tag:blogger.com,1999:blog-8954608646904080796.post5020267408198741728..comments2021-01-20T10:21:19.759-08:00Comments on Edward Feser: Frege on what mathematics isn’tEdward Feserhttp://www.blogger.com/profile/13643921537838616224noreply@blogger.comBlogger99125tag:blogger.com,1999:blog-8954608646904080796.post-8671866516584828742019-07-08T10:55:53.184-07:002019-07-08T10:55:53.184-07:00Don Jindra
Given these four propositions, you hav...<b>Don Jindra</b><br /><br />Given these four propositions, you have given:<br /><br />1/ All symbols can be considered in isolation.(FALSE)<br />2/ No symbols can be considered in isolation.(TRUE)<br />3/ Some symbols can be considered in isolation.(FALSE)<br />4/ Some symbols cannot be considered in isolation.(FALSE)<br /><br />Your thesis is this proposition:<br /><b>Symbols cannot be considered in isolation.</b><br /><br />LEMMA:Symbols, aka, abstract concepts, have no meaning apart from this material world.<br /><br />Symobols = abstract concepts<br /><br />Therefore, we have the proposition:<br /><b>Abstract concepts cannot be considered in isolation.</b><br /><br />Is this what your proposition means?<br />Philip Randhttps://www.blogger.com/profile/09143527524267821692noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-5398147808979190672019-07-08T09:22:32.988-07:002019-07-08T09:22:32.988-07:00Philip Rand,
"Symbols cannot be considered i...Philip Rand,<br /><br />"Symbols cannot be considered in isolation. Your proposition is conflating sign/symbol, i.e. abstract/concrete. This defeats your thesis."<br /><br />I can't decipher what you intend to say. You seem to be suggesting something about signifier/signified. What do you think this has to do with me?<br /><br />No symbols can be considered in isolation = true. Symbols, aka, abstract concepts, have no meaning apart from this material world. There's nothing self-defeating in this.<br /><br />Stanford isn't accurate but you are? Unless you can show that Frege did not believe in abstract objects, and was speaking metaphorically or esoterically, I have to take his words at face value. He was a platonist. <br /><br /><br /><br />Don Jindrahttps://www.blogger.com/profile/05550378223563435764noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-58069181517458787602019-07-07T09:10:38.940-07:002019-07-07T09:10:38.940-07:00Don Jindra
Your proposition:
Symbols cannot be co...<b>Don Jindra</b><br /><br />Your proposition:<br /><b>Symbols cannot be considered in isolation.</b><br />Your proposition is conflating sign/symbol, i.e. abstract/concrete<br /><br />This defeats your thesis.Philip Randhttps://www.blogger.com/profile/09143527524267821692noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-1016968020042224292019-07-07T08:52:15.974-07:002019-07-07T08:52:15.974-07:00Don Jindra
The statement:
Symbols cannot be consi...<b>Don Jindra</b><br /><br />The statement:<br /><b>Symbols cannot be considered in isolation.</b><br />is your own statement, not mine... you explain to me why it is wrong...<br /><br />Stanford isn't accurate.<br /><br />Frege's system concerns how thoughts can refer to particulars, i.e. he uses this concept of <i>sense</i> which is an abstract object; Frege was never particularly clear, but it is similar to sense-data infused with physical object interpretation.<br /><br />It is a problem dealt with in the analytical theory of reference, i.e. the territory of Mill, Russell, Strawson, Kripke, Evans, etc.<br /><br />Frege believed that you could solve the problem of non-existence only by treating them all as pure definite descriptions. These thoughts are referential in a way that exceeds their descriptive exactness, so that if they fail of reference there is no real thought at all.<br /><br />You have not responded to:<br /><br />Here are four propositions... indicate which are true OR false.<br /><br />1/ All symbols can be considered in isolation.<br />2/ No symbols can be considered in isolation.<br />3/ Some symbols can be considered in isolation.<br />4/ Some symbols cannot be considered in isolation.Philip Randhttps://www.blogger.com/profile/09143527524267821692noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-47355989260942138162019-07-07T07:18:07.978-07:002019-07-07T07:18:07.978-07:00ErotemeObelus,
