ellis@spar.UUCP (Michael Ellis) (08/01/85)
> >>> [Rich Rosen] >> >>>> [me] >>>> Please note that, if evolution is true [I believe it has much essential >>>> truth], then the present complexity was there from the beginning, only >>>> it was dormant -- exactly like a seed.... >You miss the point. I was saying that the position above only has meaning if >you assume a creator who "designed" the complexity. Then you are saying that the existence of a seed-like proto-universe would imply a Creator? >> Do you agree that science ought not to be concerned with souls? >No, of course not, though apparently you seem to. Whatever gave you that idea? >I just love the way some people choose to divide the world arbitrarily into >these physical and non-physical categories based solely on their limits of >observation, and then seek to cage science (that awful thing!) into examining >only the "physical", claiming that their pet "nonphysical" ideas should be >free of the shackles of science, which really means "let's not examine these >things rigorously because such thinking might debunk these notions >the way they got rid of geocentrism hundreds of years ago". What notions? What pet theories? Who said science should be shackled? >And then they use deceptive debasing terminology to describe science like >"it's soulless". Uncle! I take it back! Science has a Soul, as you wish. I am sorry to have offended you. I was mistaken. >What is it that you have against rigorous objectified >examination using verifiable evidence? That's all the heinous science is >after all. I am very fond of `rigorous objectified examination'. >Why should such examination have "limits"? The limits are intrinsic and not externally imposed. That means it is unable to do certain things, just as a blind person cannot see. For example, I would not judge the merits of a musical composition using the scientific method. >> In the absence of OBJECTIVE evidence, such things MAY lack OBJECTIVE >> existence. We agree. >> But is that the only kind of existence that is meaningful? > >Since other so-called evidence is rife with the flaws of preconception, >presumption, faulty patterning of the mind imposed on events, it ain't >worthwhile evidence. I do not agree. Suppose I wish to determine whether I like a musical composition. I listen to it. If it pleases me, I take that as evidence that I like it. Or suppose I experience the sensation I refer to as `love' whenever a certain person enters my dreams, thoughts, or physical presence. I take that as evidence that I love them. I also take that as evidence for the existence of love, in fact. That is perfectly valid evidence, as far as I can tell. >> Most people attribute existence to at least a few kinds of nonobjective >> things -- like beauty, meaning, awareness, causality, science, >> schroedinger probability waves, probably `physical objects', and maybe >> music, time, space... Clearly SOME meaningful things exist that have >> little or no objective existence whatsoever. > >We're talking about constructs and patterns designed by the mind to REPRESENT >reality, not reality. Do you claim to know what reality IS? I do not have the slightest idea. The closest I have are my direct sensations -- sometimes they are `rocklike', sometimes they are `lovelike', sometimes they are `musiclike', sometimes they are even `causalitylike' -- but they are all equally real. If you know how to tell which are more real than others, please enlighten us, my friend. -michael -ps I will remove net.origins from subsequent followups to this topic
rlr@pyuxd.UUCP (Rich Rosen) (08/03/85)
Watch this, this is interesting. | > >>> [Rich Rosen] >> >>>> [me] | | >>>> Please note that, if evolution is true [I believe it has much essential | >>>> truth], then the present complexity was there from the beginning, only | >>>> it was dormant -- exactly like a seed.... | | >You miss the point. I was saying that the position above only has meaning if | >you assume a creator who "designed" the complexity. | | Then you are saying that the existence of a seed-like proto-universe | would imply a Creator? Wait a minute. Take a '>>>>' quote from you, then take a '>' quote from me that wasn't in response to the '>>>>' quote, and then twist again, like we did last summer? What the hell is going on? >>I just love the way some people choose to divide the world arbitrarily into >>these physical and non-physical categories based solely on their limits of >>observation, and then seek to cage science (that awful thing!) into examining >>only the "physical", claiming that their pet "nonphysical" ideas should be >>free of the shackles of science, which really means "let's not examine these >>things rigorously because such thinking might debunk these notions >>the