First-Order Logic and Social Contract Theory

[Animus]

So, I'm reading this book titled "Moral Psychology Volume 1: The Evolution of Morality, Adaptations and Innateness". I've come across some rather interesting data provided by Lida Cosmides and John Tooby.

First of all, the authors present a typical Wason Selection Task like the following:

You are shown a set of four cards placed on a table each of which has a number on one side and a colored patch on the other side. The visible faces of the cards show 3, 8, red and brown. Which card(s) should you turn over in order to test the truth of the proposition that if a card shows an even number on one face, then its opposite face is red? Wason selection task, http://en.wikipedia.org/w/index.php?tit ... =338009127 (last visited Jan. 21, 2010)

Using First-Order logic this problem is easily solvable. However, 70% to 95% of participants get this wrong. The task dissolves to a simple "If P Then Q" statement, all of the cards correspond to states of this first-order logical statement. The 3 card corresponds to Not-P, 8 card corresponds to P, Red card corresponds to Q, and the brown card corresponds to Not-Q. If you haven't figured it out, the correct answer is to turn over the card corresponding to P and the card corresponding to Not-Q. In this case the answer is [8] and [Brown].

Cosmides and Tooby suspected that using Social Contract Theory the correct answers could be obtained from most participants by rephrasing the selection task in the form of cheater detection. Consider the following example:

Teenagers who don't have their own cars usually end up borrowing their parent's cars. In return for the privilege of borrowing the car, the Carters have given their kids the rule,

"If you borrow my car, then you have to fill up the tank with gas."

Of course, teenagers are sometimes irresponsible. You are interested in seeing whether any of the Carter teenagers broke this rule.

The cards below represent four of the Carter teenagers. Each card represents one teenager. One side of the card tells whether or not a teenager has borrowed the parents' car on a particular day, and the other side tells whether or not that teenager filled up the tank with gas on that day.

Which of the following card(s) would you definitely need to turn over to see if any of these teenagers are breaking their parents' rule: "If you borrow my car, then you fill up the tank with gas." Don't turn over any more cards than are absolutely necessary.

[Borrowed Car] [Did not borrow car] [filled up tank with gas] [ did not fill up tank with gas]

- Moral Psychology by Walter Sinnot-Armstrong, p. 79, fig 2.2

In this latter case most people select P & Not-Q, the correct answers, however they are not selected for logical reasons. An illogical inference is made based on a reverse of the original statement "If you fill the tank up with gas, you can borrow my car." Reversing the original statement in First-Order Logic would be invalid, try this out with the first example.

"if a card shows an even number on one face, then its opposite face is red"
"if a card shows red on one face, then its opposite face is an even number"

The two statements aren't equivalent, and I had no idea that with typical social contracts one could get away with reversing the statements. To reverse the social contract about borrowing the car is to create a different rule, in that case there is a sense of entitlement that arises from filling the tank with gas. "Last time I borrowed the car I filled it with gas, so I am entitled to borrow it again.". Apparently this is normal thinking, its illogical in this case, but the answers given are the correct answers, whereas in the first case the correct answers are not given by the vast majority of participants.

Interesting insight into the operations of the human mind.

[IJesusChrist]

At first I really didn't find the first test that interesting - then I realized I had gotten it wrong.

Interesting that the mind correlates the two if P then Q & if Q then P as the equivalent, however in these cases they aren't.

In nature I wonder how often this type of statement is needed to be known though...

[David Quinn]

To me, the analysis is flawed in that the wording of the Watson test is contrived and ambiguous, and relies on the general population's lack of specialized training in formal logic. This confusion and ignorance is then manipulated by the researchers to reach the conclusions they want.

At best, all it proves is that most people don't need specialized skills in formal logic in dealing with their everyday life. It doesn't seem to have anything to say about human psychology in general, although it does reveal the psychology of the academics who like to conduct this kind of research.

On the flip side, one often meets academics who are proficient in formal logic, but can't reason to save themselves out in the larger world. Their logical skills, while good enough, perhaps, within the strict guidelines of the impersonal, trivial realm of academia, tend to diminish rapidly when faced with issues that are personal and too close to the bone.

Where is the research which investigates this rather remarkable phenomenon, I wonder?