"No they were not ignoramus&q...ErotemeObelus,<br /><br />"No they were not ignoramus" is not an "argument." You're pandering to yourself.Don Jindrahttps://www.blogger.com/profile/05550378223563435764noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-73403175285318627062019-07-07T07:07:20.111-07:002019-07-07T07:07:20.111-07:00Philip Rand,
From Stanford's Encyclopedia of...Philip Rand,<br /><br />From Stanford's Encyclopedia of Philosophy:<br /><br />"Platonism is the view that there exist such things as abstract objects — where an abstract object is an object that does not exist in space or time and which is therefore entirely non-physical and non-mental. Platonism in this sense is a contemporary view. It is obviously related to the views of Plato in important ways, but it is not entirely clear that Plato endorsed this view, as it is defined here. In order to remain neutral on this question, the term ‘platonism’ is spelled with a lower-case ‘p’. The most important figure in the development of modern platonism is Gottlob Frege."<br /><br />I'll have to read the whole book to see what Frege is up. My supposition is that he's trying to sell the idea that our abstract notion of "green" is indeed preceded by concrete "greenness" present in objects. But, more importantly, this is not the case with numbers. Numbers have no presence in concrete objects. One way or another, he'll probably make the argument that we "discover" numbers, and that we can discover only what's already there on some plane of existence. This is where I'll part ways with him.<br /><br /><br />"Symbols cannot be considered in isolation , i.e. The concrete and the abstract cannot be considered in isolation, undermines your own conclusion."<br /><br />If you explain why you think so I'll explain why you're wrong.<br /><br /><br />By the way, "nothing in the intellect unless first in sense" does not fully describe my thinking. I believe in a human nature. Our sensing of the environment is regulated by that. IOW, we have intellectual predispositions. <br /><br /><br />Don Jindrahttps://www.blogger.com/profile/05550378223563435764noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-30164747506589124692019-07-06T22:34:31.667-07:002019-07-06T22:34:31.667-07:00If one merely claims someone is ignorant of some f...<b>If one merely claims someone is ignorant of some fact, that's not an ad hominem. You went beyond that.</b><br /><br />No I didn't. You could cross out the word "ignoramus" and it wouldn't affect my argument one bit. Therefore it wasn't an <i>ad hominem</i>BalancedTryteOperatorshttps://www.blogger.com/profile/06109864288446595298noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-19810611615009887442019-07-06T20:04:08.509-07:002019-07-06T20:04:08.509-07:00Don Jindra
Frege is considering this concrete and...<b>Don Jindra</b><br /><br />Frege is considering this <i>concrete</i> and <i>abstract</i> relation from a <i> Phenomenological</i> standpoint.<br /><br />Like Aquinas he would most likely agree with:<br /><i>nihil in intellectu nisi prius sensu</i>.<br /><br />Which in many respects reflects your own position.Philip Randhttps://www.blogger.com/profile/09143527524267821692noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-43848410083357635982019-07-06T19:38:39.882-07:002019-07-06T19:38:39.882-07:00Don Jindra
Yes. What Frege is concerned with are...<b>Don Jindra</b><br /><br />Yes. What Frege is concerned with are expressions of <i>collection</i>, <i>aggregate</i>.<br /><br />However, what Frege is trying to explain in your quote is the distinction between the <i>concrete</i> preceding the <i>abstract</i>.<br /><br />What he is trying to convey is that counting consolidates the concrete and thus the hetrogeneous notion of plurality into the <i>homogeneous abstract number concept</i> which makes mathematics possible.<br /><br />Frege is not Platonic.<br /><br />However, your own conclusion that:<br /><br /><b>Symbols cannot be considered in isolation</b> , i.e. The <i>concrete</i> and the <i>abstract</i> cannot be considered in isolation, undermines your own conclusion.Philip Randhttps://www.blogger.com/profile/09143527524267821692noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-12176597498075729352019-07-06T11:36:29.291-07:002019-07-06T11:36:29.291-07:00grodrigues,
