I'm not sure what the distinction is doing here at all. You introduced it. But presumably, extensionally, X is a cup if and only if X is a cup. Extensionally, we are able to substitute salva veritate. I'm not sure that works for P2. Especially with the vacillation between "seen" and "used as".I'm not sure how that distinction applies to that premise. — Michael
This is the sort of argument that an anti-realist might make:
P1. A cup exists if and only if there exists some X such that X is a cup
P2. For all X, X is a cup only if X is being seen or used as a cup
C1. Therefore, a cup exists only if there exists some X such that X is being seen or used as a cup — Michael
I'm not sure what the distinction is doing here at all. You introduced it. But presumably, extensionally, X is a cup if and only if X is a cup. — Banno
I am hunting around for something to tie down your idea. — Banno
I don't see any difference between "being used as a cup" & "having potential for being used as a cup" , both carry the same purpose as far as they allow us to group objects under a universal like "cup" — Sirius
Simply saying that X is a cup if and only if X is a cup or that X is a king if and only if X is a king is vacuous, and doesn't address any philosophical dispute. — Michael
extensionally, X is a cup if and only if X is a cup. Extensionally, we are able to substitute salva veritate — Banno
If an alien species from another planet saw Moore with his raised hand, they might be just as certain as Moore that something with a specific meaning was taking place, but within their alien language game the sense of the event would be entirely different that it is for Moore. It would not be a question of doubting Moore’s assertion, but of his assertion being irrelevant to their perspective. — Joshs
It does not matter how we specify the set, or how we order its elements, or indeed how many times we count its elements. All that matters are what its elements are. — Open Logic p. 25
Not too sure about that...And I should clarify, you talk about "all truths being known" in reference to Fitch's paradox, but the relevant claim under consideration is "all truths are knowable", a subtle but important difference. — Michael
(K Paradox) ∀p(p→◊Kp)⊢∀p(p→Kp). — Fitch’s Paradox of Knowability
if the only things that are true are the things that we know to be true — Banno
Not following that. — Banno
Fitch’s paradox of knowability (aka the knowability paradox or Church-Fitch Paradox) concerns any theory committed to the thesis that all truths are knowable. Historical examples of such theories arguably include Michael Dummett’s semantic antirealism (i.e., the view that any truth is verifiable), mathematical constructivism (i.e., the view that the truth of a mathematical formula depends on the mental constructions mathematicians use to prove those formulas), Hilary Putnam’s internal realism (i.e., the view that truth is what we would believe in ideal epistemic circumstances), Charles Sanders Peirce’s pragmatic theory of truth (i.e., that truth is what we would agree to at the limit of inquiry), logical positivism (i.e., the view that meaning is giving by verification conditions), Kant’s transcendental idealism (i.e., that all knowledge is knowledge of appearances), and George Berkeley’s idealism (i.e., that to be is to be perceivable).
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The great problem for the middle way is Fitch’s paradox. It is the proof that shows (in a normal modal logic augmented with the knowledge operator) that “all truths are knowable” entails “all truths are known”.
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