<div dir="auto"><div dir="auto">My definition is consistent with that. The only state of affairs excluded by A implies B is A is true and B is not. <div dir="auto"><br></div><div dir="auto">The truth table for A implies B is:</div><div dir="auto"><br></div><div dir="auto">A B A implies B</div><div dir="auto"><br></div><div dir="auto">T T T</div><div dir="auto">T F F</div><div dir="auto">F T T</div><div dir="auto">F F T</div><div dir="auto"><br><div dir="auto"><div dir="auto"><br><div data-smartmail="gmail_signature" dir="auto">---<br>Frank C. Wimberly<br>140 Calle Ojo Feliz, <br>Santa Fe, NM 87505<br><br>505 670-9918<br>Santa Fe, NM</div></div></div></div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Tue, Dec 27, 2022, 10:57 AM glen <<a href="mailto:gepropella@gmail.com" target="_blank" rel="noreferrer">gepropella@gmail.com</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">Well, I'm probably confused because I'm trying (and failing) to read this at the moment:<br>
<br>
Paradoxes and Inconsistent Mathematics<br>
<a href="https://ndpr.nd.edu/reviews/paradoxes-and-inconsistent-mathematics/" rel="noreferrer noreferrer noreferrer" target="_blank">https://ndpr.nd.edu/reviews/paradoxes-and-inconsistent-mathematics/</a><br>
<br>
But I'm on Eric's side, here. "A⇒B" does not mean B can only be true when/if A is true. A can be false while B is true. But when A is true, B must also be true. So the set of conditions where B obtains can be larger than the set of conditions where A obtains.<br>
<br>
<br>
On 12/27/22 09:22, Frank Wimberly wrote:<br>
> A implies B is false iff A is true and B is false.<br>
> <br>
> ---<br>
> Frank C. Wimberly<br>
> 140 Calle Ojo Feliz,<br>
> Santa Fe, NM 87505<br>
> <br>
> 505 670-9918<br>
> Santa Fe, NM<br>
> <br>
> On Tue, Dec 27, 2022, 10:15 AM David Eric Smith <<a href="mailto:desmith@santafe.edu" rel="noreferrer noreferrer" target="_blank">desmith@santafe.edu</a> <mailto:<a href="mailto:desmith@santafe.edu" rel="noreferrer noreferrer" target="_blank">desmith@santafe.edu</a>>> wrote:<br>
> <br>
> Are you sure Frank?<br>
> <br>
> The sentence from gtp that I highlight said:<br>
> <br>
>> "⊃" is the logical symbol for "implies." It is used to form conditional statements in which the formula on the right is true only if the formula on the left is true.<br>
> <br>
> As I understand “implies” (or just the conditional if A then B), it means that the formula on the right is true _if_ the formula on the left is true. Not “only if” as gtp is quoted to say above. Correct would be “the formula on the right is _false_ _only if_ the formula on the left is _false_. Conditional doesn’t say anything about whether B is true or false if A is not true.<br>
> <br>
> Eric<br>
> <br>
> <br>
> <br>
