A mathematician's lament

Well, Lockhart  explains it very well indeed...

Ada Lovelace Day 2011: Christine Ladd-Franklin

Posting about women in mathematics, a reminder from Ada Lovelace Day...

From Algebraic Logic to Optics and Psychology

By hook and by crook Christine Ladd managed to attend graduate courses in mathematics at Johns Hopkins University despite the fact that the university was not open to women. Jacob describes how she managed to do that:

[T]he university first announced its fellowship program in 1876, and one of the first applications to arrive was one signed "C. Ladd." The credentials accompanying the application indicated such outstanding ability that a fellowship in mathematics was awarded to the applicant, site unseen, and was accepted. When it was discovered that the "C." stood for Christine, several embarrassed trustees argued she had used trickery to gain admission, and the board immediately moved to revoke the offer. They failed to reckon, however, with the irascible Professor James J. Sylvester, stellar member of the first faculty. In 1870 Sylvester had been named the world's greatest living mathematician by the Encyclopedia Britannica, and his presence at Hopkins was a real coup for the struggling university. He was indispensable and knew it, in an ideal position to insist on virtually anything he wanted; in this case, he had read Christine Ladd's articles in English mathematical journals, and he insisted upon receiving the obviously gifted young woman as his student. Miss Ladd was admitted as a full-time graduate student in the fall of 1878. Though she held a fellowship for three years, the trustees forbade that her name be printed in circulars with those of other fellows, for fear of setting a precedent. Dissension over her continued presence forced one of the original trustees to resign.

From http://www.agnesscott.edu/lriddle/women/ladd.htm

Louise Hay: Roles Models in Logic...

Louise Hay: 1935-1989, Robert I. Soare. Association for Women
in Mathematics Newsletter 20:1 (January-February 1990) 3-4.


The life and work of logician Louise Hay are described in this article.
Born in France in 1935, she came to America in 1946 and received a B.A. from Swarthmore College and her M.A. and Ph.D. from Cornell University.

Her doctoral dissertation dealt with recursive function theory. Initially on the faculty at Mount Holyoke College, she moved to the University of Illinois at Chicago in 1968 where she combined an active research career with teaching and administrative work. She succumbed to cancer in 1989.
Her research dealt with index sets connected with recursively enumerable sets
as well as with computational complexity theory. She was very influential in
encouraging women to pursue mathematical careers.

Apparently the Logic Seminar in Chicago is called the Louise Hay Seminar, if I'm not imagining things..

Problems and materials...

(photo the Spanish Stonehenge--Dolmen of Guadalperal, uncovered by the drought 2022)
 

 

I've discussed so far with the classes:

Andrew Abbott's `Aims of Education'

the future of Philosophy, either via Ken Taylor post or Jung's article and

Wigner's `The Unreasonable Effectiveness of Mathematics in the Natural Sciences'. There is also Hamming's ``The Unreasonable Effectiveness of Mathematics" and perhaps the unreasonable effectiveness of data might be mentioned...

The unusual effectiveness of logic in CS is also good, but doesn't pack the same punch. (And the contrarian `The unreasonale effectiveness of data' is another nail in a perforated coffin, added much later, Sept 2015.)


There are questions that I did not find a good source like `what is a reasonable classification of the sub-areas of philosophy?' Mind you I also have not found one about the sub-areas of logic: I'm told that the classification into proof theory, model theory, recursion theory and set theory was Sack's, but I don't know where he did it...

Anyway I want to keep here a list of other questions and other articles that I think are cool enough to try to force the students to read. Must re-check the Canon of Tech, they had some good suggestions, like Vannevar Bush's `As we may think' article.

Phil50 First lecture

NEW (03/31/11): Since I now believe the course is set up in SUNET's CourseWork, I will stop posting materials here. Email me if you have problems.

Here are the slides, the questionnaire (for Friday) and the first real assignment.

PHIL50 Basics, for the time being...

Stanford University, Spring 2011
PHIL50 Introduction to Logic

Professor: Valeria de Paiva (PhD Cantab)
Email: valeria.depaiva@gmail.com
Lectures: MW 10:00-10:50 Room 206 EDUC
BOOK: Language, Proof and Logic,
John Barwise, John Etchemendy
University of Chicago Press
ISBN 157586374X


WARN­ING! Do not buy a used copy of the text! The copy of the soft­ware that comes with the book can only be reg­istered once. If you can­not reg­is­ter the soft­ware, you can­not sub­mit so­lu­tions to home­work ex­er­cises of take-home exam prob­lems or have the cor­rect­ness of your so­lu­tions au­to­mat­i­cally checked for you prior to sub­mit­ting them.

HOME­WORK/QUIZZES: Each week, there will be ei­ther a home­work as­sign­ment due or a quiz. In ad­di­tion, there will be a midterm exam and a final exam. Each exam will con­sist of an (open-book, open-notes) take-home part and a (closed-book, closed-notes) in-class part.

