We consider the problem of induction over languages containing binary relations and outline a way of interpreting and constructing a class of probability functions on the sentences of such a language. Some principles of inductive reasoning satisfied by these probability functions are discussed, leading in turn to a representation theorem for a more general class of probability functions satisfying these principles.

This paper attempts to place Goodman's "New Riddle of Induction" within the context of a subjectivist understanding of inductive logic. It will be argued that predicates such as 'grue' cannot be denied projectible status in any a priori way, but must be considered in the context of a situation of inductive support. In particular, it will be argued that questions of projectibility are to be understood as a variety of questions about the ways a given sample is random. Various examples (...) are considered, including cases when 'grue' (as opposed to 'green') should be projected, and some remarks are offered on what is meant when it is claimed that a sample is random (in ways relevant to inductive support) and how such randomness is determined. The view presented helps to make clear the relation between such apparently non-projectible predicates as 'grue' and the concept of being examined. (shrink)

Nelson Goodman's new riddle of induction wears many faces. In one of its guises the new riddle of induction appears as the problem of providing a general account of the distinction between projectible and non-projectible predicates. This is the form of the riddle which is supposed to point up a lacuna in the foundations of confirmation theories such as Carnap's which, Goodman charges, work only to the extent that one builds into them just the right predicates. As a new riddle (...) of induction, the problem of distinguishing projectible from non-projectible predicates has the virtue that it is in fact new—a virtue not shared by some other forms of the riddle.Philosophers had recognized previously that some predicates are more projectible than others in the sense that, for instance, the prediction that a certain toss of a die will turn up an even face is safer and more likely to be true than the prediction that the same toss will turn up six. (shrink)

My dissertation explores the ways in which Rudolf Carnap sought to make philosophy scientific by further developing recent interpretive efforts to explain Carnap’s mature philosophical work as a form of engineering. It does this by looking in detail at his philosophical practice in his most sustained mature project, his work on pure and applied inductive logic. I, first, specify the sort of engineering Carnap is engaged in as involving an engineering design problem and then draw out the complications of design (...) problems from current work in history of engineering and technology studies. I then model Carnap’s practice based on those lessons and uncover ways in which Carnap’s technical work in inductive logic takes some of these lessons on board. This shows ways in which Carnap’s philosophical project subtly changes right through his late work on induction, providing an important corrective to interpretations that ignore the work on inductive logic. Specifically, I show that paying attention to the historical details of Carnap’s attempt to apply his work in inductive logic to decision theory and theoretical statistics in the 1950s and 1960s helps us understand how Carnap develops and rearticulates the philosophical point of the practical/theoretical distinction in his late work, offering thus a new interpretation of Carnap’s technical work within the broader context of philosophy of science and analytical philosophy in general. (shrink)