Insider WTF
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Did anybody else notice, in the Logic Test[^] linked to in the Insider, that the person who wrote the answers to the test[^] used the wrong logical visualiations? In the explanations for the first two answers, the Venn diagram was used (without any any indication of what was and was not a valid zone, mind you), when clearly what was intended was to show that
do ⊆ d ⊆ q
and
female logicians ⊆ clear thinkers
AND
lawyers ⊆ clear thinkersIn each case, Euler diagrams should have been used, showing the subsets wholly contained inside the supersets, as shown in the Wikipedia entry on Venn diagrams[^]. Venn (and Euler) diagrams are supposed to make the visualization of logic easier, but this article does nothing to aid in said visualization - in fact adding to the confusion, especially in the first question, where the Venn diagram clearly shows cases of Donald not quacking, and only the (completely unexplained) presence of a red X shows us that there is some significance to the intersection of all three. Which significance is unexplained in the diagram, and passed over in the commentary. I can only assume that the inclusion of an article about logic with such a glaring flaw placed so prominently must be the result of our esteemed editors being tied up by an evil, evil monkey and forced to watch in horror as the monkey (I'm not adding monkey as a suffix to another word, so it's still okay, right?) proceeded to send the Insider with one mistake in it. I hope that was the only mistake in it, anyway! Perhaps the fact that there were so few interesting links in today's episode were another? I hope everyone else scored 100% on the test, like I did, though. :cool:
i hated that logic test. for some questions, you had to use knowledge that wasn't given in the premises:
Question 11. a) Men are from Mars. b) Women are from Venus. Conclusion Therefore men and women will never understand each other.
the premises say nothing about "understanding". based on the premises alone, we can't validate the conclusion. we have to use outside knowledge to validate it. but other questions require that we disregard any outside knowledge we already have:
Question 10. a) Jenny lives in Paris. b) Paris is in New Zealand. Conclusion Therefore Jenny lives in New Zealand.
because there are cities called "Paris" all over the world[^], the conclusion must be false. Jenny could live in the US or France or Canada or Kiribati. but they say the conclusion is "Valid (but not true because Paris is not in New Zealand!)". in this one, we have to disregard all outside knowledge and assume that the only Paris in the world is the (fictional) one in New Zealand. mega BS
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i hated that logic test. for some questions, you had to use knowledge that wasn't given in the premises:
Question 11. a) Men are from Mars. b) Women are from Venus. Conclusion Therefore men and women will never understand each other.
the premises say nothing about "understanding". based on the premises alone, we can't validate the conclusion. we have to use outside knowledge to validate it. but other questions require that we disregard any outside knowledge we already have:
Question 10. a) Jenny lives in Paris. b) Paris is in New Zealand. Conclusion Therefore Jenny lives in New Zealand.
because there are cities called "Paris" all over the world[^], the conclusion must be false. Jenny could live in the US or France or Canada or Kiribati. but they say the conclusion is "Valid (but not true because Paris is not in New Zealand!)". in this one, we have to disregard all outside knowledge and assume that the only Paris in the world is the (fictional) one in New Zealand. mega BS
Scored 100%, hip hip hooray. :-\
Chris Losinger wrote:
for some questions, you had to use knowledge that wasn't given in the premises: Question 11. a) Men are from Mars. b) Women are from Venus. Conclusion Therefore men and women will never understand each other. the premises say nothing about "understanding". based on the premises alone, we can't validate the conclusion. we have to use outside knowledge to validate it.
The way I understood it none of the questions required/allowed you to use outside understanding (I'm pretty sure ducks dont bark in real life, although I could be mistaken:confused:). I took it that the fact this question didn't say anything about understanding meant that I couldn't conclude that men and women will never understand each other. While that conclusion may be true :rolleyes: there was nothing in the facts given that could really lead you to that conclusion, so false it was. Just my two cents on it.
