tag:blogger.com,1999:blog-8954608646904080796.post1265144239042753193..comments2022-08-19T19:00:29.821-07:00Comments on Edward Feser: Meta-abstraction in the physical and social sciencesEdward Feserhttp://www.blogger.com/profile/13643921537838616224noreply@blogger.comBlogger75125tag:blogger.com,1999:blog-8954608646904080796.post-22726749381838922312021-04-16T20:44:11.057-07:002021-04-16T20:44:11.057-07:00Thanks for sharing a great article.
You are provid...Thanks for sharing a great article.<br />You are providing wonderful information, it is very useful to us.<br />Keep posting like this informative articles.<br />Thank you.<br /><br />Get to know about <a href="https://www.webtechmantra.com/content-com-android-browser-home/" rel="nofollow">content://com.android.browser.home</a>sammuhttps://www.blogger.com/profile/02258154158548575977noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-31040713621811436242021-04-08T01:54:52.399-07:002021-04-08T01:54:52.399-07:00Hakan evden eve Nakliyat
Halkalı evden eve Nakliya...<a href="http://www.hakanevdenevenakliyat.com" rel="nofollow">Hakan evden eve Nakliyat</a><br /><a href="http://www.halkalinakliyat.org" rel="nofollow">Halkalı evden eve Nakliyat</a><br /><a href="http://www.sinopnakliyat.gen.tr" rel="nofollow">sinop evden eve Nakliyat</a><br /><a href="http://www.cakirevdenevenakliyat.com" rel="nofollow">çakır evden eve Nakliyat</a><br /><a href="http://www.karadeniznakliyat.gen.tr" rel="nofollow">karadeniz evden eve Nakliyat</a><br /><a href="http://www.sinopasansorlutasimacilik.com" rel="nofollow">sinop asansörlü taşımacılık</a>Sinop Asansörlü Taşımacılıkhttps://www.blogger.com/profile/09170713383497883828noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-73000499387534898992021-03-29T10:13:54.379-07:002021-03-29T10:13:54.379-07:00@grodrigues,
Also, here's an argument Alex P...@grodrigues,<br /><br /><br />Also, here's an argument Alex Pruss uses to justify the idea that non-measurable constructs still have probability bounds:<br /><br /><i>"Imagine you're randomly throwing a dart at a round target C. Let A be a nonmeasurable subset of C. Suppose you also have a fair coin.<br /><br />Now, let E be this event: you hit A with the dart AND your coin lands heads. Then the probability of E is less than or equal to the probability of heads, which is 1/2. So we have an upper bound on E. Yet E is nonmeasurable.<br /><br />Similarly, we can get lower bounds. Let F be: you hit A with the dart OR your coin lands heads. Then the probability of F is at least 1/2." </i><br /><br /><br />What do you think of that?JoeDnoreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-72722130956461589182021-03-29T08:37:41.461-07:002021-03-29T08:37:41.461-07:00@grodrigues,
Understood, though since the creatio...@grodrigues,<br /><br />Understood, though since the creation of a non-measurable set would have to involve a concrete application of AC which <b>isn't undefined itself,</b> this would be one of the major distinguishing features of NS over brute facts. The very principle of AC isn't unintelligible and has an order to it - is that correct?<br /><br />Also, since one uses AC to create a non-measurable set by bringing together members from other things, could one then create different non-measurable sets based on what "elements" are brought to the table or how they are "arranged"?<br /><br />If so, this crucial element of how they would be created via AC seems to bring some intelligibility to them which helps them make sense.JoeDnoreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-41749396830870631522021-03-29T07:34:48.713-07:002021-03-29T07:34:48.713-07:00@JoeD:
"Especially so if brute facts are jus...@JoeD:<br /><br />"Especially so if brute facts are just a special type or subset of nonmeasurability, or if it's just the universal concept of Nonmeasurability applied to causation or explanation."<br /><br />Non-measurability is a property that subsets of a measure space have. I have no idea what "universality" you are talking about, certainly not when connected to causality. Brute facts are contingent facts, states of affairs, events, whatever that have no reason, raison d'être, explanation, etc. They are distinct things.<br /><br />"That is, in order to create a NS set one has to use the Axiom of Choice and actually choose particular members of other sets to do that."<br /><br />To show that non-measurable sets exist one has to use some (relatively strong) choice principle, in the exact same sense that to show that infinite sets exist one has toi use the axiom of infinite (e.g. there are no infinite sets in the topos of finite sets, or there are no non-measurable sets in ZF + DC + LM). If a set is non-measurable it is non-measurable and that is it, that is, non-measurability is a property like cardinality or other set-like properties. In the mathematical context, it is so necessarily and that is it, that is the whole explanation. Assuming non-measurable sets could be instantiated, the causal explanation needed/lacking would be of their origin, not in their being non-measurable. If their production and coming to be relied on some divine fiat involving a more or less concrete application of AC then that would be the explanation. An analogy: electrons have spin 1/2, because necessarily electrons have spin 1/2. The explanation needed/lacking would be of their origin or in other contingent properties like their state, energy, momentum or what have you.grodrigueshttps://www.blogger.com/profile/12366931909873380710noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-87497861006148296342021-03-27T09:39:19.524-07:002021-03-27T09:39:19.524-07:00@grodrigues,
