> I have to agree with Jack that the ice cream example is flawed. I think > the authors had in mind an argument that if (p -> q) and (q -> p) are > true, then p and q are logically equivalent. I don't see how that would > relate to modus ponens. The example is unfortunate. I wouldn't go as > far as Jack has and generalize that one should not take seriously > anything the authors have to say about proof. >
I guess I'm not nearly so tolerant. These folks represent themselves as experts, accept NSF finds and then speak as fools. Surely, Mr. Hirsch, who is listed as "Chair" of the 9-12 working group, must bear at least _some_ responsibility for the product. What about the fact that some one of those 6 people wrote this? Is this sort of thing standard for the Standards? What about the commission in charge of the whole thing? (Thomas A. Romberg, (Chair), Iris M. Carl, Christian R. Hirsch, F. Joe Crosswhite, Glenda Lappan, John A. Dossey, Dale Seymour, James D. Gates, Lynn A. Steen, Shirley M. Frye, Paul R. Trafton, Shirley A. Hill and Norman Webb.) While I may be wrong, I strongly suspect they _all_ of them had an opportunity to read the drafts and the final document and make comments. In fact, I would guess they were paid to do so. Do they share any responsibility here?
I see no way to put a good "spin" on this. Put the two groups together and ask which of the following is most likely true: (a) None of these folks know the meaning of converse. (b) Someone pointed it out but the person (or persons) in charge did not understand. (c) Those who know the meaning of converse took the NSF money but did not look over what was written. (d) _?_.
If a physician recommends that I have brain surgery to correct a knee problem, I assure you I will be skeptical of any other advise that person might give. I would not be able to consider this "unfortunate" or simply a "flaw" and conclude that it does not reflect on the physician's competence.