So, either we know that something is true or false or we cannot say anything about its truthness or falseness. — Alkis Piskas
3. p∧¬Kp→◊K(p∧¬Kp)
The logic is straightforward and results in a contradiction. — Michael
If this existential claim is true, then so is an instance of it:
(1)p∧¬Kp.
Now consider the instance of KP substituting line 1 for the variable p
in KP:
(2)(p∧¬Kp)→◊K(p∧¬Kp)
It doesn't make any difference expressed in notation. 3 does not follow from 1 and 2. — Isaac
the problem seems trivially solved by saying that some proposition exists for which it is not possible to know the truth. — Isaac
I see, OK, but I'm not familiar with either intuitionist or paraconsistent logic. I never use and never need to use such terms. 1) They render a discussion to a literary one, 2) They require special knowledge from all the persons involved in the discussion, which might not be available, 3) They might be confusing and/or irrelevant to the subject that is discussed and, most importantly, 4) They do not really add anything that is of essence or importance.You suggest three truth-values - "true", "false" or "cannot say". My bolding. All I was wondering is what variation you might choose. I'm aware of two choices. Intuitionist logic, such that statements are not true until proven, and paraconsistent logic, rejecting ex contradictione quodlibet. — Banno
However, I do not claim omniscience. Instead, I would argue that truth implies knowledge. This is the conclusion of the argument, after all: for all p, if p is true, then it is known that p is true. The reason that the (NonO) statement is false is because p is true implies p is known, so there cannot be any p for which p is true and p is unknown. The reason that p is true implies p is known is because p cannot be true without knowing the meaningful proposition represented by p. Again, this results from the equivocation over the meaning of p and the truth of p. — Luke
p→♢Kp — Banno
It's taken as true by various philosophical notions, explicitly or more often implicitly. Those notions that do so must explain how they deal with Fitch.
The argument doesn't asserting it, but uses it hypothetically to show that consequence, — Banno
andThen that's a denial of the knowability principle. — Michael
No. Just a hypothetical. If p then q. — Banno
So is our conclusion to be that those who thinks that only things that have been proved true are true is muddled, or that Fitch's paradox is faulty? — Banno
I think it's trivially true that the knowabilty principle cannot apply to propositions about our own knowledge — Isaac
is it really a problem to say that all meaningful propositions, except propositions like "this statement is false", have a truth value? Or is that special pleading? — Michael
Perhaps we can say (as me and Banno discussed in the other thread) that empirical truths are subject to the knowability principle, but that the truth of self-referential knowledge claims, counterfactuals, predictions, mathematics, etc. work differently? — Michael
I wasn't complaining. I just gave you FOUR reasons why I, personally don't use a specialized language. And also because you asked me what kind of logic I'm using, most probably assuming that I would or should know ...Not much point in complaining about he use of specialised language in a thread on logic. — Banno
the whole field of 'truth', and 'knowledge' is made into a quagmire by the use of a JTB definition of knowledge. — Isaac
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