Online research in philosophy

This paper deals with, prepositional calculi with strong negation (N-logics) in which the Craig interpolation theorem holds. N-logics are defined to be axiomatic strengthenings of the intuitionistic calculus enriched with a unary connective called strong negation. There exists continuum of N-logics, but the Craig interpolation theorem holds only in 14 of them.

A semantical proof of Craig's interpolation theorem for the intuitionistic predicate logic and some intermediate prepositional logics will be given. Our proof is an extension of Henkin's method developed in [4]. It will clarify the relation between the interpolation theorem and Robinson's consistency theorem for these logics and will enable us to give a uniform way of proving the interpolation theorem for them.

We review some known results about the Ramsey property for partitions of reals, and we present a certain two-person game such that if either player has a winning strategy then a homogeneous set for the partition can be constructed, and conversely. This gives alternative proofs of some of the known results. We then discuss possible uses of the game in obtaining effective versions of Ramsey's theorem and prove a theorem along these lines.

It is usually taken for granted that orthodox quantum theory poses a serious problem for scientific realism, in that the theory is empirically extraordinarily successful, and yet has instrumentalism built into it. This paper stand this view on its head. I argue that orthodox quantum theory suffers from a number of serious (if not always noticed) defects precisely because of its inbuilt instrumentalism. This defective character of orthdoox quantum theory thus undermines instrumentalism, and supports scientific realism. I go on to consider whether there is here the basis of a general argument against instrumentalism.

This is an immediate conse-quence of a more general combinatorial theorem called Ramsey’s theorem, but it is much simpler to state. We call this adjacent Ramsey theory.

It is often thought that questions of reference are crucial in assessing scientific realism, construed as the view that successful theories are at least approximately true descriptions of the unobservable; realism is justified only if terms in empirically successful theories generally refer to genuinely existing entities or properties. In this paper this view is questioned. First, it is argued that there are good reasons to think that questions of realism are largely decided by convention and carry no epistemic significance. An alternative conception of realism is then proposed, which focuses on the Ramsey sentences of scientific theories, constructed in the manner of David Lewis's 'How to define theoretical terms'. It is argued that because the Ramsey sentence of a theory preserves the epistemically significant part of the theory's content without generating commitments to any particular conclusions about reference, the realism issue is better addressed by asking whether Ramsey sentences of theories, rather than the theories themselves, are approximately true.

Scientific realists often appeal to some version of the conjunction objection to argue that scientific instrumentalism fails to do justice to the full empirical import of scientific theories. Whereas the conjunction objection provides a powerful critique of scientific instrumentalism, I will show that mathematical instrumentalism escapes the conjunction objection unscathed.

The method of Ramsey sentences has been proposed for handling theoretical constructs within a scientific system. Essentially it consists of constructing a certain "monolithic" sentence for an entire theory. In this present paper several improvements are suggested which help to overcome some of the awkward features of the method. In particular we have here many Ramsey sentences rather than just one, each erstwhile primitive theoretical term giving rise to a Ramsey sentence. Such a sentence in effect defines what we call a Ramsey constant. Using Ramsey constants, we attempt to improve the method in important logical and semantical respects. It is suggested also that such constants are of interest for the philosophy of mathematics.

In the present paper I want to do two things. First, I want to discuss Ramsey’s own views of Ramsey-sentences. This, it seems to me, is an important issue not just (or mainly) because of its historical interest. It has a deep philosophical significance. Addressing it will enable us to see what Ramsey’s lasting contribution in the philosophy of science was as well as what its relevance to today’s problems is. Since the 1950s, where the interest in Ramsey’s views has mushroomed, there have been a number of different ways to read Ramsey’s views and to reconstruct Ramsey’s project. The second aim of the present paper is to discuss the most significant and controversial of this reconstruction, viz., structuralism. After some discussion of the problems of structuralism in the philosophy of science, as this was exemplified in Bertrand Russell’s and Grover Maxwell’s views and has re-appeared in Elie Zahar’s and John Worrall’s thought, I will argue that, for good reasons, Ramsey did not see his Ramsey-sentences as part of some sort of structuralist programme. I will close with an image of scientific theories that Ramsey might have found congenial. I will call it Ramseyan humility.

In mathematical logic, Craig’s Theorem (not to be confused with Craig’s Interpolation Theorem) states that any recursively enumerable theory is recursively axiomatizable. Its epistemological interest concerns its possible use as a method of eliminating “theoretical content” from scientific theories.