Your idea that the subjects are not taking the question seriously is a good one.
I had a discussion with someone about a very similar real life ‘Linda’. It was finally resolved by realizing that the other person didn’t think of ‘and’ and ‘or’ as defined terms that always differed and was quite put out that I thought he should know that. To put it in ‘Linda’ terms: he know that Linda was a feminist and doubted that she was a teller. This being the case the ‘and’ should be thought of as an ‘or’ and b was more likely than a. Why would anyone think differently? It kind of blew my mind that I was being accused of being sloppy or illogical by using the fixed defined meaning for ‘and’ and ‘or’. I have since that time noticed that people actually often have this vagueness about logical terms.
I generally think of “and” and “or” in the strict senses, but, by the same token, I get really annoyed when I use the word “or” (which, in English, is ambiguous about whether it is meant in the exclusive or inclusive sense) and people say “yes” or “true”.
English already has words like “both” to answer in that question, which tells you in one syllable that the “exclusive or” reading is false but the “inclusive or” reading is true. This is not a standard part of symbolic logic curriculum, and is simply helpful rather than a sign of having taken such a class and learned a technical jargon that borrowed the word “or” to strictly mean “inclusive or”.
I’d never head of someone generously interpreting an “and” as an “or” (or vice versa) but it makes sense to me that it would be common and helpful in the absence of assumed exposure to a technical curriculum with truth tables and quantified predicate logic and such (at least when a friendly discussion was happening, instead of a debate).
I generally think of “and” and “or” in the strict senses, but, by the same token, I get really annoyed when I use the word “or” (which, in English, is ambiguous about whether it is meant in the exclusive or inclusive sense) and people say “yes” or “true”.
People actually do that when not trying to be annoying? That’s surprising.
Yeah, I would say “both” or “yes, it could be either” depending on what I meant. I also use “and/or” whenever I mean the inclusive or, though that’s frowned on in formal writing.
That suggests another variant of the Linda problem: replace the “and” with “and also”, and leave the rest unchanged. If this makes a big difference, it would suggest that many of the people who fail on the Linda problem fail for linguistic reasons (they have the wrong meaning for the word “and”) rather than logical reasons.
Many subjects fail to recognize that when a 6-sided die with 4 green faces and 2 red faces will be rolled several times, betting on the occurrence of the sequence GRRRRRG is dominated by betting on the sequence RRRRRG, when the subject is given the option to bet on either at the same payoff. This (well, something similar, I didn’t bother to look up the actual sequences used) is cited as evidence that more is going on than subjects misunderstanding the meaning of “and” or “or”. Sure, some subjects just don’t use those words as the experimenters do, and perhaps this accounts for some of why “Linda” shows such a strong effect, but it is a very incomplete explanation of the effect.
Explanations of “Linda” based on linguistic misunderstandings, conversational maxims, etc., generally fail to explain other experiments that produce the same representativeness bias (though perhaps not as strongly) in contexts where there is no chance that the particular misunderstanding alleged could be present.
I would not say that this person replaced “and” by “or”. I guess they considered the statement “Lisa is a bank teller and a feminist” to be “50%” true if Lisa turns out to be a feminist but not a bank teller.
The formula used would be something like P(AB)=1/2*(P(A)+P(B))
Your idea that the subjects are not taking the question seriously is a good one.
I had a discussion with someone about a very similar real life ‘Linda’. It was finally resolved by realizing that the other person didn’t think of ‘and’ and ‘or’ as defined terms that always differed and was quite put out that I thought he should know that. To put it in ‘Linda’ terms: he know that Linda was a feminist and doubted that she was a teller. This being the case the ‘and’ should be thought of as an ‘or’ and b was more likely than a. Why would anyone think differently? It kind of blew my mind that I was being accused of being sloppy or illogical by using the fixed defined meaning for ‘and’ and ‘or’. I have since that time noticed that people actually often have this vagueness about logical terms.
I generally think of “and” and “or” in the strict senses, but, by the same token, I get really annoyed when I use the word “or” (which, in English, is ambiguous about whether it is meant in the exclusive or inclusive sense) and people say “yes” or “true”.
English already has words like “both” to answer in that question, which tells you in one syllable that the “exclusive or” reading is false but the “inclusive or” reading is true. This is not a standard part of symbolic logic curriculum, and is simply helpful rather than a sign of having taken such a class and learned a technical jargon that borrowed the word “or” to strictly mean “inclusive or”.
I’d never head of someone generously interpreting an “and” as an “or” (or vice versa) but it makes sense to me that it would be common and helpful in the absence of assumed exposure to a technical curriculum with truth tables and quantified predicate logic and such (at least when a friendly discussion was happening, instead of a debate).
People actually do that when not trying to be annoying? That’s surprising.
Yeah, I would say “both” or “yes, it could be either” depending on what I meant. I also use “and/or” whenever I mean the inclusive or, though that’s frowned on in formal writing.
That suggests another variant of the Linda problem: replace the “and” with “and also”, and leave the rest unchanged. If this makes a big difference, it would suggest that many of the people who fail on the Linda problem fail for linguistic reasons (they have the wrong meaning for the word “and”) rather than logical reasons.
Many subjects fail to recognize that when a 6-sided die with 4 green faces and 2 red faces will be rolled several times, betting on the occurrence of the sequence GRRRRRG is dominated by betting on the sequence RRRRRG, when the subject is given the option to bet on either at the same payoff. This (well, something similar, I didn’t bother to look up the actual sequences used) is cited as evidence that more is going on than subjects misunderstanding the meaning of “and” or “or”. Sure, some subjects just don’t use those words as the experimenters do, and perhaps this accounts for some of why “Linda” shows such a strong effect, but it is a very incomplete explanation of the effect.
Explanations of “Linda” based on linguistic misunderstandings, conversational maxims, etc., generally fail to explain other experiments that produce the same representativeness bias (though perhaps not as strongly) in contexts where there is no chance that the particular misunderstanding alleged could be present.
Good idea. At the next such situation, I’ll try that. Hopefully it will not be soon but you never know.
I would not say that this person replaced “and” by “or”.
I guess they considered the statement “Lisa is a bank teller and a feminist” to be “50%” true if Lisa turns out to be a feminist but not a bank teller.
The formula used would be something like P(AB)=1/2*(P(A)+P(B))