quinta-feira, 23 de outubro de 2014

Russell's Unobjectionable Statement

In his book a "A History of Western Philosophy", Bertrand Russell concludes that something which is unperceived, such as an "unperceived house" is unobjectionable, in the sense that it cannot be proved to be true or false (at least logically). I partially disagree, I think that such a statement, in certain cases, can be proved to be true or false. This is not so much a critique, as an extension of thought on this issue. Consider the list of existing houses that are perceived by us:

{h1,h2,h3,h4,...hn}.

We do not perceive an unlimited number of existing houses, therefore this list is necessarily limited, since "perception" of a house requires a mental concept of a certain house that we suppose to exist. If someone states "Actually, there is an unperceived house which you are not considering", I will add this house to the list of existing houses, with the only difference being that this one cannot be perceived.

{h1, h2, h3, h4,...hn, h1(unp.)}.

Now we have n+1 houses in our list of existing houses, n perceived, 1 unperceived. Then I will ask if there are more houses which are unperceived. If there are not, then it is refuted. If there is, I will add one more:

{h1, h2, h3, h4,...hn, h1(unp.), h2,(unp.)}.

Now, if we do this a sufficient number of times, the statement "There is unperceived house which you are not considering" must necessarily be, at some point onward, false, since the number of existing houses on the (observable) universe is, by definition, finite, since matter and energy are finite in this case. However, whenever we can accurately evaluate the quantity of matter or energy present in a certain region of spacetime, we know not only that this statement must be false at a certain point, but we can even estimate at which point it is false, rendering the statement logically objectionable. Thus, the statement "A exists unperceived" is only unobjectionable (both logically and empirically) when we consider an infinite universe with infinite mass and energy.

quinta-feira, 9 de outubro de 2014

Time and Causality

Suppose A and B to be simultaneous events happening at time t.

If C imples A that implies B (C -> A -> B) then no time passes from A to B because both arise at the same time. It follows that C -> A -> B is indistinguishible from C -> B -> A, or from C -> A and C -> B. Therefore, it is not possible to infer causality on two simultaneous events, or, put another way, to infer causality is to implicitly state dt > 0 between any two events.