tag:blogger.com,1999:blog-8954608646904080796.post5685083774185368012..comments2021-04-22T09:18:28.853-07:00Comments on Edward Feser: Eric MacDonald’s assisted intellectual suicideEdward Feserhttp://www.blogger.com/profile/13643921537838616224noreply@blogger.comBlogger164125tag:blogger.com,1999:blog-8954608646904080796.post-48179891140792661692011-08-23T18:19:44.807-07:002011-08-23T18:19:44.807-07:00Empiricism ought to matter, right?
It sure does.....<i>Empiricism ought to matter, right?</i><br /><br />It sure does... and studies of the Ugandan ABC approach have shown that it's benefits are exaggerated at best.StoneTopnoreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-82990550201990872792011-08-23T12:22:10.873-07:002011-08-23T12:22:10.873-07:00I cannot see how the informal argument establishes...<i>I cannot see how the informal argument establishes that the human mind has more arithmetical power</i><br /><br />If it were merely arithmetical power, then there might not be an issue. But not all human powers are algorithmic. But you are right; this is way off to the side.TheOFloinnhttps://www.blogger.com/profile/14756711106266484327noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-53570198329658280282011-08-23T12:16:02.918-07:002011-08-23T12:16:02.918-07:00It's the idea that for an HIV+ person, sex wit...<i>It's the idea that for an HIV+ person, sex with a condom is worse than sex without a condom</i> <br /><br />Which the Pope pointed out. A technological object is not right or wrong in itself; it is the usage thereof. Just as a robber who uses an unloaded gun to rob a bank is showing the glimmering of moral growth in that he now cares at least a little bit for <i>other people,</i> without implying that bank robbery is permissible, so too does the use of a condom to prevent the spread of disease while engaged in hedonistic profligacy, without implying that hedonistic profligacy (or the objectification of women) is permissible.TheOFloinnhttps://www.blogger.com/profile/14756711106266484327noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-1592110510028196542011-08-23T12:11:23.017-07:002011-08-23T12:11:23.017-07:00"underneath" we still only have a posite...<i>"underneath" we still only have a posited and rather ineffable "stuff" we call matter and energy. </i> <br /><br />That's what Aristotle and Aquinas said, so I don't think it qualifies as an objection to hylepmorphism. You are certainly right to point out that this is a better model than the atomist model. <br /><br />There is a digest overview here:<br />http://home.comcast.net/~icuweb/c02002.htm#3TheOFloinnhttps://www.blogger.com/profile/14756711106266484327noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-40338455720082168422011-08-23T11:28:56.078-07:002011-08-23T11:28:56.078-07:00@TheOFloinn:
"S = "Lucas can't asse...@TheOFloinn:<br /><br />"<i>S = "Lucas can't assert the truth of statement S."<br /><br />This statement is true but cannot be asserted by Lucas. This shows that Lucas himself is subject to the same limits that he describes for machines, as are all people, and so Lucas's argument is pointless.<br /><br />This glosses over the distinction between "true" and "provable-within-the-system" that matters so much to Lucas and Goedel. "Assert" is not the same as "prove-within-the-system."</i>"<br /><br />I have only read the feferman pdf, and I confess that I am still not convinced. Since this is completely off-topic, I will try to be as brief as possible.<br /><br />Let S be the ideal system alleged by the die-hard mechanicist to encapsulate the arithmetical humanly provable theorems and G its Gödel sentence. The only thing we are allowed to conclude form Gödel's theorem is that S is consistent iff G is true -- and this much is provable within S itself. So convincing ourselves of the truth of G is the same as convincing ourselves of the consistency of S, so that there is no reason to assert that we (the human mind) have more provable power than S has.<br /><br />Lucas responds to this objection with an *informal* argument: if S were inconsistent then it would fail to distinguish truth from falsehood (by the principle that from a contradiction anything follows) and the human mind certainly can do it, so we have a cogent argument to accept, on the die-hard mechanicist hypothesis, that S is consistent, from which it follows that G is true. Thus we are entitled to reject S as encapsulating the human mind's ability to do arithmetic.<br /><br />I am not particularly interested in playing the devil's advocate and defending the die-hard mechanicist (may his ideas fester, rot and pass away into eternal oblivion), nevertheless I will venture the following.<br /><br />1. Gödel's theorem *by itself* cannot do the work Lucas intends to as evinced by the fact that he has to resort to an informal argument to establish the consistency of S.<br /><br />2. I cannot see how the informal argument establishes that the human mind has more arithmetical power: it is a non-formalizable argument and relying on the claim of the mechanicist. The fact that the mechanicist claims that S is consistent does not translate into the capacity for the human mind to assert the consistency of S, which is what is needed to conclude that we have more arithmetical power than S.