way they got rid of geocentrism hundreds of years ago". > What notions? What pet theories? Who said science should be shackled? YOU did, by insisting that certain things are "not in the realm" of science, BECAUSE they have names like "non-physical", "souls", etc. (Really putting the cart before the horse: making claims about aspects of the universe as being definitively beyond science so that one can then say science can't investigate them, which really simply means that they should not be subject to serious (scientific) inquiry.) >>And then they use deceptive debasing terminology to describe science like >>"it's soulless". > Uncle! I take it back! Science has a Soul, as you wish. > I am sorry to have offended you. I was mistaken. If you want to play manipulative emotional games with words, do it on your own time. You talk about things that have a soul, eh? Show me something that DOES, definitively, so that science by comparison can be soulless. >>What is it that you have against rigorous objectified >>examination using verifiable evidence? That's all the heinous science is >>after all. > I am very fond of `rigorous objectified examination'. Except, apparently, when it comes to "souls" and such. After all "soulless" science should stay away from examining things to DO relate to souls, shouldn't it? >>Why should such examination have "limits"? > The limits are intrinsic and not externally imposed. What are they? And why don't they apply to "certain things"? > That means it is unable to do certain things, just as a blind person > cannot see. For example, I would not judge the merits of a musical > composition using the scientific method. But you could examine what aspects of a piece MAKE it a "good" piece in a very scientific way. >>Since other so-called evidence is rife with the flaws of preconception, >>presumption, faulty patterning of the mind imposed on events, it ain't >>worthwhile evidence. > I do not agree. Oh. I see. Thank you for clarifying that with such powerful reasoning. :-? > Suppose I wish to determine whether I like a musical composition. > I listen to it. If it pleases me, I take that as evidence that I > like it. Just because YOU cannot determine the factors that contribute to your liking or not liking a piece of music doesn't mean that those factors do not exist. They are simply beyond your scope because you choose not to think about them in the way. > Or suppose I experience the sensation I refer to as `love' whenever a > certain person enters my dreams, thoughts, or physical presence. I take > that as evidence that I love them. I also take that as evidence for > the existence of love, in fact. Same thing. Why one set of reactions for one person and another for another? Because of those same sorts of factors. It all has a very real basis, though you may choose to avoid it. > That is perfectly valid evidence, as far as I can tell. Well, since "love" is a word to describe what happens when all those factors come together, it "exists". But, alas, you don't care about what got it to be that way. >>> Most people attribute existence to at least a few kinds of nonobjective >>> things -- like beauty, meaning, awareness, causality, science, >>> schroedinger probability waves, probably `physical objects', and maybe >>> music, time, space... Clearly SOME meaningful things exist that have >>> little or no objective existence whatsoever. >>We're talking about constructs and patterns designed by the mind to REPRESENT >>reality, not reality. > Do you claim to know what reality IS? No, you do. Funny, though, what your basis for such knowledge is. And what does it have to do with the point I made above. > If you know how to tell which are more real than others, please > enlighten us, my friend. I thought I just did, and I didn't think it was very "enlightening", I thought it was pretty straightforward. -- "There! I've run rings 'round you logically!" "Oh, intercourse the penguin!" Rich Rosen ihnp4!pyuxd!rlr
beth@sphinx.UChicago.UUCP (Beth Christy) (08/13/85)
[This line should be gone by the time you see it] From: rlr@pyuxd.UUCP (Rich Rosen), Message-ID: <1410@pyuxd.UUCP>: > |> >>> [Rich Rosen] >> >>>> [me] > | > |>>>>Please note that, if evolution is true [I believe it has much essential > |>>>>truth], then the present complexity was there from the beginning, only > |>>>>it was dormant -- exactly like a seed.... > | > |>You miss the point. I was saying that the position above only has meaning > |>if you assume a creator who "designed" the complexity. > | > |Then you are saying that the existence of a seed-like proto-universe > |would imply a Creator? > > Wait a minute. Take a '>>>>' quote from you, then take a '>' quote from me > that wasn't in response to the '>>>>' quote, and then twist