>> On Dec 27, 2022, at 11:46 AM, Frank Wimberly <<a href="mailto:wimberly3@gmail.com" rel="noreferrer noreferrer" target="_blank">wimberly3@gmail.com</a> <mailto:<a href="mailto:wimberly3@gmail.com" rel="noreferrer noreferrer" target="_blank">wimberly3@gmail.com</a>>> wrote:<br>
>><br>
>> I've taken courses in formal logic at multiple levels. All that notation is familiar and the explanation seems correct if vacuous.<br>
>><br>
>> ---<br>
>> Frank C. Wimberly<br>
>> 140 Calle Ojo Feliz,<br>
>> Santa Fe, NM 87505<br>
>><br>
>> 505 670-9918<br>
>> Santa Fe, NM<br>
>><br>
>> On Tue, Dec 27, 2022, 3:19 AM David Eric Smith <<a href="mailto:desmith@santafe.edu" rel="noreferrer noreferrer" target="_blank">desmith@santafe.edu</a> <mailto:<a href="mailto:desmith@santafe.edu" rel="noreferrer noreferrer" target="_blank">desmith@santafe.edu</a>>> wrote:<br>
>><br>
>> Interesting. Lack of global awareness duly noted.<br>
>><br>
>> But also, can you check me on this?:<br>
>><br>
>> > On Dec 26, 2022, at 7:21 PM, glen <<a href="mailto:gepropella@gmail.com" rel="noreferrer noreferrer" target="_blank">gepropella@gmail.com</a> <mailto:<a href="mailto:gepropella@gmail.com" rel="noreferrer noreferrer" target="_blank">gepropella@gmail.com</a>>> wrote:<br>
>> ><br>
>> > This exchange was interesting. I've never seen ⊃° used.<br>
>> ><br>
>> > ⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄<br>
>> > me: What is the difference between ⊃ and ⊢.<br>
>> ><br>
>> > gpt: The symbol "⊃" is the logical symbol for "implies." It is used to form conditional statements in which the formula on the right is true only if the formula on the left is true. For example, the formula "A ⊃ B" can be read as "A implies B," and it means that if A is true, then B must also be true.<br>
>><br>
>> Am I somehow blanking on ordinary sign-flips, or mistaking left and right?<br>
>><br>
>> Seems B Is true _if_ A is true. B is false _only if_ A is false == If A is true, then B must also be true.<br>
>><br>
>> Given that English is not ensured to have any global internal logical consistency, one can see making sentences that don’t close internally. But in areas where English is capable of being used with internal consistency, I am surprised to see an “only if” transposed with an “if” everywhere. Did I completely misunderstand what “implies” means?<br>
>><br>
>><br>
>> On all this I feel completely exposed: I thought I remembered from Quine’s little book on propositional calculus that “implies” isn’t even an elementary operator; only enters in a context like modus ponens for proofs. In first-order logic one was supposed to write expressions such as “B or not(A)” to mean “if A then B”. And there was some other symbol (even simpler than the entails) for that conditional.<br>
>><br>
>> Eric<br>
>><br>
>><br>
>><br>
>> -. --- - / ...- .- .-.. .. -.. / -- --- .-. ... . / -.-. --- -.. .<br>
>> FRIAM Applied Complexity Group listserv<br>