<br /><br />3. There is still the possibility that S is inconsistent. The inconsistency could be buried so deep or its proof so long that it would be beyond the human powers to grasp it (this connects with the recent programme of Voevodsky). I find this implausible but cannot really refute it, and Lucas only says that he leaves it to others to develop the hypothesis and demolish it.grodrigueshttps://www.blogger.com/profile/12366931909873380710noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-60315983575671112362011-08-23T10:26:43.754-07:002011-08-23T10:26:43.754-07:00Yet, Uganda's ABC program: Abstain, Be Faithfu...<i>Yet, Uganda's ABC program: Abstain, Be Faithful, Condom had been remarkably successful, and the Ugandan health minister wrote in Der Spiegel that it was plainly inhumane for Western aid agencies to insist on condoms as the only approach, given that that approach had failed consistently in the past. Encouraging sexual license seemed to matter more to them, he said, that stemming the spread of AIDS. <br /><br />Empiricism ought to matter, right?</i><br /><br />Now who's issuing the false dichotomies? I have no problem at all with "ABC." It's the idea that for an HIV+ person, sex with a condom is worse than sex without a condom -- whatever else one is justified to believe about abstinence and fidelity -- that I find abhorrent, and almost obviously so.Another Mattnoreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-10590172132176905822011-08-23T10:01:19.760-07:002011-08-23T10:01:19.760-07:00Euclid's proposition regarding the relationshi...<i>Euclid's proposition regarding the relationship between a secant and a tangent drawn to the same point on a circle is also [figuratively] light years from the five postulates and five common notions. Yet one does not need "a number of other assumptions" to attain it. <br /><br />Likewise, the proposition that a space is compact iff it is both countably compact and metacompact is light years from the eleven axioms of set theory; but no additional assumptions are needed to get there. <br /><br />That you don't see the deductive path from the axioms to the theorem, or understand that it might require an extended chain of reasoning does not mean it does not exist.</i><br /><br /><br />I'm in total agreement with you on this matter. In my field (music theory and composition) it's amazing how much of the structure of Western music is implied by just a few number-theoretical features of the integers 7 and 12. Yet, in all the "natural law" explications regarding homosexuality I've read, there has always been a subtle unjustified pivot somewhere, and it's almost always linguistic. Subtle changes in orientation with squishy words like "good" or more precise ones like "teleological" can get you a lot further than would be justified otherwise. Similarly, there are often subtle pivots from epistemological issues to ontological ones in the deductive chain which I also think are unjustified. They've always read as so many unearned "therefores." If you have a good recommendation I'll put it on my list of things to read.<br /><br /><br /><br /><i>So which do you deny? <br />a) That compound bodies are made of matter? <br />b) That the matter of compound bodies are some particular form of matter? <br />c) That every thing is some thing? (That matter and form are inextricably bound up in compound beings?) <br /><br />Consider sodium and chlorine. Both are made of the same matter: protons, electrons, and neutrons; but they differ in their form: the number and arrangement of these parts. And what makes one a poisonous gas and the other a flammable metal is exactly that form. (For that matter, that their compound is a tasty table condiment and essential to human life is likewise a formal cause ("emergent property") from the molecular form of their compound.)</i><br /><br /><br />Nope, this isn't good enough for me. You could keep going in this atomization project -- neutrons and protons are both "made of" quarks (but "made of" at this scale is a metaphor that makes it just intuitive enough to grasp, since quarks are not isolable), and they (the hadrons) have different properties that emerge from their form (in this case the combination of quarks), fair enough. So far we just have form (or behavior) but "underneath" we still only have a posited and rather ineffable "stuff" we call matter and energy. We're presented with elementary particles and our intuitions scream <i>"but what are they MADE of?"</i> Saying "matter" doesn't really get you anywhere because from an observational standpoint ALL you have is behavior and form -- at that scale the distinctions among bits of matter are only meaningful in terms of the behavior they exhibit and not some "underlying substance." We may never have the tools to reduce it out further in a way that is supported by observation, so on the point that there "is something" that "fleshes out" the form/behavior we're only justified in remaining agnostic, until it is observed and the observation subsumed under a theory. At that scale it's not even clear what "something" and "nothing" mean, or if it's meaningful in the first place.<br /><br />Of course, this is all complicated in our language about it because the verb "to be" has both epistemological and ontological senses (and probably many more besides) and it's sometimes hard to distinguish which sense is meant or which one is meaningful in the context.Another Mattnoreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-92185240566466740322011-08-22T20:37:08.050-07:002011-08-22T20:37:08.050-07:00You mean first order Peano arithmetic.
