Exercise 6.12

Exercise 6.12.

I've come back to this question as I couldn't prove it before, but I still can't do it. Any ideas of how to approach it, its starting to drive me crazy. How do I get the Dodec(f) by itself?

Nevermind, just got it to work.

Care to share how?
I could really do with a few pointers here.

Cheers,

AndreB Wrote:
-------------------------------------------------------
> Care to share how?
> I could really do with a few pointers here.
>
> Cheers,

Look at Negation 3, it was a big help.

Thanks - I think I've procrastinated enough now
Time for some coffee, then back to the books.
I took 2 days leave to get this assignment done, but I'm struggling a lot more than I anticipated.
Silly me.

Thanks for the tip - I'll take a look at it as soon as I've had my coffee.

I fully understand the Negation 3 exercise, and how to contradict !Dodec(e) and Small(e) in Ex 6.12, however my disjunction elimination in this exercise does not work.
It all works out logically in my head, however my head and fitch are having a hard time communicating.

AndreB Wrote:
-------------------------------------------------------
> I fully understand the Negation 3 exercise, and
> how to contradict !Dodec(e) and Small(e) in Ex
> 6.12, however my disjunction elimination in this
> exercise does not work.
> It all works out logically in my head, however my
> head and fitch are having a hard time
> communicating.

You need three subproofs, one for each of the items in the disjunction i.e. 3. You must then prove Dodec(e) for each of them. Once you do that you can use disjunction elimination to prove Dodec(e) on the main proof.

Hope I didn't give too much away, let me know if you need more tips.

Hi jeanbodemer,

I really appreciate the help. I've gone through it several times again and came up with the idea that I'm missing a single link, the same with 6.13. With this one I get the first 2, but as you have pointed out, I need to prove the 3rd sub proof - and that's the one i'm stuck on.

Any ideas - and no you did not give too much away.
I could really use some more help here - if you don't mind.

Thanks again,
AndreB

Sorry, just realised that I was talking about the wrong function above. It should be Dodec(f).

First subproof is:

~Dodec(e)
----------
_|_ (don't laugh)            _|_ intro
Dodec(f)                     _|_ elim

Then same as above for Small(e)

and then another subproof for Dodec(e) where you can just use a reit.

The use your elim on premise 3 and the above 3 subproofs.

Easy (not really, I sat with this for hours)

Hi jeanbodemer

I've tried what you suggested, and my ||Elim still fails.
My proof looks more or less as follows:

|1. Dodec(e)
|2. ~Small(e)
|3. ~Dodec(e) || Dodec(f) || Small(e)
--
| |4. ~Dodec(e)
| ---
| |5. ^ (AKA - Contradiction) ^Intro: 1, 4
| |6. Dodec(f) ^Elim: 5
| |
| |7. Small(e)
| ---
| |8. ^ (AKA - Contradiction) AnaCon: 2, 6
| |9. Dodec(f) ^Elim: 8
|
| |10. Dodec(e)
| ---
| |11. Dodec(e) Reit: 10
|
| 12. Dodec(f) ||Elim: 3, 4-6, 7-9, 10-11


Any ideas as to where I'm going wrong. I don't quite understand why Dodec(e) is needed if we are given this as a premise, and we have contradicted the possibilty of ~Dodec(e).

Sorry once again to trouble you, but I'm stuck.
Cheers,

Oops - Line 8 should have read:
| |8. ^ (AKA - Contradiction) ^Intro: 2, 7

Copy and paste is sometimes a pain when you are an idiot

10 and 11 should be Dodec(f)

Now, will you look at that - it worked.
Thanks a million Jean.
Let's see if this rather tired brain can get through a few more.
Thanks again.