1) You're right it doesn't ...@grodrigues,<br /><br /><br />1) You're right it doesn't strictly prove brute facts exist, but it can be used to make brute facts more likely and argue for their probable existence, since one of the main problematic things about BFs is their lack of defined probability which implies skepticism and agnosticism.<br /><br />Especially so if brute facts are just a special type or subset of nonmeasurability, or if it's just the universal concept of Nonmeasurability applied to causation or explanation.<br /><br /><br />2) The paper in question would be “On the Law of Large Numbers for nonmeasurable identically distributed random variables”, so if you want to read it you can look for that.<br /><br /><br />3) One more thing - could one argue that mathematical nonmeasurable sets are radically unlike brute facts in that they are selected and have a certain order to them?<br /><br />That is, in order to create a NS set one has to use the Axiom of Choice and actually choose particular members of other sets to do that. The existence of NS depends on choosing in contexts where there is an infinite amount of things and no distinguishing features for otherwise natural choice functions - and that choice isn't a brute fact in itself.<br /><br />Heck, even if a Nonmeasurable Set or Object wasn't constructed by conscious and rational humans but by machines it would have this trait. <br /><br />The only way to get rid of this internal order would seem to make the NS set pop into existence out of nothing with no procedure of generating it by choice. <br /><br />What do you think?JoeDnoreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-82605037031084727012021-03-27T05:36:44.959-07:002021-03-27T05:36:44.959-07:00@JoeD:
"Their lack of any causes or explanat...@JoeD:<br /><br />"Their lack of any causes or explanations intrinsically is what entails no defined probability."<br /><br />You have made my point for me. To repeat, I can understand brute facts have no explanations, not even probabilistic ones, but if there is some event or other for which there is no defined probability (leaving aside all the care needed to make this rigorous), there is no reason to start panicking as if the impending doom of brute facts is upon us. It just follows that such a scenario has this in common with brute facts: it has no defined probability.<br /><br />About the 2), I understand and I concur with Pruss's remark from the qualitative difference between brute facts and events, to call it that, with undefined probability. It is another way of stating my above point. I do *not* understand the argument he seems to be advancing about probability bounds. He seems to be saying that 0 <= P(E) <= 1 but P(E) is undefined -- so what the heck is he saying?<br /><br />Then he continues by assuming that there are measurable sets F, G such that F <= E <= G from which he "derives" the probability bound P(F) <= P(E) <= P(G). Same point as before: P(E) is undefined so the inequality P(F) <= P(E) <= P(G) is non-sensical. It *seems* as though if such a scenario is possible that we would have such a probability bound, but I repeat, if P(E) is undefined what is the meaning of such would-be bound? The limit of the ratios of hits to throws does *not* exist so what are we talking about when we are talking about P(E) and would-be bounds? I suppose I would have to look up his 2013 paper, mentioned at the second paragraph from the end, after Halperin's result on the existence of saturated non-measurable sets. In it he develops a "plausible mathematical model of an infinite sequence of independent identically distributed saturated nonmeasurable random variables", so I guess it depends on what "plausible" means here.<br /><br />In summary, I have no problem with his final conclusion of a priori ruling out non-measurable sets. I just think the argument can be shortened to "if they could be instantiated they would have undefined probability (in some scenario or other) and it could not be checked, confirmed or disconfirmed" and leave it at that. In other words, the argument for disallowing them is an epistemological one, and it only impinges on the actual world (the only one that matters, by the way). Whether God could create a world in which such sets are instantiated is a different question altogether.grodrigueshttps://www.blogger.com/profile/12366931909873380710noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-88210900548024433232021-03-26T16:16:25.368-07:002021-03-26T16:16:25.368-07:00With the volcano, I'm thinking of the good old...With the volcano, I'm thinking of the good old legal concept of an Act of God, i.e., there are things that are "outside human control ... for which no person can be held responsible" (says Wikipedia) and which are beyond our power to "figure out" -- worth pondering, perhaps.David McPikehttps://www.blogger.com/profile/04997702078077124822noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-60431883038387445742021-03-26T16:09:15.668-07:002021-03-26T16:09:15.668-07:00@Tony:
