[math-fun] "Pushing" and "popping" for deductions about inter-referential sentences
I just realized (painfully close to my deadline) that my essay on self-referential sentences could really benefit from a terminological distinction that I may have to coin. It's the distinction between Deduction style #1: If P says "Q is true", and P is true, then Q is true. and Deduction style #2: If P says "Q is true", and Q is true, then P is true. I'm tempted to call them "pushing" and "popping", respectively. And now that I think about it, I'm wondering whether Hofstadter used exactly this nomenclature in "Godel, Escher, Bach". I can't decide whether it's merely the sort of thing Hofstadter would do, or something he actually did! And I can't seem to locate my copy of GEB. Can someone with a handy copy look up "push" and "pop" in the index? Thanks, Jim Propp
Look up the book on amazon and click on "look inside". You will be able to search for words in the book. I'm not sure just how much of the book is searched. Also you can see the book's index which idoes include "pushing" and "popping". You can also use the Search Inside This Book feature to search for these words to get some context. I found this easier than looking for my copy of GEB. On Tue, Nov 15, 2016 at 11:17 PM, James Propp <jamespropp@gmail.com> wrote:
I just realized (painfully close to my deadline) that my essay on self-referential sentences could really benefit from a terminological distinction that I may have to coin.
It's the distinction between
Deduction style #1: If P says "Q is true", and P is true, then Q is true.
and
Deduction style #2: If P says "Q is true", and Q is true, then P is true.
I'm tempted to call them "pushing" and "popping", respectively. And now that I think about it, I'm wondering whether Hofstadter used exactly this nomenclature in "Godel, Escher, Bach". I can't decide whether it's merely the sort of thing Hofstadter would do, or something he actually did! And I can't seem to locate my copy of GEB. Can someone with a handy copy look up "push" and "pop" in the index?
Thanks,
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Hofstadter's use of "push" and "pop" was not, I think, the one Jim is proposing. In Hofstadter's use, "push" means "temporarily assume that P is true", and "pop" means "stop assuming that P is true". On Wed, Nov 16, 2016 at 5:03 AM, W. Edwin Clark <wclark@mail.usf.edu> wrote:
Look up the book on amazon and click on "look inside". You will be able to search for words in the book. I'm not sure just how much of the book is searched. Also you can see the book's index which idoes include "pushing" and "popping". You can also use the Search Inside This Book feature to search for these words to get some context. I found this easier than looking for my copy of GEB.
On Tue, Nov 15, 2016 at 11:17 PM, James Propp <jamespropp@gmail.com> wrote:
I just realized (painfully close to my deadline) that my essay on self-referential sentences could really benefit from a terminological distinction that I may have to coin.
It's the distinction between
Deduction style #1: If P says "Q is true", and P is true, then Q is true.
and
Deduction style #2: If P says "Q is true", and Q is true, then P is true.
I'm tempted to call them "pushing" and "popping", respectively. And now that I think about it, I'm wondering whether Hofstadter used exactly this nomenclature in "Godel, Escher, Bach". I can't decide whether it's merely the sort of thing Hofstadter would do, or something he actually did! And I can't seem to locate my copy of GEB. Can someone with a handy copy look up "push" and "pop" in the index?
Thanks,
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Yes, that sounds right. And the web confirms it. Thanks! Jim Propp On Wed, Nov 16, 2016 at 10:39 AM, Allan Wechsler <acwacw@gmail.com> wrote:
Hofstadter's use of "push" and "pop" was not, I think, the one Jim is proposing. In Hofstadter's use, "push" means "temporarily assume that P is true", and "pop" means "stop assuming that P is true".
On Wed, Nov 16, 2016 at 5:03 AM, W. Edwin Clark <wclark@mail.usf.edu> wrote:
Look up the book on amazon and click on "look inside". You will be able to search for words in the book. I'm not sure just how much of the book is searched. Also you can see the book's index which idoes include "pushing" and "popping". You can also use the Search Inside This Book feature to search for these words to get some context. I found this easier than looking for my copy of GEB.
On Tue, Nov 15, 2016 at 11:17 PM, James Propp <jamespropp@gmail.com> wrote:
I just realized (painfully close to my deadline) that my essay on self-referential sentences could really benefit from a terminological distinction that I may have to coin.
It's the distinction between
Deduction style #1: If P says "Q is true", and P is true, then Q is true.
and
Deduction style #2: If P says "Q is true", and Q is true, then P is true.
I'm tempted to call them "pushing" and "popping", respectively. And now that I think about it, I'm wondering whether Hofstadter used exactly this nomenclature in "Godel, Escher, Bach". I can't decide whether it's merely the sort of thing Hofstadter would do, or something he actually did! And I can't seem to locate my copy of GEB. Can someone with a handy copy look up "push" and "pop" in the index?
Thanks,
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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participants (3)
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Allan Wechsler -
James Propp -
W. Edwin Clark