The article begins by distinguishing a number of theses which, in the past, have sometimes been lumped together under the heading of 'anti-realism'. One of the theses is that there is something wrong with truth-conditional theories of meaning (what a truth-conditional theory of meaning is a matter discussed at some length), another is what I take to be the central thesis of anti-realism, that all truths are knowable. Several writers on the subject, such as Wright and Prawitz, have defended the (...) latter thesis while jettisoning the former. I argue that this position is exactly the wrong way around. Given the 'meaning is use' principle, which is also called the 'manifestation requirement', a very powerful case can be made that true theory of meaning cannot be truth-conditional. But I argue that, given the current state of our logical knowledge, there is no good reason for concluding from this that a true theory of meaning must be of the 'verificationist' type, as Dummett seems to think, and still less for thinking that anti-realism follows. I end by examining theories of meaning against Dummett's criticisms. (shrink)

In An Intimate Relation: Studies in the History and Philosophy of Science (presented to Robert E. Butts on his 60th Birthday).

William R. Stirton; III*—The Logical Status of ‘Exists’, Proceedings of the Aristotelian Society, Volume 95, Issue 1, 1 June 1995, Pages 37–50, https://doi.org/.

William R. Stirton; III*—The Logical Status of ‘Exists’, Proceedings of the Aristotelian Society, Volume 95, Issue 1, 1 June 1995, Pages 37–50, https://doi.org/.

The article investigates a system of polymorphically typed combinatory logic which is equivalent to Gödel’s T. A notion of (strong) reduction is defined over terms of this system and it is proved that the class of well-formed terms is closed under both bracket abstraction and reduction. The main new result is that the number of contractions needed to reduce a term to normal form is computed by an ε 0-recursive function. The ordinal assignments used to obtain this result are also (...) used to prove that the system under consideration is indeed equivalent to Gödel’s T. It is hoped that the methods used here can be extended so as to obtain similar results for stronger systems of polymorphically typed combinatory terms. An interesting corollary of such results is that they yield ordinally informative proofs of normalizability for sub-systems of second-order intuitionist logic, in natural deduction style. (shrink)

The main purpose of this article is to argue that Crispin Wright and Bob Hale have not succeeded in overcoming the well-known ‘Julius Caesar objection’ to their proposed definition of the phrase ‘the number of’. It is hoped that the article will also help to clarify what would actually be needed in order to overcome this objection.

This article investigates a theory of type assignment (assigning types to lambda terms) called ETA which is intermediate in strength between the simple theory of type assignment and strong polymorphic theories like Girard’s F (Proofs and types. Cambridge University Press, Cambridge, 1989). It is like the simple theory and unlike F in that the typability and type-checking problems are solvable with respect to ETA. This is proved in the article along with three other main results: (1) all primitive recursive functionals (...) of finite type are representable in ETA; (2) every term typable in ETA has a unique normal form; (3) there is a function defined by ${{\varepsilon}_0}$ -recursion which takes every typable term to a natural number which is an upper bound to the lengths of all βη-reduction sequences starting with that term. (shrink)

Sections 1 through 4 define, in the usual inductive style, various classes of object including one which is called the “combinatory terms of polymorphic type”. Section 5 defines a reduction relation on these terms. Section 6 shows that the weak normalizability of the combinatory terms of polymorphic type entails the weak normalizability of the lambda terms of polymorphic type. The entailment is not vacuous, because the combinatory terms of polymorphic type are indeed weakly normalizable, as is proven in Sect. 7 (...) using Tait and Girard’s computability predicates. The remainder of the paper is devoted to arguing that interesting consequences would follow from the existence of an “ordinally informative” proof, i.e. one which uses transfinite induction over recursive ordinal numbers and otherwise finitary methods, of normalizability for as large a class of the terms as possible. (shrink)

By "proper name" I mean a proper name in Frege's sense, i.e., a singular term. The "problem" mentioned in the title is whether the subject-term of an existential statement can be a proper name. I concentrate on examining some of the existing attempts to define "proper name" and conclude that, whatever answer is given to the question just posed, the authors of these attempts (Dummett, C Wright and B Hale) will have to modify some of their beliefs. My own favored (...) solution is to say that it can, sometimes denoting a non-existent object. (shrink)

Proof-theoretic semantics is an approach to logical semantics based on two ideas, of which the first is that the meaning of a logical connective can be explained by stipulating that some mode of inference, e.g., a natural deduction introduction or elimination rule, is permissible. The second idea is that the soundness of rules which are not stipulated outright may be deduced by some proof-theoretic argument from properties of the rules which are stipulated outright. I examine the first idea. My main (...) conclusion is that the idea is more problematic, and requires more discussion, than has been generally realized. I mention five problems which will have to be overcome before the idea can be accepted as definitely viable. (shrink)

This article tackles the current deficit in the supply of cadaveric organs by addressing the family veto in organ donation. The authors believe that the family veto matters—ethically as well as practically—and that policies that completely disregard the views of the family in this decision are likely to be counterproductive. Instead, this paper proposes to engage directly with the most important reasons why families often object to the removal of the organs of a loved one who has signed up to (...) the donor registry—notably a failure to understand fully and deliberate on the information and a reluctance to deal with this sort of decision at an emotionally distressing time. To accommodate these concerns it is proposed to separate radically the process of information, deliberation and agreement about the harvesting of a potential donor's organs from the event of death and bereavement through a scheme of advance commitment. This paper briefly sets out the proposal and discusses in some detail its design as well as what is believed to be the main advantages compared with the leading alternatives. (shrink)

Ethical decision theory may not be sufficiently well developed to furnish reliable guidelines to people involved in complex decision making that involves conflict between ethical considerations and business imperatives such as making a profit. In conditions of ethical uncertainty hindsight bias may occur, and this study reports on an exploration of hindsight bias effects among participants in continuing education in business programmes. Perceptions of business ethics were found to differ among groups within the sample depending on what they thought had (...) been the outcome of the ethical decision concerned. (shrink)

Although sex selection calls for careful thought, it seems in many cases to be neither intrinsically objectionable nor likely to have bad consequences.