Identity.

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WokSz
 
Reply Mon 23 Mar, 2009 06:30 am
Hey guys,

I'm doing predicate calculus at the moment, and I'm having trouble understanding the concept of 'identity.' I'd appreciate any help with the following questions on it. I need to formalise these inferences in first order logic, with identity. Then I need to determine whether or not they are valid modulo the theory of identity and if either one of them is invalid then provide a counter example.

(i) George Eliot is not George Orwell. Therefore, if George Eliot wrote Middlemarch, George Orwell did not.
(ii) There are at least two good reasons to be a metaphysical realist. Therefore, it is not the case that there is exactly one good reason to be a metaphysical realist.

Once again I would appreciate any help! Smile
 
kennethamy
 
Reply Mon 30 Mar, 2009 06:44 am
@WokSz,
WokSz wrote:
Hey guys,

I'm doing predicate calculus at the moment, and I'm having trouble understanding the concept of 'identity.' I'd appreciate any help with the following questions on it. I need to formalise these inferences in first order logic, with identity. Then I need to determine whether or not they are valid modulo the theory of identity and if either one of them is invalid then provide a counter example.

(i) George Eliot is not George Orwell. Therefore, if George Eliot wrote Middlemarch, George Orwell did not.
(ii) There are at least two good reasons to be a metaphysical realist. Therefore, it is not the case that there is exactly one good reason to be a metaphysical realist.

Once again I would appreciate any help! Smile

i. It is logically possible that both Georges wrote Middlemarch .Counterexample, if Newton invented the calculus, then Leibniz did not. But both invented the calculus (separately)

ii. is obviously valid.
 
Ultracrepidarian
 
Reply Fri 1 May, 2009 04:43 am
@WokSz,
Formalize in first order logic? You've got me. Is that like replacing the words with letters and signs.

[E (the sign for "Is" but upside down) O]
Three dots (E[M]) ---> O (E[W])

Something like that for the first one. But I don't know the signs and I probably went a little too far in turning not one, but two things upside down. You might have to add a couple of brackets or move them around, but that's basically it.

Btw, I agree with Kennethamy

---------- Post added at 05:48 AM ---------- Previous post was at 05:43 AM ----------

Jesus Christ! You better not copy that and turn it in. I think I made a mistake in second half.
 
GoshisDead
 
Reply Fri 1 May, 2009 12:15 pm
@Ultracrepidarian,
Isn't an upsidedown E still and E?
 
Ultracrepidarian
 
Reply Fri 1 May, 2009 12:30 pm
@GoshisDead,
Os too. I like turning things upside down. With these letters you can do it as often as you like and who would be the wiser?
 
Saint Michael
 
Reply Tue 5 May, 2009 08:29 am
@GoshisDead,
GoshisDead;60849 wrote:
Isn't an upsidedown E still and E?


Flip it sideways and it resembles a 3.
 
Ultracrepidarian
 
Reply Tue 5 May, 2009 06:41 pm
@Saint Michael,
I think you're on to something.
 
 

 
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