I have never said nor implied that ma...grodrigues,<br /><br />I have never said nor implied that mathematicians don't "do mathematics and communicate with each other about the subject meaningfully." If mathematicians disagree violently on the status of mathematical objects, why do you call me an "arrogant doofus" when I take sides? Seriously. Why?<br /><br />You seem to think I have no respect for mathematics. But I have a great deal of respect for it and those who are good at it. I wish I remembered all the math I once knew.<br /><br />I've been reading Frege's THE FOUNDATION OF ARITHMETIC.<br /><br />Under "Is Number a property of external things?", #22, page 28, there is some text that's very similar to what I wrote some days ago:<br /><br />"Baumann rejects the view that numbers are concepts extracted from external things: 'The reason being that external things do not present us with strict units; they present us with isolated groups or sensible points, but we are at liberty to treat each one of these itself again as a many.' And it is quite true that, while I am not in a position, simply by thinking of it differently, to alter colour or hardness of a thing in the slightest, I am able to think of the Iliad either as one poem, or as 24 Books, or as some large Number of verses. Is it not in totally different senses that we speak of a tree as having 1000 leaves and again as green leaves?"<br /><br />Frege elaborates on this distinction between color and number and uses a card deck as an example. He ends the section with this:<br /><br />"The Number 1, on the other hand, or 100 or any other Number, cannot be said to belong to the pile of playing cards in its own right, but at most to belong to it in view of the way in which we have chosen to regard it; and even then not in such a way that we can simply assign the Number to it as a predicate. What we choose to call a complete pack is obviously an arbitrary decision, in which the pile of playing cards has no say. But it is when we examine the pile in light of this decision, that we discover perhaps that we can call it two complete packs. Anyone who did not know what we call a complete pack would probably discover in the pile any other Number you like before hitting on two."<br /><br />Yet when I say basically the same thing, I'm an "arrogant doofus."<br /><br />Nevertheless, I think the "arrogant doofus" named Frege is correct about this. But I think it ultimately undermines his platonic conclusion. I'm reading on because I'm interested in seeing how he tries to resolve it.<br /><br /><br />Don Jindrahttps://www.blogger.com/profile/05550378223563435764noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-53908287284581246982019-07-06T09:32:44.957-07:002019-07-06T09:32:44.957-07:00Don Jindra
You are correct despite godrigues stat...<b>Don Jindra</b><br /><br />You are correct despite <b>godrigues</b> stating (twice):<br /><br /><i>None of the other equations are tautologies in this sense neither can they proved from 0 = 0 or reduced in any way whatsoever to 0 = 0. <b>This is a mathematical fact with a simple demonstration</b></i><br /><br /><b>He has yet to provide any demonstration.</b><br /><br />Remember, a man with experience is never at the mercy of a man with an argument.Philip Randhttps://www.blogger.com/profile/09143527524267821692noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-13310946402056327552019-07-06T07:23:31.886-07:002019-07-06T07:23:31.886-07:00@Don Jindra:
"You're not listening."...@Don Jindra:<br /><br />"You're not listening."<br /><br />You're not talking. I laid out my reasons. Any response? No, so yeah, dishonesty.<br /><br />"If you have an understanding of math "quite independently of the ontological status of mathematical objects" then I simply ask that you demonstrate that you do."<br /><br />It is simply an empirical fact that mathematicians do mathematics and communicate with each other about the subject meaningfully, and yet disagree violently on what exactly is the status of mathematical objects. It is my impression that Platonism is over-represented (and many are atheists to boot) but you can find the whole spectrum of positions. This is not specific to mathematics. For an example, physicists do quantum mechanics all day long and yet they disagree violently what the theory is actually telling us about reality in itself.<br /><br />You really are one of the most arrogant doofus I have ever met online, completely ignorant about the subject he pontificates about and completely unaware of his own ignorance.<br /><br />"Are you trying to be ignorant? It sure seems like you are."<br /><br />As opposed to you actually being one?<br /><br />Enough bantering with an idiot.grodrigueshttps://www.blogger.com/profile/12366931909873380710noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-86661792057148715812019-07-06T06:39:27.396-07:002019-07-06T06:39:27.396-07:00grodrigues,