"The computer industry is the only industry that is more fashion-driven than women's fashion. Maybe I'm an idiot, but I have no idea what anyone is talking about. What is it? It's complete gibberish. It's insane. When is this idiocy going to stop?" -- Oracle CEO Larry Ellison
-
Did anybody else notice, in the Logic Test[^] linked to in the Insider, that the person who wrote the answers to the test[^] used the wrong logical visualiations? In the explanations for the first two answers, the Venn diagram was used (without any any indication of what was and was not a valid zone, mind you), when clearly what was intended was to show that
do ⊆ d ⊆ q
and
female logicians ⊆ clear thinkers
AND
lawyers ⊆ clear thinkersIn each case, Euler diagrams should have been used, showing the subsets wholly contained inside the supersets, as shown in the Wikipedia entry on Venn diagrams[^]. Venn (and Euler) diagrams are supposed to make the visualization of logic easier, but this article does nothing to aid in said visualization - in fact adding to the confusion, especially in the first question, where the Venn diagram clearly shows cases of Donald not quacking, and only the (completely unexplained) presence of a red X shows us that there is some significance to the intersection of all three. Which significance is unexplained in the diagram, and passed over in the commentary. I can only assume that the inclusion of an article about logic with such a glaring flaw placed so prominently must be the result of our esteemed editors being tied up by an evil, evil monkey and forced to watch in horror as the monkey (I'm not adding monkey as a suffix to another word, so it's still okay, right?) proceeded to send the Insider with one mistake in it. I hope that was the only mistake in it, anyway! Perhaps the fact that there were so few interesting links in today's episode were another? I hope everyone else scored 100% on the test, like I did, though. :cool:
Oh yeah. :cool: However I know little to nothing about Venn (or even if) diagrams so am glad that was not the subject of the test.
Henry Minute If you open a can of worms, any viable solution *MUST* involve a larger can.
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Did anybody else notice, in the Logic Test[^] linked to in the Insider, that the person who wrote the answers to the test[^] used the wrong logical visualiations? In the explanations for the first two answers, the Venn diagram was used (without any any indication of what was and was not a valid zone, mind you), when clearly what was intended was to show that
do ⊆ d ⊆ q
and
female logicians ⊆ clear thinkers
AND
lawyers ⊆ clear thinkersIn each case, Euler diagrams should have been used, showing the subsets wholly contained inside the supersets, as shown in the Wikipedia entry on Venn diagrams[^]. Venn (and Euler) diagrams are supposed to make the visualization of logic easier, but this article does nothing to aid in said visualization - in fact adding to the confusion, especially in the first question, where the Venn diagram clearly shows cases of Donald not quacking, and only the (completely unexplained) presence of a red X shows us that there is some significance to the intersection of all three. Which significance is unexplained in the diagram, and passed over in the commentary. I can only assume that the inclusion of an article about logic with such a glaring flaw placed so prominently must be the result of our esteemed editors being tied up by an evil, evil monkey and forced to watch in horror as the monkey (I'm not adding monkey as a suffix to another word, so it's still okay, right?) proceeded to send the Insider with one mistake in it. I hope that was the only mistake in it, anyway! Perhaps the fact that there were so few interesting links in today's episode were another? I hope everyone else scored 100% on the test, like I did, though. :cool:
Wow, you are a serious geek. :) I could care less about the diagrams, if you need diagrams to think logically then you're in the wrong business. ;) Yup 100%. To be honest I was surprised I got 100% because I burned through them going with my gut each time and not spending any time trying to parse it out logically.
"It's so simple to be wise. Just think of something stupid to say and then don't say it." -Sam Levenson
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i hated that logic test. for some questions, you had to use knowledge that wasn't given in the premises:
Question 11. a) Men are from Mars. b) Women are from Venus. Conclusion Therefore men and women will never understand each other.
the premises say nothing about "understanding". based on the premises alone, we can't validate the conclusion. we have to use outside knowledge to validate it. but other questions require that we disregard any outside knowledge we already have:
Question 10. a) Jenny lives in Paris. b) Paris is in New Zealand. Conclusion Therefore Jenny lives in New Zealand.
because there are cities called "Paris" all over the world[^], the conclusion must be false. Jenny could live in the US or France or Canada or Kiribati. but they say the conclusion is "Valid (but not true because Paris is not in New Zealand!)". in this one, we have to disregard all outside knowledge and assume that the only Paris in the world is the (fictional) one in New Zealand. mega BS
Chris Losinger wrote:
for some questions, you had to use knowledge that wasn't given in the premises
Whoops! That was the whole point of the test, it's a "logic" test not a geography test. I think it was quite clever how they worded some of the questions to intentionally throw people off if they weren't thinking purely logically.
