FOM: "profound changes"

Moshe' Machover moshe.machover at
Wed Aug 12 16:55:53 EDT 1998

At 2:24 am +0100 12/8/98, Harvey Friedman wrote, inter alia:

>And just to indicate that what I am
>concerned about has nothing whatsoever to do specifically with recursion
>theorists or recrusion theory, let me generalize about the pattern that I
>have witnessed in other subareas of mathematical logic. I suspect that it
>occurs in other areas of mathematics as well.

>From personal experience I can confirm that it certainly does. HF's
assessment in the paragraphs which follow are an uncannily accurate
description of the situation I found in the area of the measurement of
voting power (a sub-area of social choice, aka public choice) in which I
have been working for a number of years and which is quite remote from
logic. In fact, the situation here is if anything worse, because it is an
applied subject. So many people do a lot of empirical or semi-empirical
work, `applying' the mathematics to real-life situations as though they
were using cooking recipes, without giving a thought to `higher
intellectual goals ... for instance, the reasons why these
basic structures were defined in the first place - and the strengths and
weaknesses of these basic structures for the purposes they were created

>People in the field realize that some basic structures are hard to analyze,
>and that if one works hard enough, one can start to get some structural
>information. At some point, initial breakthroughs in this vein are made by
>some people, which creates a stir. These people become the opinion makers
>of the field, and have students extending their results. Then research in
>the field starts getting evaluated more and more by what structural
>information it reveals about these basic structures, and less and less by
>any higher intellectual goals.
>By higher intellectual goals, I mean, for instance, the reasons why these
>basic structures were defined in the first place - and the strengths and
>weaknesses of these basic structures for the purposes they were created
>for. The field starts getting redefined in terms of the structural analysis
>of these particular basic structures. Other issues that were predominant -
>perhaps at an informal level only - in the early stages of the subject,
>become downplayed, or even marginalized.
>In late stages of this process, researchers start to forget what any of
>these higher intellectual goals are or were ever conceived to be.
>Eventually, the students no longer come into contact in any substantial way
>with any higher intellectual goals.
>Before going any further, let me indicate how this is manifested in
>practice. Some people will do research that doesn't fall into this focused
>mode. In some cases their research deals directly with the higher
>intellectual goals - at least more directly than the focused structural
>studies that dominate the field. But they find that their careers are
>seriously restricted compared to people working on the focused structural
>studies. They find that the major places of employment are populated mainly
>by the people who made the initial breakthroughs in the focused structural
>studies, and their students, and the students of their students, etcetera,
>who have become accustomed to automatically evaluating research in terms of
>the focused structual studies. In a tight labor market, these people (doing
>research that doesn't fall into the focused mode) may even become
>In any case, the distinction between the careers of those who concentrate
>on the focused structural studies and those who don't becomes well known
>and reinforces itself.
>Another strong factor in the equation is the peer review method of awarding
>grants. When money is tight, mixed reviews will generally kill funding.
>Reviewers will naturally reserve their high praise for work that is very
>much like theirs; high praise for work very much like theirs is essentially
>the same as high praise for their own work. Consideration of higher
>intellectual goals could make such a system fairer. But consideration of
>higher intellectual goals becomes so remote a consideration that it plays
>essentially no role. The difficulties involved in getting funding for
>virtually anything outside the focused structural studies become
>insurmountable for almost anyone.

I am sure this is the situation in quite a number of areas!

  %%  Moshe' Machover                 | E-MAIL: moshe.machover at %%
  %%  Department of Philosophy        | FAX (office)*: +44 171 873 2270  %%
  %%  King's College, London          | PHONE (home)*: +44 181 969 5356  %%
  %%  Strand                          |                                  %%
  %%  London WC2R 2LS                 |  * If calling from UK, replace   %%
  %%  England                         |    +44 by 0                      %%

More information about the FOM mailing list