Misconception One: Many of our students are convinced that so-called psychics can successfully predict the future (usually at some cost to the persons wishing information on the future).

Misconception Two: Some philosophers of science have maintained that in assessing data as evidence for a theory, it makes no difference whether the data were known before or only after the theory had been created

Brief Account of the Effect: The teacher, brandishing a book by the historian and philosopher of science Charles Sanders Peirce, announces that a reading of this book has given the teacher psychic powers, i.e., the ability successfully to predict some events. When expressions of disbelief have subsided, the teacher offers to demonstrate this ability. From an ordinary box of playing cards, the teacher withdraws the deck and removes the four Jacks, placing them on a stand so that all can see. The Jacks are face up. The teacher informs the students that a volunteer is to select one of these four cards and that the teacher al-ready knows which card will be selected. The teacher then randomly recruits a student and asks the student to come forward. The teacher hands the student the teacher's ball point pen and invites the student to touch it to any one of the four Jacks. The teacher announces that he(she) already knows which Jack will be chosen. The student then touches, say, the Jack of Hearts. The teacher then asks the student to turn this card over. On the back, the student finds a handwritten message: "You will choose this card." Expression of awe and stunned wonderment soon give way to cat calls of the form: "All the cards say that. Turn the other three cards over." The teacher then turns over the other three Jacks, none of which contains a message! Shocked silence and increased interest follow. This enables the teacher either (a) to begin to charge large fees for psy-chic sessions, or (b) to engage the students in a discussion of how this works and what significances this may have.

Comment on the Successfulness of the Effect: I have tried this demonstration perhaps two dozen times, usually in classes but also at social gatherings of historians and philosophers of science. It has never failed to work, nor has anyone ever divined how it was done. As I recall, two of the HPS persons who witnessed this demonstration were Thomas Kuhn and Carl Hempel.

Class Discussion of the Effect (and Explication of How to Perform this Feat): Part One: The Method Revealed: Having thus attracted the students' attention, I tend to give in to their entreaties to explain how the trick works. What I do is to remove the Jack of Hearts, leaving three Jacks, and invite another student to come forward. That student takes the pen and touches it to one of the remaining Jacks, say, the Jack of Diamonds. The student is then invited to unscrew the ball point pen. In it the student finds a note stating: "You will pick the Jack of Diamonds." When further expressions of amazement have died down, I remove the Jack of Diamonds and invite a third student to come forward to touch a card. That student touches, say, the Jack of Spades. I then hand the student the Peirce volume, within which the student finds a note saying: "You will pick the Jack of Spades." Expressions of amazement, especially from brighter students, have usually subsided somewhat by this point. I proceed then immediately to remove the Jack of Spades and ask yet another student to come forward and to select a card. When that student touches the Jack of Clubs (which is, of course, the only remaining card), I inform the student that I knew this would be the card chosen and hand the student the card box, in which the student finds a note saying: "You will choose the Jack of Clubs." Most students have by this point divined my method and recognized that this psychicÕs powers would be severely constricted were I to be required to specify beforehand how I will indicate my foreknowledge as to which card will be touched! Perhaps also some have become slightly more skeptical of other persons claiming psychic powers.

Part Two A: Discussion of Psychic Powers This experience gives those students who lean toward believing in psychic powers some reason to be skeptical of persons making such claims. This can be reinforced in various ways, e.g., by noting that although various psychics have made correct predictions, this may simply be by chance. Most of their predictions are as faulty -- as the French say, even a stopped clock is right twice a day -- but the few that are correct attract undue attention. Or one can note that at times psychics succeed by making predictions so vague that they cannot but be true. Herodotus tells of a king who was informed by an oracle that if the king invaded a neighboring country, a great kingdom would fall. This prediction in fact turned out to be correct -- problem was that it was the king's own kingdom that fell.

Part Two B: Discussion of Whether Historical Factors Are Significant in Evaluating Scientific Theories. In his classic text Philosophy of Natural Science, the distinguished philosopher of science Carl Hempel discussed the question whether in evaluating the evidence for a theory, it makes any difference whether the empirical evidence was known before the theory was created or whether that evidence was predicted by the theory. Hempel's position seems to be that

from a logical point of view, the strength of the support that a hypothesis receives from a given body of data should depend only on what the hypothesis asserts and what the data are; the question of whether the hypothesis or the data were presented first, being a purely historical matter, should not count as affecting the confirmation of the hypothesis.[1]

Having for many years used Hempel's book in a course I taught and believing that although most claims made in that text deserve support, this was not one of them, I was anxious to find a way to challenge this position.