Equivale...<i>You mean first order Peano arithmetic.</i> <br /><br />Equivalent to first order logic. <br /><br /><i>I have not read Lucas' response, if any</i> <br /><br />If one of them was <br /><br /><i>S = "Lucas can't assert the truth of statement S."<br /><br />This statement is true but cannot be asserted by Lucas. This shows that Lucas himself is subject to the same limits that he describes for machines, as are all people, and so Lucas's argument is pointless.</i> <br /><br />This glosses over the distinction between "true" and "provable-within-the-system" that matters so much to Lucas and Goedel. "Assert" is not the same as "prove-within-the-system." <br /><br />You can find Lucas' papers here:<br />http://users.ox.ac.uk/~jrlucas/<br />just scroll down to <br />I Gödelian Papers<br /><br />In particular, we have Lucas on Feferman here:<br />http://users.ox.ac.uk/~jrlucas/Godel/feferman.pdfTheOFloinnhttps://www.blogger.com/profile/14756711106266484327noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-52698567619737974962011-08-22T19:31:50.082-07:002011-08-22T19:31:50.082-07:00@TheOFloinn:
"What Gödel's theorem demon...@TheOFloinn:<br /><br />"What Gödel's theorem demonstrated was that in any consistent computational system {Ui} strong enough to support first order logic there are true sentences in {Ui} that cannot be proven in {Ui}."<br /><br />You mean first order Peano arithmetic.<br /><br />"This has several consequences: a theory of everything is unknowable, the human mind is not a computer, etc."<br /><br />I am very wary of Gödelian arguments propping "the human mind is not a computer". Feferman responds to Penrose's argument in "Penrose's Gödelian argument" (available online) and Torkel Franzen does it in his book "Gödel's theorem -- an incomplete guide to its use and abuse". He also points out (briefly) flaws in Lucas' argument. On the other hand, I have not read Lucas' response, if any, so I will stick to the "am very wary". Note the only thing I am disputing here is whether Gödel's theorems can be used to support the conclusion "the human mind is not a computer" not the conclusion itself, which I heartily endorse, but on other grounds.grodrigueshttps://www.blogger.com/profile/12366931909873380710noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-21430885411462730292011-08-22T18:26:32.985-07:002011-08-22T18:26:32.985-07:00The problem with empiricism is as noted by Russell...The problem with empiricism is as noted by Russell the problem of induction: no number of specific empirical instances suffice to establish a universal. Yet science depends upon the ability to induce universals. From Fido, Rover, Spot, and Lassie, we induce the non-empirical idea of "dog." From numerous instances of falling objects, we induce the non-empirical idea of "gravity."<br /><br />Hume's solution was to deny that "dog" and "gravity" (and "cause"!) exist at all. This could be fatal to science, if practicing scientists actually took him seriously. <br /><br />Some discussion can be found here:<br />http://thomism.wordpress.com/2011/08/21/an-aristotelian-thomistic-response-to-russells-problem-of-induction/TheOFloinnhttps://www.blogger.com/profile/14756711106266484327noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-29078873376564312072011-08-22T18:15:15.057-07:002011-08-22T18:15:15.057-07:00Someone over on Coyne’s site [MacDonald takes down...<i>Someone over on Coyne’s site [MacDonald takes down Feser’s theology] argues that:<br /><br /><b>Cantor’s Continuum Hypothesis has been shown to be logically independent from the usual axioms of mathematics. Mathematicians can freely assume it to be either true or false.</b><br /><br />So presumably there would be some conclusions that would follow if it was true and some if it was false.</i> <br /><br />Egads. Someone who would write that probably relies on Wikipedia for his sources. The proof of the unprovability of some theorems within a given system is precisely that the same results follow whichever one assumes. That is, neither CH nor not-CH entails a contradiction with the remainder of mathematics. <br /><br />Mathematicians generally regard CH as true, not only for aesthetic reasons, but because of the following peculiarity: <br /><br />The Axiom of Choice (Axiom IX) has always seemed non-axiomatic (like Euclid's parallel postulate), but it has been proven that AC <i>cannot</i> be derived from Axioms I-X. Neither can CH be derived from I:X+AC. However, if we drop AC from the axioms and adopt CH instead, AC <i>can</i> be derived from I:X+CH. Which is cool. <br /><br />What Gödel's theorem demonstrated was that in any consistent computational system {Ui} strong enough to support first order logic there are true sentences in {Ui} that cannot be proven in {Ui}. That is, the set of true sentences exceeds the set of provable sentences, rather like the set of real numbers exceeds the set of rational numbers. IOW, you cannot compute every true thing. <br /><br />This has several consequences: a theory of everything is unknowable, the human mind is not a computer, etc.TheOFloinnhttps://www.blogger.com/profile/14756711106266484327noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-66465712147793391992011-08-22T17:44:51.367-07:002011-08-22T17:44:51.367-07:00I will have a very hard time being charitable to i...