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By Yousif Mustafa, Clara Maingi

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Sample text

From these observables one can specify an initial set of states, namely, one for each assignment of values to the three attributes. The gas in the laboratory is in exactly one of these states at a time. Which state it is in can be determined by measurement. The set of possible states is pared down by further investigation. Boyle's law tells us that only those states in which the product of the pressure and the volume is some specific multiple of the temperature are possible. This gives us a way of understanding information flow.

These form the tokens of a classification. Each toss x has, we assume, some state state(x) E { (n, m} 1 1 ::; n , m ::; 6}. For example, the state of (d1 , dz, t} is ( 1 , 5) if and only if d1 lands at t with the numeral 1 showing and dz lands at t with the numeral 5 showing. The types of our classification are, then, the events over Q, that is, subsets a s; Q, and x F= a if and only if the state of x is in a . A s these examples illustrate, w e sometimes take the tokens of a classification to be structureless mathematical objects, while at other times we give them struc­ ture so as to relate them to other tokens of other classifications more effectively.

Information and the Elimination of Possibilities A familiar idea in the philosophy of language is that the semantic value of a statement is given by the set of "possible worlds" in which it is true. This can be used to give an account of information content: r being F carries the information that s is G if in all the possible worlds compatible with k and in which r is F, s is G (and there is at least one possible world compatible with k in which s is not G). Possible-Worlds Information Content: To a person with prior knowledge k, Applying this account to epistemology, we see that it gives us a counterfactual account: whether one knows that p depends not only on the facts of this world but also on what goes on in other possible worlds.

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