate, there are always llamas!<br /><br />The point, as you no doubt know, is that the concave/vex distinction exhausts the possibilities. It is A or B and these are +/- values of one another. That's nice, and that's what makes for a nice explanation. The way the question is posed is that there are integral values possible, hence it is reasonable to ask why not 3, 4, etc. The reframing pre-empts this question and leaves the only possible answers as also the right ones. Explanation, as I see it, looks to find just these kinds of predicates, ones that frame questions in the right way.Norberthttps://www.blogger.com/profile/15701059232144474269noreply@blogger.comtag:blogger.com,1999:blog-5275657281509261156.post-32092589216278086452013-08-13T17:21:56.496-07:002013-08-13T17:21:56.496-07:00What about flat?What about flat?David Pesetskyhttps://www.blogger.com/profile/09666557087629655596noreply@blogger.comtag:blogger.com,1999:blog-5275657281509261156.post-58306236394240421732013-08-13T15:25:41.120-07:002013-08-13T15:25:41.120-07:00Because concave and convex exhaust the options. 1,...Because concave and convex exhaust the options. 1,2 do not. It is precisely in finding ways to frame issues so that the extant exhausts the possible and no more that subserves explanation. Norberthttps://www.blogger.com/profile/15701059232144474269noreply@blogger.comtag:blogger.com,1999:blog-5275657281509261156.post-25618041950574936062013-08-13T15:22:10.580-07:002013-08-13T15:22:10.580-07:00Why is it more of an "explanation" to sa...Why is it more of an "explanation" to say that a camel's back can be convex or concave than to say that it can have one or two humps? It's certainly no more parsimonious.Andy Farmerhttps://www.blogger.com/profile/16968137307258749074noreply@blogger.comtag:blogger.com,1999:blog-5275657281509261156.post-52811206168177621442013-08-13T15:21:17.619-07:002013-08-13T15:21:17.619-07:00This comment has been removed by the author.Andy Farmerhttps://www.blogger.com/profile/16968137307258749074noreply@blogger.comtag:blogger.com,1999:blog-5275657281509261156.post-68856226684805059502013-08-12T14:06:03.354-07:002013-08-12T14:06:03.354-07:00I can let others decide on how high the price is. ...I can let others decide on how high the price is. I've registered my vote. Norberthttps://www.blogger.com/profile/15701059232144474269noreply@blogger.comtag:blogger.com,1999:blog-5275657281509261156.post-26654976689908106742013-08-12T12:57:48.572-07:002013-08-12T12:57:48.572-07:00This comment has been removed by the author.Anonymoushttps://www.blogger.com/profile/03443435257902276459noreply@blogger.comtag:blogger.com,1999:blog-5275657281509261156.post-1609400873885085342013-08-12T11:24:07.535-07:002013-08-12T11:24:07.535-07:00The price for purchasing 'Problems of Projecti...The price for purchasing 'Problems of Projection is $19.95. That is, if your library doesn't have a subscription to Lingua. Most libraries do, and most likely the article is automatically accessible from your laptop computer at the office. Elsevier also makes Lingua accessible for free in various developing countries through their Hinari programs. Admittedly, Elsevier makes money from us. But $19.95, while unusual, is hardly exorbitant. What did you pay for your cappucino's today?Anonymoushttps://www.blogger.com/profile/02659974295352713609noreply@blogger.com