-

[Jamesh]

I would have turned the red card over to confirm that RED-EVEN is consistent. We are geared to test reality by what we see repeated, not by logical analysis. We predict by seeing patterns, not comparing differences.

I think the instructions need to say a) there are no other colours and b) rephrase to "Which card(s) should you turn over in order to best test the truth of the propositions that"

Also, the references are EVEN-RED, it does not ask one to test any proposition relating to ODD-BROWN

So to me, even if I got it wrong, I’d still think I was correct to choose the EVEN-RED cards.

Mind you, for the following example it is far clearer as to what one is testing, and I'd imagine most would get this one right.

"David planted a lovely garden with flowers of every color. He has not been able to enjoy it, though, because deer from the forest nearby have been nibbling on his plants, killing some of them.

He would like to keep the deer out of his garden. His grandmother said that in the old days, she kept deer away by spraying an herbal tea -- lacana -- in her garden. She said:

"If you spray lacana tea on your flowers, deer will stay out of your yard."

This sounded dubious. So David convinced some of his neighbors to spray their flowers with lacana tea, to see what would happen. You are interested in seeing whether any of the results of this experiment violate Grandma's rule.

The cards below represent four yards near David's house. Each card represents one yard. One side of the card tells whether or not lacana tea was sprayed on the flowers in a yard, and the other side tells whether or not deer stayed out of that yard.

Which of the following cards would you definitely need to turn over to see if what happened in any of these yards violated Grandma's rule:

"If you spray lacana tea on your flowers, deer will stay out of your yard."

Don't turn over any more cards than are absolutely necessary.

sprayed with lacana tea
not sprayed with lacana tea
deer stayed away
deer did not stay away"

[Animus]

To me, the analysis is flawed in that the wording of the Watson test is contrived and ambiguous, and relies on the general population's lack of specialized training in formal logic. This confusion and ignorance is then manipulated by the researchers to reach the conclusions they want.

At best, all it proves is that most people don't need specialized skills in formal logic in dealing with their everyday life. It doesn't seem to have anything to say about human psychology in general, although it does reveal the psychology of the academics who like to conduct this kind of research.

Oh come on David, I know you have a bad taste for Academics, but I think you missed the point. The point was to see if regular people made logical inferences or arrived at their beliefs by other means. Some of it is ambiguous, as 50% of logicians get some Wason Selection tasks wrong, depending on how they are formulated. There is a lot more discussion in the chapters surrounding this than I was able to post. The issue was how people faired when the statements were presented differently.

It doesn't seem ambiguous to me and I had no problem selecting the correct answer. this is probably, as you say, the result of knowing what to look for. But that's precisely the point... most people don't know how to think about it logically.

[Animus]

I would have turned the red card over to confirm that RED-EVEN is consistent. We are geared to test reality by what we see repeated, not by logical analysis. We predict by seeing patterns, not comparing differences.

I think the instructions need to say a) there are no other colours and b) rephrase to "Which card(s) should you turn over in order to best test the truth of the propositions that"

Also, the references are EVEN-RED, it does not ask one to test any proposition relating to ODD-BROWN

So to me, even if I got it wrong, I’d still think I was correct to choose the EVEN-RED cards.

Mind you, for the following example it is far clearer as to what one is testing, and I'd imagine most would get this one right.

"David planted a lovely garden with flowers of every color. He has not been able to enjoy it, though, because deer from the forest nearby have been nibbling on his plants, killing some of them.

He would like to keep the deer out of his garden. His grandmother said that in the old days, she kept deer away by spraying an herbal tea -- lacana -- in her garden. She said:

"If you spray lacana tea on your flowers, deer will stay out of your yard."

This sounded dubious. So David convinced some of his neighbors to spray their flowers with lacana tea, to see what would happen. You are interested in seeing whether any of the results of this experiment violate Grandma's rule.

The cards below represent four yards near David's house. Each card represents one yard. One side of the card tells whether or not lacana tea was sprayed on the flowers in a yard, and the other side tells whether or not deer stayed out of that yard.

Which of the following cards would you definitely need to turn over to see if what happened in any of these yards violated Grandma's rule:

"If you spray lacana tea on your flowers, deer will stay out of your yard."

Don't turn over any more cards than are absolutely necessary.

sprayed with lacana tea
not sprayed with lacana tea
deer stayed away
deer did not stay away"

Your example is logically identical though.

