Curse

MMSDome · Jul 16, 2009, 12:02 AM // 00:02

Ok first off if any of you have done logic problems in the past I would appreciate your help on this one.

The problem is: Derive from no premises: ((A → B) → A) → A)

And the answer to this is:

D] Derive from no premises: ((A → B) → A) → A)

--------------->
1. | (A → B) → A _____Assump [A]
2. | ~(A → B) v A _____1 Imp
3. | ~(~A v B) v A ____2 Imp
4. | (~~A & B) v A __ _ 3 DeM
5. | (A & B) v A _____ 4 DN
6. | A v (A & B) ______ 5 Comm
7. | (A v A) & (A v B) __ 6 Dist
8. | A v A __________ 7 Simp
9. | A ______________ 8 Rep.
-----------------
10. ((A → B) → A) → A) 1-9 CP

Now my question is from lines 3 to 4 my teacher uses DeM but he does not make the B in line 4 ~B. I am wondering if he is wrong and I caught his error or if I am just not seeing the problem. In case you need refreshing on logic problems the rule of DeM, or DeMorgan is:

~(p v q) :: ~p & ~q
~(p & q) :: ~p v ~q

Your help is much appreciated

Akuma · Jul 16, 2009, 12:06 AM // 00:06

what the hell

kostolomac · Jul 16, 2009, 12:20 AM // 00:20

Sorry I can't help, I don't know much about logic in mathematics.

Winterclaw · Jul 16, 2009, 02:42 AM // 02:42

It's been a long time since I looked at logic problems. However just by looking at it, it seems like he does have a typo.

However some negations have rules on which on gets negated and which one doesn't if depending on their sign and operator, so I'd check that out. It could be that he did two steps at once.

Lavoc · Jul 16, 2009, 01:46 PM // 13:46

42 <3

12 chars

Shursh · Jul 16, 2009, 02:07 PM // 14:07

i don't know much about math logic, but it would seem that there needs to be a ~ in front of that B on line 4. why would it only be added to the A? operator rules say that the ~ should be applied to both.

or i could be completely wrong...who knows...

Fril Estelin · Jul 16, 2009, 02:35 PM // 14:35

Quote:

Originally Posted by MMSDome

Now my question is from lines 3 to 4 my teacher uses DeM but he does not make the B in line 4 ~B. I am wondering if he is wrong and I caught his error or if I am just not seeing the problem.

Yes he made a mistake, it should be ~B.

http://en.wikipedia.org/wiki/Contraposition

But it doesn't change the proof, because ~B disappears from 7 to 8.

P.S.: what kind of course is this?

Picuso · Jul 16, 2009, 02:38 PM // 14:38

Quote:

Originally Posted by MMSDome

Now my question is from lines 3 to 4 my teacher uses DeM but he does not make the B in line 4 ~B. I am wondering if he is wrong and I caught his error or if I am just not seeing the problem.

He has to be wrong. As you say, line 4 would be:
(A & ~B) v A

(I've done too many logic problems this year XD)

MMSDome · Jul 16, 2009, 09:19 PM // 21:19

Quote:

Originally Posted by Fril Estelin

Yes he made a mistake, it should be ~B.

http://en.wikipedia.org/wiki/Contraposition

But it doesn't change the proof, because ~B disappears from 7 to 8.

P.S.: what kind of course is this?

It is a philosophy course on elementary logic, totally not what I was expecting but it was either this or calculus.

Turns out the teacher was wrong and pretty much said the same thing you did, Fril.

Thanks to all who helped, attempted to help, and akuma.

pumpkin pie · Jul 17, 2009, 03:06 AM // 03:06

This proof it, I have no logic what so ever! I don't even understand what the question is about.

Konig Des Todes · Jul 17, 2009, 04:13 AM // 04:13

Quote:

Originally Posted by MMSDome

It is a philosophy course on elementary logic, totally not what I was expecting but it was either this or calculus.

Since when do philosophy courses on logic - which would mean using words - use mathematical logic? I covered this is general mathematics.

I guess the teacher is just lazy to write out the lines and did it the short way with mathematical/symbolic logic...

Fril Estelin · Jul 17, 2009, 05:29 AM // 05:29

Quote:

Originally Posted by MMSDome

It is a philosophy course on elementary logic, totally not what I was expecting but it was either this or calculus.

Quote:

Originally Posted by Konig Des Todes

Since when do philosophy courses on logic - which would mean using words - use mathematical logic? I covered this is general mathematics.

I guess the teacher is just lazy to write out the lines and did it the short way with mathematical/symbolic logic...

Actually, it's not so surprising at all. Philosophers have always been avid logicians (well some of them

). In fact, during the Renaissance, a lot of the mathematicians who founded the basis of current classical logics were also doing philosophy, physics, religion, etc. (and there were quite a number of German ones!)

I even found absolutely fascinating (and quite basic) logic work from some philosophers on the nature of time during my PhD. Philosophers perfectly understand the tool nature of logic, as this example funnily illustrates: despite the mistake, the proof is actually right

.

Just FYI (and your prof's), there are more advanced logic that are much less "mechanical" (for lack of a better word), like the modal logics where instead of using operators AND and OR, you use operators like "I believe that" or "I know that" or "I am obliged by the fact" etc. But their framework is a lot more difficult to explain, but better fits the more complex "human" problems such as philosophy.

Konig Des Todes · Jul 17, 2009, 07:30 AM // 07:30

Fril, I think you misunderstanding me. It's not so much that philosophy class is having logic. It's the way in which it is used. Usually what the OP denoted is used in mathematics courses - understandable to be used by mathematicians gone philosophers or a mathematician who also works as a philosopher.

So what I was commenting on was more of a philosophy course (which is fine arts) using mathematics methods. Like I said in my previous post, I guess the teacher is lazy and uses the shorthand method (like how people are even lazier on the internet and uses leet speak or shortened words

)

Fril Estelin · Jul 17, 2009, 07:46 AM // 07:46

Quote:

Originally Posted by Konig Des Todes

So what I was commenting on was more of a philosophy course (which is fine arts) using mathematics methods. Like I said in my previous post, I guess the teacher is lazy and uses the shorthand method (like how people are even lazier on the internet and uses leet speak or shortened words

)

No he's not, he's simply rigorous. It's quite common to try to explain a logic problems in natural language (see Guru where everyone draws conclusions from axions in a logically wrong way because you simple use words "so" or "as a consequence"), only to discover that language is not rigorous because interpretation of certain terms can differ, leading to ambiguity.

It's possible that A and B have a very precise meaning in the example given here, and that he's talking about them more than about their logical relationship.

Although I admit that this proof is quite complex for a philosophy course.