<i>I will have a very hard time being charitable to ideas that seem to be, on their face, as plainly inhumane as this.</i><br /><br />Yet, Uganda's ABC program: <b>A</b>bstain, <b>B</b>e Faithful, <b>C</b>ondom had been remarkably successful, and the Ugandan health minister wrote in <i>Der Spiegel</i> that it was plainly inhumane for Western aid agencies to insist on condoms as the only approach, given that that approach had failed consistently in the past. Encouraging sexual license seemed to matter more to them, he said, that stemming the spread of AIDS. <br /><br />Empiricism ought to matter, right?TheOFloinnhttps://www.blogger.com/profile/14756711106266484327noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-58351588427768584252011-08-22T17:38:55.865-07:002011-08-22T17:38:55.865-07:00consider non-Euclidean geometry... Until it was “p...<i>consider non-Euclidean geometry... Until it was “proven” to correlate with actual space it seems it was only a consistent set of axioms and theorems with a rather pallid claim to knowledge and utility.</i> <br /><br />Pallid to whom? Surely you don't suppose that a master in mathematics could be ignorant of the utility of mathematics, nor that the truth of mathematics is independent of its utility! And which 'non-Euclidean geometry' do you refer to? Riemannian? Lobachevskian? And what do you mean by 'correlate with actual space'? Mathematics can be useful for modeling the physics, but as the great George E. P. Box once said, "All models are wrong. Some are useful." <br /><br />Hume was of course a champion of empiricism to the extent that he advocated burning all books that were not empirical in nature. This put him in a bad case vis a vis mathematics, which the Cartesians hoped to use to give conclusions in the physics the same absolute certainty as conclusions in mathematics. So he declared mathematics to be an honorary form of empiricism. <br /><br />Meanwhile, empiricism had given us a world-flood, phlogiston, beams coming from the eyes, N-rays, polywater, and other cute things. All falsifiable, and all eventually falsified. That is the nature of empiricism (evidentia naturalis): the next fact may prove everything wrong.TheOFloinnhttps://www.blogger.com/profile/14756711106266484327noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-30634714400792611432011-08-22T17:28:45.746-07:002011-08-22T17:28:45.746-07:00Any participation in an abortion results in automa...<i>Any participation in an abortion results in automatic excommunication.</i> <br /><br />Ex-communi-cation means 'excluded from communion.' It is automatic for any mortal sin whatever. We hear more about it with respect to abortion because proponents of abortion constantly affirm it as a positive good or at worst a no-big-deal. This can confuse well-meaning people and create a 'stumbling block' (lit. 'scandal'). In the same manner, some of the same-minded folks were formally excommunicated in the early 20th century for espousing eugenics, and in the 1950s were threatened with excommunication by the archbishops of New Orleans and St. Louis for espousing segregation. No one needs to denounce a sin that everyone realizes is a sin. <br /><br />Hope this helps.TheOFloinnhttps://www.blogger.com/profile/14756711106266484327noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-68584402105948943692011-08-22T17:12:15.633-07:002011-08-22T17:12:15.633-07:00This is light years from any specific argument aga...<i>This is light years from any specific argument against homosexuality, say, which requires a number of other assumptions</i> <br /><br />Euclid's proposition regarding the relationship between a secant and a tangent drawn to the same point on a circle is also [figuratively] light years from the five postulates and five common notions. Yet one does not need "a number of other assumptions" to attain it. <br /><br />Likewise, the proposition that a space is compact iff it is both countably compact and metacompact is light years from the eleven axioms of set theory; but no additional assumptions are needed to get there. <br /><br />That you don't see the deductive path from the axioms to the theorem, or understand that it might require an extended chain of reasoning does not mean it does not exist. <br />+ + + <br /><i>I'd quibble pretty deeply with the "matter and form" assumption</i> <br /><br />So which do you deny? <br />a) That compound bodies are made of matter? <br />b) That the matter of compound bodies are some particular form of matter? <br />c) That every thing is some thing? (That matter and form are inextricably bound up in compound beings?) <br /><br />Consider sodium and chlorine. Both are made of the same matter: protons, electrons, and neutrons; but they differ in their form: the number and arrangement of these parts. And what makes one a poisonous gas and the other a flammable metal is exactly that form. (For that matter, that their compound is a tasty table condiment and essential to human life is likewise a formal cause ("emergent property") from the molecular form of their compound.)<br /><br />Hope this helps.TheOFloinnhttps://www.blogger.com/profile/14756711106266484327noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-84961371656631680752011-08-22T16:07:30.587-07:002011-08-22T16:07:30.587-07:00@Steersman (continued):