[David Quinn]

To me, the analysis is flawed in that the wording of the Watson test is contrived and ambiguous, and relies on the general population's lack of specialized training in formal logic. This confusion and ignorance is then manipulated by the researchers to reach the conclusions they want.

At best, all it proves is that most people don't need specialized skills in formal logic in dealing with their everyday life. It doesn't seem to have anything to say about human psychology in general, although it does reveal the psychology of the academics who like to conduct this kind of research.

Oh come on David, I know you have a bad taste for Academics, but I think you missed the point. The point was to see if regular people made logical inferences or arrived at their beliefs by other means. Some of it is ambiguous, as 50% of logicians get some Wason Selection tasks wrong, depending on how they are formulated. There is a lot more discussion in the chapters surrounding this than I was able to post. The issue was how people faired when the statements were presented differently.

Fair enough.

It doesn't seem ambiguous to me and I had no problem selecting the correct answer. this is probably, as you say, the result of knowing what to look for. But that's precisely the point... most people don't know how to think about it logically.

To me, that particular test is very ambiguous, as the test question can be interpreted in at least three different ways, each of which leads to three different "correct" answers. So at best, the test only proves that most people are not able to guess which particular interpretation the researchers have in mind.

-

[Animus]

To me, the analysis is flawed in that the wording of the Watson test is contrived and ambiguous, and relies on the general population's lack of specialized training in formal logic. This confusion and ignorance is then manipulated by the researchers to reach the conclusions they want.

At best, all it proves is that most people don't need specialized skills in formal logic in dealing with their everyday life. It doesn't seem to have anything to say about human psychology in general, although it does reveal the psychology of the academics who like to conduct this kind of research.

Oh come on David, I know you have a bad taste for Academics, but I think you missed the point. The point was to see if regular people made logical inferences or arrived at their beliefs by other means. Some of it is ambiguous, as 50% of logicians get some Wason Selection tasks wrong, depending on how they are formulated. There is a lot more discussion in the chapters surrounding this than I was able to post. The issue was how people faired when the statements were presented differently.

Fair enough.

It doesn't seem ambiguous to me and I had no problem selecting the correct answer. this is probably, as you say, the result of knowing what to look for. But that's precisely the point... most people don't know how to think about it logically.

To me, that particular test is very ambiguous, as the test question can be interpreted in at least three different ways, each of which leads to three different "correct" answers. So at best, the test only proves that most people are not able to guess which particular interpretation the researchers have in mind.

-

Please expand on the different interpretations.

[Animus]

The correct interpretation is literal

if a card shows an even number on one face, then its opposite face is red

this is like saying all apples are fruits (but not all fruits are apples).

So in the example, the four cards [3][8][Red][Brown], the [8] satisfies the condition (P) while the [3] does not. Even if the [3] had [Red] on the other side, this wouldn't have any bearing on the rule. Its the equivalent of a banana belonging to our fruit family as well as apples. The [Red] card satisfies the original statement (Q) but whatever happens to be on the other side of it does not indicate whether or not the rule is correct. If it were our fruit example, one side could say [Fruit] and the other side could be a whole range of different things. We might find an [Apple] on the other side, but that won't tell us if all [Apple]s are on the flip-side of [Fruit]. The [Brown] card can tell us more about the rule because it has the potential of invalidating the rule if it happens to have an even number on the other side of it. In the fruit example it would be like [Apple] on one side versus [Vegetable] on the other.

In no apparent linguistic formulation would the Not-P and Q conditions need to be selected, unless the reverse of the original statement was assumed to be true. If the original statement were given as such

if a card shows an even number on one face, then its opposite face is red and if a card shows red on one face then its opposite will be an even number

then the other cards would become logically relevant.

The oddity that Tooby and Cosmides were pointing out was the in examples like the first involving numbers and colors people in general only selected the P condition, but when the task involved social contracts like the second rule the reverse of the statement was assumed and the Not-Q condition was selected. But if the reverse of the statement were actually true then all the conditions would be relevant to the rule.

For example, all apples are fruit and all fruit are apples; [Apple][Corn][Vegetable][Fruit]

In this case most people would select [Apple] and [Vegetable], but in fact all four cards are relevant to the rule. If [Corn] has [Fruit] on its flip-side then the latter half of the rule is nullified, likewise if [Fruit] has something besides [Apple] on its flip-side.

