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By D I Blockley

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2 theory may be a basic theory for all physics and one micro-state may only be predicted from another by statistical means, it does not necessarily follow that the overall behaviour of macro-states cannot be related to each other by nonstatistical means. This, of course, is the reason why the theory of structural analysis has been able to develop as far as it has without recourse to statistics. However, the major inlplication of the success of quantum theory, as we have seen earlier, is clear. Science can no longer claim to be 'true' or even approaching 'the truth'.

However, this does not deny that the conclusion is a useful one. We shall find that since mathematics is based on a more complex deductive system, it rllay be argued that it is also analytic although its axioms are synthetic. We will return to these ideas in Chapter 5 when considering the nature of the mathematics of uncertainty and its reliance on set theory, which itself is grounded on deductive logic. For the moment it is important to note that the logic is based upon two truth values, a statement is either true or false.

In order for the air to be warm it is necessary that the sun be shining. Gemignani states these conditions formally as follows: Condition A is a sufficient condition for condition B, provided B always occurs when A occurs. That is, we have If A , then B. Condition A is a necessary condition for B, provided B cannot occur unless A also occurs. That is, B only if A. e. A if and only i f B . Sec. 51 Deduction 5 It should be noted that if A is a sufficient condition for B, even though. ::^; distinction to be made later with regard to reasons for structur; failure.

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