merjet

Correspondence and Coherence blog

73 posts in this topic

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Thanks, Merlin, for the information on Beyond Self-Interest and the particular paper in it by Virginia Held: “Mothering versus Contract.” I imagine it would be worthwhile to compare and assimilate Held’s ideas with Kathleen Touchstone’s Then Athena Said.

Oh, I see now that someone else noticed the connection to Prof. Touchstone’s book and mentioned it in a comment in your blog. Thanks for sharing the link there to Objectivity Archive. By the way, a year or two ago, Kathleen mentioned to me that she is working on another book. I don’t know the topic or the schedule.

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There is a review of Kathleen Touchstone’s Then Athena Said in The Journal of Ayn Rand Studies 8.2 (link). Since it is more than 5 years old, it can be read online for free with a JSTOR account, which can also be had for free.  

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Yes, and I have some remarks on Then Athena Said online in the thread here.

 

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14 minutes ago, merjet said:

Here is some ecological rationality for you:  Never pee in the water in which you are standing.   You make have to drink it some day....

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3 minutes ago, BaalChatzaf said:

Here is some ecological rationality for you:  Never pee in the water in which you are standing.   You make have to drink it some day....

Heh. Here is another. Never pee while wearing a poncho in gusty winds.  

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pertaining to "A Little Logic Puzzle" :  

That is the fallacy of asserting the consequent.  which says  if a implies b  and b is asserted  then a follows.

if you construct a truth table for ((a => b)  &  b) => a  you will see the expression is not a tautology hence is not a valid inference form.

"=>"  stands for implies and "&"  for "and"

The algebraic logic  formulated by George Boole  in 1850  includes Aristotle's syllogistic as a special case. Way back when,  Aristotle developed syllogistic categorical logic  and the Stoics developed  logic  based on conditionals.  The Stoic logic invented by Crysypus is mostly lost and the syllogistic logic  based on categorical  statements   survived and was not improved upon until Leibniz  attempted to reformulate logic  (he was a bit ahead of  his time)  and George Boole and Gotleib Frege succeeded in the 19 th century.  It was Boole's formulation of conditional logic  what was applicable to expressing the logic of electronic computing machines. 

Aristotle's syllogistic   was correct as far as it went,  but  it could not handle binary relations well.   Consider  If  all tigers are animals   then the tail of a tiger is the tail of an animal.   Or   if x is the tail of a tiger   then  x  is the tail of an animal.  The binary relation x is the tail  of  y   is no expressible  in categorical form. The best one can  do   is   all lion's tails   are animal tail's  therefore if x is a lion's tail  then x is an animal's tail  which is a conditional statement.  The categorical version is all lion's tails are animal's tails.    which does not follow from all lions are animals in the Aristotelian syllogistic.  There is nothing wrong with Aristotle's logic but it is inflexible and somewhat constipated. 

One wonders if the work of the Stoic school has survived long enough to be taken into the Islamic domains  could it have migrated back into Europe  in the late middle ages?   The only reason that Aristotle's work even partially survived is that much of it was taken up by Islamic scholars and part of the Ulima (Muslim learning)  and migrated back into Europe (the Byzantine empire)  when Christian scholars when to the Muslim world to learn and thing or two. It was the Ulima that kept much of Greek thinking alive until middle ages in Europe.  A great deal was lost when Julius Caesar burned down the library at Alexandria and later on the Christians burned  what was not burned by Caesar.  
 

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3 hours ago, BaalChatzaf said:

Aristotle's syllogistic   was correct as far as it went,  but  it could not handle binary relations well.   Consider  If  all tigers are animals   then the tail of a tiger is the tail of an animal.   Or   if x is the tail of a tiger   then  x  is the tail of an animal.  The binary relation x is the tail  of  y   is no expressible  in categorical form.

You sound like a broken record, and Fred Sommers' term logic handles binary (and higher) relations very well.

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17 minutes ago, merjet said:

You sound like a broken record, and Fred Sommers' term logic handles binary (and higher) relations very well.

