From: "Robert I. Soare" Sender: Computability Theory To: COMP-THY@LISTSERV.ND.EDU Date: Fri, 16 Jul 1999 19:12:33 -0500 ========================================================================= ****************** SECTION 5 ***************************** 7/16/99 CONCLUSION: The search for truth in scholarly and scientific disciplines calls for the most scrupulous methods, for careful logical support of our position, and full supporting evidence and open debate rather than closed door discussions. We should tolerate, even welcome, criticism and views contrary to our own, because only in full and open discussion can we test the validity of our hypotheses. Robert Maynard Hutchins, former president of the University of Chicago, and founder of the Great Books Program, wrote that we must be ever ready to test our ideas in the open forum of ideas, subjecting them to continual reexamination, and be ready to replace them by others if they are refuted. OPEN NOT CLOSED DEBATE: Harvey Friedman (FOM, July 15, 1999) apparently agrees with Hutchins when he argues that we discussion and criticism of areas of logic and the work of logicians should take place in open debate rather than "behind closed doors." I completely agree and will give some consequences of this principle. SETTING PRIORITIES: Suppose an invited speaker, and later self appointed "reviewer," at the AMS Boulder meeting in Boulder had had a "thesis" that "priority methods are almost completely absent from applied recursion theory." During the week long meeting he could have brought it up OPENLY with the roughly 60 participants since they included most of leading experts in computability in the world. He could have brought this up either in several of the lectures, in small groups, or privately experts on this question. Since this thesis is NOT a philosophical assertion, but is immediately provable or refutable from readily available FACTS, it could have been quickly answered by perhaps half of the participants, (as the Kucera application to Knight's question was settled). Instead the "reviewer" waited until he had returned home to his computer to advance it as fact to a relatively CLOSED forum of FOM subscribers, a list which contains few of the Boulder participants, and relatively few who were in a position to supply the information necessary to decide the issue. TOPOLOGY: Suppose the same "reviewer" at the same Boulder conference heard two lectures on announced connections between computability theory and differential topology, and had private conversations with the two lecturers who explained, for example, how computably enumerable sets and degrees are applied to measure the depth of local minima on a manifold. (It was made clear that this was an ANNOUNCED result only bacause the topologists had not written it up.) If in any doubt about the STATEMENT of the announced results, that "reviewer," anticipating his future writeup of the meeting, could have asked in the OPEN forum of the meeting or asked either lecturer what the correct statement was. Instead he returned to his computer and wrote to the CLOSED FORUM of his FOM list no statement of the announced results, which he said had not been backed up. The FOM list probably contained almost no one who could state the geometry results of the Nabutovsky-Weinberger paper 2, and thus who could have shed light on Simpson's misunderstanding. I think that Hutchins and probably Harvey would agree that in this case, discussion of this misunderstanding in the OPEN FORUM of the Boulder meeting would have been much better than its later presentation unclarified on the CLOSED FORUM OF FOM. THE FOM LIST: OPEN OR CLOSED? Of course, technically the FOM is open to all interested participants who qualify. However, there are many very knowledgeable people who do not subscribe for many reasons, personal, professional, ethical, practical, and otherwise. In the example above, it hardly seems fair to consider it the ONLY forum, or even the LEADING forum for discussion on issues of computability theory, when so few of the 60 prominent researchers at Boulder, or the roughly 150 on the comp-thy mailing list of Cholak, are also on the FOM list. Even if they were ALL on list, there is not equal access by all participants, because the moderator, Mr. Simpson can edit or omit the submissions if he chooses. This power alone (even if never exercised) may have an intimidating effect on people who want to make comments which may be unpopular with him. I do not imply any improper behavior on Simpson's part, just that in a debate in which he is involved, this gives him a advantage which would not be the case in an open debate at Boulder with 60 people in the same room all on equal footing. I am sure that these two incidents were simply oversights on Simpson's part and not intensional, but they illustrate the need for more open forums than FOM. UNFOUNDED ALLEGATIONS: When Hutchins said that we must have open criticism and debate, I do not think he intended to include unfounded allegations which have no logical basis or basis in evidence. Yet Harvey wrote (Jul 15): > "It makes the fields better because the criticism usually leads to an > invigorating new and related line of research. THIS IS TRUE EVEN IF THE > CRITICISM IS ILL INFORMED AND UNFRIENDLY." Surely Harvey MEANT that unfriendly, even severe, criticism is all right, but it must have some basis in fact and logic. Allegations which are entirely unfounded in logic and fact and which are continually repeated behind closed doors are aa great attraction for the untutored mind: 1. No effort is required to construct a logical analysis, or to search for supporting evidence. 2. It is comforting to repeat them to others in the same closed circle who will nod readily, and never ask for justification. 3. If repeated often enough, the allegation takes on a life of its own, and some people even accept if it they do not know the facts. On a social scale this has happened many times this century to certain groups on the basis is religious or racial prejudice, terrible human consequences. On a scientific scale it happened when the authorities condemned Galileo for his support of the Copernican theory, a judgement they did not reverse for 300 years, in spite of the evidence. On a smaller scale it goes on every day in our personal and scientific lives. I am sure that Harvey Friedman and Steve Simpson condemn unfounded careless allegation as much as I. We can begin by casting out false allegations, which have been repeated (perhaps accidentally) over years, and are clearly refuted. FALSE CLAIM: "priority methods are almost completely absent from applied recursion theory." ANSWER: (See above discussion.) FALSE CLAIM: Computably enumerable sets to not have many applications to other areas of mathematics. ANSWER: In addition to all the well known ones this is again refuted by the papers in "applications" and by many quotes in the Nabutovsky-Weinberger papers. FALSE CLAIM: Turing degrees are not useful in other areas of mathematics. ANSWER: Nabutovsky-Weinberger, "In order to space out our critical points suitably around Met(M), we will also vary the `seed' group in terms of degree of unsolvability." ---------------------------------------------------------------------------- Let us all examine our assumptions in open forums of discussion, with the greatest number of experts on the questions, and scrupulously test them. If they pass, let us proclaim them. If they fail, let us discard them and never more repeat them. ========================================================================= NOTE: If you have comments on any of these issues please send them to the UNIVERSITY OF CHIGAGO FOUNDATIONS OF MATHEMATCS MAILING LIST, UC-FOM list: soare@math.uchicgo.edu The wider the list of participants and email list the more open the discussion.