"Dismissing it as you do with &#...grodrigues,<br /><br />"Dismissing it as you do with 'You said something to the effect that more complex equations can't be proven from 0=0. But that has nothing to do with what I'm saying.' is once again, shameless dishonesty."<br /><br />You're not listening. I suppose you give yourself permission to call me dishonest when you don't listen. This post was yet another evasion. <br /><br />"When the topic is mathematics, there is a difference between a mathematician and a coding monkey."<br /><br />Are you trying to be ignorant? It sure seems like you are. If you have an understanding of math "quite independently of the ontological status of mathematical objects" then I simply ask that you demonstrate that you do. But instead you're obsessed with making this personal.<br /><br /><br /><br />Don Jindrahttps://www.blogger.com/profile/05550378223563435764noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-83307992988414969012019-07-06T05:49:42.799-07:002019-07-06T05:49:42.799-07:00@Philip Rand:
I do not think it is worth clutteri...@Philip Rand:<br /><br />I do not think it is worth cluttering the combox with further replies to the incoherent screaming coming from a padded cell.<br /><br />Peace be with you.grodrigueshttps://www.blogger.com/profile/12366931909873380710noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-36455641816817696212019-07-06T04:59:55.949-07:002019-07-06T04:59:55.949-07:00grodrigues
A tautology is valid/true in ANY inter...<b>grodrigues</b><br /><br />A tautology is valid/true in ANY <i>interpretation</i>.<br /><br />I list your tabled statements:<br />A) "2 + 2 = 4" is a tautology in a different sense that "0 = 0" is a tautology. (FALSE)<br /><br />Let; a=b=1<br />ARITHMATIC: 1 + 1 = 2<br />GEOMETRY: 1 + 1 = sqrt(2)<br /><br />B) equations are not tautologies (TRUE)<br />I demonstrated this.<br />C) e = mc^2 is not reducible to 0 = 0 (TRUE)<br />I demonstrated this.<br />D) e = mc^2 cannot be proved from 0 = 0 (TRUE)<br />I demonstrated this.<br />Philip Randhttps://www.blogger.com/profile/09143527524267821692noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-37448136569832386832019-07-06T04:47:25.548-07:002019-07-06T04:47:25.548-07:00@Phil Rand:
"What I suggest you do is to plo...@Phil Rand:<br /><br />"What I suggest you do is to plot each function on a graph."<br /><br />Oh dear, with all the nutcases in all the blogs of the internet world I happened to bump the dimwit that is even more obnoxious and insufferable than me.<br /><br />"Then compare the differences between all four conceptions of 0=0."<br /><br />What you wrote is not even an accurate characterization of what I said. And in the cases where it is (or it could be patched to be) there is no inconsistency. 0 = 0 is quite obviously an *instance* of the logical axiom that everything is self-identical. If on the other hand, we interpret the symbol 0 as the constant function x |-> 0 then 0 = 0 is perfectly good equation with solution set (or equalizer) the universal set (say the real numbers if you take them for domain). A tautology is a formula in propositional calculus that is always true, which is obviously the case with 0 = 0 (depending on how you do things you may have to extend propositional calculus, say with the constant symbol 0, but this is a minor detail). There is no contradiction anywhere, except maybe in that empty skull of yours.<br /><br />Your ignorant stupidity about these things is so obvious and blatant, that I suspect that "I am a theoretical physicist, expert in condensed matter physics, quantum ab initio EOS, and information-physics." is just bullshit. Despite my jab a theoretical physicist needs quite a lot more beyond calculus: GR needs differential geometry, QM needs functional analysis, representation theory, etc. That or the state of education in theoretical physics is a complete sham.<br /><br />As the Son of Ya'Kov suggested, stop doing drugs, they are turning what little is left of your brain into mush.grodrigueshttps://www.blogger.com/profile/12366931909873380710noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-44598425959270868982019-07-05T21:12:07.761-07:002019-07-05T21:12:07.761-07:00grodrigues