>> Fridays 9a-12p Friday St. Johns Cafe / Thursdays 9a-12p Zoom <a href="https://bit.ly/virtualfriam" rel="noreferrer noreferrer noreferrer" target="_blank">https://bit.ly/virtualfriam</a> <<a href="https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fbit.ly%2fvirtualfriam&c=E,1,FACgozR-UqqCXQNuQwGDcUKOr9F8z9par_ZMWYigt5pt0zR5SRseqvtZvhgeXNhXZtJbOBMArZ894NdK7CRcE5elLELfxS5zueuLVPCUFvPwUnQ_&typo=1" rel="noreferrer noreferrer noreferrer" target="_blank">https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fbit.ly%2fvirtualfriam&c=E,1,FACgozR-UqqCXQNuQwGDcUKOr9F8z9par_ZMWYigt5pt0zR5SRseqvtZvhgeXNhXZtJbOBMArZ894NdK7CRcE5elLELfxS5zueuLVPCUFvPwUnQ_&typo=1</a>><br>
>> to (un)subscribe <a href="http://redfish.com/mailman/listinfo/friam_redfish.com" rel="noreferrer noreferrer noreferrer" target="_blank">http://redfish.com/mailman/listinfo/friam_redfish.com</a> <<a href="https://linkprotect.cudasvc.com/url?a=http%3a%2f%2fredfish.com%2fmailman%2flistinfo%2ffriam_redfish.com&c=E,1,Yhc5E5ab9UmYYG9HMLYkBuVWFStwPqiriJeHKTJEVbJx3gSi011Mhs_3KW7idMNg-N0XMR9DgpMC7rPIdS9XeZlcJ2U4se1WrqkjRwr_&typo=1" rel="noreferrer noreferrer noreferrer" target="_blank">https://linkprotect.cudasvc.com/url?a=http%3a%2f%2fredfish.com%2fmailman%2flistinfo%2ffriam_redfish.com&c=E,1,Yhc5E5ab9UmYYG9HMLYkBuVWFStwPqiriJeHKTJEVbJx3gSi011Mhs_3KW7idMNg-N0XMR9DgpMC7rPIdS9XeZlcJ2U4se1WrqkjRwr_&typo=1</a>><br>
>> FRIAM-COMIC <a href="http://friam-comic.blogspot.com/" rel="noreferrer noreferrer noreferrer" target="_blank">http://friam-comic.blogspot.com/</a> <<a href="https://linkprotect.cudasvc.com/url?a=http%3a%2f%2ffriam-comic.blogspot.com%2f&c=E,1,KjGjIbhNXx_Jkk8XVQeh0lyM3M6RydNqm286xij8qR8oHoHQcqigRNdtrPlFd2b8B98pogaXmWG6I4JoFfoHshueOTb-xfV86hrPhgpGlYoxVjU,&typo=1" rel="noreferrer noreferrer noreferrer" target="_blank">https://linkprotect.cudasvc.com/url?a=http%3a%2f%2ffriam-comic.blogspot.com%2f&c=E,1,KjGjIbhNXx_Jkk8XVQeh0lyM3M6RydNqm286xij8qR8oHoHQcqigRNdtrPlFd2b8B98pogaXmWG6I4JoFfoHshueOTb-xfV86hrPhgpGlYoxVjU,&typo=1</a>><br>
>> archives: 5/2017 thru present <a href="https://redfish.com/pipermail/friam_redfish.com/" rel="noreferrer noreferrer noreferrer" target="_blank">https://redfish.com/pipermail/friam_redfish.com/</a> <<a href="https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fredfish.com%2fpipermail%2ffriam_redfish.com%2f&c=E,1,tKP0RmBbn5aXqMMP90FfZRUgR4SeRNAbCIPIHTmOOMKvYU9wbJQX8c6NaqJZF-ALbi5h5pfwbbR6XC7VfiNBZH8WQJvHUbf391P9nkUqxn-_LgrnFkGB5kRXKEY,&typo=1" rel="noreferrer noreferrer noreferrer" target="_blank">https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fredfish.com%2fpipermail%2ffriam_redfish.com%2f&c=E,1,tKP0RmBbn5aXqMMP90FfZRUgR4SeRNAbCIPIHTmOOMKvYU9wbJQX8c6NaqJZF-ALbi5h5pfwbbR6XC7VfiNBZH8WQJvHUbf391P9nkUqxn-_LgrnFkGB5kRXKEY,&typo=1</a>><br>
>> 1/2003 thru 6/2021 <a href="http://friam.383.s1.nabble.com/" rel="noreferrer noreferrer noreferrer" target="_blank">http://friam.383.s1.nabble.com/</a> <<a href="http://friam.383.s1.nabble.com/" rel="noreferrer noreferrer noreferrer" target="_blank">http://friam.383.s1.nabble.com/</a>><br>
