allzermalmer

Truth suffers from too much analysis

Posts Tagged ‘Knowability’

The Aim is the Search for Universal Laws

Posted by allzermalmer on October 22, 2013

I would rather discover one true cause than gain the kingdom of Persia.
Read more at http://www.brainyquote.com/quotes/authors/d/democritus.html#Ti0otIFKyo1RksRu.99“I would rather discover one true cause than gain the kingdom of Persia1. There exists at least one (empirical) principle that is true at describing an invariable relationship of the empirical world. (expressed) 2. There exists at least one possible (empirical) principle that is true at describing an invariable relationship¬† of the empirical world.¬† (expressed or not express3. There exists at least one invariable relationship of the empirical world.

“I would rather discover one true cause than gain the kingdom of Persia.” Democritus

Question: “Does there exist one true cause?”

The answer to this question, is answered in the affirmative by some and answered in the negative by some.

Affirmative: There does exist at least one causal relationship between events.
Negative: There doesn’t exist at least one causal relationship between events.

Both answers to the question are logically possible. There is no self-contradiction in either proposition. So it is possible that there does exist at least one causal relationship between events & it is possible that there doesn’t exist at least one causal relationship between events.

Suppose that we have someone similar to Democritus, they would be searching for at least one true causal relationship. It is possible that they don’t find what they are searching for since it is possible that there doesn’t exist at least one causal relationship between events.

So we can have the Aim of Searching for Universal Laws, but that doesn’t mean that what we search for is true or that we will find what we search for. In both cases we would neither be able to find what we search for (since it doesn’t exist) nor search for what is true (since it isn’t true).

We can have a methodological principle that there does exist at least one causal relationship between events. All our actions would be consistent with this methodological principle, but none of this is asserting that there actually does exist at least one causal relationship between events because it is possible that there doesn’t actually exist at least one causal relationship. This implies that our assertion was false, which implies that we didn’t find at least one true causal relationship.

The whole endeavor would be predicated on a fiction, and everything produced within the endeavor would be fictional as well. Even the single processes, or plural processes, used in this endeavor would only have input of fictions and output of fictions. It would be similar to comic books, having fictional characters as input in their process and fictions as the output in their process.

Suppose that there actually does exist a causal relationship between events. It is logically possible that both there exists at least one causal relationship between events & we don’t know this one causal relationship between events. However, it is logically impossible that we know both there exists at least one causal relationship between events & we don’t know this one causal relationship between events.

Suppose we know that both there exists at least one causal relationship between events & we don’t know this one causal relationship between events. It follows that, we know there exists at least one causal relationship between events and we know we don’t know this one causal relationship between events. We know there exists at least one causal relationship between events & we don’t know this one causal relationship between events. This is a contradiction, so it is necessary we don’t know both there exists at least one causal relationship between events & we don’t know this one causal relationship between events. From all this it follows we don’t know there exists at least one causal relationship. Since we don’t know there exists at least one causal relationship, it means that we can’t know that there exists at least one causal relationship.

The very Aim of the Search for Universal Laws would be of something that you can’t possibly know, even if you did obtain what you were searching for.

 

 

 

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Paradox of Knowability

Posted by allzermalmer on April 12, 2013

Theorem 5: If there is some true proposition which nobody knows (or has known or will know) to be true, then there is a true proposition which nobody can know to be true

“There are truths that cannot be known. For suppose that all truths can be known. Then all truths actually are known. Otherwise, we may suppose for some p that p but it is not known that p. Then it can be known that p but it is not known that p. But when it is known that thus and such, it is known that thus and it is known that such. So it could be known that p and known that it is not known that p. But what is known is true. So it could be known that p and not known that p. But that is a contradiction, and no contradiction can be true. So all truths are actually known.” W.D. Hart

(1) Assume that if X is true then possible to know that X is true. (2) Then, if X is true & do not know that X is true, then possible to know that both X is true & do not know X is true. (3) But, not possible to know that both X is true & do not know X is true. (4) Not both X is true & do not know X is true. (5)  If X is true then do not not know that X is true. (6) If X is true then know that X is true.

What if the World is non-omniscient? This would mean that nobody knows all truths, and nobody ever will. Therefore, there are unknowable truths. If some truth is unknown, then that it is unknown is itself unknowable; Because the world is non-omniscient, there is some unknowable truth. If there at exists at least one Truth, such that Truth is true and Truth is unknown, then there exists at least one Truth, such that Truth is unknown and Truth is unknowable. If there does not exist at least one Truth, such that Truth is unknown and Truth is unknowable, then there does not exist at least one Truth, such that Truth is true and Truth is unknown.

It is possible that it is known by someone at some time that both X is true & It is not known by someone at some time that X is true. It is possible that both It is known by someone at some time that X is true & It is not known by someone at some time that X is true (reduction ad absurdum)

Non-Omniscience: X is true & It is not known by someone at some time that X is true.

Verdicality (KV): If it is known by someone at some time that X is true, then X is true.

Distribution (KC): If it is known by someone at some time that both X is true & Y is true, then both it is known by someone at some time that X is true & It is known by someone at some time that Y is true.

Non-Contradiction (LNC): It is not possible that both X is true & X is not true.

Clousure (CP): If X is true implies Y is true & it is possible that X is true, then it is possible that Y is true.

Knowability (KP): If X is true then it is possible that it is known by someone at some time that X is true.

(1) Assume that X is true & It is not known by someone at some time that X is true

(2) It is possible that it is known by someone at some time that both X is true & It is not known by someone at some time that X is true. (By KP & (1).

(3) It is known by someone at some time that both X is true & It is not known by someone at some time that X is true. It is known by someone at some time that X is true & It is known by someone at some time that it is not known by someone at some time that X is true.

(4) It is known by someone at some time that both X is true & it is not known by someone at some time that X is true. It is known by someone at some time that X is true & It is not known by someone at some time that X is true. (By Simp, VK, and Adjunction (and Transitivity implication))

(5) It is possible that both It is known by someone at some time that X is true & It is not known by someone at some time that X is true. (by CP)

(6) It is not possible that both It is known by someone at some time that X is true & It is not known by someone at some time that X is true. (by LNC)

(7) It is necessary that not both X is true & X is not true.

*(8) X is true & It is known by someone at some time that X is true. (by Reduction Ad Absurdim)

Thus, If X is true, then it is known by someone at some time that X is true:: If it is not known by someone at some time that X is true, then X is not true.

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