# Is it possible to prove the invalidity of logic without using logic?

Is it possible to validly invalidate logic without using logic?

Mere assertion gives rise to the question, "How do you know?".

At that point, you end up having to use logic to justify the thesis that... logic is invalid... lol

Or instead of trying to use logic to justify it, you can appeal to rank assertion or divine revelation. But these are both questionable bases (plural of basis) because two contradictory ideas would both be true...

So then does the impossibility of this feat actually prove of the validity of logic?

• I think you may run into a linguistic issue that the word "proof" is closely entwined with the concept of logic, as is the word "invalidate." However, if an individual does not treat "proof" and "logic" as closely entwined, then there would be potential to have such proofs for that individual. To break free of this, you may have to step beyond the simple words, and look at what behaviors you associate with individuals after such a "proof" occurs. That may free you from the linguistic troubles. – Cort Ammon Apr 9 '15 at 4:50
• Yes. Logically, an argument can't be valid and invalid at the same time. But if we dismiss the rules of logic, then nothing forbids concluding invalid arguments are also valid. ;) – David H Apr 9 '15 at 7:13
• absolutely correct, @CortAmmon I'm aware of the issues, but couldn't think of a better term to eliminate this nuance. Got any suggestions? I didn't think it would detract too much from the main point I was making though. I'm definitely interested in this, and am wondering how might you word it. – ahnbizcad Apr 9 '15 at 7:24
• If the OP covers all cases, would it be a proof? It's like talking about the set of A and !A. If both of those sets have property X, then everything has property X (or at least within A and !A's category [e.g. numbers], in this case, claims of truth) – ahnbizcad Apr 9 '15 at 7:26
• Normally, logic is taken as axiomatic. – James Kingsbery Apr 9 '15 at 17:54

I would say it is impossible to invalidate logic as a whole, just as it is impossible to disprove "science." Logic, at it's base, is the formalization of rational thought. If/when a more reliable method of reasoning becomes available, that becomes logic (and the old methods of reasoning are either adapted or abandoned).

In that way, though, it is very possible for one method of logical reasoning to prove that some other method of logical reasoning is unreliable. Reductio ad Absurdum is an ancient technique often used for such purposes, and the history of logical reasoning is filled examples of old methods of logical reasoning giving way to more improved versions.

You cannot "absolutely" validate or invalidate some argument/principle without using logic, i.e. the "tools" for manufacturing arguments/proofs.

What you can do is to use some logical principles that you are considering "safe" or provisionally well-founded to argue against some other purported principles that you want to reject, like Intuitionism that rejects the "unrestricted" use of the Law of Excluded Middle.

• So the world of platonic forms attacks what you said at the root postulate level. "There is an ideal world of forms, unreachable, invisible, intangible, etc". This is a premise, postulate that attempts to undermine any safe or provisionally well-founded logical principles. How can the platonic world of forms be argued with, or "established" to be true or false? – ahnbizcad Apr 9 '15 at 16:58

Demonstration may be a valid approach.

I've heard many inspirational quotes which fall along the line of, "When someone says you can't be something, the best way to prove them wrong is to go out and be it."

• But that only clinches the argument only if it's a matter of providing a counterexample, in this case, yourself. – ahnbizcad Apr 9 '15 at 16:15
• Or proving an example. One of the classic arguments that shows up in religion is that a deity "proves" they exist by showing so many amazing things that one can only assume that deity exists. – Cort Ammon Apr 9 '15 at 16:38
• We're taking about the same thing. If things so amazing and groundbreaking, defying physics occurred, that would tentatively poke a hole in the idea of "there is no god". But without the god actually making ITSELF present, communicate, and open to observation, and instead only does some external "miracles", those "miracles" could simply be yet undigested phenomenon by current theoretical understanding. – ahnbizcad Apr 9 '15 at 16:55
• May I suggest a place to look to extend this conversation: Formal Systems. It sounds like your definition of "proof" is "proof by a formal system," which is a mathematical concept. If so, then your answer is simplified greatly. The wikipedia page is reasonable in its handling of the term. – Cort Ammon Apr 9 '15 at 17:46
• Also worth noting but not necessarily part of your question is that logic does get interesting and frayed as you go down the rabbit hole. Eventually logic does run square into Godel's Incompleteness Theorems. While his theorem are logic (thus not an answer to your question) they do show the edges of what logic can and cannot do. – Cort Ammon Apr 9 '15 at 18:00