>><br>
>> -. --- - / ...- .- .-.. .. -.. / -- --- .-. ... . / -.-. --- -.. .<br>
>> FRIAM Applied Complexity Group listserv<br>
>> Fridays 9a-12p Friday St. Johns Cafe / Thursdays 9a-12p Zoom <a href="https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fbit.ly%2fvirtualfriam&c=E,1,_spTYZpBgzfulo-KvqI8rEzXQnNQEKBsbLisXTlr_mycwxyzjQtVPPo1I2aErQUHbLfg7bzp1CSukQ6vEKVwLfp3fRDVEBuHthgGKeICow,,&typo=1" rel="noreferrer noreferrer noreferrer" target="_blank">https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fbit.ly%2fvirtualfriam&c=E,1,_spTYZpBgzfulo-KvqI8rEzXQnNQEKBsbLisXTlr_mycwxyzjQtVPPo1I2aErQUHbLfg7bzp1CSukQ6vEKVwLfp3fRDVEBuHthgGKeICow,,&typo=1</a> <<a href="https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fbit.ly%2fvirtualfriam&c=E,1,_spTYZpBgzfulo-KvqI8rEzXQnNQEKBsbLisXTlr_mycwxyzjQtVPPo1I2aErQUHbLfg7bzp1CSukQ6vEKVwLfp3fRDVEBuHthgGKeICow,,&typo=1" rel="noreferrer noreferrer noreferrer" target="_blank">https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fbit.ly%2fvirtualfriam&c=E,1,_spTYZpBgzfulo-KvqI8rEzXQnNQEKBsbLisXTlr_mycwxyzjQtVPPo1I2aErQUHbLfg7bzp1CSukQ6vEKVwLfp3fRDVEBuHthgGKeICow,,&typo=1</a>><br>
>> to (un)subscribe <a href="https://linkprotect.cudasvc.com/url?a=http%3a%2f%2fredfish.com%2fmailman%2flistinfo%2ffriam_redfish.com&c=E,1,YGWVR0l_mWGwkSJgcqb-4MaGx3TabLJ_UEXMsf4RfIVpJRtH_z_87WR9YzqtbWedPsYxpzY2Yf3GoTs9r4QlS5pDCpsUsuqqStf7wZD5TgfO7B13p230BxY,&typo=1" rel="noreferrer noreferrer noreferrer" target="_blank">https://linkprotect.cudasvc.com/url?a=http%3a%2f%2fredfish.com%2fmailman%2flistinfo%2ffriam_redfish.com&c=E,1,YGWVR0l_mWGwkSJgcqb-4MaGx3TabLJ_UEXMsf4RfIVpJRtH_z_87WR9YzqtbWedPsYxpzY2Yf3GoTs9r4QlS5pDCpsUsuqqStf7wZD5TgfO7B13p230BxY,&typo=1</a> <<a href="https://linkprotect.cudasvc.com/url?a=http%3a%2f%2fredfish.com%2fmailman%2flistinfo%2ffriam_redfish.com&c=E,1,YGWVR0l_mWGwkSJgcqb-4MaGx3TabLJ_UEXMsf4RfIVpJRtH_z_87WR9YzqtbWedPsYxpzY2Yf3GoTs9r4QlS5pDCpsUsuqqStf7wZD5TgfO7B13p230BxY,&typo=1" rel="noreferrer noreferrer noreferrer" target="_blank">https://linkprotect.cudasvc.com/url?a=http%3a%2f%2fredfish.com%2fmailman%2flistinfo%2ffriam_redfish.com&c=E,1,YGWVR0l_mWGwkSJgcqb-4MaGx3TabLJ_UEXMsf4RfIVpJRtH_z_87WR9YzqtbWedPsYxpzY2Yf3GoTs9r4QlS5pDCpsUsuqqStf7wZD5TgfO7B13p230BxY,&typo=1</a>><br>
>> FRIAM-COMIC <a href="https://linkprotect.cudasvc.com/url?a=http%3a%2f%2ffriam-comic.blogspot.com%2f&c=E,1,VZHhoxvwV3O3HoDR22IXaL0brXD2f5UITFIIRFrhhDVotM51qEn028C93zmqUufNXjGtfdN3w9mWfwXbhnL2Y4-7O_N0mAb0_vbQXKWRjEI,&typo=1" rel="noreferrer noreferrer noreferrer" target="_blank">https://linkprotect.cudasvc.com/url?a=http%3a%2f%2ffriam-comic.blogspot.com%2f&c=E,1,VZHhoxvwV3O3HoDR22IXaL0brXD2f5UITFIIRFrhhDVotM51qEn028C93zmqUufNXjGtfdN3w9mWfwXbhnL2Y4-7O_N0mAb0_vbQXKWRjEI,&typo=1</a> <<a