I agree, "scientism" is not the ...@Tony: <br />I agree, "scientism" is not the culprit. I continue to be baffled as to why Feser thinks it is relevant. Scientism is, I take it, a species of Bad Philosophy of Science, and BPoS is arguably relevant (although the problem mostly seems to be Bad Science, i.e., BS rather than BPoS), but not scientism in particular. <br /><br />As for what scientism is, I wouldn't have said it was either of the options you mention. I thought it was the straightforwardly naive (usually completely unanalyzed) claim that the only real knowledge is scientific knowledge. <br /><br />Anyway, certainly a good scientist can be a bad philosopher of science (or bad at public policy), just as a good person can be a poor moral philosopher. <br /><br />As for figuring out what to do in case of a Really Bad Disease, I wonder if that's a bit like getting hit by a small volcanic eruption, and hoping that now we'll know better how to handle a 30 times bigger eruption. Maybe... not? Or maybe it's like starting a small fire on an ant hill and wondering, as you watch the ants freak out, if this will help them figure out how to deal with a 30 times bigger fire in the future. (Obviously ants aren't even potentially rational so it's an imperfect analogy, but...)David McPikehttps://www.blogger.com/profile/04997702078077124822noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-60694201535724175902021-03-26T08:20:16.937-07:002021-03-26T08:20:16.937-07:00@grodrigues,
Part 2 of 2
"But this reason...@grodrigues,<br /><br />Part 2 of 2 <br /><br /><br /><i>"But this reasoning <b>is mistaken.</b> To see this, we need to sharpen our hypothesis N a little more. There are non-measurable sets A where we can say things about the frequency with which A will be hit. For instance, it could be that although A is non-measurable, <b>it contains</b> a measurable set A1 of area (0.74)T and is <b>contained in</b> a measurable set A2 of area (0.76)T. (Think of A as 74% of the target plus a nonmeasurable set localized to an area containing only 2% of the target.) But the dart will hit A1 about 74% of the time, and A2 about 76% of the time. Whenever the dart hits A1, it hits A, and whenever it hits A, it hits A2, so <b>we would expect</b> the dart to hit A approximately 74% to 76% of the time. And so our observed frequency would be <b>no surprise.</b> The mere fact that A is nonmeasurable <b>does not rule out probabilistic predictions</b> about frequencies, because a nonmeasurable set might be “quite close” to measurable sets like A1 and A2 that bracket A from below and above."</i><br /><br /><i>"However some sets are not only nonmeasurable, but <b>saturated nonmeasurable.</b> Set A is saturated nonmeasurable provided that all of A’s measurable subsets have <b>measure zero</b> and all measurable subsets of the complement of A <b>are also</b> of measure zero. Given the Axiom of Choice, for Lebesgue measure on the real line, there not only are nonmeasurable sets, but <b>there are</b> saturated nonmeasurable sets (Halperin 1951). When A is saturated nonmeasurable, <b>no method</b> of generating predictions by bracketing a the probabilities into an interval, like the one from 74% to 76%, will work. The only measurable subsets of A will have zero area and the only measurable supersets of A will have area T. So our bracketing will only tell us the <b>trivial fact</b> that the frequency will be between 0 and 1, inclusive." </i><br /><br /><i>"Let M then be the hypothesis that A is saturated nonmeasurable. Can we say that given M, the frequency is unlikely to be near 0.750?<br />The answer turns out to be negative <b>even if we have infinitely many</b> observations. Pruss (2013) has given a plausible mathematical model of an infinite sequence of independent identically distributed saturated nonmeasurable random variables, and it follows from his Theorem 1.3 that for any nonempty interval I which is a proper subset of [0, 1], the event that the limiting frequency of the events is in I is itself saturated nonmeasurable..." </i><br /><br /><i>"So in our case above, if I is some small interval like [0.740, 0.760] centered on 0.750, there is <b>nothing probabilistic</b> we can say about the observed frequency being in I when the target set is nonmeasurable as the event of the frequency being in I is then <b>saturated nonmeasurable.