PROBABILITY: THROW OF A
DIE
The fourth law of logic is
absolutely indispensable in physics. We use it every day and do not
realize it in probability. But what after all is probability? Let us use
a very simple example to get at the answer to that question. Let us use
the face of a die turned up. How can I model that, before the die is
thrown?
Now we can only think by operationalism. To operate and output
something is to automatically put it in the past. It's happened, it's
gone, the moment you do it. To perceive an object is to put it in the
past. To determine it is to put it in the past. To observe it is to put
it in the past. There is no observed, perceived, detected, measured, or
determined present. That is, there is no separated, exclusive,
determined present such as is specified by the first three laws of logic—the
fourth law is the present, by the way—but
in observational physics which deals with determined, observed past
phenomena, there exists no present. The future has not yet been
observed, so it also is the unobserved. Only the past therefore is the
observed. How then can one ever hope to model the unobserved present or
the unobserved future?
If I look at the problem of the die with one face up, it is in the
past. When I see it, it is in the past. When I think it, it is in the
past. So if all I can observe, think, or perceive is the die in the
past, how can I ever model it in the future? It's very simple! If I
drive any problem set to its absolute boundary limit, it turns into its
own opposite by the fourth law of logic, by the law of the boundary. So
how do I do that with this problem of the die?
The problem set is specified by the condition "the perceived die
with one face up"; this is the most recent past. Now simply find all the
most immediate pasts you can get to meet the condition specified, and
gather them all up together, and they then must turn into and comprise
precisely the opposite, the immediate future. In this problem set, I can
construct and collect six such pasts, each consisting of the perceived
die with one face up. So by the fourth law of logic, those six faces up
collected together as an ensemble represent the future and in fact are
identical to the future. The present, which is simply the boundary
between the most immediate past and the most immediate future, was
specified by applying the fourth law of logic in the first place: the
identity of the most immediate past and the most immediate future, being
binocular, is unperceived, but it is the present nonetheless. So that is
what probability is—an application
of the fourth law of logic, so that the most immediate future can be
represented in terms of the most immediate past—and
physicists and mathematicians have been doing this ever since they have
been doing physics and mathematics.
Without the fourth law of logic, there exists no rigorous logical
basis for probability! So the fourth law is a very useful law indeed. We
have simply failed to realize that we have been applying it all along.
The ontological problem can also be solved as follows: to state that
"A is not" is to state that "A is" is not; to absent a
presented thing is to first present it; to be "not-being" is a clear
statement of the problem. By the first three laws of logic, the problem
is not soluble. By the fourth law, it is simple since being and
not-being can be identified. All distinction between present (being) and
absent (not being) can be lost. |