href="https://linkprotect.cudasvc.com/url?a=http%3a%2f%2ffriam-comic.blogspot.com%2f&c=E,1,VZHhoxvwV3O3HoDR22IXaL0brXD2f5UITFIIRFrhhDVotM51qEn028C93zmqUufNXjGtfdN3w9mWfwXbhnL2Y4-7O_N0mAb0_vbQXKWRjEI,&typo=1" rel="noreferrer noreferrer noreferrer" target="_blank">https://linkprotect.cudasvc.com/url?a=http%3a%2f%2ffriam-comic.blogspot.com%2f&c=E,1,VZHhoxvwV3O3HoDR22IXaL0brXD2f5UITFIIRFrhhDVotM51qEn028C93zmqUufNXjGtfdN3w9mWfwXbhnL2Y4-7O_N0mAb0_vbQXKWRjEI,&typo=1</a>><br>
>> archives: 5/2017 thru present <a href="https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fredfish.com%2fpipermail%2ffriam_redfish.com%2f&c=E,1,JwWnj-6UkTnEBOrj37sp44TnxhxZ5pzs-MTlWtgAfQjQRxaufe58Yo48fhJwo3DKPN1ERx4ANXtSxhjsUUDsM38mkbM4nYQCIN4pmv-AUD_FxdrE-q8,&typo=1" rel="noreferrer noreferrer noreferrer" target="_blank">https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fredfish.com%2fpipermail%2ffriam_redfish.com%2f&c=E,1,JwWnj-6UkTnEBOrj37sp44TnxhxZ5pzs-MTlWtgAfQjQRxaufe58Yo48fhJwo3DKPN1ERx4ANXtSxhjsUUDsM38mkbM4nYQCIN4pmv-AUD_FxdrE-q8,&typo=1</a> <<a href="https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fredfish.com%2fpipermail%2ffriam_redfish.com%2f&c=E,1,JwWnj-6UkTnEBOrj37sp44TnxhxZ5pzs-MTlWtgAfQjQRxaufe58Yo48fhJwo3DKPN1ERx4ANXtSxhjsUUDsM38mkbM4nYQCIN4pmv-AUD_FxdrE-q8,&typo=1" rel="noreferrer noreferrer noreferrer" target="_blank">https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fredfish.com%2fpipermail%2ffriam_redfish.com%2f&c=E,1,JwWnj-6UkTnEBOrj37sp44TnxhxZ5pzs-MTlWtgAfQjQRxaufe58Yo48fhJwo3DKPN1ERx4ANXtSxhjsUUDsM38mkbM4nYQCIN4pmv-AUD_FxdrE-q8,&typo=1</a>><br>
>> 1/2003 thru 6/2021 <a href="http://friam.383.s1.nabble.com/" rel="noreferrer noreferrer noreferrer" target="_blank">http://friam.383.s1.nabble.com/</a> <<a href="http://friam.383.s1.nabble.com/" rel="noreferrer noreferrer noreferrer" target="_blank">http://friam.383.s1.nabble.com/</a>><br>
> <br>
> -. --- - / ...- .- .-.. .. -.. / -- --- .-. ... . / -.-. --- -.. .<br>
> FRIAM Applied Complexity Group listserv<br>
> Fridays 9a-12p Friday St. Johns Cafe / Thursdays 9a-12p Zoom <a href="https://bit.ly/virtualfriam" rel="noreferrer noreferrer noreferrer" target="_blank">https://bit.ly/virtualfriam</a> <<a href="https://bit.ly/virtualfriam" rel="noreferrer noreferrer noreferrer" target="_blank">https://bit.ly/virtualfriam</a>><br>
> to (un)subscribe <a href="http://redfish.com/mailman/listinfo/friam_redfish.com" rel="noreferrer noreferrer noreferrer" target="_blank">http://redfish.com/mailman/listinfo/friam_redfish.com</a> <<a href="http://redfish.com/mailman/listinfo/friam_redfish.com" rel="noreferrer noreferrer noreferrer" target="_blank">http://redfish.com/mailman/listinfo/friam_redfish.com</a>><br>
> FRIAM-COMIC <a href="http://friam-comic.blogspot.com/" rel="noreferrer noreferrer noreferrer" target="_blank">http://friam-comic.blogspot.com/</a> <<a href="http://friam-comic.blogspot.com/" rel="noreferrer noreferrer noreferrer" target="_blank">http://friam-comic.blogspot.com/</a>><br>
