Mathematical Logic & Foundations Chart (w/ further updates)

Mathematical Logic & Foundations Chart (w/ further updates)

The above photo is a detail from a large, hand drawn chart entitled “Mathematical Logic and Foundations, 1847-1947.” It was made in 1976 by Joel Friedman (I believe this Joel Friedman, emeritus at UC Davis). A print of it has been hanging up in the University of South Carolina Department of Philosophy for as long as anyone here can remember. I do not know whether it was widely distributed or how many copies still exist. I photographed it (two photos, stitched together, owing to the size and detail), and you can view the whole thing here.

UPDATE (10/29/14): Dana Tulodziecki (Purdue) writes in: “I saw your post about the Math Logic poster and thought the two attached letters might be of interest to you.  They were found in Ted Ulrich’s old office (now mine).” And what she attached was a letter that Joel Friedman, the chart’s creator, sent along with copies of the chart, and an accompanying note from— wait hold on a sec, I just got an email—

Well, tollens my ponens will you look at that, it’s an email from Joel Friedman! Just as I am typing this update! Seriously! I had written him the other day but hadn’t heard back yet. Let’s see what he has to say…

“Yes, I am the author of the ML Chart you have posted.” Check.

“Apparently your website is so popular that four of my own UCD Philosophy colleagues emailed me about it afterwards.” [Blushing.]

” I have about 20 copies left.” A few folks contacted me about wanting to purchase copies; now’s your chance! (Contact Friedman, not me.)

Was it ever published?

At the very beginning, I tried to get my Chart published by a number of publishing companies, but alas, they all concluded it would not be cost effective.  Even Prometheus Publishers, after doing a marketing analysis, concluded they couldn’t make it cost effective, even though they liked the Chart very much.  Perhaps this problem can now be overcome.  I don’t know.  In any case, I copyrighted this Chart and self-published it long ago.

And now for the chart’s background and creation:

I finished my doctoral dissertation at UCLA in 1966, in logic and foundations of set theory, providing a new theory, called STC (“the set theory of proper classes”), which turned out to be stronger than the von Neumann/Bernays/Goedel theory of sets and proper classes.  (For example, Tarski’s Axiom of Strongly Inaccessible Cardinals can be derived in my STC.)  My doctoral supervisor was the prominent logician and philosopher of mathematics, Abraham Robinson.  He was a real prince of a man, as well as a great mathematical logician.  From 1966 to 1971, logic and foundations was my exclusive field of research, and I was hired at UC Davis in 1967 to teach various courses in this area.  After 1971, I branched out into other areas of philosophy, over the decades, primarily philosophy of mathematics and science, metaphysics, philosophy of mind, and early modern philosophy (Descartes, Spinoza, and Leibniz).  Over the last 15 years, during my retirement, I have focused my research primarily in modal logic and philosophy of mathematics and science, developing a new philosophy called Modal Platonism (MP), first begun when I was a Visiting Fellow at Princeton University (1998-99), working with Bas van Fraassen.  I can tell you this MP project is still thrilling to me.  Lately during the last several years, I’ve been consulting about MP, with my old teacher/mentor at UCLA, David Kaplan, who was also on my doctoral committee with Robinson.  Altogether van Fraassen, Otávio Bueno, Kaplan, and Bernard Molyneux (a UCD colleague) have been most instrumental in spurring me on to the completion of this project.  My latest draft paper is called: “Modal Platonism is a Threat to Platonism”.

Anyways, logic and foundations has remained my passion periodically, in one form or another, especially since 1965, nearly 50 years ago, when I began working on my dissertation under Robinson. But at some point, around 1975, I got the idea of making an ML chart while living in San Francisco for the summer.  The idea was to make a chart of the greatest mathematical logicians (including mathematical foundationalists), during the Golden Age of ML, from 1847 to 1947, listing their main technical results inside the “bubbles” under their names.   What is unique about my Chart is that you can estimate the importance of each great mathematical logician by the size of the bubble containing his/her results.   Note that De Morgan and Boole are giants in the Chart, because they are first, but the real giants are Frege, Cantor, Russell, Hilbert, Post, Skolem, Tarski, von Neumann, and Goedel, at least according to the bubbles in the Chart.  After writing up a final draft of my Chart, in my own poor handwriting, I hired a philosophy graduate student, Christina Waters [here?], to write up this same final draft using her wonderful penmanship in India ink.  I then had the first hundred copies printed by a professional, using his Heidelberg Press.  In its day, that was a high-tech machine.

Professor Friedman seems pleased that his chart has been given a “new life.” Pretty neat! Anyway, where was I? Oh yes, apart from the aforementioned letter from Friedman (which the above excerpts from his email render largely superfluous) there was an accompanying note from a fan of the chart:


logic poster letter from Quine pic copy


Thanks to Dana Tulodziecki for sending this along, and to Joel Friedman for filling us in on the story of his wonderful chart.

UPDATE 2 (10/31/14): Josef Kay (UC Davis) comments below: “Joel Friedman and I are meeting tomorrow to discuss the possibility of making the chart available as a print for online order. David Goldman has recommended looking into as a means of selling prints, which seems like it might be a good choice. If anyone else has any advice or recommendations for how to go about doing this (e.g. if there is a better alternative website), I’d appreciate the input. I’ll report the outcome to this blog.”

UPDATE 3 (10/31/14): Friedman sent Christian Koons (Bowling Green) a photo of a photocopy of his diagram of Spinoza’s Ethics, which he passed on to me—thanks, Christian!—and which I post below. If anyone wants to send a higher res version along, I can post that, as well.

Friedman Spinoza Chart

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