[math-fun] Contacting Ray Smullyan
Does anyone on the list have contact info for Smullyan? I want to send him my paradoxical pair of sentences "If the premise of this implication does not contain the letter p, then two is not even" and its formal contrapositive "If two is even, then the premise of this implication contains the letter p" (the first is true whereas the second is false); more importantly, I want to find out if he knows of other, better sentences of this kind. (I haven't read all his books; it's possible that he had this idea years before I did, and implemented it in a better way.) I should probably send my question to Hofstadter too, but that seems less urgent. (The last time I saw Smullyan, he did not look that well.) Jim Propp
The Lehman College math / comp. sci. webpage lists this e-address: rsmullyan@verizon.net <mailto:rsmullyan@verizon.net>. (But this person is listed as "Raymond", not "Ray".) —Dan
On Jan 19, 2016, at 7:31 AM, James Propp <jamespropp@gmail.com> wrote:
Does anyone on the list have contact info for Smullyan?
I want to send him my paradoxical pair of sentences "If the premise of this implication does not contain the letter p, then two is not even" and its formal contrapositive "If two is even, then the premise of this implication contains the letter p" (the first is true whereas the second is false); more importantly, I want to find out if he knows of other, better sentences of this kind. (I haven't read all his books; it's possible that he had this idea years before I did, and implemented it in a better way.)
I should probably send my question to Hofstadter too, but that seems less urgent. (The last time I saw Smullyan, he did not look that well.)
Thanks, Dan; I tried that address and got a response from Smullyan a few hours later! Writing to Smullyan put me in mind of an observation my friend the mathematician Michael Larsen made back when we were in college: the sentence "If M is invertible, then M^{-1} is invertible" is a true proposition in linear algebra, whereas its contrapositive "If M^{-1} is not invertible, then M is not invertible" is just plain silly. I was also reminded of a quip of Alan McKay's: "Like a ski resort full of girls looking for husbands and husbands looking for girls, the situation is not as symmetrical as it might seem." Combining the two, one might consider the true sentence "If a woman is married, then her husband is married"; its contrapositive is "If a woman's husband is single, then she's single too" --- which seems not only true but eminently fair. :-) Jim Propp On Tue, Jan 19, 2016 at 3:01 PM, Dan Asimov <asimov@msri.org> wrote:
The Lehman College math / comp. sci. webpage lists this e-address:
rsmullyan@verizon.net <mailto:rsmullyan@verizon.net>.
(But this person is listed as "Raymond", not "Ray".)
—Dan
On Jan 19, 2016, at 7:31 AM, James Propp <jamespropp@gmail.com> wrote:
Does anyone on the list have contact info for Smullyan?
I want to send him my paradoxical pair of sentences "If the premise of this implication does not contain the letter p, then two is not even" and its formal contrapositive "If two is even, then the premise of this implication contains the letter p" (the first is true whereas the second is false); more importantly, I want to find out if he knows of other, better sentences of this kind. (I haven't read all his books; it's possible that he had this idea years before I did, and implemented it in a better way.)
I should probably send my question to Hofstadter too, but that seems less urgent. (The last time I saw Smullyan, he did not look that well.)
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On Jan 20, 2016, at 8:05 AM, James Propp <jamespropp@gmail.com> wrote:
. . .
Writing to Smullyan put me in mind of an observation my friend the mathematician Michael Larsen made back when we were in college: the sentence "If M is invertible, then M^{-1} is invertible" is a true proposition in linear algebra, whereas its contrapositive "If M^{-1} is not invertible, then M is not invertible" is just plain silly.
I was also reminded of a quip of Alan McKay's: "Like a ski resort full of girls looking for husbands and husbands looking for girls, the situation is not as symmetrical as it might seem."
Combining the two, one might consider the true sentence "If a woman is married, then her husband is married"; its contrapositive is "If a woman's husband is single, then she's single too" --- which seems not only true but eminently fair. :-)
The last of these reminds me of the truism: "If your parents didn't have any children, then you won't have any children and your children won't have any children, either." Though the contrapositive of this seems plainly true also. —Dan
On Wed, Jan 20, 2016 at 10:24 AM, Dan Asimov <asimov@msri.org> wrote:
The last of these reminds me of the truism: "If your parents didn't have any children, then you won't have any children and your children won't have any children, either."
