Jesus and Mo, Faith and Reason
Jesus and Mo is a webcomic which I enjoy on occasion, the most recent comic involves Jesus and Mo talking with the barmaid about how, while they have exhausted every argument for their religious beliefs, they are still right for having them. Because even though logic and reason have shown those beliefs to be invalid, Logic and Reason is based on Faith as well. So the Barmaid’s arguments are circular.
What follows is the single most brilliant bit of logic ever. I simply must explain it.
The argument from the prophets is as follows:
Premises
- Their arguments for their respective faiths have been shown invalid by logic. That is, Faith is shown invalid by Logic, because Faith based beliefs are circular. (”I believe this because it’s true, it’s true because I believe it”)
- Logic is based on faith in the belief that logical principles are valid.
- Circular arguments are Logically invalid.
Conclusion
- Since Logic is based on faith, it too is a circular argument, because Faith based beliefs are circular.
Error
- You cannot use logic to disprove the validity of logic, because insodoing, you disprove the validity of your own proof.
Thats right, they showed readily that if logic were based on faith, that logic would be a circular, invalid arguement. The problem was that, in order to show that circular argument is invalid, you must use logic. However, if logic itself is invalid, then circular arguments are okay, which means Logic as a belief system is okay, but we’ve previously shown that logic as a belief system isn’t okay, since it denys a circular argument.
This is a stronger result than it may seem, it states that the rules of logic cannot be shown to be invalid. Because insodoing you must use logic, and if you were to complete your proof, then your proof would immediately be invalid.
There exists no logical proof that logic is invalid.
This is why we, as rationalists, rely on logic so heavily, we know — in fact, we can prove, that logic cannot be proven false by logical means. Logic doesn’t just not require faith, it logically can’t admit faith on any level, since doing so would be admitting a contradiction in logic, which is illogical.
Logic is so much fun.
I use the argument the other way. If I were to prove with logic that logic is valid (whatever is the meaning of “valid” to you), this is meaningless. Because, either
a) the logic is valid. So it produces always right results. Between those, there is: “logic is valid”.
b) the logic is invalid. So it can produce wrong results. Between those, there can be: “logic is valid”.
In both cases you (can) get “logic is valid”
So, you can prove neither logic is valid nor is valid.
Well, this all is a funny and quite interesting reasoning, but way long from being complete. In fact, this is just the top of what in modern logic the Gödel Incompleteness Theorems did discover.
The problems about those reasonings are:
- you must define what “valid” or “invalid” means to you. This is connected with concepts like completeness, consistence or provability which are far from being simple.
- there is a system of truths (the world). Here you have true facts and false facts (but is it so neat the distinction?). Then you have lots of ways to determine what’s wrong or true. Which is to say…
- …you must define what “logic” is for you. There are at least some ten kinds of logics tipically used for different reasons (propositional, predicative, predicative of 2nd order, modal, …). Often, in one logic you can prove the completeness of the other one, or its consistence, or some other properties.
The problem in fact is that the logic we use everyday is often a mix of these logics, and not always a correct or proved mix. On the other side, if we were to never use it, because of the previous reasoning (you can neither prove logic’s validity nor invalidity)… well, we could as well stand still all day, because none of our actions could be justified :-). That is to say that the logic we use is proved by… experimentation on the real world!
Comment by RedGlow — June 27, 2008 @ 11:56 am
Firstly, I sure do think there is a consistent, constant definition of logical validity floating around out there. In fact, I would typically call any (philosophical, at least) stance ‘valid’ if there exists some ‘proof’ (in the sense of an informal proof like that of critical thinking) that it is true.
Secondly, You’re not really using the argument the other way. In fact, you’re argument is the same as mine. I argue that trying to prove Logic is invalid will invariably invalidate your proof. That is, in _any_ consistent logic L, there cannot exist a logically consistent proof P which asserts the inconsistency of L, because that would be a contradiction with the fact that we are operating within a consistent logic. More formally, forall P in L, |- Con(L), no P |- ~Con(L), by definition of Con(L). Where Con(L) iff L is consistent.
Applying that same logic the other way only shows that we can have a consistent logic assert it’s own consistency. But that’s just a trivial result from the hypothesis.
This is practically copied from any number of books on the GIT, with a bit of R&W’s Principia thrown in for good measure, though, it’s been a while since I’ve used modern notation for these things.
However, all of this formal logic stuff is mostly irrelevant, as we are really talking about informal logic and critical thinking, which is a bit more loose-moralled about ouroboros arguments like this one. In this informal setting, J&M have accepted as a premise that the barmaids logic shows that Faith-based positions are illogical positions, and by extension, anything derived from a faith-based position is illogical. So by asserting that Logic is a Faith based position, they conclude that all things asserted by Logic must be illogical. This is done in an effort to show all of their previous arguments are at least on equal footing with logical arguments. Insodoing, however, one finds that by asserting the invalidity of logic, and _all_ it’s results, that the assertion made must also be invalid. Formally, if IF is informal logic, FA is Faith based arguments, then J&M’s argument results in the following, given P as their proof of the result.
Given:
Con(IF), (FA |- x) => ~x, P => (FA |- IF)
However, we can then see that, by extension, the following:
Thm: IF |- p, therefore FA |- p, therefore ~p
Now, we constructed the given in Consistent logic, therefore we can say that
IF |- P’, where P’ = P => (FA |- IF)
But, by Thm: we have ~P’, however, we have shown that (or, moreso pretended to show that) IF |- P => (FA |- IF), and moreover that IF |- P. So we have that IF |- P /\ IF |- ~P, therefore the proof (which you’ll note was not given) cannot exist, since it’s a contradiction of IF’s Consistency.
Hopefully that all made sense. Thanks for the comment!
Comment by admin — June 27, 2008 @ 1:10 pm