I received some help from reading a section of Charles Sanders Peirce's "Lessons from the History of Science." In a section discussing reasoning from samples, Peirce stressed that for inferences supported by samples, it is necessary not only that the samples be random, but also that the inferences to be tested be formulated before the sample is examined rather than being based on or drawn from the sample. To illustrate the necessity of his second requirement, Peirce constructed a sample consisting of five randomly selected items; in particular, he randomly chose five eminent historical figures and examined their birth and death dates. Peirce's data was as follows [2]:

From this sample, Peirce formulated five inferences, all of which are fully supported by the sample, and all of which are obviously wrong! In particular, the sample indicated:
(1) 75% of eminent men are born in years ending in 0.
(2) 75% of eminent men die in Autumn.
(3) 100% of eminent men die on a day of the month that is an integral multiple of 3.
(4) 100% of eminent men die in years (Y) with the following property: 2Y + 1 = N, where NÕs last digit is identical to the next to last digit of Y. Take, for example, 1594. Then 2¥1594 + 1 = 3189. The last digit of 3189 is 9, which is the same as the second digit of Y.
(5) "All eminent men who were living in any year ending in forty-four died at an age which after subtracting four becomes divisible by eleven. All others die at an age which increased by ten is divisible by eleven."[3]

The absurdity of these five inferences, despite the fact that the each is fully supported by the sample, suggests how important the historical order is. Had the investigator been required to formulate possible inferences before examining the sample, almost certainly none of these inferences would have come to mind. Note that the problem is not the size of the sample nor its randomness. A sufficiently ingenious investigator, presented with a sample of much larger size, might formulate further inferences, which would be not only well supported by the sample, but also patently wrong.

As all teachers know, however, it is one thing to have a logical argument; it is another to convince students of the force of the argument. This is where the card trick can work its magic. Students come to see that the trick works only because the presenter has not beforehand revealed how he or she will indicate foreknowledge.

Some Hints on How to Enhance the Effectiveness of the Demonstration and Discussion

• The most striking form in which to reveal the presenter's supposed foreknowledge is by having the note written on the back of the card. Consequently the effect will be enhanced by increasing the likelihood that this will happen. The way to do this is to mark one of the two middle cards. For some reason, students are suspicious of those on the ends and tend to choose one of the two middle cards.
• Magic stores sometimes sell oversized playing cards. These should be of use to teachers having large classes.
• Persons may find the effect enhanced by using cards marked with ESP symbols or by varying the four methods of revealing the item chosen. For example, one might prepare a note for any of the following: on the back wall or ceiling of the room, on a slide or overhead, in a sealed envelope lying on the desk, on a corner of the blackboard, on the back of a student paper, or some other location where it will become visible only when the presenter calls attention to it.
• One useful source I have found for methods of combating belief in psychics, astrologers, and such is the magazine Skeptical Inquirer. See also Joe Nickel, Barry Karr, and Tom Genoni (eds.), The Outer Edge: Classic Investigations of the Paranormal (Amherst, New York: Committee for the Scientific Investigation of Claims of the Paranormal, 1996).

Conclusion

As noted, this demonstration can be used either to call attention to the problematic character of claims made by psychics or to combat a well known claim about scientific method.

Notes
1. Carl G. Hempel, Philosophy of Natural Science (Englewood Cliffs, N.J.: Prentice-Hall, Inc., 1966), p. 38.
2. Charles Sanders Peirce, Essays in the Philosophy of Science, ed. by Vincent Tomas (Indianapolis: Bobbs-Merrill, 1957), p. 218.
3. Peirce, Essays, p. 219. Illustrations: Baring was alive in 1744, so he satisfies the first condition. He lived to the age 70, from which we subtract 4, which yields 66, which is divisible by 11. Custine fails to meet the first condition, but satisfies the claim because having lived 34 years, if we add 10 to 34, we get 44, which is divisible by 11.