The truism needs some refinement in the face of adoption and surrogate births. -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
Actually, I just noticed the heterosexism in my original email. "If a woman is married then her husband is married" is false (though if the woman's husband isn't married, her wife is!). Jim On Wednesday, January 20, 2016, James Propp <jamespropp@gmail.com> wrote:
Thanks, Dan; I tried that address and got a response from Smullyan a few hours later!
Writing to Smullyan put me in mind of an observation my friend the mathematician Michael Larsen made back when we were in college: the sentence "If M is invertible, then M^{-1} is invertible" is a true proposition in linear algebra, whereas its contrapositive "If M^{-1} is not invertible, then M is not invertible" is just plain silly.
I was also reminded of a quip of Alan McKay's: "Like a ski resort full of girls looking for husbands and husbands looking for girls, the situation is not as symmetrical as it might seem."
Combining the two, one might consider the true sentence "If a woman is married, then her husband is married"; its contrapositive is "If a woman's husband is single, then she's single too" --- which seems not only true but eminently fair. :-)
Jim Propp
On Tue, Jan 19, 2016 at 3:01 PM, Dan Asimov <asimov@msri.org <javascript:_e(%7B%7D,'cvml','asimov@msri.org');>> wrote:
The Lehman College math / comp. sci. webpage lists this e-address:
rsmullyan@verizon.net <javascript:_e(%7B%7D,'cvml','rsmullyan@verizon.net');> <mailto: rsmullyan@verizon.net <javascript:_e(%7B%7D,'cvml','rsmullyan@verizon.net');>>.
(But this person is listed as "Raymond", not "Ray".)
—Dan
On Jan 19, 2016, at 7:31 AM, James Propp <jamespropp@gmail.com <javascript:_e(%7B%7D,'cvml','jamespropp@gmail.com');>> wrote:
Does anyone on the list have contact info for Smullyan?
I want to send him my paradoxical pair of sentences "If the premise of this implication does not contain the letter p, then two is not even" and its formal contrapositive "If two is even, then the premise of this implication contains the letter p" (the first is true whereas the second is false); more importantly, I want to find out if he knows of other, better sentences of this kind. (I haven't read all his books; it's possible that he had this idea years before I did, and implemented it in a better way.)
I should probably send my question to Hofstadter too, but that seems less urgent. (The last time I saw Smullyan, he did not look that well.)
math-fun mailing list math-fun@mailman.xmission.com <javascript:_e(%7B%7D,'cvml','math-fun@mailman.xmission.com');> https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
These discussions about properties of a nonexistent object require nontrivial interpretation, which can't be done mathematically. Better, I think, to say that some "propositions" have no truth value (perhaps because they are not actually propositions). The classic example is "The present King of France is bald." Reasoning about the empty set cannot help us here. One can defend the proposition by saying, "Show me one hair from the present King of France's head!" One can attack it by saying, "Show me his shiny scalp!" I think "propositions" like "So-and-so's husband is not married" have the same problem. The statement "Chris has no husband" does not straightforwardly imply "Chris's husband is unmarried"; it can only have that implication under some fairly gnarly rule of interpretation, which I challenge anybody to verbalize. On Wed, Jan 20, 2016 at 2:01 PM, James Propp <jamespropp@gmail.com> wrote:
Actually, I just noticed the heterosexism in my original email. "If a woman is married then her husband is married" is false (though if the woman's husband isn't married, her wife is!).
Jim
On Wednesday, January 20, 2016, James Propp <jamespropp@gmail.com> wrote:
Thanks, Dan; I tried that address and got a response from Smullyan a few hours later!
Writing to Smullyan put me in mind of an observation my friend the mathematician Michael Larsen made back when we were in college: the sentence "If M is invertible, then M^{-1} is invertible" is a true proposition in linear algebra, whereas its contrapositive "If M^{-1} is not invertible, then M is not invertible" is just plain silly.
I was also reminded of a quip of Alan McKay's: "Like a ski resort full of girls looking for husbands and husbands looking for girls, the situation is not as symmetrical as it might seem."
Combining the two, one might consider the true sentence "If a woman is married, then her husband is married"; its contrapositive is "If a woman's husband is single, then she's single too" --- which seems not only true but eminently fair. :-)
Jim Propp
On Tue, Jan 19, 2016 at 3:01 PM, Dan Asimov <asimov@msri.org <javascript:_e(%7B%7D,'cvml','asimov@msri.org');>> wrote:
The Lehman College math / comp. sci. webpage lists this e-address:
rsmullyan@verizon.net <javascript:_e(%7B%7D,'cvml','rsmullyan@verizon.net');> <mailto: rsmullyan@verizon.net <javascript:_e(%7B%7D,'cvml','rsmullyan@verizon.net');>>.
