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By Walter Philipp

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Extra info for Almost sure invariance principles for partial sums of weakly dependent random variables

Sample text

It is a consequence of (i) above that the ratio T(a) - T(b) T(c) - T(d) is invariant for given objects a, b, c, and d, no matter which scale of temperature is used to measure it. It is a further important consequence that the average of two temperatures is also invariant in the following sense: If the temperature of the object a is midway between those of band c, that will be so no matter which scale is employed to measure temperature: T(a) = T(b) - T(c) 2 is either true for all scales, T, of temperature or true for none.

These dispositions conflict if the agent when hungry encounters a packaged yellow mushroom. Of course, the set of beliefs consisting of (i), (ii) and (v) There are packaged yellow mushrooms. is inconsistent, and thus upon encountering a packaged yellow mushroom, the agent has an inconsistent set of beliefs. But if we, the observers, know (v) to be true, and know also that the agent disbelieves it, then our account of his beliefs (i) and (ii) in terms of the dispositions (iii) and (iv) can't be quite right, since we attribute to him dispositions not both of which can be his.

This argument may lead us to judge the denial of the premise. Similarly, in the case of believing a negation, we may allow what is negated, a part of the content, to be before the mind, and think of the judgment, which carries conviction with it, as applying only to the whole content judged. Mentalistic theories which allow distinct sorts of acts of the mind allow also for a different sort of treatment oflogical connectives than do theories such as Hume's:18 We may think of judging not-A, for example, asjudging A negatively, or, simply, as denying A, where denying and affirming are different species or judgment.

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