again, like we > did last summer? What the hell is going on? Calm down, son, he was just appeasing those folks who think we provide too much context for discussion. The "'>' quote" from you was in fact in response to the "'>>>>' quote" from ... shoot, is that Mike? There was just some other stuff in between that doesn't really matter. But anyway, he's responding to your last statement which is correctly quoted, even if not all of the context is provided. And you're avoiding answering his question. *Do* you think that a proto-universe with inherent potential complexity similar to that of a seed would imply a creator? >> What notions? What pet theories? Who said science should be shackled? > >YOU did, by insisting that certain things are "not in the realm" of science, >BECAUSE they have names like "non-physical", "souls", etc. So saying that something has limits is shackling it? You can't see ultraviolet light, you poor shackled creature, you. Get real, Rich. That's a pretty emotional appeal coming from a "science uber alles" kind of fellow. :-) >(Really putting >the cart before the horse: making claims about aspects of the universe >as being definitively beyond science so that one can then say science can't >investigate them, which really simply means that they should not be subject >to serious (scientific) inquiry.) Huh? Does anybody understand this? >>>Why should such examination have "limits"? > >> The limits are intrinsic and not externally imposed. > >What are they? And why don't they apply to "certain things"? Why don't *what* apply to "certain things"? Limits? Limits apply to everything. Even (gasp) science. >> That means it is unable to do certain things, just as a blind person >> cannot see. For example, I would not judge the merits of a musical >> composition using the scientific method. > >But you could examine what aspects of a piece MAKE it a "good" piece in a >very scientific way. Could you? Even tho there's never complete agreement on which music is "good"? Even tho people's tastes vary over time? Even if you could nail down all the factors that induce Mike to say "this music is good", could you use that information to predict *anything* about what he'll say in 2 years? And could you use it to predict anything about anybody else? If you really can do this, you should, 'cause you'd make big bucks in the record business. When you do, send us all postcards from Tinsel Town and we'll remember you with new respect. But until you do, I'd say the burden of proof is on you to show how music can be scientifically judged as "good". >> I do not agree. > >Oh. I see. Thank you for clarifying that with such powerful reasoning. :-? I *loathe* people who respond to the first sentence of a paragraph before they even read what follows. Whatsa matter, Rich, can't comprehend an entire paragraph at once? His reasoning followed on the very next line. >Well, since "love" is a word to describe what happens when all those factors >come together, it "exists". But, alas, you don't care about what got it to >be that way. One may well end up being able to scientifically determine when someone is in love and why. It may well just be a chemical reaction. But I really don't see how, even in theory, one can scientifically determine whether or not an individual is married, or has recently broken a law, or is president. And marriage and crime and the presidency certainly seem to be real things with real consequences. Please either explain why they're not real, or give me some clue as to how one would approach them scientifically. Or, of course, you could concede that science doesn't apply to everything. >>>>Most people attribute existence to at least a few kinds of nonobjective >>>>things -- like beauty, meaning, awareness, causality, science, >>>>schroedinger probability waves, probably `physical objects', and maybe >>>>music, time, space... Clearly SOME meaningful things exist that have >>>>little or no objective existence whatsoever. > >>>We're talking about constructs and patterns designed by the mind to >>>REPRESENT reality, not reality. > >> Do you claim to know what reality IS? > >No, you do. So you *don't* know what reality is. Well, if you don't know what the definition of reality is, then on what basis do you say that beauty, meaning, awareness, ... don't fit it? Come on, now, do something new and THINK about what you're saying. You seemed to be saying that they're not real because they're "constructs and patterns designed by the mind to REPRESENT reality". Well, but why does that make them not real? Is it because they're constructs and patterns? Is it because they're designed by the mind? Numbers are constructs/patterns designed by the mind to represent reality. After all, there's no such physical thing as