"And since we are ta...@Steersman (continued):<br /><br />"<i>And since we are talking about mathematics, what exactly are your credentials that I should believe you instead of the mathematical community?</i><br /><br />Couple of years of university math and a couple of years of math associated with a 2 year program in control system theory and applications plus more than a few years of reading and studying various odds and ends. And yours are?"<br /><br />You made several statements that implied that mathematics is not knowledge, without providing arguments; thus it made sense to ask what kind of mathematical knowledge you have that allows you to do them. From our exchanges, my impression is that your arguments are largely based on ignorance (using the word in the etymological sense, not as an insult).<br /><br />As far as my credentials: undergraduate studies in physics with a very strong mathematical component, a phd in mathematics, published papers in peer-reviewed journals, seminar talks. And while I am not a mathematician (I do not have a university teaching position), I am attached to a research group in a university math department and part of my time is devoted to mathematical research.<br /><br />""Bolyai ends his work by mentioning that it is not possible to decide through mathematical reasoning alone if the geometry of the physical universe is Euclidean or non-Euclidean; this is a task for the physical sciences."<br /><br />Presumably a piece of information, of knowledge, of some value and, as indicated, not accessible or “provable” [decidable] by mathematics alone – somewhat related to the point I was trying to make."<br /><br />Not, it is not related *at all* to your point. What Bolyai is saying is that whether physical space is Euclidean or not is a contingent, not a necessary fact, and thus it can only be decided by experimental evidence not by mathematical reasoning alone. From our modern POV this is a obvious, but it was not in the historical time of Bolyai. This has nothing to do with the status of mathematical axioms *qua* mathematical axioms.<br /><br />"<i>Seems to me that in general one can’t really have a sound argument unless one has empirical evidence that in fact the premises are true.<br /><br />Is this claim an exception to the general claim?</i><br /><br />Seems that is the basis of the definition for sound provided in the above link, although the “in general” might not then be applicable. And while one might “quibble” about the definition of “true” – a non-trivial point I gather – it seems to me a good starting point is “corresponding to some fact about reality” based on observation: empirical evidence."<br /><br />You misunderstand my question. You claim that: "in general one can’t really have a sound argument unless one has empirical evidence that in fact the premises are true." so I ask if this claim itself falls in the general class -- and then you have to prove that itself or the premises establishing it are empirically valid -- or is not, and then you have to answer why exactly does this claim not fall under the general class of claims needing, or its premises needing, empirical verification.grodrigueshttps://www.blogger.com/profile/12366931909873380710noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-13285190730661616162011-08-22T16:05:34.506-07:002011-08-22T16:05:34.506-07:00@Steersman:
"Is mathematics knowledge? If it...@Steersman:<br /><br />"<i>Is mathematics knowledge? If it is, then TheOFloinn is absolutely, one hundred per cent correct.</i><br /><br />Ok, I’ll concede that it is knowledge"<br /><br />Then TheOFloinn is 100% correct, because every mathematical theorem can be put in the form if ... then ... and you can add to the premises, your basic axioms, etc.<br /><br />"but my question – poorly phrased, mea culpa – was essentially whether it is true in the sense of it, or aspects of it, corresponding to true features of “reality”." <br /><br />This is not a mathematical question but a question for the empirical sciences. All you can say is that some parts of mathematics are useful in formulating physical theories or have some sort of practical application, others do not, that is all. The talk of corresponding to true features of reality is meaningless, because experimental verification only verifies the model or physical theory not the underlying mathematical apparatus. Is this distinction so hard to grasp?<br /><br />"Cantor’s Continuum Hypothesis has been shown to be logically independent from the usual axioms of mathematics. Mathematicians can freely assume it to be either true or false."