Talk:Fitch's paradox of knowability

From Wikipedia, the free encyclopedia

Socrates
Philosophy Portal
This article is within the scope of the WikiProject Philosophy, which collaborates on articles related to philosophy. To participate, you can edit this article or visit the project page for more details.
Stub This article has been rated as Stub-Class on the quality scale.
Low This article has been rated as low-importance on the importance scale.

[edit] Lengthy deleted text

The following text has been added by various contributors:

A concise statement of Fitch's paradox is: "It is impossible for all truths to be knowable unless all truths are known, because the fact of an unknown truth existing is unknowable."
As a simple example, suppose that your friends are considering throwing you a surprise party. It is then impossible for you to even know that the statement "My friends are throwing me a surprise party" is true; if you ever did know that, then the party would no longer be a surprise, and the statement would become false. Thus, you can know that this statement is false, but it's impossible for you to ever know that it is true. In spite of this, it is perfectly possible for that statement to be true; all of your friends can know about it and it will remain true as long as you don't know about it.
That example covered the knowledge of only one person, but it can be taken further. There is an old children's riddle: "What was the tallest mountain in the world before Mount Everest was discovered?" The answer is "Mount Everest", because Mount Everest still existed - and was still, in fact, the tallest mountain in the world - even before it was discovered; we just didn't know it.
Thus, prior to the discovery of Mount Everest, the statement "Mount Everest (or, to be pedantic, the mountain that would later be named Mount Everest) is the tallest mountain in the world, but nobody knows it" was perfectly true. However, just as with the "surprise party" statement, it was impossible for anyone to know that it was true - because as soom as anyone knows it, it becomes false.
The paradox, therefore, is that if we assume that there are some statements that are true which we are not yet aware of - undiscovered scientific principles, information about the future, secrets yet to be revealed, and similar - then for any such statement, the fact that "(the statement) is true, but we don't know it" is true, but it's impossible for us to ever know it. Thus, there must be some true statements which are unknowable, and thus not all truths are knowable. This is a very uncomfortable conclusion, but the only escape - assuming that we already know all there is to know, so that no statements of the form above can exist and be true - is even more uncomfortable.

The above text is not about Fitch's paradox. It is perhaps about the paradox of the knower, which is quite different. --- Charles Stewart 19:48, 18 August 2005 (UTC)


I wrote the text above based on the first of the two linked pages, namely http://plato.stanford.edu/entries/fitch-paradox/, which describes the paradox (translated from formal logic notation) as:

  • Suppose knowability: For all propositions p, if p is true then p can be known at some time.
  • Suppose non-omniscience: There exist some proposition(s) p such that all p are true but no p is known at any time.
  • Instantiate: There exists a particular proposition p such that p is true and p is not known at any time.
  • Substitute above statement into knowability: if the proposition that, "There exists a particular proposition p such that p is true and p is not known at any time" is true, then it can be known at some time.
  • Modus Ponens: since we are assuming that "There exists a particular proposition p such that p is true and p is not known at any time" is indeed true, then it must indeed be possible for "There exists a particular proposition p such that p is true and p is not known at any time" to be known.
  • But it can't be, because as soon as you know it, you know p, and then the part of the conjunction stating that "p is not known at any time" becomes false.

The "surprise party" example describes a single knower, but the later example concerning Everest is intended to apply to the whole range of agents capable of knowing things, which yields Fitch's Paradox as above. -- Hyphz