a 3.4. Nevertheless, numbers are real, and, in fact, your science depends on them quite heavily. So what is it about beauty, meaning, awareness, ... that makes you think they're not real? And why? >> If you know how to tell which are more real than others, please >> enlighten us, my friend. > >I thought I just did, and I didn't think it was very "enlightening" [....] At last something I can agree with. It most certainly was *not* enlightening. Try to say something cogent that *will* enlighten as to why science can be applied to everything. >"There! I've run rings 'round you logically!" Dream on. -- --JB (Beth Christy, U. of Chicago, ..!ihnp4!gargoyle!sphinx!beth) "Oh yeah, P.S., I, I feel, feel like, I am in a burning building And I gotta go." (Laurie Anderson)
rlr@pyuxd.UUCP (Rich Rosen) (08/14/85)
> Calm down, son, he was just appeasing those folks who think we provide > too much context for discussion. The "'>' quote" from you was in fact in > response to the "'>>>>' quote" from ... shoot, is that Mike? There was > just some other stuff in between that doesn't really matter. But anyway, > he's responding to your last statement which is correctly quoted, even if > not all of the context is provided. [BETH CHRISTY] Sorry to disappoint you. What he quoted was not only not me, it was him! Furthermore, taken out of context as it was, it obscured the original point: that referring to specific intended complexity built into as "seed" was implying a designer (note the word intended). This is very different from claiming that the potential for complexity was there, because saying that makes no assumptions about intentions or planned complexity. > And you're avoiding answering his > question. *Do* you think that a proto-universe with inherent potential > complexity similar to that of a seed would imply a creator? No, of course not. >> What notions? What pet theories? Who said science should be shackled? > >YOU did, by insisting that certain things are "not in the realm" of science, >BECAUSE they have names like "non-physical", "souls", etc. > So saying that something has limits is shackling it? You can't see > ultraviolet light, you poor shackled creature, you. Get real, Rich. Get clear. Be good with it. (Sorry, wrong discussion.) Insisting that something has limits when you cannot prove that a limiting point exists, or insisting that going beyond the limits you specify is invalid (perhaps because you are afraid of what scientific inquiry might discover about the nature fo what you claim lies beyond those limits), that is indeed shackling. Or an attempt at it. > That's a pretty emotional appeal coming from a "science uber alles" > kind of fellow. :-) One has a right to become emotionally charged about seeing fuzzy thinking allowed to masquerade as knowledge about reality. >>(Really putting >>the cart before the horse: making claims about aspects of the universe >>as being definitively beyond science so that one can then say science can't >>investigate them, which really simply means that they should not be subject >>to serious (scientific) inquiry.) > Huh? Does anybody understand this? I usre do. And people who don't presume that their eccentric wishful thinking notions MUST represent reality do too. But allow to go slowly. One might reasonably ask if the reason the anti-scientists talk so loudly about "the limits of science", and insist that science cannot properly investigate their claims about a "super-natural", is really because of the fact that if such investigation of the nature of those claims and their evidence and origin were to occur, it would show how shabby, how rooted in wishful thinking, they really are. >>>>Why should such examination have "limits"? >>> The limits are intrinsic and not externally imposed. >>What are they? And why don't they apply to "certain things"? > Why don't *what* apply to "certain things"? Limits? Limits apply to > everything. Even (gasp) science. Then tell us all what they are so that we'll know not to go beyond them by accident. :-? It sounds at this point like you'd just rather we didn't go beyond "certain" limits, because doing so, investigating the probability of reliability for certain beliefs that have a basis only in wishful thinking, might not be too pleasant. >>> That means it is unable to do certain things, just as a blind person >>> cannot see. For example, I would not judge the merits of a musical >>> composition using the scientific method. >>But you could examine what aspects of a piece MAKE it a "good" piece in a >>very scientific way. > Could you? Even tho there's never complete agreement on which music is > "good"? Even tho people's tastes vary over time? Even if you could nail > down all the factors that induce Mike to say "this music is