"It's so simple to be wise. Just think of something stupid to say and then don't say it." -Sam Levenson
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i hated that logic test. for some questions, you had to use knowledge that wasn't given in the premises:
Question 11. a) Men are from Mars. b) Women are from Venus. Conclusion Therefore men and women will never understand each other.
the premises say nothing about "understanding". based on the premises alone, we can't validate the conclusion. we have to use outside knowledge to validate it. but other questions require that we disregard any outside knowledge we already have:
Question 10. a) Jenny lives in Paris. b) Paris is in New Zealand. Conclusion Therefore Jenny lives in New Zealand.
because there are cities called "Paris" all over the world[^], the conclusion must be false. Jenny could live in the US or France or Canada or Kiribati. but they say the conclusion is "Valid (but not true because Paris is not in New Zealand!)". in this one, we have to disregard all outside knowledge and assume that the only Paris in the world is the (fictional) one in New Zealand. mega BS
Actually, for the most part, the test itself was okay.
Chris Losinger wrote:
for some questions, you had to use knowledge that wasn't given in the premises: Question 11. a) Men are from Mars. b) Women are from Venus. Conclusion Therefore men and women will never understand each other. the premises say nothing about "understanding". based on the premises alone, we can't validate the conclusion. we have to use outside knowledge to validate it.
This is a classic example of ignoring outside information. You're supposed to determine whether or not a logical statement is true or not from the information given.
Chris Losinger wrote:
but other questions require that we disregard any outside knowledge we already have:
This is standard practice in logic courses. In order to make ensure that you actually understand the underlying logic, rather than merely picking the answer that you "know" to be true, any good test of logical ability will have some questions with untrue premises, and thus untrue conclusion; yet the logic itself is valid. Thus all ducks bark, because the premises support this conclusion. They will also do the opposite, as in the marsupials question, where despite our outside knowledge that kangaroos are marsupials, the premises don't suppost this. All these questions use only the premises given, and if you're using any outside knowledge (that Paris isn't actually in Australia, or that more than one Paris exists, when the premise specifically states that (Implied "The") Paris is in Australia), then you're not actually evaluating the logic correctly. The only problem I had with the test itself was the last question, where the premises themselves were ambiguous: as the answer key stated, is the first premise a definition or merely the result of observations? It's stated as a definition, yet the presence of the second premise suggests that it's not. The only real way around this quandary is to assume that this is a definition, but that observations don't necessarily reveal what is the case: even though water is defined as H2O, it's possible that somebody will try to observe water using a procedure that falsely shows it to NaCl, or something like that (the explanation the answer key gives actually destroys the integrity of the logical statement). But this question is so ambiguous, there could be a perfectly reasonable explanation for
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Wow, you are a serious geek. :) I could care less about the diagrams, if you need diagrams to think logically then you're in the wrong business. ;) Yup 100%. To be honest I was surprised I got 100% because I burned through them going with my gut each time and not spending any time trying to parse it out logically.
"It's so simple to be wise. Just think of something stupid to say and then don't say it." -Sam Levenson
Diagrams? We don't need no stinking diagrams! I agree, I could care less about the diagrams as well. I certainly didn't feel any need to start diagramming logical constructions, as these were plenty easy enough to just look at and solve. What I object to is that the author found it necessary to include diagrams to show his logic - and then used the wrong ones. Sure, go ahead, diagram it for the people who can't wrap their minds around elementary logic - but do it right! Sheesh!
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Did anybody else notice, in the Logic Test[^] linked to in the Insider, that the person who wrote the answers to the test[^] used the wrong logical visualiations? In the explanations for the first two answers, the Venn diagram was used (without any any indication of what was and was not a valid zone, mind you), when clearly what was intended was to show that
do ⊆ d ⊆ q
and
female logicians ⊆ clear thinkers
AND
lawyers ⊆ clear thinkersIn each case, Euler diagrams should have been used, showing the subsets wholly contained inside the supersets, as shown in the Wikipedia entry on Venn diagrams[^]. Venn (and Euler) diagrams are supposed to make the visualization of logic easier, but this article does nothing to aid in said visualization - in fact adding to the confusion, especially in the first question, where the Venn diagram clearly shows cases of Donald not quacking, and only the (completely unexplained) presence of a red X shows us that there is some significance to the intersection of all three. Which significance is unexplained in the diagram, and passed over in the commentary. I can only assume that the inclusion of an article about logic with such a glaring flaw placed so prominently must be the result of our esteemed editors being tied up by an evil, evil monkey and forced to watch in horror as the monkey (I'm not adding monkey as a suffix to another word, so it's still okay, right?) proceeded to send the Insider with one mistake in it. I hope that was the only mistake in it, anyway! Perhaps the fact that there were so few interesting links in today's episode were another? I hope everyone else scored 100% on the test, like I did, though. :cool:
Trevortni wrote:
I can only assume that the inclusion of an article about logic with such a glaring flaw placed so prominently must be the result of our esteemed editors being tied up by an evil, evil monkey and forced to watch in horror as the monkey (I'm not adding monkey as a suffix to another word, so it's still okay, right?) proceeded to send the Insider with one mistake in it. I hope that was the only mistake in it, anyway! Perhaps the fact that there were so few interesting links in today's episode were another?