[IJesusChrist]

I have to say this is more of a 'you have to know what to look for'.

It's interesting in that we don't use this type of logic, i.e. this type of situation where p->q but not necessarily q->p.

This is taught in logic classes for a reason - it's not a common occurence in nature (I dont think?)

[Animus]

I have to say this is more of a 'you have to know what to look for'.

It's interesting in that we don't use this type of logic, i.e. this type of situation where p->q but not necessarily q->p.

This is taught in logic classes for a reason - it's not a common occurence in nature (I dont think?)

Actually, this logic applies to every determination of causal processes. The statement 'IF P then Q' is best understood as representing a sufficient causal conditional.

Consider this, you are riding in the passenger seat of a friend's car. Your friend is screaming down a highway marked at 80kmh, but your friend is doing 100Kmh and passing many of the other motorists on the highway. Your friend gets stuck behind two slower drivers doing the speed limit and exclaims "Fucking retards, move it!". Your friend has made a causal attribution, attributing the speed of the other drivers to them being "fucking retards". This can be formulated as; If the driver is a fucking retard, they will drive the speed limit. Is this necessarily true? Of course its not. In this case your friend has made a fundamental attribution error. If your friend was being serious he might look to different set of causal conditions; the driver is submissive to authority and only drives the posted limit, the driver has sophisticated knowledge of the mathematics of force and realizes that speed limits are chosen for good reason given the physical science involved, or any number of reasons besides the one given. Its not clear how the reason given is even a valid reason at all.

Then lets suppose your friend passes these slower drivers and continues his route down the highway. After some time passes another vehicle comes flying past you at 130kmh and your friend yells "Wow! What an asshole!" is it really likely to be the case that this other driver is an 'Asshole'. Couldn't it be the case that the is rushing to the hospital while reeling in agony from a gall stone, or maybe his wife in the passenger seat is going into labor. Is 'Asshole' even a sufficient condition? All assholes drive 130kmh on an 80kmh road? No of course not. your friend is just making the attributions based on his relative position. To the first two drivers he might be the 'asshole', to the latter driver he might be the 'fucking retard'. All of these attributions are egoic relational attributions and not causal attributions.

We are endlessly faced with making such attributions and by and large we get it wrong more than we get it right.

[Tomas]

I have to say this is more of a 'you have to know what to look for'.

It's interesting in that we don't use this type of logic, i.e. this type of situation where p->q but not necessarily q->p.

This is taught in logic classes for a reason - it's not a common occurence in nature (I dont think?)

Actually, this logic applies to every determination of causal processes. The statement 'IF P then Q' is best understood as representing a sufficient causal conditional.

Consider this, you are riding in the passenger seat of a friend's car. Your friend is screaming down a highway marked at 80kmh, but your friend is doing 100Kmh and passing many of the other motorists on the highway. Your friend gets stuck behind two slower drivers doing the speed limit and exclaims "Fucking retards, move it!". Your friend has made a causal attribution, attributing the speed of the other drivers to them being "fucking retards". This can be formulated as; If the driver is a fucking retard, they will drive the speed limit. Is this necessarily true? Of course its not. In this case your friend has made a fundamental attribution error. If your friend was being serious he might look to different set of causal conditions; the driver is submissive to authority and only drives the posted limit, the driver has sophisticated knowledge of the mathematics of force and realizes that speed limits are chosen for good reason given the physical science involved, or any number of reasons besides the one given. Its not clear how the reason given is even a valid reason at all.

Then lets suppose your friend passes these slower drivers and continues his route down the highway. After some time passes another vehicle comes flying past you at 130kmh and your friend yells "Wow! What an asshole!" is it really likely to be the case that this other driver is an 'Asshole'. Couldn't it be the case that the is rushing to the hospital while reeling in agony from a gall stone, or maybe his wife in the passenger seat is going into labor. Is 'Asshole' even a sufficient condition? All assholes drive 130kmh on an 80kmh road? No of course not. your friend is just making the attributions based on his relative position. To the first two drivers he might be the 'asshole', to the latter driver he might be the 'fucking retard'. All of these attributions are egoic relational attributions and not causal attributions.

We are endlessly faced with making such attributions and by and large we get it wrong more than we get it right.

Very good, Annie. You win a cookie.

