[FOM] informal poll special terms in logic
hmflogic at gmail.com
Mon May 8 00:24:44 EDT 2017
> Reply with a vote to jbaldwin at uic.edu. Feel free to ignore some items.
> Do not reply to the list unless you really have something to say.
> I will summarize the results and perhaps kick of a discussion after I have tallied the results.
> Do you regard the following distinctions as `archaic' or `specialized' (i.e. only used by some areas of logic) or `unknown to you'?
> 1) pure versus applied logic
> 2) pure versus applied model theorem
> 3) recursive versus computable
> 4) valid sentence versus valid argument
> 5) Fratur N to name a structure rather Roman N
> John Baldwin
Very coincidentally, I think, I just contributed briefly to some
ongoing correspondence at mailing lists associated with the Ohio State
University mathematics community concerning related kinds of questions
for mathematics generally. I attach a copy of this very recent
correspondence. I have kept only my name on this correspondence
because the two other writers might not want this to be more public.
---------- Forwarded message ----------
From: Harvey Friedman <hmflogic at gmail.com>
Date: Sun, May 7, 2017 at 7:27 AM
Subject: Re: [Math-emeriti] "pure" mathematics and "impure" mathematics
In the legitimate and important movement to replace the term "pure
mathematics" with "theoretical mathematics", perhaps the use of
"theoretical physics" should be cited? Note that the physicists were
not so stupid as to fall into the trap of adopting the term "pure
So who now wants to draft a position paper on this for ultimate
presentation to the AMS, MAA, SIAM, and IMU (at least)? Perhaps key to
this movement is to get the Journals to refer to "theoretical
mathematics" and erase all their uses of "pure mathematics".
The physicists use "theoretical physics, experimental physics". Should
we go for "theoretic mathematics, experimental mathematics?" Probably
our applied math friends would not want to go there, and rather keep
"applied". Note that the physicists do use "applied physics", and that
has a somewhat different meaning than "experimental physics".
Harvey M. Friedman
On Sat, May 6, 2017 at 1:41 PM, xxx wrote:
> Dear xxx:
> You finish your end-of-the-year essay by:
> Therefore, it is to our advantage to substitute “theoretical” for “pure”
> in referring to abstract and rigorous mathematics.
> Let me draw your attention to the little known fact that mankind uses more
> than one language. For instance, I don't know if you ever heard of these, but
> there are languages called German and Russian.
> As far as I know, in Russian they use both words "теоретическая/theoretical"
> or "Чистая/clean/pure/unadulterated" see, e.g.,
> I personally never heard of any Russian using the "pure" word, only
> the "theoretical" one.
> If you ever meet a German person, maybe you can find out what Germans use.
> Wikipedia says:
> reine Mathematik, auch als theoretische Mathematik
> so German must also use both words.
> I asked a Hungarian and he told me that it is definitely
> "elm\'eleti/theoretical" in that exotic language; see
> It appears that the British are to be blamed for introducing the word "pure"
> to describe theoretical math; google "Sadleirian Chair".
> I wonder how many people, in addition to the Hungarians, are mathepolitically
> Sincerely, xxx
May 5, 2017
> Dear Colleague,
> This past semester I completed a poll among ten members of our academic community, five from our Mathematics Department and five from the outside. The latter included college councelors and a dean from one of our colleges. The poll consisted of having them answer the following question:
> “What is the first thing that comes to mind when you assess ‘pure’ mathematics?” The result produced the following off-the-cuff answers:
> 1. “it has no motivation in applications”
> 2. “it has no application, even though I understand it is beautiful” 3. (i) “lack of motivation;”, (ii) ”Who cares!”
> 4. (i) “lack of applications”; (ii) ”lack of people who care”
> 5. “don’t talk to the general public [about “pure” mathematics]” 6. “not useful”
> 7. “no practicality, no usefulness, no bearing on anything”
> 8. “beautiful, but does not care about applications”.
> 9. “implies mathematics is contaminated”
> 10. “is outside the context of the real world”
> The criticism implied by these answers is summarized bluntly by # 7: “pure” mathematics has “no practicality, no usefulness, no bearing on anything”. Conversely, mathematics which is practical and useful is viewed as “contaminated”, i.e. “impure”, because it is about the world.
> What the ten answers highlight is an error originated by Plato and promoted by seventeenth and eighteenth century philosophers. They claimed that there is a fundamental cleavage in knowledge, including quantitative knowledge; it divides mathematics into two mutually exclusive (and jointly exhaustive) types, “pure” and “impure”.
> Many, if not most, mathematicians by and large do not worry about the chaotic and dire cultural consequences of epistemic errors such as “pure” mathematics. They unwittingly embrace this error by simply equating “pure” mathematics to being abstract and logically rigorous and then by committing the other part of the same Platonic error: denigrating applications.
> However, both logical rigor and applications are crucial. Without the first, we cannot be certain that our statements are true; without the second, it does not matter whether or not they are true. The pure-impure dichotomy drives a wedge between the two. It is a breach between (a) the physical world (reality) and (b) conceptual and mathematical statements about it. This dichotomy presents the following Hobson’s choice: conceptual statements in terms of rigorous and non-trivial mathematics are “pure” and hence are disconnected from the world, while physically concrete observations about it that are formulated in terms of mathematical statements are “impure” and mathematically trivial at best. “Pure” mathematics is one of the symptoms of a philosophic auto-immune contageon, known in technical philosophy as the analytic-synthetic dichotomy1. It is a dogma according to which a “necessarily” true proposition cannot be factual, while a factual proposition cannot be “necessary”. This contageon latches itself onto the very base of the thinkers who embrace it. Indeed, it is an important historical fact that this dogma, which is devastating for science and mathematics2, has been at the root of the collapse of philosophy (during the past two centuries) into rank irrationalism3, a belief that reality and scientific theories are “social constructs” based on peer pressure, and that reason is not valid or useful.
> The “pure” mathematics terminology4, with its implied pure-impure dichotomy, serves only to introduce confusion, and should be abandoned. What is required in this context is the appreci- ation and the acquisition of the appropriate method of thinking, the means of forming concepts from concretes, of inductive reasoning5, the means of generalizing from the particulars to abstract principles.
> Therefore, it is to our advantage to substitute “theoretical” for “pure” in referring to abstract and rigorous mathematics.
> Sincerely, xxx
> 1https://campus.aynrand.org/works/1967/01/01/the-analytic-synthetic-dichotomy 2Page 75-77 in Explaining Postmodernism by Stephen R.C. Hicks.
> 3ibid. pp 78-83
> 4 “Theoretical Mathematics” would be a superior terminology. This is
> discussed in the “Preface” at
> 5THE LOGICAL LEAP: Induction in Physics by David Harriman https://people.math.osu.edu/gerlach.1/TheLogicalLeap/TheLogicalLeapReviewPhysTodayFinalVersionOct2010.pdf
SO - the above is the relevant correspondence to date from OSU.
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