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         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.  |