good", could > you use that information to predict *anything* about what he'll say in 2 > years? And could you use it to predict anything about anybody else? If > you really can do this, you should, 'cause you'd make big bucks in the > record business. Someone beat me to it. > But until you do, I'd say the burden > of proof is on you to show how music can be scientifically judged as "good". You'll note that I never said that: I said that the components of a piece can be analyzed scientifically, and determine its internal elements. >>> I do not agree. >>Oh. I see. Thank you for clarifying that with such powerful reasoning. :-? > I *loathe* people who respond to the first sentence of a paragraph before > they even read what follows. Whatsa matter, Rich, can't comprehend an > entire paragraph at once? His reasoning followed on the very next line. Good for you and your loathing. You also seem to loathe clearcut rational reasoning, but that won't stop the rest of us. If you loathe awful horrible people like me, then don't bother discussing things with me. His statement was a separate "paragraph", and what's more I answered the points in the subsequent section. >>Well, since "love" is a word to describe what happens when all those factors >>come together, it "exists". But, alas, you don't care about what got it to >>be that way. > One may well end up being able to scientifically determine when someone > is in love and why. It may well just be a chemical reaction. But I > really don't see how, even in theory, one can scientifically determine > whether or not an individual is married, or has recently broken a law, or > is president. And marriage and crime and the presidency certainly seem > to be real things with real consequences. Please either explain why > they're not real, or give me some clue as to how one would approach them > scientifically. Or, of course, you could concede that science doesn't > apply to everything. You really don't listen to anything anyone has to say, do you? I'm not going to repeat at length what several other people have posted articles about regarding your position. Frank Adams in <581@mmintl.UUCP> rebutted all your points very well. Where was your answer to HIM? I quite frankly don't have the time nor the desire to reproduce that here. This is really not worth continuing, since Ms. Christy has not listened to a single point made by me or anyone else on this topic. -- "Wait a minute. '*WE*' decided??? *MY* best interests????" Rich Rosen ihnp4!pyuxd!rlr
beth@sphinx.UChicago.UUCP (Beth Christy) (08/14/85)
From: rlr@pyuxd.UUCP (Rich Rosen), Message-ID: <1494@pyuxd.UUCP>: >If you loathe awful >horrible people like me, then don't bother discussing things with me. It's a deal. -- --JB (Beth Christy, U. of Chicago, ..!ihnp4!gargoyle!sphinx!beth) "Oh yeah, P.S., I...I feel...feel like...I am in a burning building And I gotta go." (Laurie Anderson)
beth@sphinx.UChicago.UUCP (Beth Christy) (08/14/85)
I agreed in a posting of an hour or so ago to stop even trying to talk sense with Mr. Rosen, but I do have one last thing to add: From: rlr@pyuxd.UUCP (Rich Rosen), Message-ID: <1494@pyuxd.UUCP>: >You really don't listen to anything anyone has to say, do you? I'm not >going to repeat at length what several other people have posted articles >about regarding your position. Frank Adams in <581@mmintl.UUCP> rebutted >all your points very well. Where was your answer to HIM? I quite frankly >don't have the time nor the desire to reproduce that here. This is really >not worth continuing, since Ms. Christy has not listened to a single point >made by me or anyone else on this topic. Two points: 1) I didn't see Mr. Adams response. Since I assume the rest of the net did, would someone email it to me, and (assuming it has some meaningful content, unlike ...) I'll be happy to respond to it. (I'm only following the discussion that appears in net.origins (which is twice stupid - I'm probably missing half the articles, and it doesn't belong here anyway) - was his response only posted to one of the other groups?) 2) I do find it rather amusing that Mr. Rosen has the time and desire to engage in fights about "You said that. I did not, you did.", but doesn't "have the time nor the desire" to actually answer serious questions regarding his position. I'm happy to stop trying to discuss things with him, and look forward to more a meaningful exchange with Mr. Adams. -- --JB (Beth Christy, U. of Chicago, ..!ihnp4!gargoyle!sphinx!beth) "Oh yeah, P.S., I...I feel...feel like...I am in a burning building And I gotta go." (Laurie Anderson)
rlr@pyuxd.UUCP (Rich Rosen) (08/15/85)