<br /><br />Yes, Goedel proved that CH is true in the V=L model while Cohen, using his forcing method, constructed a ZFC model where ~CH holds. The last sentence is problematic because mathematicians do *not* freely assume that CH is true or false, precisely because its status is unclear (although set-theorists tend to think that it is false). My impression is that the common attitude among mathematicians is that if they find out that a question turns out to depend on the status of CH, they will simply move on and ask a different question. Among the experts in set-theory the attitude is of course different, because they will assume all sorts of axioms independent of ZF(C) to do their work, since part of their work is precisely the study and the justification of *new* axioms strong enough to decide CH and other questions.<br /><br />"So presumably there would be some conclusions that would follow if it was true and some if it was false. But since, as Wikipedia notes, the hypothesis is neither provable nor disprovable (at least using ZF) any of those conclusions would seem likewise. Those arguments might be valid – true premises leading to true conclusions – but they would not be known to be sound – all the premises being true. Which highlights my point: one would have the knowledge that “if the premise is true then the conclusion is true”, but one would not have the knowledge that the premise, and thereby the conclusion, is true – the latter being, I would think, somewhat of a more important and valuable result than the former."<br /><br />There are some misconceptions here. I do not have the time to elucidate them all (so feel free to dismiss me), but here go some points as it pertains to the current discussion. First, soundness as the article linked defines it is largely irrelevant to the point TheOFloinn made because theorems in mathematics are usually in the conditional if ... then ... form. So the question of whether hypothesis are true, while obviously important, is irrelevant for the current matter. Second, it is not true that premises must be empirically verifiable to be asserted true (as you assert below) -- this is obvious, since every statement can be used as a premise in an argument, it would mean that every statement must be empirically verifiable to be qualified as true. But the statement "every statement must be empirically verifiable to be true", which you take to be true, is itself not empirically verifiable. In other words, there are other forms, other than empirical verification, to justify the truth value of some premise -- see my point above about CH. Third, I have the impression that somehow you think that the status of CH can be decided by an appeal to the empirical sciences. It cannot, so your point is moot.grodrigueshttps://www.blogger.com/profile/12366931909873380710noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-67158482449532069832011-08-21T22:43:05.853-07:002011-08-21T22:43:05.853-07:00grodrigues said: Is mathematics knowledge? If it i...<i>grodrigues said: Is mathematics knowledge? If it is, then TheOFloinn is absolutely, one hundred per cent correct.</i><br /><br />Ok, I’ll concede that it is knowledge, but my question – poorly phrased, mea culpa – was essentially whether it is true in the sense of it, or aspects of it, corresponding to true features of “reality”. Someone over on Coyne’s site [MacDonald takes down Feser’s theology] argues that:<br /><br /><i>Cantor’s Continuum Hypothesis has been shown to be logically independent from the usual axioms of mathematics. Mathematicians can freely assume it to be either true or false.</i><br /><br />So presumably there would be some conclusions that would follow if it was true and some if it was false. But since, as Wikipedia notes, the hypothesis is neither provable nor disprovable (at least using ZF) any of those conclusions would seem likewise. Those arguments might be <a href="http://wiki.ironchariots.org/index.php?title=Validity_vs._soundness" rel="nofollow">valid</a> – true premises leading to true conclusions – but they would not be known to be sound – all the premises being true. Which highlights my point: one would have the knowledge that “if the premise is true then the conclusion is true”, but one would not have the knowledge that the premise, and thereby the conclusion, <b>is</b> true – the latter being, I would think, somewhat of a more important and valuable result than the former. <br /><br /><i>And since we are talking about mathematics, what exactly are your credentials that I should believe you instead of the mathematical community?</i><br /><br />Couple of years of university math and a couple of years of math associated with a 2 year program in control system theory and applications plus more than a few years of reading and studying various odds and ends. And yours are? <br /><br /><i>And do you actually know differential geometry and its applications? Its history …? Surely you must, judging by the confidence you pronounce such valuative sentences as "it was only a consistent set of axioms and theorems with a rather pallid claim to knowledge and utility".