Tough crowd :(( What kind of items can I invent to make it more interesting? I held off on this year's Darwin Awards winner (for fear of offending folk), all the Apple news (really, $179 to replace the battery, and 30c/song I already paid you for?), and a game site (figuring you hard-working folk wouldn't appreciate the distraction).
-------------- TTFN - Kent
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Trevortni wrote:
I can only assume that the inclusion of an article about logic with such a glaring flaw placed so prominently must be the result of our esteemed editors being tied up by an evil, evil monkey and forced to watch in horror as the monkey (I'm not adding monkey as a suffix to another word, so it's still okay, right?) proceeded to send the Insider with one mistake in it. I hope that was the only mistake in it, anyway! Perhaps the fact that there were so few interesting links in today's episode were another?
Tough crowd :(( What kind of items can I invent to make it more interesting? I held off on this year's Darwin Awards winner (for fear of offending folk), all the Apple news (really, $179 to replace the battery, and 30c/song I already paid you for?), and a game site (figuring you hard-working folk wouldn't appreciate the distraction).
-------------- TTFN - Kent
Nah, it's actually nice, every once in a while, to not be opening enough windows off of the Insider to warrant using all the fingers on both hands. I think you allow me such a break every.... oh.... how long ago was the last blue moon? It's usually pretty interesting, but - hey! I do need to get work done every once in a while, right?
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Actually, for the most part, the test itself was okay.
Chris Losinger wrote:
for some questions, you had to use knowledge that wasn't given in the premises: Question 11. a) Men are from Mars. b) Women are from Venus. Conclusion Therefore men and women will never understand each other. the premises say nothing about "understanding". based on the premises alone, we can't validate the conclusion. we have to use outside knowledge to validate it.
This is a classic example of ignoring outside information. You're supposed to determine whether or not a logical statement is true or not from the information given.
Chris Losinger wrote:
but other questions require that we disregard any outside knowledge we already have:
This is standard practice in logic courses. In order to make ensure that you actually understand the underlying logic, rather than merely picking the answer that you "know" to be true, any good test of logical ability will have some questions with untrue premises, and thus untrue conclusion; yet the logic itself is valid. Thus all ducks bark, because the premises support this conclusion. They will also do the opposite, as in the marsupials question, where despite our outside knowledge that kangaroos are marsupials, the premises don't suppost this. All these questions use only the premises given, and if you're using any outside knowledge (that Paris isn't actually in Australia, or that more than one Paris exists, when the premise specifically states that (Implied "The") Paris is in Australia), then you're not actually evaluating the logic correctly. The only problem I had with the test itself was the last question, where the premises themselves were ambiguous: as the answer key stated, is the first premise a definition or merely the result of observations? It's stated as a definition, yet the presence of the second premise suggests that it's not. The only real way around this quandary is to assume that this is a definition, but that observations don't necessarily reveal what is the case: even though water is defined as H2O, it's possible that somebody will try to observe water using a procedure that falsely shows it to NaCl, or something like that (the explanation the answer key gives actually destroys the integrity of the logical statement). But this question is so ambiguous, there could be a perfectly reasonable explanation for
Trevortni wrote:
You're supposed to determine whether or not a logical statement is true or not from the information given.
maybe you didn't read the first example i provided.
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Trevortni wrote:
You're supposed to determine whether or not a logical statement is true or not from the information given.
maybe you didn't read the first example i provided.
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well, i'm pretty sure i read what i wrote.