(But this person is listed as "Raymond", not "Ray".)
—Dan
On Jan 19, 2016, at 7:31 AM, James Propp <jamespropp@gmail.com <javascript:_e(%7B%7D,'cvml','jamespropp@gmail.com');>> wrote:
Does anyone on the list have contact info for Smullyan?
I want to send him my paradoxical pair of sentences "If the premise of this implication does not contain the letter p, then two is not even" and its formal contrapositive "If two is even, then the premise of this implication contains the letter p" (the first is true whereas the second is false); more importantly, I want to find out if he knows of other, better sentences of this kind. (I haven't read all his books; it's possible that he had this idea years before I did, and implemented it in a better way.)
I should probably send my question to Hofstadter too, but that seems less urgent. (The last time I saw Smullyan, he did not look that well.)
math-fun mailing list math-fun@mailman.xmission.com <javascript:_e(%7B%7D,'cvml','math-fun@mailman.xmission.com');> https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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I may be wrong, but I think philosophers of language tend to interpret "the" statements as saying, first of all, that what follows the "the" exists and is unique, and then whatever further is said the "the" thing. So if we agree to this, any statement about "the" King of France (presuming a current time frame) is just false. –Dan
On Jan 20, 2016, at 2:19 PM, Allan Wechsler <acwacw@gmail.com> wrote:
These discussions about properties of a nonexistent object require nontrivial interpretation, which can't be done mathematically. Better, I think, to say that some "propositions" have no truth value (perhaps because they are not actually propositions). The classic example is "The present King of France is bald." Reasoning about the empty set cannot help us here. One can defend the proposition by saying, "Show me one hair from the present King of France's head!" One can attack it by saying, "Show me his shiny scalp!"
I think "propositions" like "So-and-so's husband is not married" have the same problem. The statement "Chris has no husband" does not straightforwardly imply "Chris's husband is unmarried"; it can only have that implication under some fairly gnarly rule of interpretation, which I challenge anybody to verbalize.
Shouldn't there be an intermediate category for pseudo-propositions that are well-formed syntactically but not well-grounded semantically? I don't think such pseudo-propositions deserve to be included in the truth/falsity game. Do philosophers agree with me? Jim On Wednesday, January 20, 2016, Dan Asimov <asimov@msri.org> wrote:
I may be wrong, but I think philosophers of language tend to interpret "the" statements as saying, first of all, that what follows the "the" exists and is unique, and then whatever further is said the "the" thing.
So if we agree to this, any statement about "the" King of France (presuming a current time frame) is just false.
–Dan
On Jan 20, 2016, at 2:19 PM, Allan Wechsler <acwacw@gmail.com <javascript:;>> wrote:
These discussions about properties of a nonexistent object require nontrivial interpretation, which can't be done mathematically. Better, I think, to say that some "propositions" have no truth value (perhaps because they are not actually propositions). The classic example is "The present King of France is bald." Reasoning about the empty set cannot help us here. One can defend the proposition by saying, "Show me one hair from the present King of France's head!" One can attack it by saying, "Show me his shiny scalp!"
I think "propositions" like "So-and-so's husband is not married" have the same problem. The statement "Chris has no husband" does not straightforwardly imply "Chris's husband is unmarried"; it can only have that implication under some fairly gnarly rule of interpretation, which I challenge anybody to verbalize.
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My impression is that almost all pseudo-philosophers of language would agree with you. —Dan
On Jan 20, 2016, at 3:24 PM, James Propp <jamespropp@gmail.com> wrote:
Shouldn't there be an intermediate category for pseudo-propositions that are well-formed syntactically but not well-grounded semantically? I don't think such pseudo-propositions deserve to be included in the truth/falsity game. Do philosophers agree with me?
Jim
On Wednesday, January 20, 2016, Dan Asimov <asimov@msri.org> wrote:
I may be wrong, but I think philosophers of language tend to interpret "the" statements as saying, first of all, that what follows the "the" exists and is unique, and then whatever further is said the "the" thing.
So if we agree to this, any statement about "the" King of France (presuming a current time frame) is just false.