</i><br /><br />Actually what I really said was “… it <b>seems</b> it was only a consistent set of axioms and theorems with a rather pallid claim to knowledge and utility” – an impression, not an ex cathedra statement. But no, I don’t know (much) about (differential) geometry, although I see from the Wikipedia article on Non-Euclidean geometry – most of which I don’t follow all that well – that elliptic geometry is applicable to the surfaces of spheres so, if that was the case, then presumably it would have some direct and tangible applications – and I would stand corrected. But I also note a comment about the mathematician Janos Bolyai:<br /><br /><i>Bolyai ends his work by mentioning that it is not possible to decide through mathematical reasoning alone if the geometry of the physical universe is Euclidean or non-Euclidean; this is a task for the physical sciences.</i><br /><br />Presumably a piece of information, of knowledge, of some value and, as indicated, not accessible or “provable” [decidable] by mathematics alone – somewhat related to the point I was trying to make.<br /><br /><i>"Seems to me that in general one can’t really have a sound argument unless one has empirical evidence that in fact the premises are true."<br /><br />Is this claim an exception to the general claim?</i><br /><br />Seems that is the basis of the definition for <b>sound</b> provided in the above link, although the “in general” might not then be applicable. And while one might “quibble” about the definition of “true” – a non-trivial point I gather – it seems to me a good starting point is “corresponding to some fact about reality” based on observation: empirical evidence.<br /><br /><i>note: you should probably also inform us what you mean by the qualifier "sound" as it applies to arguments.</i><br /><br />As indicated in the above link I think I am, now and there at least, using it in the correct sense – learn something new everyday. But thanks for not automatically assuming I was using it incorrectly.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-91975509593254378422011-08-21T16:35:35.760-07:002011-08-21T16:35:35.760-07:00this still does precisely nothing in the way of en...<i>this still does precisely nothing in the way of entailing that the covering up of sex abuse was the most appropriate course of Catholic action.<br /></i><br /><br />So why was there a cover up? Why do such things continue to this day? Such as the case involving Rev. Shawn Ratigan in Kansas (where the bishop failed to report the possible abuse by Ratigan for months despite agreeing to report such instances immediately)?<br /><br />This is not an isolated incident... it is one of many... and if the priests and bishops who are teaching "Catholic Morality" don't believe in it then how can it be seen as valid?StoneTopnoreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-15579280856518184012011-08-21T07:56:00.563-07:002011-08-21T07:56:00.563-07:00@Steersman:
"You were okay until the end. Em...@Steersman:<br /><br />"<i>You were okay until the end. Empirical evidence is all well and good for natural philosophy, but it is not the way of mathematics or metaphysics. Mathematics disregards empiricism entirely, and so achieves absolutely certain knowledge. (Empiricism leads to tentative 'falsifiable' knowledge, properly 'opinion.')</i><br /><br />Really don’t follow or agree with that at all. For example, consider non-Euclidean geometry which has been a bit of a bone of contention with Mr. Munro. Until it was “proven” to correlate with actual space it seems it was only a consistent set of axioms and theorems with a rather pallid claim to knowledge and utility."<br /><br />Sigh. Here we go again...<br /><br />Is mathematics knowledge? If it is, then TheOFloinn is absolutely, one hundred per cent correct. If it is not, then what are the literally thousands of mathematicians wasting their time on? Maybe you should dismiss all mathematical departments and retain of mathematics only what can be deemed useful? You would *not* like the outcome, let me tell you that. And since we are talking about mathematics, what exactly are your credentials that I should believe you instead of the mathematical community? And maybe the "usefulness" criteria can be applied to other disciplines other than mathematics? Pray tell us, what goes the way of the trash can next?<br /><br />How do you measure "utility"? If you measure "utility" as it directly concerns the building of physical theories then you are just going in circles and effectively denying that mathematics is an autonomous, independent discipline -- and we are back at my paragraph above. And do you actually know differential geometry and its applications? Its history before an application was found in general relativity? Surely you must, judging by the confidence you pronounce such valuative sentences as "it was only a consistent set of axioms and theorems with a rather pallid claim to knowledge and utility".<br /><br />"Seems to me that in general one can’t really have a sound argument unless one has empirical evidence that in fact the premises are true."<br /><br />Is this claim an exception to the general claim? If it is not, then to substantiate it, deductive argument of whatever kind is not enough and you must present us with the necessary empirical evidence. If it is, then inform us why exactly you are not special-pleading? What is so special about this particular claim?