The argument is:
Everyone likes Mandy. Mandy likes nobody but Andy. Therefore, Mandy and Andy are the same person.
We translate it and prove it:
- (x)Lxm
- (x)[¬ (x=a) ⊃¬ Lmx] • Lma
- ∴m = a
- Lmm ......... 1UI x/m
- (x)[¬ (x=a) ⊃¬ Lmx] ......... 2Simp.
- ¬ (m=a) ⊃¬ Lmm ......... 5UI x/m
- m = a ......... 4,6MT
You advise that in terms of logic the formulation provides the solution indicated but you don't clarify as to whether in terms of grammar the solution is the same. I ask because 'If English then Logic' suggests it is, whereas my knowledge of English tells me that, on the contrary, it cannot be inferred that Mandy and Andy are the same person. Or am I just confused? LOL
ReplyDeleteRegards,
a
We have 2 premises and a conclusion. The first premise says that everyone likes Mandy. Since the premise does not explicitly say that everyone except Mandy likes Mandy,we take it to mean that Mandy is included in 'everyone'. So Mandy likes herself too. The second premise says that Mandy likes nobody except Andy - at this stage we could conclude that Andy is herself or indeed Andy is any of the remaining persons in the set of everybody. However, since the second premise states explicitly that Mandy does not like all those remaining persons, then it follows that the only person Mandy likes is Andy, that is, herself. So Mandy is Andy.
ReplyDeleteI'll go over the Mandy-Andy argument again in the next post. Should be fun.
ReplyDeleteThankyou for setting aside my last few posts as indeed they were difficult to understand - just goes to show how the circuitry of brains differs. After my low I still couldn't leave the problem alone and, concentrating on my declaration that Andy was exempted from the set 'nobody' I did a few short critical path sketches to help me find out what I was seeing but not able to put into words. And finally I discovered why I instinctively knew the answer you presented was 'wrong'. You can imagine my great relief at discovering that I was not mentally retarded LOL :)
ReplyDeleteIn the form shown in your blog post we are presented by two independent premises. In the first premise Mandy is include in 'everyone' because everyone means everyone.
In the second premise Andy is exempted from 'nobody' but of course Mandy is not. As per the first premise we must logically include Mandy in the set 'nobody' just as we include her in the set 'everyone' in the first premise. So the second premise tells us that Mandy does not like herself. It becomes glaringly obvious when you change the order of the the two premises. The two premises are contradictory in that in one we learn Mandy likes herself, in the other we learn she does not.
My brother's adamance in arguing your case that everyone is everyone (and that people often use words incorrectly) is what closed my brain circuit and made me realise what I was trying to say all along.
As to the use of everyone in everyday language, it indeed often does not include everyone - but that's a different discussion.
I must add, so you don't get wrong idea, that when I said 'wrong' I was referring to the written form of the conundrum and not the formulaic solution as this I assume :) contains a qualified version of the original premises.
ReplyDeleteWhilst trying to fix my brain circuitry the Barber's paradox kept popping up in my head and it seems like the two premises may represent a similar paradox.
Regards,
a