tag:blogger.com,1999:blog-4010478591191633760.post5193238167600891706..comments2024-03-22T08:04:05.869-07:00Comments on 魚之樂: 哲學的啟發 --- 兩個實例Unknownnoreply@blogger.comBlogger40125tag:blogger.com,1999:blog-4010478591191633760.post-36644947941290338712014-05-21T03:32:19.787-07:002014-05-21T03:32:19.787-07:00Anything that you could put into this form will (m...Anything that you could put into this form will (most likely??) be a paradox:<br /><br />A: x is M<br />B: x is N<br />(a): A -> B<br />(b): ~B -> ~A <br /><br />The uncertainty is in case you put things like "God" or "infinite" into M and N, trying to test its limit.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-4010478591191633760.post-47544070996190788322014-05-21T03:28:24.749-07:002014-05-21T03:28:24.749-07:00The paradox cannot be solved statistically because...The paradox cannot be solved statistically because it is a side-effect of a fault in the Logic tool-set, rather than a problem caused by the population of ravens or lions.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-4010478591191633760.post-22703930952904223822014-05-21T01:59:53.070-07:002014-05-21T01:59:53.070-07:00As a computer scientist, I am trained in both logi...As a computer scientist, I am trained in both logic and statistics. I am very well aware that pure logic doesn't care about population and quantities. But I have clearly stated that I am offering a different point of view using mathematics right at the beginning of my comment. Unless you have arguments to support you, please don't call my view wrong. You know you don't have to comment.<br /><br />BTW, Spork would be able to use statistical methods as well.<br /><br />SiriusAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-4010478591191633760.post-31388887104974768972014-05-20T22:46:14.693-07:002014-05-20T22:46:14.693-07:00//This is a paradox when M is not N. //
黑色, 鳥, DN...//This is a paradox when M is not N. //<br /><br />黑色, 鳥, DNA相信只是涵蓋了烏鴉,但都不是烏鴉,只是涵蓋範圍收窄。<br />那麼:<br />(a) 所有烏鴉都是這種DNA的鳥。(b) 所有非這種DNA的鳥都不是烏鴉。<br />還算不算是paradox?<br /><br />Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-4010478591191633760.post-33332877911655936002014-05-20T18:23:57.041-07:002014-05-20T18:23:57.041-07:00Pure Logic doesn't care about "ravens&quo...Pure Logic doesn't care about "ravens", "lions", population and quantity. The latter are for Statistics.<br /><br />Just pretend you are Spock of "Star Trek", will you?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-4010478591191633760.post-21669858947251184432014-05-20T18:15:54.598-07:002014-05-20T18:15:54.598-07:00You assumed that it has to be a logic operator.
T...You assumed that it has to be a logic operator.<br /><br />This "paradox" matter has been solved. Different people might use different approach to uncover its mystery. Probably the logic table is the easiest and simplest way to demonstrate why (a) and (b) are not logical equivalent (as in below).<br /><br />Because the source of the problem is Logic, applying logic operations would lead an investigator to go around full circles. Thus one needs to apply a different set of operators, hoping that they would do some good.<br /><br />If you apply the known logic operations as if doing mathematics, (a) and (b) will always yield the SAME answer, implying that they are logical equivalent, leading to confirm the paradox. But human intelligence tells that there must be a catch in the paradox. Finding the catch solves the mystery.<br /><br />The terms "ravens" and "black" create distractions, thus one needs to overlook the alphabets but go back to pure Logic mode. i.e. treating them as "symbols" instead of the words "ravens" and "black".<br /><br />By introducing "r" for "T(rue) maybe", "A -> B" can no longer be rewritten as "~A or B", and that is the catch, as it was the source of the paradox in the first place.<br /><br />One may eat with a fork, a spoon, a pair of chopsticks, a knife, a stick, and even with our own hands. And the case is closed.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-4010478591191633760.post-84475104201488630002014-05-20T17:33:47.215-07:002014-05-20T17:33:47.215-07:00You are correct that "raven" and "b...You are correct that "raven" and "black" can be changed to anything, say, P and Q. But the raven paradox only occurs when the pool of P is significantly smaller than the pool of non-P. For example, <br /><br />(c) All male lions have mane.<br />(d) All lions without mane are not male.<br /><br />Since the number of male and non-male (female) lions are roughly equal, we are able to naturally take evidence for (d) as also evidence for (c). And the raven paradox does not occur.<br /><br />SiriusAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-4010478591191633760.post-34272689425727258582014-05-20T13:07:52.624-07:002014-05-20T13:07:52.624-07:00//You assumed.//