</b> In particular, we <b>cannot</b> say that the frequency is <b>unlikely</b> to be near 0.750 (nor that it’s <b>likely</b> to be near). The observation of a frequency close to 0.750 is <b>neither surprising nor to be expected</b> given that the target set is saturated nonmeasurable."</i><br /><br /><i>"Our probabilistic reasoning thus cannot disconfirm hypotheses of saturated nonmeasurability. Such hypotheses endanger all our local scientific inferences from observed frequencies to chancy dispositions, inferences central to our epistemic practices. Yet our local scientific inferences are, surely, good. If we cannot disconfirm saturated nonmeasurability hypotheses a posteriori, then we need to do so <b>a priori.</b>" </i><br /><br />What do you think of this?JoeDnoreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-20018362765763636022021-03-26T08:18:41.494-07:002021-03-26T08:18:41.494-07:00@grodrigues,
Part 1 of 2
1) Well the context in ...@grodrigues,<br /><br />Part 1 of 2<br /><br />1) Well the context in this case is about probability of occurrence, which is the measure that lacks definition. And it seems straightforward as to how undefined probability is connected to brute facts - because brute facts have undefined probability.<br /><br />Their lack of any causes or explanations intrinsically is what entails no defined probability.<br /><br />2) Well, here is how Alex Pruss put it: https://alexanderpruss.blogspot.com/2019/09/classical-probability-theory-is-not.html<br /><br /><br /><i>"I think there is some reason independent of the PSR to doubt the actual causal implementability of nonmeasurable mathematical constructs. Cf. the chapter on the Axiom of Choice in my book on the paradoxes of infinity."</i><br /><br /><i>"I also think there is a difference between (a) the <b>extreme nonmeasurability</b> of uncaused contingent events and (b) the kind of nonmeasurability you would have in a concrete situation like <b>throwing a dart</b> at a nonmeasurable target. In (a), there are <b>no probabilities at all</b> attachable to the event. But in (b), <b>there are probabilistic bounds,</b> since the probability of hitting the nonmeasurable target is less than the probability of throwing the dart which in turn is less than one. Thus, (b) leads to <b>less</b> in the way of sceptical worries than (a)."</i><br /><br /><br />And here is a paper by Pruss about PSR and probability: https://alexanderpruss.blogspot.com/2016/02/the-principle-of-sufficient-reason-and.html<br /><br />He basically applies Bayes to nonmeasurable events - which is what brute facts are supposed to be.<br /><br />As for the 17-page article, here are some extracts about the dart throwing example and why brute facts are mathematically nonmeasurable things:<br /><br /><br /><i>"So suppose coins are being flipped in this roundabout way. A dart with a perfectly defined tip (say, infinitely sharp or perfectly symmetrical) is uniformly randomly thrown at <b>a circular target.</b> There is a region A of the target marked off, and a detector generates a heads toss (maybe in a very physical way: it picks up the coin and places it heads up) whenever the dart lands in A; otherwise, it generates a tails toss."</i><br /><br /><i>"The chance of the coin landing heads now should be equal to <b>the proportion of the area</b> of the target lying within A, and we can elaborate Cp to the hypothesis that the area of A is pT, where T is the area of the whole target. Given the observation of approximately 750 heads, it seems reasonable to infer that probably the area of A is approximately (3/4)T. But what if <b>an area cannot be assigned</b> to the marked region A? Famously, given the Axiom of Choice, there are sets that have no area—not in the sense that they have zero area (like the empty set, a singleton or a line-segment), but in the sense that our standard Lebesgue area measure cannot assign them any area, not even zero. In such a case, there will also be <b>no well-defined chance</b> of the dart hitting A, and hence no well-defined chance of heads. Let N be the hypothesis that A has no area, i.e., is non-measurable."</i><br /><br /><i>"Now, here is a fascinating question. If N were true, <b>what would we be likely to observe?</b> Of course, if we perform 1000 tries, we will get some number n of heads, and n/1000 will then be a frequency between 0 and 1. We might now think as follows. This frequency can equally well be any of the 1001 different numbers in the sequence 0.000, 0.001, . . . , 0.999, 1.000. It seems <b>unlikely,</b> then, that it’s going to be near 0.750, and so C3/4 (and its neighbors) is still <b>the best hypothesis</b> given that the actual frequency is 0.750." </i>JoeDnoreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-57151243953248486062021-03-26T07:03:04.111-07:002021-03-26T07:03:04.111-07:00@JoeD:
