Is this a correct RAA proof?

[Protoman2050]

Originally Posted by 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.

Really? Cool! And, what sort of "boring descriptors"...how are mine interesting compared to what you learned? What would your method call "reductio" and "principle of explosion"? Logic is only bland when you start mixing it w/ math.

[VideCorSpoon]

Take the indirect proof for example.

This is the indirect proof in proof format.


Here are three different different titles for that particular method of inference rule of the top of my head.

Herrick would say that is a "indirect proof."
(To prove P. Indent, assume ~P, derive a contraditction, end the indentation, assert P)
Prospesel would say that is "Dash I" (literally... -I)
(-A depends on whatever assumptions B &-B depends on (less the assumption a)
Bergmann would not even use conditional proofs, though he incorporates more than the official inference rules.

So three different people with three different takes on the exact same thing. Herrick is by far the easiest to understand from what I have seen. But they are all technical descriptors. Yours are interesting because they incorporate an abstract concept towards the technical rule. It's not interesting in a bad way, just interesting in particular because that technical title helps understand the concept in a broader way.

Reductio ad absurdum is called indirect proof and principle of explosion is called conditional proof. Same thing, different names.

Yeah, I hear what you are saying about logic when math gets involved. I had an interesting conversation with Zentetic11235 on discrete mathematics, number theory, and topology which only underlines my precarious distance from mathematical logic. Still interesting though, you should not be deterred from it, but once you learn it mathematically, its probably 99.9% certain that you would go back to the propositional method.

[Protoman2050]

Originally Posted by VideCorSpoon

Take the indirect proof for example.

This is the indirect proof in proof format.


Here are three different different titles for that particular method of inference rule of the top of my head.

Herrick would say that is a "indirect proof."
(To prove P. Indent, assume ~P, derive a contraditction, end the indentation, assert P)
Prospesel would say that is "Dash I" (literally... -I)
(-A depends on whatever assumptions B &-B depends on (less the assumption a)
Bergmann would not even use conditional proofs, though he incorporates more than the official inference rules.

So three different people with three different takes on the exact same thing. Herrick is by far the easiest to understand from what I have seen. But they are all technical descriptors. Yours are interesting because they incorporate an abstract concept towards the technical rule. It's not interesting in a bad way, just interesting in particular because that technical title helps understand the concept in a broader way.

Reductio ad absurdum is called indirect proof and principle of explosion is called conditional proof. Same thing, different names.

Yeah, I hear what you are saying about logic when math gets involved. I had an interesting conversation with Zentetic11235 on discrete mathematics, number theory, and topology which only underlines my precarious distance from mathematical logic. Still interesting though, you should not be deterred from it, but once you learn it mathematically, its probably 99.9% certain that you would go back to the propositional method.

I thought conditional proof was where you assume the antecedent of a conditional to prove the consequent, ie Conditional proof - Wikipedia, the free encyclopedia.

[VideCorSpoon]

No, you have it right, but Herrick uses the conditional proof as its own inference (rather than just as the name of the” if, then” statement.) Different names for different methods.

The conditional you posited is right (the one from wiki), but that is the basic conditional, as in conditional, bi-conditional, conjunction, and disjunction.

The way the conditional proof works is this. Say for your conclusion you wanted to get a conditional, i.e. P-->Q . You would have to indent, assume P, end with Q , and assert P -->Q as your conclusion. This is one of my favorite inference rules. It’s basically a big all encapsulating argument, like a hypothetical syllogism, but also incorporates different inferences and replacements.

[Protoman2050]

So, what are the other methods of proving my, um, thingie?

[VideCorSpoon]

Oops! Sorry about that, I did it but I got side tracked.

This is one way. But this is one of the simpler ways to do it, which also reveals the problems in the argument. Usually if you have to use double negation or communication, there is room for refinement in the conveyance. Those two are also severe word play when you see the literal structure of the proof.

[Protoman2050]

Originally Posted by VideCorSpoon

Oops! Sorry about that, I did it but I got side tracked.

This is one way. But this is one of the simpler ways to do it, which also reveals the problems in the argument. Usually if you have to use double negation or communication, there is room for refinement in the conveyance. Those two are also severe word play when you see the literal structure of the proof.

I see. Another way?

[VideCorSpoon]

Suffice to say there a number of ways to do it. It's all how you manipulate the rules and construct your argument. You can expand the argument by extrapolating from the rules you used to derive excess steps from them, but then that wouldn't be logical.

To further your own argument (with the proof that I did) you would have to revise #3 K (because a double negative is the same as if there were no negative at all) and flip #1 juxtaposition to have a logically flowing argument.

This would mean that the unknown variable, syntax, has to be accounted for in truth functional logic.

[Protoman2050]

Originally Posted by VideCorSpoon

To further your own argument (with the proof that I did) you would have to revise #3 K (because a double negative is the same as if there were no negative at all) and flip #1 juxtaposition to have a logically flowing argument.

This would mean that the unknown variable, syntax, has to be accounted for in truth functional logic.

Elaborate, please.

[VideCorSpoon]

elaborate on your request for an elaboration. LOL! just kidding! what exactly are you unclear about? The argument honing or the syntax comment?