<br /><br />note: you should probably also inform us what you mean by the qualifier "sound" as it applies to arguments. "Soundness" has a very specific technical meaning in mathematics, and I want to be sure I am not misunderstanding you.grodrigueshttps://www.blogger.com/profile/12366931909873380710noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-77794107054563832952011-08-21T04:33:29.019-07:002011-08-21T04:33:29.019-07:00Can I suggest that the term 'New Atheist' ...Can I suggest that the term 'New Atheist' is inappropriate.<br /><br />A more accurate and descriptive term would be 'Fundamentalist Atheist'. This reflects the rigid, intransigent polemicism that they practice.labnuthttps://www.blogger.com/profile/12216731311329758699noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-7292530510284689852011-08-20T23:14:54.941-07:002011-08-20T23:14:54.941-07:00Brian said: That just means you don't really h...<i>Brian said: That just means you don't really have a grasp of what theistic personalism means.</i><br /><br />Certainly not in all of its ramifications. But I had the basic idea which was clarified and corroborated by Dr. Feser: “The theistic personalist or neo-theist conceives of God essentially as a person comparable to human persons, only without the limitations we have.”Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-85146057167055197292011-08-20T22:55:32.616-07:002011-08-20T22:55:32.616-07:00Another Matt:
"Was this not an analogy for p...Another Matt:<br /><br /><b>"Was this not an analogy for protected sex involving an HIV+ male prostitute? If I remember correctly this was huge news when it broke because it potentially reversed 2) and 3) from above as doctrine. "Naturally," yes, but why was that even controversial in the first place, in a way that required an explication from on high?"</b><br /><br />For a few reasons. In the first place, the embargo on the book was broken early by the Vatican newspaper, which printed the "controversial" quote in isolation from its context AND with a bad translation from the German that mangled what was actually said. Yes, the Vatican newspaper did that. That misunderstanding is what all the news stories in America ran with.<br /><br />Second, the press does not know a thing about Catholicism. It really does not. And so 9/10 things you read about Catholicism in the press is simply not true, making a clarification from the Vatican always necessary. I woke up the following morning to my local news station, and the reporter said that the Pope reversed Church doctrine! *sigh* Apparently, people still think that the charism of Infallibility extends to everything the pope says.<br /><br />Lastly, the press, or at least a lot of the press, has a clear anti-Catholic bias.<br /><br />All of this came together to make one big ****storm making a clarification necessary.Brianhttps://www.blogger.com/profile/18065529769651450157noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-43322414664834592552011-08-20T22:45:23.770-07:002011-08-20T22:45:23.770-07:00Steersman:
“He cannot be affected by anything in t...Steersman:<br /><b>“He cannot be affected by anything in the created order” [a curious use of the personal pronoun given that theistic personalism is apparently a heresy].</b><br /><br />That just means you don't really have a grasp of what theistic personalism means.Brianhttps://www.blogger.com/profile/18065529769651450157noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-70567643024653355782011-08-20T22:23:45.917-07:002011-08-20T22:23:45.917-07:00This is the fallacy known as a "false dichoto...<i>This is the fallacy known as a "false dichotomy."</i><br /><br />Yep, I was being deliberately provocative, but my question still stands. Correct me if I'm wrong, but the Pope JPII pronouncement I quoted above seems to imply that if you have AIDS, then the list of actions regarding sex, from most moral to least moral is:<br /><br />1) Remain abstinent.<br />2) Have unprotected sex with your spouse.<br />3) Have sex with your spouse using a condom.<br />4) Have sex with someone who isn't your spouse.<br /><br />The last one isn't quite implied in the quote but I'm going to infer it from what I know about Church teaching. I have no argument with 1), but the ordering of 2) and 3) is extremely morally offensive to me on its own, and the reasoning behind it (that it offends the dignity of the individual more to use a condom than to contract AIDS, assuming that a sexual act between husband and wife is "committed") that much more offensive. I will have a very hard time being charitable to ideas that seem to be, on their face, as plainly inhumane as this.<br /><br /><br /><i>Naturally, as the pope said recently, it is better to rob a bank with an unloaded gun than with a loaded gun, since it shows the robber with some concern over the well-being of the Other; but the real problem is in the bank-robbing.</i><br /><br />Was this not an analogy for protected sex involving an HIV+ male prostitute? If I remember correctly this was huge news when it broke because it potentially reversed 2) and 3) from above as doctrine. "Naturally," yes, but why was that even controversial in the first place, in a way that required an explication from on high?Another Mattnoreply@blogger.com