TOP­ICS TO BE COV­ERED:

1. Why logic? Computational thinking for philosophers? (1 lec­ture):

2. Propo­si­tional Log­ics (approx 10 lec­tures):
• The syn­tax and se­man­tics of propo­si­tional log­ics
• The log­i­cal con­nec­tives.
• Build­ing truth ta­bles to test for­mal va­lid­ity, both "by hand" and using Boole.
. The dis­tinc­tion be­tween im­pli­ca­tion and im­pli­ca­ture
. "Fitch" and formal proofs.

3. First-Or­der Log­ics (approx 10 lec­tures):
• The syn­tax and se­man­tics of first-or­der log­ics
• Ex­press­ing your­self in first-or­der log­ics
• Build­ing struc­tures to demon­strate for­mal in­va­lid­ity, by hand and using Tarski's World
• Con­struct­ing for­mal de­duc­tions to demon­strate for­mal va­lid­ity, by hand and using Fitch


4. Modal Propo­si­tional Log­ics (3 lec­tures):
• Deontic, epistemic, tem­po­ral, dy­namic, and gen­eral modal propo­si­tional log­ics

5. Wrap-up (1 lec­ture):
• Spe­cial em­pha­sis on the ques­tion of how much sup­port a for­mal de­riva­tion of a propo­si­tion pro­vides for be­liev­ing it to be true

COEN260 Basics

Santa Clara University, Spring 2011
COEN 260 Truth Deduction and Computation

Professor: Valeria de Paiva (PhD Cantab)
Email: valeria.depaiva@gmail.com
Lectures: MW 7:10-9:00 Room 106 Bannan
BOOK: Language, Proof and Logic,
John Barwise, John Etchemendy
University of Chicago Press
ISBN 157586374X


Cat­a­log De­scrip­tion: In­tro­duc­tion to math­e­mat­i­cal logic and se­man­tics of lan­guages for the com­puter sci­en­tist. In­ves­ti­ga­tion of the re­la­tion­ships among what is true, what can be proved, and what can be com­puted in the for­mal lan­guages for propo­si­tional logic, first order pred­i­cate logic, el­e­men­tary num­ber the­ory, and the type-free and typed lambda cal­cu­lus. Pre­req­ui­site: COEN 19 or AMTH 240 and COEN 70. (4 units)

WARN­ING NOTE ON BOOK: WARN­ING! Do not buy a used copy of the text! The copy of the soft­ware that comes with the book can only be reg­isted once. If you can­not reg­is­ter the soft­ware, you can­not sub­mit so­lu­tions to home­work ex­er­cises of take-home exam prob­lems or have the cor­rect­ness of your so­lu­tions au­to­mat­i­cally checked for you prior to sub­mit­ting them.

HOME­WORK/QUIZZES: Each week, there will be ei­ther a home­work as­sign­ment due or a quiz. In ad­di­tion, there will be a midterm exam and a final exam. Each exam will con­sist of an (open-book, open-notes) take-home part and a (closed-book, closed-notes) in-class part.

TOP­ICS TO BE COV­ERED:

1. What is Computational Thinking? How does logic fit into it? (1 lec­ture):

2. Propo­si­tional Log­ics (7 lec­tures):
• The syn­tax and se­man­tics of propo­si­tional log­ics
• The log­i­cal con­nec­tives.
• Build­ing truth ta­bles to test for­mal va­lid­ity, both "by hand" and using Boole.
. The dis­tinc­tion be­tween im­pli­ca­tion and im­pli­ca­ture
. "Fitch" and formal proofs.

3. First-Or­der Log­ics (7 lec­tures):
• The syn­tax and se­man­tics of first-or­der log­ics
• Ex­press­ing your­self in first-or­der log­ics
• Build­ing struc­tures to demon­strate for­mal in­va­lid­ity, by hand and using Tarski's World
• Con­struct­ing for­mal de­duc­tions to demon­strate for­mal va­lid­ity, by hand and using Fitch

4. Lambda-Calculus (3 lec­tures):
• The syn­tax and se­man­tics of lambda-calculus, typed and untyped. Curry-Howard isomorphism.
• A quick look at some real-world tools for ap­ply­ing higher-or­der log­ics to soft­ware en­gi­neer­ing prob­lems

5. Modal Propo­si­tional Log­ics (1 lec­ture):
• The syn­tax and se­man­tics of tem­po­ral, dy­namic, and gen­eral modal propo­si­tional log­ics

6. Wrap-up (1 lec­ture):
• Spe­cial em­pha­sis on the ques­tion of how much sup­port a for­mal de­riva­tion of a propo­si­tion pro­vides for be­liev­ing it to be true