>>If you loathe awful >>horrible people like me, then don't bother discussing things with me. > It's a deal. [BETH CHRISTY] I just have to wonder if you loathe all horrible people who disagree with you. No matter. You didn't seem to like answering rebuttals (from me and others) anyway, so it's just as well. Good day. -- "to be nobody but yourself in a world which is doing its best night and day to make you like everybody else means to fight the hardest battle any human being can fight and never stop fighting." - e. e. cummings Rich Rosen ihnp4!pyuxd!rlr
rlr@pyuxd.UUCP (Rich Rosen) (08/15/85)
> Two points: > 1) I didn't see Mr. Adams response. Since I assume the rest of the > net did, would someone email it to me, and (assuming it has some > meaningful content, unlike ...) Thanks for showing off your attitude towards anyone holding to a contrary position to yours. Don't project your inability to engage in a serious discussion with someone holding an opposing opinion onto others. > 2) I do find it rather amusing that Mr. Rosen has the time and desire > to engage in fights about "You said that. I did not, you did.", > but doesn't "have the time nor the desire" to actually answer > serious questions regarding his position. I'm happy to stop > trying to discuss things with him, and look forward to more a > meaningful exchange with Mr. Adams. The words "snotty attitude" don't even begin to describe your noisemaking, Beth. What do you call the previous articles that took a contrary stance to your holy position, if not answering the questions put forth? Never mind, forget I asked, a crass remark is sure to follow from you if I seriously ask that question expecting an answer. Good riddance, Beth. I'll stink to discussions with people who have positions, not people who whine and complain about someone else's position just because they don't like it, or are afraid of it. -- "Do I just cut 'em up like regular chickens?" Rich Rosen ihnp4!pyuxd!rlr
franka@mmintl.UUCP (Frank Adams) (08/20/85)
In article <969@sphinx.UChicago.UUCP> beth@sphinx.UChicago.UUCP (Beth Christy) writes: > Numbers are constructs/patterns designed by the mind to >represent reality. After all, there's no such physical thing as a 3.4. >Nevertheless, numbers are real, and, in fact, your science depends on >them quite heavily. Are numbers real? This is not obvious. There is a great deal of disagreement on this subject -- not least among mathematicians. Have you ever heard of intuitionism? Mathematical philosophers basically fall into three groups. One is the formalists, who insist they are just manipulating rules, and that any applicability to anything else is strictly incidental. The intuitionists believe that mathematical objects (numbers, for short), are solely constructs of the mind. They conclude that the only valid proofs are those which show how to accomplish the thing being proved. In particular, they deny the "law of the excluded middle": that for any proposition P, either P is true or P is false. Thus one cannot prove P by showing that not-P is contradictory. The third group, which is probably the largest, thinks numbers are real, but doesn't really know what they are. A good answer to that question would be most appreciated.
westling@cvl.UUCP (Mark Westling) (08/22/85)
Keywords: In article <608@mmintl.UUCP> franka@mmintl.UUCP (Frank Adams) writes: > Mathematical philosophers basically fall into three groups. One is the > formalists, who insist they are just manipulating rules, and that any > applicability to anything else is strictly incidental. > The intuitionists believe that mathematical objects (numbers, for short), > are solely constructs of the mind. ... > The third group, which is probably the largest, thinks numbers are real, > but doesn't really know what they are. A good answer to that question > would be most appreciated. From my limited knowledge of mathematical philosophy, it looks like the biggest group wasn't mentioned. The idea that numbers exist on their own was put forth last (I think) by Kant. Kant believed that mathematical reasoning could not be derived from logic, but rather from intuitive, a priori notions of time and space: arithmetic arises from time, and geometry arises from space. A major point was his claim that the figure is essential to all geometric proofs. He also believed in the necessity of Euclid's axioms, which are naturally based on intuition. The school of thought which was not mentioned in the original posting is the one founded by Frege and expanded by Russell. Two major results provided the incentive for dismissing Kant's ideas. Riemann and Lobachevsky showed that, in pure mathematics, non-Euclidean geometry also works, so there is no a priori need for Euclid's axioms. What happens in the real world is irrelevant; we're talking strictly about mathematical truth. Peano strengthened symbolic logic and set theory. Frege took the