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Scored 100%, hip hip hooray. :-\
Chris Losinger wrote:
for some questions, you had to use knowledge that wasn't given in the premises: Question 11. a) Men are from Mars. b) Women are from Venus. Conclusion Therefore men and women will never understand each other. the premises say nothing about "understanding". based on the premises alone, we can't validate the conclusion. we have to use outside knowledge to validate it.
The way I understood it none of the questions required/allowed you to use outside understanding (I'm pretty sure ducks dont bark in real life, although I could be mistaken:confused:). I took it that the fact this question didn't say anything about understanding meant that I couldn't conclude that men and women will never understand each other. While that conclusion may be true :rolleyes: there was nothing in the facts given that could really lead you to that conclusion, so false it was. Just my two cents on it.
"The computer industry is the only industry that is more fashion-driven than women's fashion. Maybe I'm an idiot, but I have no idea what anyone is talking about. What is it? It's complete gibberish. It's insane. When is this idiocy going to stop?" -- Oracle CEO Larry Ellison
wags77 wrote:
he way I understood it none of the questions required/allowed you to use outside understanding
actually, they all do. without outside understanding, you can't tell nouns from verbs from prepositions from adjectives. you don't know what it means to "bark" (does it mean to make a noise like a dog, or to be a dog?). the problems happen when the trick in the question gets too close to the things you have to know to understand the question itself. evs
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wags77 wrote:
he way I understood it none of the questions required/allowed you to use outside understanding
actually, they all do. without outside understanding, you can't tell nouns from verbs from prepositions from adjectives. you don't know what it means to "bark" (does it mean to make a noise like a dog, or to be a dog?). the problems happen when the trick in the question gets too close to the things you have to know to understand the question itself. evs
Okay, I concede that you may need to use some outside understanding
Chris Losinger wrote:
tell nouns from verbs from prepositions from adjectives
although I'm not entirely sure you need to know what barking means
Chris Losinger wrote:
you don't know what it means to "bark" (does it mean to make a noise like a dog, or to be a dog?).
to come to a conclusion for that question... Question 7. a) All ducks bark. b) Donald is a duck. Conclusion Therefore Donald barks. All I need to know is that all ducks do it and Donald is a duck so he must do it, whatever "it" happens to be isn't really important to the question.
"The computer industry is the only industry that is more fashion-driven than women's fashion. Maybe I'm an idiot, but I have no idea what anyone is talking about. What is it? It's complete gibberish. It's insane. When is this idiocy going to stop?" -- Oracle CEO Larry Ellison
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well, i'm pretty sure i read what i wrote.
Very well: you want a more verbiose answer? Frankly, I'm having trouble deciding whether you passed that question without realizing it, or failed it miserably. Regardless of which answer you selected. You spoke rightly when you said that
Chris Losinger wrote:
based on the premises alone, we can't validate the conclusion.
That was the point of the question: based on the premises alone, you can't validate the conclusion. Thus the conclusion is invalid. Thus the answer key says the answer is invalid. You did read the answer key, right? Though the answer key (as previously noted) is not very good. And it does show in this question as well: It would have been so easy to point out that the premises said nothing about understanding. The author could have pointed out that the premises were nonsense statements in the first place (though that would have required pointing out that this is irrelevant to the strict application of logic). The author should have pointed out that there was absolutely nothing in the premises to support the proposed conclusion. But instead, the author supplied evidence outside of the logical structure to show (empirically), rather than show (logically) that the conclusion was wrong, rather than invalid, as was intended. Thus, in the context of the answer key, the question was bad, because the author failed to explain the logic; but in the of the test itself, the question was perfectly valid: it requires you to ignore, rather than import, outside knowledge, in order to correctly determine that the conclusion was not, as you stated, supported by the premises.
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wags77 wrote:
he way I understood it none of the questions required/allowed you to use outside understanding
actually, they all do. without outside understanding, you can't tell nouns from verbs from prepositions from adjectives. you don't know what it means to "bark" (does it mean to make a noise like a dog, or to be a dog?). the problems happen when the trick in the question gets too close to the things you have to know to understand the question itself. evs
a.) All shizzywigs blurgle. b.) Plurlp is a shizzywig. Conclusion: Plurlp blurgles. You do need to know the language of propositional logic. THAT'S IT. Do you consider knowing what "+", "-", "*", and "/" mean to be outside information when determining the answer to a math problem? This is a test of your ability to read, understand, and properly apply the language of propositional logic. To complain about needing to understand what's being tested is just.... just.... Please don't force me to finish that insult.