"If nonmeasurability is basically bei...@JoeD:<br /><br />"If nonmeasurability is basically being undefined, and nonmeasurable sets with no defined size can exist, and those same sets in some contexts imply undefined probability which is the same as for brute facts, then the possibility of nonmeasurable sets existing lends more credibility to brute facts being possible as well. At least that's the argument."<br /><br />Non-measurability is not being measurable, or not having its measure defined, with the context specifying what measure we are talking about. I am not being pedantic for the sake of pedantry: Solovay showed that the existence of measurable cardinals (a statement independent of ZFC) is equiconsistent with the existence of a sigma-additive extension of the Lebesgue measure to *all* subsets of the real line (this is not inconsistent with Banach-Tarski type results as these rely on the measure being invariant over a non-amenable group such as the group of rotations in R^3). The connection of "Undefined probability" to "brute facts" is baffling, meaning, I can see why brute facts do not have causes (or explanations -- I tend to view all explanations as causal), not even probabilistic ones, but not the reverse and certainly not "the same".<br /><br />"To clarify the scenario - it's specifically that the Probability of hitting the nonmeasurable target is LESSER than the Probability of throwing the dart which is in turn LESSER than 1 or absolute certainty. This is in fact likely a DIFFERENCE between nonmeasurable sets and brute facts since brute facts don't have any probability bounds while this scenario at least does."<br /><br />The probability of hitting the non-measurable set is undefined so it is not lesser or greater than anything whatsoever.<br />grodrigueshttps://www.blogger.com/profile/12366931909873380710noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-57482057526128835252021-03-25T20:35:19.566-07:002021-03-25T20:35:19.566-07:00@One Brow
I had never heard of it before, so than...@One Brow<br /><br />I had never heard of it before, so thanks for the tip. I read a post from the guy(i think) about hylemorphism and i can see how you could use the concept in a non-aristotelian context. <br /><br />But i don't know if Daniel sees himself as non-aristotelian. From his post, he does not seems to find a problem between his more computational view of the idea and Aristotle himself. I don't know if the greek actually believed in life after death and all that, that seems pretty controversial,so maybe they are not THAT diferent. <br /><br /><br />@JoeD<br /><br />Its been a while since i saw the debate, so i could be exaggerating. But i remember he saying something like that yes, thought i doubt that he is a realist on universals. Oppy seemed to me to see our mathematics as derived from reality. <br /><br />I even remember that when asked by Dr. Craig on why we have these laws and not others he replied that they are necessary*, in the sense that it could not be others(which i agree). But again, its been a while, so watching the debate would be more trustworth. <br /><br />*a strange thing is that i remember Oppy wanting to finish the whole question of the origin of the laws there, like if he thought that a thing being necessary means that it can't have any explanation, but i could be remembering wrongTalmidhttps://www.blogger.com/profile/04267925670235640337noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-52631345115397120672021-03-25T14:03:58.437-07:002021-03-25T14:03:58.437-07:00@Unknown,
And couldn't one describe brute fac...@Unknown,<br /><br />And couldn't one describe brute facts as a type of selection as well? It may not be caused or explained, but a particular brute fact is distinct from other brute facts, so when something specific happens brutely it was in a sense selected since this particular thing happened for no reason, which is by definition distinct from another thing.<br /><br />So you could say <b> nothing selected </b> it, rather than denying that selection applies to brute facts or that we cannot speak of selection in any way regarding brute facts.JoeDnoreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-81176409203483185632021-03-25T11:17:17.796-07:002021-03-25T11:17:17.796-07:00@Talmid,
Wait, did Oppy actually say that there i...@Talmid,<br /><br />Wait, did Oppy actually say that there is most likely real structure in reality to explain why math is so good at modelling the world?<br /><br />Did that really happen?JoeDnoreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-46726798270397097702021-03-25T11:08:23.027-07:002021-03-25T11:08:23.027-07:00@Unknown,
One more thing came to mind - the Axiom...@Unknown,<br /><br />One more thing came to mind - the Axiom of Choice generates nonmeasurable sets from selection, but that itself can be said to be something we have to do to discover NS sets, not that it creates them.<br /><br />For example, if a nonmeasurable set were created ex nihilo - either by God or if that happened as a brute fact - it would have members that we would usually generate via particular selection, but in itself the recently created NS set wasn't created by selection; rather, all of its members are part of its definition or internal structure which came into being with it.<br /><br />So it seems the selection of sets via AoC doesn't constrain them from being brute if they popped into existence rather than being generated via a method.JoeDnoreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-33702651288656368822021-03-25T11:02:08.923-07:002021-03-25T11:02:08.923-07:00@grodrigues,