[David Quinn]

To me, that particular test is very ambiguous, as the test question can be interpreted in at least three different ways, each of which leads to three different "correct" answers. So at best, the test only proves that most people are not able to guess which particular interpretation the researchers have in mind.

Please expand on the different interpretations.

1) The researcher's interpretation. 8 and brown to be overturned.

2) What I would call the "literal interpretation". "Which card(s) should you turn over in order to test the truth of the proposition that if a card shows an even number on one face, then its opposite face is red?" Only 8 to be overturned. The other three cards are irrelevant because at the commencement of the test they do not show an even number.

3) What I would call the "exact correspondence interpretation". The two statements, "If even number, then red" and "If red, then even number" are equivalent and interchangeable. The test proposition is that a card with an even number on one side will always have red on the other, and vice versa. Any or all cards to be overturned. Each card, at the commencement of the test, has the same potential to prove or disprove the proposition.

-

[IJesusChrist]

Animus, what eventually its coming down to is that in the world we live in, it is more often (hopefully) beneficial to make the assumption that 'If P then Q = Q then P' However this is not logical, it is (probably) the safer route in our world...

This is interesting though, or beginning to be anyway.

I'm pondering what this would affect in both the ancient world and the modern world with survival.

Lets say you go out in the woods. You come back and you tell everyone you ate a mushroom, and feel sick. Using If P then Q, if Q then P logic, we would deduce that if you are poisoned, then you ate a mushroom.

This doesn't sound beneficial at all!

Let's see this then - You go out and see cows grazing, and a baby cow drinking mother's milk, so you... erm... get some milk. You deduced that If you drink milk, you will feel good, so if you feel good, you have drank milk... or maybe... Hmmmm now I'm starting to see psychology come in atlast! I'll give this more thought.

[Animus]

To me, that particular test is very ambiguous, as the test question can be interpreted in at least three different ways, each of which leads to three different "correct" answers. So at best, the test only proves that most people are not able to guess which particular interpretation the researchers have in mind.

Please expand on the different interpretations.

1) The researcher's interpretation. 8 and brown to be overturned.

ok

2) What I would call the "literal interpretation". "Which card(s) should you turn over in order to test the truth of the proposition that if a card shows an even number on one face, then its opposite face is red?" Only 8 to be overturned. The other three cards are irrelevant because at the commencement of the test they do not show an even number.

I think the test assumes an elementary understanding of English grammar. It might be slightly biased in that regard. It was shown that when people were repeatedly explained what they should be looking for they eventually understood it ("Naturally"). Otherwise given the context, it seems pretty obvious that the task is to "test the truth of the proposition that ...". In which case its not specifying only to turn over cards that currently show an even face. Its actually quite difficult for me to see how it could be interpreted as you suggest. It strikes me as a failure to understand basic grammar or to adequately familiarize one's self with the task.

3) What I would call the "exact correspondence interpretation". The two statements, "If even number, then red" and "If red, then even number" are equivalent and interchangeable. The test proposition is that a card with an even number on one side will always have red on the other, and vice versa. Any or all cards to be overturned. Each card, at the commencement of the test, has the same potential to prove or disprove the proposition.

-

There is nothing in the statement to indicate exact correspondence, such a statement would properly be given as 'If a card shows either an even number or the color red, the opposite face will show the other" or something to that effect, specifying exact correspondence. But this last interpretation strikes at what Tooby and Cosmides theorize in Social Contract theory. To them if a statement is given as a social exchange, then it is interpreted as exactly corresponding. Yet, even in this case, people generally fail to select the correct cards, selecting P and Not-Q rather than all four.

With this kind of test there is always room to debate the exact use of grammar and language. But there is a reasonable expectation and an unreasonable expectation. There will always be people who misinterpret as a result of cultural differences, the way that is controlled for is usually by a reasonable offset of the data, or by controlled selection of participants. To be honest, I'm not up to speed on the precise methodology of their experiments. It is however reasonable to assume that their data is roughly accurate without knowing if they applied such controls. Unless they administered the task to non-English speaking Taiwanese children before breakfast or some other ludicrous sample.

[Animus]

Animus, what eventually its coming down to is that in the world we live in, it is more often (hopefully) beneficial to make the assumption that 'If P then Q = Q then P' However this is not logical, it is (probably) the safer route in our world...

