About Prof. Mac Lane's Ph.D. Thesis
Dear all,
I have just finished translating S. Mac Lane's "Categories for the Working Mathematician" in Japanese and it will be published in June or July. However, my publisher (Springer-Verlag Tokyo) ask me to explain the title and short summary of his PhD thesis "Abbreviated Proofs in the Logical Calculus" in Japanese for his biographical note within a week. It is very old and I don't have enough time to explore it. Does anyone know information about it?
Best regards,
---- Hiroyuki Miyoshi Professor of Computer Science, Ph.D. Department of Computer Science, Kyoto Sangyo University Kyoto 603-8555, Japan +81-75-705-1463 (tel), +81-75-705-1640 (fax) hxm@cc.kyoto-su.ac.jp
18-May-2005 16:59:34 -0300,925;000000000000-0000000b
Dear all, I have just finished translating S. Mac Lane's "Categories for the Working Mathematician" in Japanese and it will be published in June or July. However, my publisher (Springer-Verlag Tokyo) ask me to explain the title and short summary of his PhD thesis "Abbreviated Proofs in the Logical Calculus" in Japanese for his biographical note within a week. It is very old and I don't have enough time to explore it. Does anyone know information about it? Best regards, ---- Hiroyuki Miyoshi Professor of Computer Science, Ph.D. Department of Computer Science, Kyoto Sangyo University Kyoto 603-8555, Japan +81-75-705-1463 (tel), +81-75-705-1640 (fax) hxm@cc.kyoto-su.ac.jp 18-May-2005 16:59:34 -0300,2527;000000000000-0000000a
I would say: In the dissertation Mac Lane tried to bring formal logic closer to mathematical practice. His specific device was to abbreviate certain commonly used sequences of steps into single steps. This did not turn out to be very useful and Mac Lane soon lost interest in it. The larger perspective, though, was to say that real proofs are not just any sequence of formally valid steps. He says real proofs are built around ``leading ideas.'' Mac Lane viewed his dissertation as a first step towards a ``structure theory'' of proofs that would recognize these leading ideas and use them to discover formally valid proofs. Throughout his career he believed that formal logic could help more with the actual discovery of proofs, if logicians would pay more attention to how actual proofs are used. ----- Original Message -----
Dear category theorists, I have received many replies to my previous message, to the list or directly to me. From Prof. Awodey's and Prof. McLarty's messages, I have understood that Prof. Mac Lane's thesis treated a foundational subject on the length of proofs in the context of the Hilbert Program, but he didn't continue this research. And Steve also suggested the recent obituaries more suitable for the source for his bibliographical note and told me that Saunders recently wrote a note about his own thesis, entitled "A late return to a thesis in logic." Prof. Johnstone informed me that it is available in his selected publication volumes. Mr. McGuire gave me an interesting suggestion on translation of the title of CWM. All of these comments are valuable for me. Thank you very much. Hiroyuki Miyoshi 27-May-2005 12:21:49 -0300,1613;000000000000-00000010
On Wed, 18 May 2005, Hiroyuki Miyoshi wrote:
Dear all,
I have just finished translating S. Mac Lane's "Categories for the Working Mathematician" in Japanese and it will be published in June or July. However, my publisher (Springer-Verlag Tokyo) ask me to explain the title and short summary of his PhD thesis "Abbreviated Proofs in the Logical Calculus" in Japanese for his biographical note within a week. It is very old and I don't have enough time to explore it. Does anyone know information about it?
The thesis is reprinted, together with a commentary in English by Mac Lane, in his Selected Papers published in 1979 by Springer-Verlag. Peter Johnstone 23-May-2005 19:32:11 -0300,1697;000000000000-0000000d
participants (3)
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Colin McLarty -
Hiroyuki Miyoshi -
Prof. Peter Johnstone