About probability - the reason why ...@grodrigues, <br /><br />About probability - the reason why the connection is made to brute facts is that brute facts also have an undefined probability. If nonmeasurability is basically being undefined, and nonmeasurable sets with no defined size can exist, and those same sets in some contexts imply undefined probability which is the same as for brute facts, then the possibility of nonmeasurable sets existing lends more credibility to brute facts being possible as well. At least that's the argument.<br /><br />To clarify the scenario - it's specifically that the Probability of hitting the nonmeasurable target is LESSER than the Probability of throwing the dart which is in turn LESSER than 1 or absolute certainty. This is in fact likely a DIFFERENCE between nonmeasurable sets and brute facts since brute facts don't have any probability bounds while this scenario at least does.<br /><br />JoeDnoreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-87604523732175007912021-03-25T10:56:24.864-07:002021-03-25T10:56:24.864-07:00@Unknown,
"There is no process of selection ...@Unknown,<br /><br /><i>"There is no process of selection through any probabilities; there is nothing that selects among any possible worlds, the brute facts are not caused, there would be nothing selecting or hitting anything."</i><br /><br />Are you referring to the argument that hitting a NS target with a dart still has probability bounds - P of hitting the target being less than P of throwing the dart, which is in turn less than certain truth or 1?<br /><br />Or are you saying that the Axiom of Choice - which is used to select elements in cases where there are no proper distinguishing features and an infinity of elements - by its very nature as a choosing function means it's NOT arbitrary as brute facts have to be?<br /><br />If the latter, that certainly seems plausible - though when I asked Alex Pruss about NS and brute facts, he did say that NS sets would lead to less skeptical worries than brute facts due to probabilistic bounds on NS constructions - the keyword being less skeptical worries, so some skeptical worries seem to still exist with NS.<br /><br />Pruss also compared NS to brute facts in his paper on probability in science and PSR - arguing how if brute facts are possible then the probability of them occurring is nonmeasurable and thus undermines science, so we need an a priori way to get rid of brute facts. <br /><br />He also compares the idea of throwing a dart at a NS target to brute facts in that they are both defeaters for any inductive expectation - the lack of meaningful probability for the dart hitting the NS target seemingly the same as the nonmeasurability of brute facts.<br /><br />Plus, nonmeasurable sets are nonmeasurable because they lack any meaningful size - they are literally called sizeless sets since their size is neither 0 not infinite - so size does not apply to them at all. They are just sets that exist, and happen to have no size.<br /><br />In the same way, brute facts would also seem to be an instance of NS since the concept of probability doesn't apply to them at all - they are literally probability-less. They are things that can happen, without probability.<br /><br />What do you think?JoeDnoreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-25417354453720158172021-03-25T10:29:57.201-07:002021-03-25T10:29:57.201-07:00@JoeD:
"So... could we still say that this i...@JoeD:<br /><br />"So... could we still say that this implies it can't be causally implemented or physically constructed - especially since physical constructibility seems like a lower level definition of constructibility that is even more limited than mathematical constructibility?"<br /><br />Could God have created a world in which the physical laws are such that in some sense, non-measurable sets can be instantiated? I don't know and I don't know how one would even begin to try to answer this question. Assuming it is possible, does that entail any skeptical worries? I have still not seen an argument for why that is so. In your contrived scenario, enclose the non-measurable set by an appropriate figure of area/volume/whatever 1 (1 what? choose whatever unit you fancy). Then the probability that a point-tipped dart hits the set is undefined. Why is that a problem? Don't know. In the frequentist interpretation, the probability is a limit of a certain ratio. Why is the non-existence of this limit somehow problematic? Shrug shoulders.grodrigueshttps://www.blogger.com/profile/12366931909873380710noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-77586141546269171992021-03-25T08:22:10.470-07:002021-03-25T08:22:10.470-07:00Just barging in, but