This is interesting though, or beginning to be anyway.

I'm pondering what this would affect in both the ancient world and the modern world with survival.

Lets say you go out in the woods. You come back and you tell everyone you ate a mushroom, and feel sick. Using If P then Q, if Q then P logic, we would deduce that if you are poisoned, then you ate a mushroom.

This doesn't sound beneficial at all!

Let's see this then - You go out and see cows grazing, and a baby cow drinking mother's milk, so you... erm... get some milk. You deduced that If you drink milk, you will feel good, so if you feel good, you have drank milk... or maybe... Hmmmm now I'm starting to see psychology come in atlast! I'll give this more thought.

If everything was the same backward as it is forward it'd be a pretty messed up world indeed.

http://www.youtube.com/watch?v=Pq0iNKQJs_U

[Pincho Paxton]

Movies try to use the missing backwards interpretation as a sales tactic. Transformers 2 made loads of money at the box office, yet when asked about it, most people hate it. Box office takings are complicated, and have no message about how good a movie really is.

Mankind has so much technology, is mankind the evolution of the genius? Send the average man's child back in time to the Cavemen as a baby. Does this child re-invent everything? The child may not even come up with the wheel. Mankind is built from the minds of the many, and the genius few. It does not reverse to us having evolved a great deal.

[David Quinn]

I've thought of another interpretation:

4) What I would call the "scientific interpretation". The test is viewed more as a scientific exercise than a logical one. As far as scientific testing is concerned, the greater the sample of test operations, the more accurate the final result will be. Hence, 8, red, and brown to be overturned.

The problem with the researcher's interpretation is that if the brown card is turned over and reveals an odd number, then the card becomes irrelevant to the test. It voids itself out of the proceedings, which then leaves a sample of 1 - namely, the 8 card. The person with a scientific bent will view this as most unsatisfactory and will know that even if the 8 card turns over to be red, nothing can be proved with such a small sample. At least by turning over the red card, the sample will increase by one.

Of course, if he was strictly scientific, he would still find this sample far too small and would assert that the test itself is meaningless, as no conclusions can be drawn from such a small sample.

So now we have at least four differing interpretations of the one test, all of which are perfectly valid (in my opinion, at least), and thus it should come as no surprise that up to 90% of participants fail to perceive the "correct" answer, and up to 50% of logicians as well. Not necessarily because people lack logical skills, but because the test is poorly-conceived to begin with.

We all know that most people have poor logical skills, but really, there must be far better ways of measuring it than this.

-

[Animus]

I've thought of another interpretation:

4) What I would call the "scientific interpretation". The test is viewed more as a scientific exercise than a logical one. As far as scientific testing is concerned, the greater the sample of test operations, the more accurate the final result will be. Hence, 8, red, and brown to be overturned.

The problem with the researcher's interpretation is that if the brown card is turned over and reveals an odd number, then the card becomes irrelevant to the test. It voids itself out of the proceedings, which then leaves a sample of 1 - namely, the 8 card. The person with a scientific bent will view this as most unsatisfactory and will know that even if the 8 card turns over to be red, nothing can be proved with such a small sample. At least by turning over the red card, the sample will increase by one.

Of course, if he was strictly scientific, he would still find this sample far too small and would assert that the test itself is meaningless, as no conclusions can be drawn from such a small sample.

So now we have at least four differing interpretations of the one test, all of which are perfectly valid (in my opinion, at least), and thus it should come as no surprise that up to 90% of participants fail to perceive the "correct" answer, and up to 50% of logicians as well. Not necessarily because people lack logical skills, but because the test is poorly-conceived to begin with.

We all know that most people have poor logical skills, but really, there must be far better ways of measuring it than this.

-

I think there is still a misunderstanding between what we are talking about. The experiment is supposed to be ambiguous, because it's about real-world social interactions and how people think about them. If it was made out to be like a modern IQ test, it would be testing something besides social reasoning. When people were told what they should be looking for to get a logical answer they succeeded at doing it. But that's not how they would have interpreted it in a real social-interaction.

Honestly David, I don't think your fourth interpretation is valid. Scientific samples don't usually include irrelevant elements. If the Red card is not useful logically speaking, its not useful scientifically either. It might be useful for determining a different rule however. If we wanted to look for trends we'd have to include the entire set, but not just to test the rule given.