> archives: 5/2017 thru present <a href="https://redfish.com/pipermail/friam_redfish.com/" rel="noreferrer noreferrer noreferrer" target="_blank">https://redfish.com/pipermail/friam_redfish.com/</a> <<a href="https://redfish.com/pipermail/friam_redfish.com/" rel="noreferrer noreferrer noreferrer" target="_blank">https://redfish.com/pipermail/friam_redfish.com/</a>><br>
> 1/2003 thru 6/2021 <a href="http://friam.383.s1.nabble.com/" rel="noreferrer noreferrer noreferrer" target="_blank">http://friam.383.s1.nabble.com/</a> <<a href="http://friam.383.s1.nabble.com/" rel="noreferrer noreferrer noreferrer" target="_blank">http://friam.383.s1.nabble.com/</a>><br>
> <br>
> <br>
> -. --- - / ...- .- .-.. .. -.. / -- --- .-. ... . / -.-. --- -.. .<br>
> FRIAM Applied Complexity Group listserv<br>
> Fridays 9a-12p Friday St. Johns Cafe / Thursdays 9a-12p Zoom <a href="https://bit.ly/virtualfriam" rel="noreferrer noreferrer noreferrer" target="_blank">https://bit.ly/virtualfriam</a><br>
> to (un)subscribe <a href="http://redfish.com/mailman/listinfo/friam_redfish.com" rel="noreferrer noreferrer noreferrer" target="_blank">http://redfish.com/mailman/listinfo/friam_redfish.com</a><br>
> FRIAM-COMIC <a href="http://friam-comic.blogspot.com/" rel="noreferrer noreferrer noreferrer" target="_blank">http://friam-comic.blogspot.com/</a><br>
> archives: 5/2017 thru present <a href="https://redfish.com/pipermail/friam_redfish.com/" rel="noreferrer noreferrer noreferrer" target="_blank">https://redfish.com/pipermail/friam_redfish.com/</a><br>
> 1/2003 thru 6/2021 <a href="http://friam.383.s1.nabble.com/" rel="noreferrer noreferrer noreferrer" target="_blank">http://friam.383.s1.nabble.com/</a><br>
<br>
-- <br>
ꙮ Mɥǝu ǝlǝdɥɐuʇs ɟᴉƃɥʇ' ʇɥǝ ƃɹɐss snɟɟǝɹs˙ ꙮ<br>
<br>
-. --- - / ...- .- .-.. .. -.. / -- --- .-. ... . / -.-. --- -.. .<br>
FRIAM Applied Complexity Group listserv<br>
Fridays 9a-12p Friday St. Johns Cafe / Thursdays 9a-12p Zoom <a href="https://bit.ly/virtualfriam" rel="noreferrer noreferrer noreferrer" target="_blank">https://bit.ly/virtualfriam</a><br>
to (un)subscribe <a href="http://redfish.com/mailman/listinfo/friam_redfish.com" rel="noreferrer noreferrer noreferrer" target="_blank">http://redfish.com/mailman/listinfo/friam_redfish.com</a><br>
FRIAM-COMIC <a href="http://friam-comic.blogspot.com/" rel="noreferrer noreferrer noreferrer" target="_blank">http://friam-comic.blogspot.com/</a><br>
archives: 5/2017 thru present <a href="https://redfish.com/pipermail/friam_redfish.com/" rel="noreferrer noreferrer noreferrer" target="_blank">https://redfish.com/pipermail/friam_redfish.com/</a><br>
1/2003 thru 6/2021 <a href="http://friam.383.s1.nabble.com/" rel="noreferrer noreferrer noreferrer" target="_blank">http://friam.383.s1.nabble.com/</a><br>
</blockquote></div></div>