next step and reduced mathematics to logic. Russell continued along these lines, adding that the set theory used in his constructions was also reducible to logic. Recently, however, Quine and others have argued that the essential part is the set theory itself, not the logic. Formalists dislike this notion because they believe that logic is generally less certain than mathematics; intuitionists dispute it because it allows the existence of propositions which are unprovable (e.g. with Goedel's incompleteness theorem, or even quantification with infinite or just unmanageably big classes: how can you claim "all X are Y" if you can't test every X empirically?). Both provide alternatives to a logical or set theoretical foundation of mathematics, but neither support a special, "Platonic" existence of numbers. (At least, that's how I understand it.) It seems to me that there is more room for ontological investigation in the philosophy of logic (especially quantification) than in the philosophy of mathematics. Any thoughts? -- -- Mark Westling ARPA: westling@cvl CSNET: westling@cvl UUCP: ...!{seismo,allegra}!umcp-cs!cvl!westling
ellis@spar.UUCP (Michael Ellis) (08/23/85)
>>Numbers are constructs/patterns designed by the mind to >>represent reality. After all, there's no such physical thing as a 3.4. >>Nevertheless, numbers are real, and, in fact, your science depends on >>them quite heavily. [Beth Christy] > >Are numbers real? This is not obvious. There is a great deal of >disagreement on this subject -- not least among mathematicians. >... >The third group, which is probably the largest, thinks numbers are real, >but doesn't really know what they are. A good answer to that question >would be most appreciated. [Frank Adams] Bertrand Russell's analysis of the nature of numbers is the most appealing I've heard. He starts with the classical paradox.. I have red apples => Each apple was red I have ten fingers => Each finger was ten??? From Russell's History of Western Philosophy (Simon and Schuster): "The complete answer, as regards propositions in which `ten' occurs is "that, when these propositions are fully analyzed, they are found to "contain no constituent corresponding to the word `ten'. To explain "this in the case of such a large number as ten would be complicated; let "us therefore, substitute `I have two hands' "This means: "There is a such that there is b such that a and b are not identical "and whatever x may be, `x is a hand of mine' is true when, and only "when, x is a or x is b "Here the word `two' does not occur. It is true that two letters a and b "occur, but we do not need to know that they are two.. Thus numbers are, "in a precise sense, formal. It is left as an exercise for the diligent reader to remove any numerical reference from: `I have ten fingers' -michael
franka@mmintl.UUCP (Frank Adams) (08/27/85)
In article <761@cvl.UUCP> westling@cvl.UUCP (Mark Westling) writes: > >From my limited knowledge of mathematical philosophy, it looks like the >biggest group wasn't mentioned. > >The idea that numbers exist on their own was put forth last (I think) by >Kant. Kant believed that mathematical reasoning could not be derived from >logic, but rather from intuitive, a priori notions of time and space: >arithmetic arises from time, and geometry arises from space. A major point >was his claim that the figure is essential to all geometric proofs. He also >believed in the necessity of Euclid's axioms, which are naturally based on >intuition. Actually, this is the idea I didn't mention. One can believe in mathematics as a description of the real world; but this leaves little room for set theory. >The school of thought which was not mentioned in the original posting is the >one founded by Frege and expanded by Russell. Two major results provided >the incentive for dismissing Kant's ideas. Riemann and Lobachevsky showed >that, in pure mathematics, non-Euclidean geometry also works, so there is no >a priori need for Euclid's axioms. What happens in the real world is >irrelevant; we're talking strictly about mathematical truth. Peano >strengthened symbolic logic and set theory. Frege took the next step and >reduced mathematics to logic. Russell continued along these lines, adding >that the set theory used in his constructions was also reducible to logic. Sorry, set theory is *not* reducible to logic. The only ones who are willing to treat it as such are the formalists -- who don't care about the existence of the mathematical objects they deal with. If one takes set theory as the foundation, the original question remains: what kind of existence do sets have? >Recently, however, Quine and others have argued that the essential part is >the set theory itself, not the logic. Actually, I think you need both.
