Solution to Fitch's Paradox
Posted: Sat Mar 23, 2024 4:07 am
As I understand it, Fitch's paradox seems to be the strange conclusion that if all truths are knowable, then all truths MUST be known. In other words, it's impossible for there to be an unknown truth if all truths are knowable.
Here's the original argument for this. I've taken the argument from wikipedia:
Suppose p is a sentence that is an unknown truth; that is, the sentence p is true, but it is not known that p is true. In such a case, the sentence "the sentence p is an unknown truth" is true; and, if all truths are knowable, it should be possible to know that "p is an unknown truth". But this isn't possible, because as soon as we know "p is an unknown truth", we know that p is true, rendering p no longer an unknown truth, so the statement "p is an unknown truth" becomes a falsity. Hence, the statement "p is an unknown truth" cannot be both known and true at the same time. Therefore, if all truths are knowable, the set of "all truths" must not include any of the form "something is an unknown truth"; thus there must be no unknown truths, and thus all truths must be known.
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I wanted to take an attempt at providing a solution to this paradox.
My solution is this: In the sentence "p is an unknown truth", we need to examine the specific word "is".
Let's say there was a ball that fell out of a bag into a forest, and no one knew for 3 years.
In the first year where no one knew, it can be said "it's unknown the ball is in the forest"... or more simply it's an unknown truth. But to be very specific what we are really saying is: "at this point in time, it's unkown the ball is in the forest".
In the second year we can say the same.
In the third year, Jimmy stumbles upon the ball. According to this paradox, it's not possible for this unknown truth to be true anymore because Jimmy now knows it. And more nonsensically this unknown truth could have never existed in the first place and all truths must be known.
This illustrates the flaw of this paradox as well as the solution. Timing must be taken into consideration for the word "is". It's logically allowed for both unknown truths to exist and for all truths to be knowable. Once an unknown truth becomes known, it doesn't become false. Because the "unknown" aspect of the statement logically could only ever apply to it for the time that no one knew about it. So statements like "p is an unknown truth" can be true because they are temporally bound and "is" can only ever refer to the time when they are unknown. To be more specific, what the sentence is truly saying is: "At a certain specific time or range of time p is an unknown truth". That solves this paradox.
Here's the original argument for this. I've taken the argument from wikipedia:
Suppose p is a sentence that is an unknown truth; that is, the sentence p is true, but it is not known that p is true. In such a case, the sentence "the sentence p is an unknown truth" is true; and, if all truths are knowable, it should be possible to know that "p is an unknown truth". But this isn't possible, because as soon as we know "p is an unknown truth", we know that p is true, rendering p no longer an unknown truth, so the statement "p is an unknown truth" becomes a falsity. Hence, the statement "p is an unknown truth" cannot be both known and true at the same time. Therefore, if all truths are knowable, the set of "all truths" must not include any of the form "something is an unknown truth"; thus there must be no unknown truths, and thus all truths must be known.
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I wanted to take an attempt at providing a solution to this paradox.
My solution is this: In the sentence "p is an unknown truth", we need to examine the specific word "is".
Let's say there was a ball that fell out of a bag into a forest, and no one knew for 3 years.
In the first year where no one knew, it can be said "it's unknown the ball is in the forest"... or more simply it's an unknown truth. But to be very specific what we are really saying is: "at this point in time, it's unkown the ball is in the forest".
In the second year we can say the same.
In the third year, Jimmy stumbles upon the ball. According to this paradox, it's not possible for this unknown truth to be true anymore because Jimmy now knows it. And more nonsensically this unknown truth could have never existed in the first place and all truths must be known.
This illustrates the flaw of this paradox as well as the solution. Timing must be taken into consideration for the word "is". It's logically allowed for both unknown truths to exist and for all truths to be knowable. Once an unknown truth becomes known, it doesn't become false. Because the "unknown" aspect of the statement logically could only ever apply to it for the time that no one knew about it. So statements like "p is an unknown truth" can be true because they are temporally bound and "is" can only ever refer to the time when they are unknown. To be more specific, what the sentence is truly saying is: "At a certain specific time or range of time p is an unknown truth". That solves this paradox.