Do you mean everyone can have hi...//You assumed.//<br /><br />Do you mean everyone can have his own definition of NOT?<br />I am not arguing with you what is the best definition of NOT. But if you insist on your definition of NOT, then " (b) is logically equivalent to NOT(NOT(b)) " does not hold.<br /><br />It is what you mention before:<br /><br />// then (a) has to be logically equivalent to NOT(NOT(b))), which is practically (b) //<br /><br />And look at what you also mention:<br /><br />//// (a): Y is Z<br />(b): non-Z is not Y<br /><br />Not(b): non-Z is Y<br />Not(Not(b)): Z is Y ////<br /><br />Does your (b) actually mean the same thing as your NOT(NOT(b)) ?<br /><br />For example:<br />If we know only "X is not clever --> X is not rich",<br />can we deduce from it "X is clever --> X is rich" ?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-4010478591191633760.post-55842682180798522622014-05-20T09:40:52.730-07:002014-05-20T09:40:52.730-07:00A: x is M
B: x is N
(a): A -> B
(b): ~B -> ~...A: x is M<br />B: x is N<br />(a): A -> B<br />(b): ~B -> ~A <br /><br />This is a paradox when M is not N. Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-4010478591191633760.post-40968825572340553932014-05-20T01:06:25.399-07:002014-05-20T01:06:25.399-07:00或者應該是這樣說,把涵蓋面收窄的意思是要令(b)句不會使得例如像紅色的蘋果和綠色的寶石等等很多無關的...或者應該是這樣說,把涵蓋面收窄的意思是要令(b)句不會使得例如像紅色的蘋果和綠色的寶石等等很多無關的東西能夠被納入考慮之列,例如試這樣說<br /><br />(a) 所有烏鴉都是這種DNA的鳥。(b) 所有非這種DNA的鳥都不是烏鴉。<br /><br />這樣(b)句的意思是否可限定了必須是「鳥」才可被考慮?不是鳥的東西例如紅色的蘋果和綠色的寶石等等很多不是鳥的東西就能夠被排除出考慮之列從而使得相關程度大為提高?若能夠依此類推當涵蓋面收窄到某種程度時或會令paradox不成立?<br /><br />Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-4010478591191633760.post-1679844781730810142014-05-19T22:07:07.100-07:002014-05-19T22:07:07.100-07:00一樣是paradox吧! 白色的天鵝, 紅色的蘋果和綠色的寶石都是支持(b)的證據.一樣是paradox吧! 白色的天鵝, 紅色的蘋果和綠色的寶石都是支持(b)的證據.浪,noreply@blogger.comtag:blogger.com,1999:blog-4010478591191633760.post-74062697204786052532014-05-19T21:29:03.025-07:002014-05-19T21:29:03.025-07:00//You have misunderstood the paradox. //
那麼請問如果把「...//You have misunderstood the paradox. //<br /><br />那麼請問如果把「黑色」這個涵蓋面很寬的詞改為涵蓋面不大於「烏鴉」這個詞的涵蓋面,例如改為:<br /><br />(a) 所有烏鴉都是這種DNA結構的。(b) 所有非這種DNA結構的東西都不是烏鴉。<br /><br />這樣又是否是paradox?<br /><br />Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-4010478591191633760.post-49513221540112508972014-05-19T13:39:04.878-07:002014-05-19T13:39:04.878-07:00You have misunderstood the paradox.
>> 就像數...You have misunderstood the paradox. <br /><br />>> 就像數學裡的分數那樣,要分母不為0才有意義一樣。<br /><br />Thus we have Calculus.<br />Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-4010478591191633760.post-80466323244354065862014-05-19T13:13:58.926-07:002014-05-19T13:13:58.926-07:00「二階意志」可能是屬於對為什麼要做一件事有更深層次的理解;若去到「三四階意志」的話,恐怕就是屬於「信...「二階意志」可能是屬於對為什麼要做一件事有更深層次的理解;若去到「三四階意志」的話,恐怕就是屬於「信仰」的地步了?<br /><br />Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-4010478591191633760.post-17858958719779072942014-05-19T12:24:24.810-07:002014-05-19T12:24:24.810-07:00//(a) 所有烏鴉都是黑色的。(b) 所有非黑色的東西都不是烏鴉。//
問題相信是因為用了「...//(a) 所有烏鴉都是黑色的。(b) 所有非黑色的東西都不是烏鴉。//<br /><br />問題相信是因為用了「黑色」這個基本上只描述了一個特徵的詞(涵蓋面很寬),來代表了還有很多其它特徵的「烏鴉」(比黑色這個詞的涵蓋面少得多);這就好比說用「黃色」來代表「中國人」那樣,於是考究「中國人」就變為了考究「黃色」的東西那樣未必都是與中國人有關。<br />可能這個假設是要有一個前者的涵蓋面不能夠大於後者才有意義,就像數學裡的分數那樣,要分母不為0才有意義一樣。<br /><br />Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-4010478591191633760.post-67437955858571473872014-05-19T10:30:20.157-07:002014-05-19T10:30:20.157-07:00In case you are not convinced:
