The Wason Selection Task, Part II
Before we sink our teeth even deeper into the Wason Selection Task, we should start by briefly reviewing conditional reasoning arguments.
Conditional reasoning generally starts with the statement "if P is true, then Q is true" or "if P, then Q" (P &rarr Q). For example, the statement "If this tree is a spruce (P), then it has needles (Q)" is a conditional statement.
There are four conditional reasoning arguments that apply to the Wason Selection Task—two of them valid and two of them invalid. Each of these introduces a different second statement. Thus, each can be identified according to the statement introduced right after the "if P, then Q" statement.
The rule given in any Wason Selection Task is considered to be a statement of the form "if P, then Q." So, the rule "every person that has an alcoholic drink is of legal age (21)" that I included in my previous post might be recast as "if alcoholic drink (P), then legal age (Q). Similarly, in the more formal version below, the rule "every card that has a D on one side has a 3 on the other" might be recast as "if D (P), then 3 (Q)."
Accordingly, each of the four answer choices in a Wason Selection Task is seen as the second statement in a conditional reasoning argument—either a statement about P (i.e., P is true [P] or P is not true [&sim P]) or a statement about Q (i.e., Q is true [Q] or Q is not true [&sim Q]).
In the "drinking" version of the selection task, for example, statements about drink type are the Ps and statements about age are the Qs:
The Ps and Qs for the more formal task would be assigned this way:
(Notice, by the way, how brilliant I was to include the html code for the tilda, "& sim," in the art, expecting it to be translated. Not one of my prouder blogging moments.)
Though the Wason Selection Task seems to be structured as a conditional reasoning task, it is not that straightforward. Participants are not asked to determine whether or not a conclusion is derived logically from statements. If that were the case, you would be shown the cards, given the "if P, then Q" statement, and simply asked, for each card, Is there a 3 on the other side? or Is there a D on the other side?
There is some evidence to suggest that people do fairly well on conditional reasoning tasks, but very poorly on the Wason Selection Task. I'll take up some interesting arguments as to why this is in Part III.
Wason Task: Part I | Part II | Part III | Part IV | Part V | Part VI
Conditional reasoning generally starts with the statement "if P is true, then Q is true" or "if P, then Q" (P &rarr Q). For example, the statement "If this tree is a spruce (P), then it has needles (Q)" is a conditional statement.
There are four conditional reasoning arguments that apply to the Wason Selection Task—two of them valid and two of them invalid. Each of these introduces a different second statement. Thus, each can be identified according to the statement introduced right after the "if P, then Q" statement.
Modus Ponens (P is true): This argument proceeds as follows: If P is true, then Q is true. P is indeed true. Therefore, Q is true. This is a valid form of reasoning. Example: If this tree is a spruce (P), then it has needles (Q). This tree is indeed a spruce (P). Therefore, this tree has needles (Q).It is important to note that the terms valid and invalid used to describe these arguments tell us nothing about the correctness of their conclusions. For example, each of these lines of reasoning is logically invalid . . .
Denying the Antecedent (P is not true): This is a fallacy and proceeds as follows: If P is true, then Q is true. P is not true. Therefore, Q is not true. Example: If this tree is a spruce (P), then it has needles (Q). This tree is not a spruce (not P). Therefore, this tree does not have needles (not Q).
Affirming the Consequent (Q is true): This is also a fallacy and proceeds as follows: If P is true, then Q is true. Q is indeed true. Therefore, P is true. Example: If this tree is a spruce (P), then it has needles (Q). This tree indeed has needles (Q). Therefore, this tree is a spruce (Q).
Modus Tollens (Q is not true): This argument proceeds as follows: If P is true, then Q is true. Q is not true. Therefore, P is not true. This is a valid form of reasoning. Example: If this tree is a spruce (P), then it has needles (Q). This tree does not have needles (not Q). Therefore, this tree is not a spruce (not P).
Affirming the Consequent: If today is June 1, then tomorrow is June 2. Tomorrow is indeed June 2. Therefore, today is June 1.. . . even though they are undeniably correct. Formal logic does not concern itself with the contents of arguments, only their form.
Denying the Antecedent: If today is June 1, then tomorrow is June 2. Today is not June 1. Therefore, tomorrow is not June 2.
The rule given in any Wason Selection Task is considered to be a statement of the form "if P, then Q." So, the rule "every person that has an alcoholic drink is of legal age (21)" that I included in my previous post might be recast as "if alcoholic drink (P), then legal age (Q). Similarly, in the more formal version below, the rule "every card that has a D on one side has a 3 on the other" might be recast as "if D (P), then 3 (Q)."
Accordingly, each of the four answer choices in a Wason Selection Task is seen as the second statement in a conditional reasoning argument—either a statement about P (i.e., P is true [P] or P is not true [&sim P]) or a statement about Q (i.e., Q is true [Q] or Q is not true [&sim Q]).
In the "drinking" version of the selection task, for example, statements about drink type are the Ps and statements about age are the Qs:
The Ps and Qs for the more formal task would be assigned this way:
(Notice, by the way, how brilliant I was to include the html code for the tilda, "& sim," in the art, expecting it to be translated. Not one of my prouder blogging moments.)
Though the Wason Selection Task seems to be structured as a conditional reasoning task, it is not that straightforward. Participants are not asked to determine whether or not a conclusion is derived logically from statements. If that were the case, you would be shown the cards, given the "if P, then Q" statement, and simply asked, for each card, Is there a 3 on the other side? or Is there a D on the other side?
There is some evidence to suggest that people do fairly well on conditional reasoning tasks, but very poorly on the Wason Selection Task. I'll take up some interesting arguments as to why this is in Part III.
Wason Task: Part I | Part II | Part III | Part IV | Part V | Part VI
Labels: education, mathematics, research