The fact referred to we call the signal or indicating fact. The thermometer is the carrier, the property of containing mercury that has risen past 98.6 is the indicating property. The proposition that Elwood has a fever is the incremental informational content of the signal. The property of having a fever is the indicated property; Elwood is the subject matter. A signal has incremental content, given a connecting fact and relative to a constraint. 1 In this case, the connecting fact (...) is that the thermometer is in Elwood’s mouth, the connecting relation is that of one thing being in the mouth of another, and the constraint C 1 is. (shrink)
Information is a notion of wide use and great intuitive appeal, and hence, not surprisingly, different formal paradigms claim part of it, from Shannon channel theory to Kolmogorov complexity. Information is also a widely used term in logic, but a similar diversity repeats itself: there are several competing logical accounts of this notion, ranging from semantic to syntactic. In this chapter, we will discuss three major logical accounts of information.
We sketch the historical and conceptual context of Turing's analysis of algorithmic or mechanical computation. We then discuss two responses to that analysis, by Gödel and by Gandy, both of which raise, though in very different ways. The possibility of computation procedures that cannot be reduced to the basic procedures into which Turing decomposed computation. Along the way, we touch on some of Cleland's views.
Kaplan says that monsters violate Principle 2 of his theory. Principle 2 is that indexicals, pure and demonstrative alike, are directly referential. In providing this explanation of there being no monsters, Kaplan feels his theory has an advantage over double-indexing theories like Kamp’s or Segerberg’s (or Stalnaker’s), which either embrace monsters or avoid them only by ad hoc stipulation, in the sharp conceptual distinction it draws between circumstances of evaluation and contexts of utterance. We shall argue that Kaplan’s prohibition is (...) also essentially stipulative, and that it is too general. The main difference between ourselves and Kaplan is that the basic carriers of a truth-value is a sentence-in-a-context; our account is utterance-based. (shrink)
Brutus wanted to kill Caesar. He believed that Caesar was an ordinary mortal, and that, given this, stabbing him (by which we mean plunging a knife into his heart) was a way of killing him. He thought that he could stab Caesar, for he remembered that he had a knife and saw that Caesar was standing next to him on his left, in the Forum. So Brutus was motivated to stab the man to his left. He did so, thereby killing (...) Caesar. We have explained Brutus’s act by citing a complex of beliefs, desires and perceptions that motivated it. Our explanation provides a causal account of Brutus’s act. The beliefs, desires and perceptions in such a motivating complex are particular cognitions. The act was also a particular, an event that occurred at a certain place and time. The cognitions caused the act.1 Our explanation also provides a rationale for Brutus’s act. The beliefs, desires and perceptions of Brutus’s that we cite had contents. The desire we cited had the content that Brutus kill Caesar. The ﬁrst belief we cited had the content that Caesar was an ordinary mortal. The act was of a certain type. The explanation provides a rationale because the contents of the cognitions mesh in a certain way with one another and with the type of the act. It was the type of act that would satisfy Brutus’s desire to kill 1 Caesar, if the beliefs we cited were true. If the person next to him is Caesar, and Caesar is mortal, and stabbing is a way of killing the mortal next to one, then an act of that type will satisfy Brutus’s desire. The beliefs in the motivating complex “close the gap” between the type of act motivated and the motivating desire. (shrink)