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Okay, I concede that you may need to use some outside understanding
Chris Losinger wrote:
tell nouns from verbs from prepositions from adjectives
although I'm not entirely sure you need to know what barking means
Chris Losinger wrote:
you don't know what it means to "bark" (does it mean to make a noise like a dog, or to be a dog?).
to come to a conclusion for that question... Question 7. a) All ducks bark. b) Donald is a duck. Conclusion Therefore Donald barks. All I need to know is that all ducks do it and Donald is a duck so he must do it, whatever "it" happens to be isn't really important to the question.
"The computer industry is the only industry that is more fashion-driven than women's fashion. Maybe I'm an idiot, but I have no idea what anyone is talking about. What is it? It's complete gibberish. It's insane. When is this idiocy going to stop?" -- Oracle CEO Larry Ellison
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Very well: you want a more verbiose answer? Frankly, I'm having trouble deciding whether you passed that question without realizing it, or failed it miserably. Regardless of which answer you selected. You spoke rightly when you said that
Chris Losinger wrote:
based on the premises alone, we can't validate the conclusion.
That was the point of the question: based on the premises alone, you can't validate the conclusion. Thus the conclusion is invalid. Thus the answer key says the answer is invalid. You did read the answer key, right? Though the answer key (as previously noted) is not very good. And it does show in this question as well: It would have been so easy to point out that the premises said nothing about understanding. The author could have pointed out that the premises were nonsense statements in the first place (though that would have required pointing out that this is irrelevant to the strict application of logic). The author should have pointed out that there was absolutely nothing in the premises to support the proposed conclusion. But instead, the author supplied evidence outside of the logical structure to show (empirically), rather than show (logically) that the conclusion was wrong, rather than invalid, as was intended. Thus, in the context of the answer key, the question was bad, because the author failed to explain the logic; but in the of the test itself, the question was perfectly valid: it requires you to ignore, rather than import, outside knowledge, in order to correctly determine that the conclusion was not, as you stated, supported by the premises.
Trevortni wrote:
Frankly, I'm having trouble deciding whether you passed that question without realizing it, or failed it miserably.
and i don't remember if i got the Mars/Venus one right or not (i got the Paris one right, i know). i took the test hours before you commented on it here. i missed two, i think. but the quiz doesn't tell you which you missed and which you didn't. it just gives the answers. but regardless, i picked these two for examples here because they fit the point i was trying to make. which i guess i failed to do.
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a.) All shizzywigs blurgle. b.) Plurlp is a shizzywig. Conclusion: Plurlp blurgles. You do need to know the language of propositional logic. THAT'S IT. Do you consider knowing what "+", "-", "*", and "/" mean to be outside information when determining the answer to a math problem? This is a test of your ability to read, understand, and properly apply the language of propositional logic. To complain about needing to understand what's being tested is just.... just.... Please don't force me to finish that insult.
Trevortni wrote:
Please don't force me to finish that insult.
you want to insult me over this? get over yourself.
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Okay, I concede that you may need to use some outside understanding
Chris Losinger wrote:
tell nouns from verbs from prepositions from adjectives
although I'm not entirely sure you need to know what barking means
Chris Losinger wrote:
you don't know what it means to "bark" (does it mean to make a noise like a dog, or to be a dog?).
to come to a conclusion for that question... Question 7. a) All ducks bark. b) Donald is a duck. Conclusion Therefore Donald barks. All I need to know is that all ducks do it and Donald is a duck so he must do it, whatever "it" happens to be isn't really important to the question.
"The computer industry is the only industry that is more fashion-driven than women's fashion. Maybe I'm an idiot, but I have no idea what anyone is talking about. What is it? It's complete gibberish. It's insane. When is this idiocy going to stop?" -- Oracle CEO Larry Ellison
ok ok. ducks and barking was a bad example. i guess it's the Venus/Mars one that really gets me. let me try it this way: both of the statements are nonsense, so of course you can't draw any conclusions from them. but in order to know they are nonsense, you really do have to know a bit about Men, Women, Mars, Venus, "from" and "understanding". and, yes, i understand why the answer to that one is what it is. i just think that one, and a couple of the other questions, are a touch sloppy.