–Dan
On Jan 20, 2016, at 2:19 PM, Allan Wechsler <acwacw@gmail.com <javascript:;>> wrote:
These discussions about properties of a nonexistent object require nontrivial interpretation, which can't be done mathematically. Better, I think, to say that some "propositions" have no truth value (perhaps because they are not actually propositions). The classic example is "The present King of France is bald." Reasoning about the empty set cannot help us here. One can defend the proposition by saying, "Show me one hair from the present King of France's head!" One can attack it by saying, "Show me his shiny scalp!"
I think "propositions" like "So-and-so's husband is not married" have the same problem. The statement "Chris has no husband" does not straightforwardly imply "Chris's husband is unmarried"; it can only have that implication under some fairly gnarly rule of interpretation, which I challenge anybody to verbalize.
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Yet some propositions about non-existent objects seem to have truth values, e.g. "Sherlock Holmes resided on Baker street." Brent On 1/20/2016 2:19 PM, Allan Wechsler wrote:
These discussions about properties of a nonexistent object require nontrivial interpretation, which can't be done mathematically. Better, I think, to say that some "propositions" have no truth value (perhaps because they are not actually propositions). The classic example is "The present King of France is bald." Reasoning about the empty set cannot help us here. One can defend the proposition by saying, "Show me one hair from the present King of France's head!" One can attack it by saying, "Show me his shiny scalp!"
I think "propositions" like "So-and-so's husband is not married" have the same problem. The statement "Chris has no husband" does not straightforwardly imply "Chris's husband is unmarried"; it can only have that implication under some fairly gnarly rule of interpretation, which I challenge anybody to verbalize.
On Wed, Jan 20, 2016 at 2:01 PM, James Propp <jamespropp@gmail.com> wrote:
Actually, I just noticed the heterosexism in my original email. "If a woman is married then her husband is married" is false (though if the woman's husband isn't married, her wife is!).
Jim
On Wednesday, January 20, 2016, James Propp <jamespropp@gmail.com> wrote:
Thanks, Dan; I tried that address and got a response from Smullyan a few hours later!
Writing to Smullyan put me in mind of an observation my friend the mathematician Michael Larsen made back when we were in college: the sentence "If M is invertible, then M^{-1} is invertible" is a true proposition in linear algebra, whereas its contrapositive "If M^{-1} is not invertible, then M is not invertible" is just plain silly.
I was also reminded of a quip of Alan McKay's: "Like a ski resort full of girls looking for husbands and husbands looking for girls, the situation is not as symmetrical as it might seem."
Combining the two, one might consider the true sentence "If a woman is married, then her husband is married"; its contrapositive is "If a woman's husband is single, then she's single too" --- which seems not only true but eminently fair. :-)
Jim Propp
On Tue, Jan 19, 2016 at 3:01 PM, Dan Asimov <asimov@msri.org <javascript:_e(%7B%7D,'cvml','asimov@msri.org');>> wrote:
The Lehman College math / comp. sci. webpage lists this e-address:
rsmullyan@verizon.net <javascript:_e(%7B%7D,'cvml','rsmullyan@verizon.net');> <mailto: rsmullyan@verizon.net <javascript:_e(%7B%7D,'cvml','rsmullyan@verizon.net');>>.
(But this person is listed as "Raymond", not "Ray".)
—Dan
On Jan 19, 2016, at 7:31 AM, James Propp <jamespropp@gmail.com <javascript:_e(%7B%7D,'cvml','jamespropp@gmail.com');>> wrote: Does anyone on the list have contact info for Smullyan?
I want to send him my paradoxical pair of sentences "If the premise of this implication does not contain the letter p, then two is not even" and its formal contrapositive "If two is even, then the premise of this implication contains the letter p" (the first is true whereas the second is false); more importantly, I want to find out if he knows of other, better sentences of this kind. (I haven't read all his books; it's possible that he had this idea years before I did, and implemented it in a better way.)
I should probably send my question to Hofstadter too, but that seems less urgent. (The last time I saw Smullyan, he did not look that well.)
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Writing to Smullyan put me in mind of an observation my friend the mathematician Michael Larsen made back when we were in college: the sentence "If M is invertible, then M^{-1} is invertible" is a true proposition in linear algebra, whereas its contrapositive "If M^{-1} is not invertible, then M is not invertible" is just plain silly.
It's still true, though -- just vacuously so.
Do all unicorns have 1 horn (by definition) or 0 (by nonexistence)?
Yes. (And, less trivially, both of the disjunctands are also true.) Best wishes, Adam P. Goucher
participants (6)
-
Adam P. Goucher -
Allan Wechsler -
Brent Meeker -
Dan Asimov -
James Propp -
Mike Stay