Timeline for What are some mathematical concepts that were (pretty much) created from scratch and do not owe a debt to previous work?
Current License: CC BY-SA 2.5
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| Jul 31, 2011 at 0:54 | comment | added | Todd Trimble | By the way, there is some interesting commentary on the matter here (see especially the quotation of Hilary Putnam): en.wikipedia.org/wiki/Ernst_Schr%C3%B6der#Influence | |
| Jul 31, 2011 at 0:04 | comment | added | Todd Trimble | What I had in mind when I wrote that was that Boole and others paved the way for the realization that logic could be mathematicized. My understanding is that Boole's work shows how propositional logic can be represented in symbolic, algebraic form. Subsequently, others like E. Schroeder and C.S. Peirce had pushed the algebraization of relational calculus quite far (including of course relational composition, closely tied to quantification). Frege in fact knew of this work but was somewhat dismissive. Anyway, pursuit of the analogies between algebra and FOL was quite vigorous before Frege. | |
| Jun 13, 2011 at 2:33 | comment | added | Jacques Carette | @Todd: have you read Boole's actual work on logic, and compared it to what Frege wrote? [I have recently read a number of papers by both.] They are really quite different. Frege's work is infused with a lot of philosophy and deep 'foundational' thinking about all of mathematics. Boole's work is fantastic, but in a different direction. | |
| Jun 12, 2011 at 12:27 | comment | added | Todd Trimble | I strongly disagree with the assessment of Frege; plenty of others helped pave the way, including for example Boole. I am a little skeptical of surreal numbers as well. | |
| May 26, 2010 at 18:59 | history | answered | Gil Kalai | CC BY-SA 2.5 |