Concerning 0=0, you tabled four positi...<b>grodrigues</b><br /><br />Concerning 0=0, you tabled four positions:<br />1/ 0 = 0 is a tautology<br />2/ 0 = 0 is a logical axiom<br />3/ 0 = 0 reduces to an equaliser<br />4/ 0 = 0 is the universal set<br /><br />What I suggest you do is to plot each function on a graph.<br /><br />Then compare the differences between all four conceptions of 0=0.Philip Randhttps://www.blogger.com/profile/09143527524267821692noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-39759727694623171022019-07-05T20:48:08.682-07:002019-07-05T20:48:08.682-07:00grodrigues
Interesting...I gave you a precise and...<b>grodrigues</b><br /><br />Interesting...I gave you a precise and accurate answer concerning the definition of 0=0<br /><br /><b>Concerning 0=0, you tabled four positions:<br />1/ 0 = 0 is a tautology<br />2/ 0 = 0 is a logical axiom<br />3/ 0 = 0 reduces to an equaliser<br />4/ 0 = 0 is the universal set<br /><br />Your final position is that "0=0" is equivalent to all four positions on account one can carve up 0=0 any way one chooses.</b><br /><br />What is extremely interesting is that your position concerning 0=0 is directly in violation of the First Principle of Thomistic Metaphysics, i.e. the Principle of Non-contradiction.<br /><br />I find it odd that I am in a dialogue with:<br />1/ An Atheist who is unaware he believes in <i>necessary truths</i>.<br />2/ A Thomist who is unaware that he does not believe in <i>necessary truths</i>.<br /><br />Weird....<br />Philip Randhttps://www.blogger.com/profile/09143527524267821692noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-25248078024265137842019-07-05T18:01:34.390-07:002019-07-05T18:01:34.390-07:00@grodrigues
I think Phil Rand is a nut case. He ...@grodrigues<br /><br />I think Phil Rand is a nut case. He tries to bug Dr. Dennis Bonnette over at the Strange Notions blog and pretends he knows how to answer Thomistic Philosophical arguments but his answers are just bizarre. <br /><br />He is smoking something.<br /><br />djindra is just being djindra.Son of Ya'Kovhttps://www.blogger.com/profile/05645132954231868592noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-3350670015474976182019-07-05T12:15:41.730-07:002019-07-05T12:15:41.730-07:00@Phil Rand:
"No, it is a matter of precision...@Phil Rand:<br /><br />"No, it is a matter of precision and accuracy."<br /><br />Giggle. Sure, it is.<br /><br />Your second iteration is absolutely irrelevant to what I said. Just go back and actually read what I wrote. I can spoon feed it to you if you need me to.<br /><br />"I am a theoretical physicist, expert in condensed matter physics, quantum ab initio EOS, and information-physics."<br /><br />This explains a lot. I was talking mathematics, don't feel ashamed if you cannot go much beyond calculus.<br /><br />@Don Jindra:<br /><br />"Your tactic was to start with a quibble about tautology."<br /><br />This is a dishonest characterization of the dialectical situation. For if you really though it was mere quibbling and not addressing your point, then why you didn't you say so earlier? Instead of for example, coming out with: "2x+2x=4x can be reduced to 0=0. It's simply false to say it cannot be. You're making yourself look foolish.". So yeah, you took me up to task and dug in your heels, quibbling or no quibbling, about *mathematical facts*. Dismissing it as you do with "You said something to the effect that more complex equations can't be proven from 0=0. But that has nothing to do with what I'm saying." is once again, shameless dishonesty.<br /><br />"My expertise on this topic doesn't play second fiddle to yours."