Law of No Contradiction, and exceptions to the rules?

[Mr. Laymen]

I'm new to the topic, but it's interesting to me.

 

From what I've read...

 

http://plato.stanford.edu/entries/contradiction/

 

It seems our intersubjective verifiability agrees with LNC and LEM as a foundation of logic.

 

But there is a debated or uncertain exception to the rules; para-consistency, rather than inconsistency. The concept I think is that some "variables", structure and function may be a contradiction intentionally, and is unlike everything else that is consistent. An exception to the rule, or is it...

 

I'm not really that familiar with Buddhism, but the example of the exception described in the text refers to a Buddhist viewpoint. I attempted to interpret how a Buddhist view might attempt to fit logic into the modal/negation square mentioned in the text. Something like the below maybe? (I have no idea what I'm really saying here, not trying to prove anything, just trying to understand more about the topic)

 

modal square

everything exists everything doesn't exist

nothing exists nothing doesn't exist

 

negation square

0=1 0≠1

0≠1 0=1

 

Am I misinterpreting this? What do other people think about this topic?

[Mr. Laymen]

...Or if no one is interested in discussing this cause it's boring, or something, can anyone suggest any decent reading material they may be aware of on the topic?

[Sato]

Hey there,

 

I've only just seen this thread, and I imagine a good couple of others haven't yet, due to time-zone conflicts and other such things. This is an interesting topic, and it'd be likely to garner some discussion, but it's best to wait a day or two before bumping. I see you're new to SFN so I'd like to extend a warm welcome.

 

Modal logic, to my understanding, studies truth with respect to a statement's world(s) of interpretations; most commonly by "necessity", that is, it is true in every world, and "possibility", that is, it is true in some world. In non-paraconsistent (consistent?) logics, a contradiction in a theory results in every theorem being true, and this is so by the standard rules of inference of classical logic. Paraconsistent logics aim to serve as logical systems which do not "explode" upon a contradiction and so can maintain some sort of usefulness.

 

Here is a very relevant paper that may come in handy to you: http://sqig.math.ist.utl.pt/pub/MarcosJ/04-M-ModPar.pdf

 

Cheers,

Sato

[Mr. Laymen]

Here is a very relevant paper that may come in handy to you: http://sqig.math.ist.utl.pt/pub/MarcosJ/04-M-ModPar.pdf

 

Γ J α iff ✸Γ S5 ✸α

 

Hahah, that looks like Vulcan? This is dense material, gonna take some effort to digest, I'll give it a shot though. Thanks!

[TheDivineFool]

As far as logic is concerned, I'm only familiar with baby logic. Contradiction is a Big NO! NO! in it.

 

In fact like the OP said, it's a foundational thing.

 

I've heard of paraconsistent logic and that it makes room for contradiction and also multi-valued logic that rejects LEM.

 

However, these logics must be tailor-made for certain spheres of experience that involve such states.

 

Everyday experience never presents contradictions and this fact is used to detect errors in it. For example if x were to say ''cola is good for health'' and y were to say ''cola is not good for health'', it is natural to doubt the truth of the statements.

 

Having said that, the LNC presents some serious problems for us. For example Zeno's paradoxes are about the impossibility of mundane experiences such as the simple act of walking from your bedroom to the bathroom. So, we're left with the dilemma of choosing between LNC and denying reality.

[Mr. Laymen]

 

However, these logics must be tailor-made for certain spheres of experience that involve such states.

 

 

What are some of the "spheres"? I assume one is the "conceptual nothingness" viewed by Buddhists as mentioned in the link of the OP, but do you know of any other concepts that make use of this?

 

or example if x were to say ''cola is good for health'' and y were to say ''cola is not good for health'', it is natural to doubt the truth of the statements.

 

 

Hahah, I'd just assume we all aren't defining "health" very accurately.

 

For example Zeno's paradoxes are about the impossibility of mundane experiences such as the simple act of walking from your bedroom to the bathroom. So, we're left with the dilemma of choosing between LNC and denying reality.

 

 

They (Paraconsistency and Zeno's Paradox) seem like a similar scenario/issue of attempting to define finite-ness accurately, while remaining relative.