..Danger Zone.
Hola.
Sorry, loyal readers, I have been a bit quiet lately.
Excuses?
Well, lack of motivation, existence of an actual life, other things to do, etc.
So I thought I’d check in, only because I thought you should know about Fitch’s Paradox of Knowability.
Why? Well, firstly, it really is very interesting. But mainly it is a cautionary tale about the use of Wikipedia’s random article button.
I was surfing Wiki today when I came across the article about this. Basically, the paradox challenges the theory of knowability which proposes that all truths are knowable, or something.
Fitch’s Paradox sort of states that “if there is an unknown truth then that it is an unknown truth is itself unknowable.”
The example Wiki gives is the question “before Mt Everest was discovered what was the highest mountain in the world?” The answer is of course Mt Everest. Which then means common sense says we could have said, before Mt Everest was discovered, that an undiscovered mountain which will be called Mt Everest is the highest mountain in the world.
The paradox points out that accepting the statement as true means the statement cannot be true, as the word ‘undiscovered’ is paradoxical.
Or something.
I am fairly sure that in my attempt to simplify and understand this I have destroyed it, like a banana.
My point is after trying to understand it, my brain started to hurt, quite a bit.
Have a care when you press the random button.
4 comments:
If a truth is unknown then surely it is simply that - unknown. This doesn't mean that it is unknowable, just unknown. If another mountain higher than Mt Everest is found then the truth will be that the higest known mountain is now mount X.
Now that doesn't mean that the new truth is unknowable, it is simply unknown at this time. That must be a different thing, I think. Thus all truths can still be knowable.
Is part of the problem one of time? A 'known' truth is present tense, a 'knowable' truth is future. Could not a present unknown truth be knowable in the future rather than unknowable? Or is that too simple?
The question of whether the existence of an unknown truth is capable of being known because it is an unknown truth.
I actually meant to remove the last sentence but forgot it in the editing.
I think the paradox is one of semantics. Saying that something is a "knowable" truth now(i.e. not known now but will be in the future) but unknown now is a paradox.
If we know that we will know an unknown truth in the future, then that truth is not unknown, merely not known now - therein lies the paradox.
Maybe.
I don't know.
In some of the discussion I have read people point out that, in reality (or common sense), the paradox can sit happily. We can assume that there are aliens out there, for example, but we don't know it now. Just because our assumption is paradoxical doesn't mean it can't be true.
I ran across a more "knowable" Theory of Knowability somewhere a while back that went something like
"All I know is that the more I know the more I know I don't know"
I find that much easier to live by!
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