Is this a correct RAA proof?

[Protoman2050]

Is this a correct RAA proof:

1. T v U
2. U -> ~K
3. K /:. T
4. ~T (RAA Assumption)
5. U (1,4, Disjunctive Syllogism)
6. ~K (2,5, Modus Ponens)
Contradiction!
7. T

Line 6 contradicts line 3, so...is this valid? I know the theorem I'm trying to prove is valid, but is my proof valid?

Thanks!

[kennethamy]

Originally Posted by Protoman2050

Is this a correct RAA proof:

1. T v U
2. U -> ~K
3. K /:. T
4. ~T (RAA Assumption)
5. U (1,4, Disjunctive Syllogism)
6. ~K (2,5, Modus Ponens)
Contradiction!
7. T

Line 6 contradicts line 3, so...is this valid? I know the theorem I'm trying to prove is valid, but is my proof valid?

Thanks!

Looks right to me, except that you should put in a step:

7. K & ~K

Then 8.
T.

[Protoman2050]

Originally Posted by kennethamy

Looks right to me, except that you should put in a step:

7. K & ~K

Then 8.
T.

1. T v U
2. U -> ~K
3. K /:. T
4. ~T (RAA Assumption)
5. U (1,4, Disjunctive Syllogism)
6. ~K (2,5, Modus Ponens)
7. K & ~K (3,6 Conjunction)
Contradiction!
8. T

Any other ways to prove this? What would this look like --and would it be convincing?-- in English?

BTW: T=God is trinity, U=God is unity, K=God can know Himself.

[VideCorSpoon]

Yup! Looks good. The only problem I see is that #7 is derived from “conjunction” inference rather than “addition.” The addition inference would require a disjunction. Not a big problem, only the citation.

[Protoman2050]

Originally Posted by VideCorSpoon

Yup! Looks good. The only problem I see is that #7 is derived from “conjunction” inference rather than “addition.” The addition inference would require a disjunction. Not a big problem, only the citation.

Of course. Now, I was talking w/ a philosophy prof, Dr Stolze, and he said that this is valid, just not a very "strong" proof of God's triunity. What does he mean? Any other ways of proving this? Btw, I know lines 4-8 are called the "proof", but what are lines 1-3 called?

[VideCorSpoon]

I don’t understand why your professor would say that it is a weak argument though. You can solve that particular proof in more than three ways (at least). The main reason that I could see as to why that particular proof would be weak is because it bases its entire weight off of the fact that “because this small part of the grander argument is problematic, the whole thing is by extension wrong.”

Funny that you asked about what lines 1-3 are called. The lines are officially called premises of the argument. Lines 1 – 3 can’t be an argument in itself even though we typically include the conclusion at the end of the given argument in order to solve the proof. That conclusion is just the reminder of what we are supposed to conclude at. So lines 1-3 are the initial parts of a grander argument. I’m not quite sure if there is an exact word for it though. If you know of one, I’m curious as well.

I’ll write up a precise proof (without nesting) for this in a little bit.

[Protoman2050]

Originally Posted by VideCorSpoon

I don’t understand why your professor would say that it is a weak argument though. You can solve that particular proof in more than three ways (at least). The main reason that I could see as to why that particular proof would be weak is because it bases its entire weight off of the fact that “because this small part of the grander argument is problematic, the whole thing is by extension wrong.”

Funny that you asked about what lines 1-3 are called. The lines are officially called premises of the argument. Lines 1 – 3 can’t be an argument in itself even though we typically include the conclusion at the end of the given argument in order to solve the proof. That conclusion is just the reminder of what we are supposed to conclude at. So lines 1-3 are the initial parts of a grander argument. I’m not quite sure if there is an exact word for it though. If you know of one, I’m curious as well.

I’ll write up a precise proof (without nesting) for this in a little bit.

I believe what he meant was that you can infer anything, not just T, from line 7, and that a "stronger" proof would not rely on the principle of explosion to work.

[VideCorSpoon]

Fair enough. I would refer to that as a weak inference, not a weak argument because it is contingent on a single line though. Is your professor supposing that a better derivation could have been used? That is, other than the fact that a nested proof is not exactly a solid argument (i.e. principle of explosion /indirect proof).

Also, I’ve noticed you are learning a very exciting adjective heavy version of logic. “Explosion” and “Reductio” etc. Which method are you learning? I learned propositional with the Herrick method. Same rules (for the most part) but different names.

[Protoman2050]

Originally Posted by VideCorSpoon

Fair enough. I would refer to that as a weak inference, not a weak argument because it is contingent on a single line though. Is your professor supposing that a better derivation could have been used? That is, other than the fact that a nested proof is not exactly a solid argument (i.e. principle of explosion /indirect proof).

Also, I’ve noticed you are learning a very exciting adjective heavy version of logic. “Explosion” and “Reductio” etc. Which method are you learning? I learned propositional with the Herrick method. Same rules (for the most part) but different names.

Nested proof? What's that? Yes, he told me that he isn't qualified enough to formally judge my proof, but to pass it on to Dr Stapp, the logic prof, b/c "she'd be quite interested in it".

I've been learning from the web, b/c when I was in HS, I took a logic class, but dropped before we got to formal proofs. "Exciting"? What does that mean?

I believe this is more formally a proof by contradiction, rather then a reductio ad absurdum proof.

[VideCorSpoon]

A nested proof is a proof that is indented into the proof and discharged before the rest of the proof can go on. Indirect and conditional proofs are nested proofs.

If you have learned propositional logic from the web, you have caught on really well. I have not been able to find any kind of really understandable logic tutorials as of yet on the web, so you have been able to pick up on a generally difficult subject to convey. Props.

I’m used to very boring descriptors for reference rules, so any more interesting titles are neat to encounter. Logic is typically very bland. No harm meant.

Also, I agree with you, it seems more a contradiction (indirect) proof than reductio (conditional) proof.