Sommers and Engleburtsen had to -extend- the logic.  Aristotle was  nowhere near what they did.   And even with term logic extended,  term logic yields no useful metamathematical results.   Goedel could not have proved the incompleteness theorems using term logic and term logic does not lend itself well to mathematical extension.  Logic stagnated until   Boole  and Frege made the breakthrough by going back to Stoic  conditional logic. 

In logic design of circuits  (necessary to get minimal  circuits)   Sommers-Engelburtsen term logic is nowhere used.   S and E  were very  clever and original, but their term logic does not lend itself very well to computer  execution.  The programming language PROLOG  and others are derived from first order logic.  Set theory was finally nailed down by being basted on  conditional logic.  Term Logic bore no mathematical fruit.   First and Higher order Predicate Logic did.

Computerization of grammar and machine translation were derived logically from the extensions of predicate logic.  Next time you use Google Translate be aware there is a lot of mathematically based logic behind it.  

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8 hours ago, BaalChatzaf said:

pertaining to "A Little Logic Puzzle" :  

That is the fallacy of asserting the consequent.  which says  if a implies b  and b is asserted  then a follows.

if you construct a truth table for ((a => b)  &  b) => a  you will see the expression is not a tautology hence is not a valid inference form.

"=>"  stands for implies and "&"  for "and"

Ba'al, the error is a distribution error.

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1 hour ago, KorbenDallas said:

Ba'al, the error is a distribution error.

In conditional logic  there is no issue of distribution.  

In conditional   terms   "all P  is Q"  means if x is a P  then x is Q.  Asserting y is a Q  does not guarantee y is a P.  Suppose  y is in Q - P  which is to say the set of Q's which are not  P's   

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1 hour ago, BaalChatzaf said:

In conditional logic  there is no issue of distribution.  

It's written as a categorical syllogism, one that has a distribution error.

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1 minute ago, KorbenDallas said:

It's written as a categorical syllogism, one that has a distribution error.

And I showed its conditional counterpart.   Anything in categorical logic can be handled by conditional logic, in particular first order predicate logic.  The converse, however, is not true.  One of the reasons why modern predicate logic was developed was to handled  binary and higher order relations  flexibly.

Conditional logic was originated by the Stoics about the same time Aristotle operated his Lyceum.  Crysippus, the Stoic was said to have write dozens, possibly hundreds of books  on logic,  but none of them have survived to this day.  We only have fragmentary references to Stoic conditional logic by other writers, but the full details are lost in time.  We are fortunate to have what we have of Aristotle.  Some of  his works were preserved by the Roman  Cicero,  others of his works  somehow got to the Islamic domains where they become a hit and were carefully studied and expanded upon.  In Europe, the study of logic mostly stagnated until the late middle ages when they returned to Europe.  R. Maimonodes  used Aristotle's logic to defend Judaism against Islam and a century later Thomas Acquinas used Aristotle's work to expound  Catholicism. 

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9 hours ago, merjet said:

Interesting, I went into solving #1 cold, without any further context.  I got the right answer, then went on to #2 and the Wiki article.  The method I used was System 1 according to the description, but when validating it I found my own answer was incorrect, then I came to the right answer, so I this was System 2 according to the description.  All this took about 1 to 1.5min..

(Pats Self on back :))

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I just looked at the problem and decided (spoiler alert) saved the most fuel without doing any calculation to speak of. I think the problem is set up to trap you in what seems obvious so I went with what I thought was the un-obvious answer. I also don't think it's close or the idea is you must do several detailed calculations and that shouldn't be what the author's about. If it's thinking fast and slow I did the fast for it took about 20 seconds. Still thinking about it as I write this if it's roughly three times the gas mileage the more economical vehicle uses, so 1/3 the fuel which magnifies the savings of the 12 - 14.

Now I'll try the second. My answer was correct. For 10,000 miles driving each, 12 - 14 saved roughly 36 gals over the 30 - 40. I took a lot of time before my young teenager arithmetic came back on line, however.

--Brant

boy genius

 

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