franka@mmintl.UUCP (Frank Adams) (08/27/85)
In article <481@spar.UUCP> ellis@spar.UUCP (Michael Ellis) writes: > > Bertrand Russell's analysis of the nature of numbers is the most > appealing I've heard. He starts with the classical paradox.. > > I have red apples => Each apple was red > I have ten fingers => Each finger was ten??? > > From Russell's History of Western Philosophy (Simon and Schuster): > > "The complete answer, as regards propositions in which `ten' occurs is > "that, when these propositions are fully analyzed, they are found to > "contain no constituent corresponding to the word `ten'. To explain > "this in the case of such a large number as ten would be complicated; let > "us therefore, substitute > `I have two hands' > "This means: > > "There is a such that there is b such that a and b are not identical > "and whatever x may be, `x is a hand of mine' is true when, and only > "when, x is a or x is b > > "Here the word `two' does not occur. It is true that two letters a and b > "occur, but we do not need to know that they are two.. Thus numbers are, > "in a precise sense, formal. > > It is left as an exercise for the diligent reader to remove any > numerical reference from: > > `I have ten fingers' > >-michael This works reasonably well for the natural numbers, and can be extended without undo difficulty to the rational numbers and even the real numbers (although the exact meaning in the latter case is not obvious). It fails when applied to, say, the complex numbers; and fails utterly when the discussion turns to set theory. There are those who only believe in mathematical objects for which a description of this type can be given. They are called finitists, and they accept even less of modern mathematics than the intuitionists do.
westling@cvl.UUCP (Mark Westling) (08/27/85)
I am posting the following for a friend. Send replies to John McLean
(arpanet: mclean@nrl-css, uucp: ...decvax!nrl-css!mclean).
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Let's keep our epistemology and ontology straight. Frank Adams was
giving the three traditional ontological views of numbers: they don't
exist, they are mental constructions, and they are real. Frege and Quine both
fall into the third camp, but they disagree on mathematical epistemology.
For Frege numbers are logical objects; we know that arithmetic is true
because the laws of arithmetic are reducible to the laws of logic. Of course,
his reduction was plagued by two problems: (1) his concept of logic was
larger than what is generally accepted as logic today (he included set
theory) and (2) his axiomatization of set theory was inconsistent. Russell
solved the second problem with the theory of types, but not the first. For
Quine, numbers exist on the grounds that Beth Christie echoed in a different
context: our best theories are committed to them. Physics needs arithmetic
and arithmetic says, among other things, that there is a number between 1 and
3. We know about numbers just like we know about any other type of
object: we construct theories about them. For people who like "isms",
Frege's view is called logicism and Quine's is called empiricism. The
latter has a distinguished hitory dating at least as far back as Mill,
and is still a hot topic as can be seen by reading Hartry Field's latest
book (whose title is something like SCIENCE WITHOUT NUMBERS).
John McLean
...!decvax!nrl-css!mclean or
mclean@nrl-css
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--
-- Mark Westling
ARPA: westling@cvl CSNET: westling@cvl
UUCP: ...!{seismo,allegra}!umcp-cs!cvl!westlingdmcanzi@watdcsu.UUCP (David Canzi) (08/31/85)
Frank Adams claims that mathematics cannot be reduced to logic. Consider a list of all theorems of mathematics, denoted T[1], T[2], etc. For each T[i], let A[i] be the conjunction of all the axioms that were assumed in proving T[i]. Then, for all i>=1, "if A[i] then T[i]" is a tautology. Mathematics consists entirely of studying logical tautologies, though the common habit of stating theorems without their axioms makes it look otherwise. Now that mathematics is known to contain only tautologies, I suppose this gives creationists grounds for attacking it. -- David Canzi This has been a test of the emergency broadcasting sytem. It was only a test. Repeat: only a test. If this had been a real emergency, you would be dead.