<br /><br />When the topic is mathematics, there is a difference between a mathematician and a coding monkey. Sorry, them's the breaks. What mathematicians do *cannot* be reduced to symbol manipulation, but is about *understanding* of their proper object, quite independently of the ontological status of mathematical objects. The fact that you keep repeating this mantra, shows the ignorance and shallowness of your so-called understanding. And this is not an ad-hominem since to discuss the central issue you want to discuss, the ontological status of mathematical objects (it is once again misleading and an indication of your ignorance that you talk in terms of "meaning"), it at least behooves a passing familiarity with what mathematicians *actually do* as opposed to whatever you imagine, based on whatever it was you learned 40 years ago. Pointing such failures is not an ad hominem because I never made the obvious fallacious move, but it goes towards showing that you do not possess any real knowledge or really, any evidence-based arguments.grodrigueshttps://www.blogger.com/profile/12366931909873380710noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-61611598616579744962019-07-05T10:39:31.020-07:002019-07-05T10:39:31.020-07:00grodrigues,
You don't like my POV, fine. But ...grodrigues,<br /><br />You don't like my POV, fine. But you in particular seem to have a need to make it personal. <br /><br />I have not left your complaints by the wayside. You have not addressed mine. Frege understood the issue to be, What do numbers mean? I'm trying to stay on topic.<br /><br />Your tactic was to start with a quibble about tautology. Then you threw out "e^ix = cos(x) + i * sin(x)" as if this sheds light on the meaning of "2". It doesn't. I pointed that out. <br /><br />You said something to the effect that more complex equations can't be proven from 0=0. But that has nothing to do with what I'm saying. I'm saying equations have equal left and right sides. So that's "a phrase or expression in which the same thing is said twice in different words" -- words in this case being mathematical symbols, but symbols nonetheless.<br /><br />This is a docudrama loosely based on how our argument went:<br /><br />ME: Sam said his autobiography is his description of his own life. He doesn't realize that sentence is a tautology.<br /><br />YOU: That's not *really* a tautology, you moron, because you can't get from there to "It's deja vu all over again." <br /><br />This is typically how your comments come across to me. <br /><br />I know what "essential nature" means around here, this being an essentialist site. But if you meant something less than that in this case, then it's probably no more relevant to this discussion than the "essential nature" of tic-tac-toe. <br /><br />As to your credentials and the weight you think they deserve, mathematicians are not the only people on the planet who regularly manipulate symbols. I've been manipulating symbols for 40 years professionally. I think I have a good understanding of what I'm doing. My expertise on this topic doesn't play second fiddle to yours.<br /><br /><br />Don Jindrahttps://www.blogger.com/profile/05550378223563435764noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-54955754454573194232019-07-05T09:56:22.440-07:002019-07-05T09:56:22.440-07:00Don Jindra
Here are four propositions... indicate...<b>Don Jindra</b><br /><br />Here are four propositions... indicate which are true & false.<br /><br />1/ All symbols can be considered in isolation.<br />2/ No symbols can be considered in isolation.<br />3/ Some symbols can be considered in isolation.<br />4/ Some symbols cannot be considered in isolation.Philip Randhttps://www.blogger.com/profile/09143527524267821692noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-60259566347163907022019-07-05T09:40:31.954-07:002019-07-05T09:40:31.954-07:00Philip Rand,
How does it sound necessary to you? ...Philip Rand,<br /><br />How does it sound necessary to you? I sure don't see it that way. Don Jindrahttps://www.blogger.com/profile/05550378223563435764noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-29411619469573058472019-07-05T08:29:47.162-07:002019-07-05T08:29:47.162-07:00Don Jindra
You state:Symbols cannot be considered...<b>Don Jindra</b><br /><br />You state:<i>Symbols cannot be considered in isolation.</i><br /><br />That sounds like a <i>necessary truth</i> to me...Philip Randhttps://www.blogger.com/profile/09143527524267821692noreply@blogger.comtag:blogger.com,1999:blog-8954608646904080796.post-64300643119289129462019-07-05T08:20:21.095-07:002019-07-05T08:20:21.095-07:00grodrigues: "I suppose this is a matter of ho...<b>grodrigues:</b> <i>"I suppose this is a matter of how we carve things up"</i><br /><br /><b>Philip Rand:</b> <i>No, it is a matter of precision and accuracy.</i>Philip Randhttps://www.blogger.com/profile/09143527524267821692noreply@blogger.com