Since "raven&...In case you are not convinced:<br /><br />Since "raven" and "black" are just "labels", what if they are changed to something like "star" and "heavy".<br />Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-4010478591191633760.post-9923320195647974662014-05-19T06:12:24.978-07:002014-05-19T06:12:24.978-07:00In reality, both (a) and (b) have infinite number ...In reality, both (a) and (b) have infinite number of objects.<br /><br />- - - -<br /><br />The paradox is about "why seeing (b) could deduce (a)". Through Logic & its logical operations as shown above, (b) could actually be rewritten to become (a).Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-4010478591191633760.post-81230475302277887802014-05-19T02:01:19.769-07:002014-05-19T02:01:19.769-07:00I'd like to express my view as a mathematician...I'd like to express my view as a mathematician/computer scientist. <br /><br />Evidence for (a) is drawn from a pool of finite ravens. whereas evidence for (b) must be drawn from a pool of infinite number of non-raven objects. It is possible to observe every raven on Earth and conclude that (a) is true. But it is impossible to observe every non-raven objects. Therefore, non-black non-raven objects are not evidences (or negligible evident).<br /><br />SiriusAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-4010478591191633760.post-85891005014952125492014-05-18T12:02:26.480-07:002014-05-18T12:02:26.480-07:00(b) may deduce (a) only if "r" ["T...(b) may deduce (a) only if "r" ["T(rue) maybe"] isn't used. Thus the paradox is due to a fault in the logic table, instead of something happening in our human world.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-4010478591191633760.post-19750943083359819382014-05-18T11:59:02.124-07:002014-05-18T11:59:02.124-07:00You assumed.You assumed.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-4010478591191633760.post-16078295846426485492014-05-18T01:58:26.596-07:002014-05-18T01:58:26.596-07:00The paradox of ravens happens because of a problem...The paradox of ravens happens because of a problem in the truth table:<br /><br />Let M be "p->q" (for easy text formatting):<br /><br /> p q M<br /> T T T<br /> T F F<br /> F T T<br /> F F T<br /><br />Suppose instead of T(rue) & F(alse), we allow a third state r for "T(rue) maybe".<br />The new truth table would be:<br /><br /> p q M<br /> T T T<br /> T F F<br /> F T r<br /> F F r<br /><br />A: x is a raven<br />B: x is black <br />(a): All ravens are black ===> A -> B ===> ~A or B<br />(b): all non-blacks are non-ravens ==> ~B -> ~A ===> ~(~B) or ~A ===> B or ~A<br /><br /> A B a b<br /> T T T T<br /> T F F F<br /> F T T T<br /> F F T T<br /><br />But if we introduce "r" for "T(rue) maybe".<br /><br /> A B a b<br /> T T T r<br /> T F F F<br /> F T r r<br /> F F r T<br /><br />Now is (a) and (b) really logical equivalent?<br /><br />From (b), at most one may deduce "some B is A" or "All B is A". It may never be used to deduce "All A is B".<br />Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-4010478591191633760.post-82474100197813721332014-05-17T15:30:13.525-07:002014-05-17T15:30:13.525-07:00you have a misconception in negation.
Let (a): &q...you have a misconception in negation.<br /><br />Let (a): "A => B".<br /><br />NOT(a) should be "A and NOT(B)". Or informally "there exists some condition satisfying A but not B"Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-4010478591191633760.post-91896383477391893502014-05-17T11:42:47.036-07:002014-05-17T11:42:47.036-07:00You are right! I slipped up!You are right! I slipped up!Joehttps://www.blogger.com/profile/03572952855079557855noreply@blogger.comtag:blogger.com,1999:blog-4010478591191633760.post-35843936841962883692014-05-17T08:19:59.149-07:002014-05-17T08:19:59.149-07:00Use brain first; ignore alphabets.Use brain first; ignore alphabets.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-4010478591191633760.post-78503032380295786212014-05-17T06:25:18.851-07:002014-05-17T06:25:18.851-07:00logic ...only T , F, 2 status.
not(T) = F , not(F...logic ...only T , F, 2 status.<br /><br />not(T) = F , not(F) = T , this is the definition of 'not' operand in logic.<br /><br />so,<br />(a) : Y is Z (this is statement, you could say "Y is Z" is true or false),<br />(b) : not Z is not Y (this is statement too).<br /><br />not(b) , in logic , it means:<br />if b is true, then not(b) is false.<br />if b is false, then not(b) is true.<br /><br />not(not Z is not Y) does not means not Z is Y...Laneserhttps://www.blogger.com/profile/07018511947417179463noreply@blogger.com