"So if NS's can act...Just barging in, but<br /><br />"So if NS's can actually exist - since they are coherent and possible and even provable in a sector of math - then it seems brute facts can also since they are just Nonmeasurability applied to things happening or being actual in terms of their lack of explanation."<br /><br />This is not what brute facts are. Pruss argues that brute facts would, if possible, have no meaningful objective probability, but the idea that if NS are possible then brute facts are possible is nonsense; brute facts are absolutely unexplained contingent events and there is nothing to properly constrain them since they are supposed to come from nothing, by nothing. There is no process of selection through any probabilities; there is nothing that selects among any possible worlds, the brute facts are not caused, there would be nothing selecting or hitting anything. Anonymoushttps://www.blogger.com/profile/01087138435392371312noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-43200731285552764962021-03-25T08:17:09.824-07:002021-03-25T08:17:09.824-07:00@grodrigues,
So... could we still say that this i...@grodrigues,<br /><br />So... could we still say that this implies it can't be causally implemented or physically constructed - especially since physical constructibility seems like a lower level definition of constructibility that is even more limited than mathematical constructibility?JoeDnoreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-65672134962045494652021-03-25T07:49:29.115-07:002021-03-25T07:49:29.115-07:00Talmid,
As I said, I'm sure no offense was in...Talmid,<br /><br />As I said, I'm sure no offense was intended.<br /><br />Have you read Camels with Hammers? Daniel Fincke was trying to create a version of hylomorphism somewhat different from the Aristotelian version. I don't know if he still is.One Browhttps://www.blogger.com/profile/11938816242512563561noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-85594732312837277392021-03-24T20:41:21.190-07:002021-03-24T20:41:21.190-07:00@One Brow
Sorry about the name :(
I'am not th...@One Brow<br /><br />Sorry about the name :(<br />I'am not that good with details, these words are kinda similar...<br /><br />Well, there sure is non-scholastic takes on hylemorphism, Aristotle himself would disagree with some of the scholastics, since they themselves disagreed with each other and people like Aquinas did inovate on the greek ideas.<br /><br /> About the non-aristotelian hylemorphism, that would be pretty interesting to know, actually. Maybe you could argue that people like the platonists, augustinians, cappadocians and others essencialists where close to that, maybe it depends on how we define things.<br /><br />BenG<br /><br />Could the nominalist get even mereological nihilism? The mereological simples would need to have particular caracteristics too which would indicate a essence, so it seems that the problem would continue.<br /><br />And yea, Dr. Craig is pretty clear on his dialogue with Cosmic Skeptic about find mereological nihilism a bizarre view. Kinda funny. Talmidhttps://www.blogger.com/profile/04267925670235640337noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-16265131226809610832021-03-24T13:56:12.781-07:002021-03-24T13:56:12.781-07:00@JoeD:
In the two passages, I am using practical ...@JoeD:<br /><br />In the two passages, I am using practical in different senses,m as witnessed by the fact that in the second passage I enclose the word in square quotes and lead with "such as there being no effective constructive procedure for the partition of the ball" -- "practical" here means "interesting to mathematicians". Yeah, the word choice is suboptimal to say the least...grodrigueshttps://www.blogger.com/profile/12366931909873380710noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-15979066532975130692021-03-24T11:48:04.107-07:002021-03-24T11:48:04.107-07:00@grodrigues,
"Non-constructibility follows, ...@grodrigues,<br /><br /><i>"Non-constructibility follows, where non-constructibility is understood in a *mathematical* sense, because if it were constructive such construction could have already been done in ZF + DC. There are a few things more that could be said, but this entails having precise descriptions of what counts as a construction. "</i><br /><br />But didn't you also say when describing the Banach-Tarski paradox in a different post that the non-constructibility also implies a few practical senses of the term that aren't technical?:<br /><br /><i>"As to the Banach-Tarski it is probably worth it to mention that its proof is unavoidably non-constructive -- non-constructive in a technical mathematical sense, but that does translate in a few more "practical" senses, such as there being no effective constructive procedure for the partition of the ball, etc." </i><br /><br />From here: http://edwardfeser.blogspot.com/2018/09/10th-anniversary-open-thread.htmlJoeDnoreply@blogger.com