pt. 1. A critique of current educational aims.--pt. 2. Reason.--pt. 3. Education and reason.

R F Dearden; Theory and Practice in Education, Journal of Philosophy of Education, Volume 14, Issue 1, 30 May 2006, Pages 17–29, https://doi.org/10.1111/j.1467-.

R F Dearden; Theory and Practice in Education, Journal of Philosophy of Education, Volume 14, Issue 1, 30 May 2006, Pages 17–29, https://doi.org/10.1111/j.1467-.

R F Dearden; Happiness and Education, Journal of Philosophy of Education, Volume 2, Issue 1, 30 May 2006, Pages 17–29, https://doi.org/10.1111/j.1467-9752.1968.

„My sole purpose in this paper is to try and correct what I take to be a common misinterpretation of Hume’s opinions on mathematics. I shall not enquire whether he was right or wrong in holding these opinions. Nor shall I offer opinions of my own.“.

R F Dearden; Play and Pleasure, Journal of Philosophy of Education, Volume 5, Issue 1, 30 May 2006, Pages 37–41, https://doi.org/10.1111/j.1467-9752.1971.tb0044.

We introduce a linear analogue of Läuchli's semantics for intuitionistic logic. In fact, our result is a strengthening of Läuchli's work to the level of proofs, rather than provability. This is obtained by considering continuous actions of the additive group of integers on a category of topological vector spaces. The semantics, based on functorial polymorphism, consists of dinatural transformations which are equivariant with respect to all such actions. Such dinatural transformations are called uniform. To any sequent in Multiplicative Linear Logic (...) , we associate a vector space of“diadditive” uniform transformations. We then show that this space is generated by denotations of cut-free proofs of the sequent in the theory MLL + MIX. Thus we obtain a full completeness theorem in the sense of Abramsky and Jagadeesan, although our result differs from theirs in the use of dinatural transformations.As corollaries, we show that these dinatural transformations compose, and obtain a conservativity result: diadditive dinatural transformations which are uniform with respect to actions of the additive group of integers are also uniform with respect to the actions of arbitrary cocommutative Hopf algebras. Finally, we discuss several possible extensions of this work to noncommutative logic.It is well known that the intuitionistic version of Läuchli's semantics is a special case of the theory of logical relations, due to Plotkin and Statman. Thus, our work can also be viewed as a first step towards developing a theory of logical relations for linear logic and concurrency. (shrink)

R F Dearden; Competition in Education, Journal of Philosophy of Education, Volume 6, Issue 1, 30 May 2006, Pages 119–133, https://doi.org/10.1111/j.1467-9752.19.

R F Dearden; Education and Politics, Journal of Philosophy of Education, Volume 14, Issue 2, 30 May 2006, Pages 149–156, https://doi.org/10.1111/j.1467-9752.198.

R F Dearden; Education and Politics, Journal of Philosophy of Education, Volume 14, Issue 2, 30 May 2006, Pages 149–156, https://doi.org/10.1111/j.1467-9752.198.

R F Dearden; Happiness and Education, Journal of Philosophy of Education, Volume 2, Issue 1, 30 May 2006, Pages 17–29, https://doi.org/10.1111/j.1467-9752.1968.

A critical and constructive discussion of philosophical questions which have particular bearing on the formulation of educational aims.

R F Dearden; Freedom and the Development of Autonomy: a reply to Victor Quinn, Journal of Philosophy of Education, Volume 18, Issue 2, 30 May 2006, Pages 271–27.

R. F. Atkinson; XIII*—Explanation in History, Proceedings of the Aristotelian Society, Volume 72, Issue 1, 1 June 1972, Pages 241–256, https://doi.org/10.1093/a.

In Chapter 4 of his essay Utilitarianism, “Of what sort of Proof the Principle of Utility is susceptible,” J. S. Mill undertakes to prove, in some sense of that term, the principle of utility. It has very commonly been argued that in the course of this “proof” Mill commits two very obvious fallacies. The first is the naturalistic fallacy which he is held to commit when he argues that since “the only proof capable of being given that an object is (...) visible, is that people actually see it. The only proof that a sound is audible is that people hear it: and so of the other sources of our experience. In like manner … the sole evidence it is possible to produce that anything is desirable, is that people do actually desire it.”1 Here Mill appears to hold that “X is desirable ”—a value judgment—follows deductively from “People desire x”—a factual statement. And the second is the fallacy of composition which seems to be involved in Mill'zs argument that since “each person's happiness is a good to that person … the general happiness, therefore, a good to the aggregate of all persons.”2. (shrink)

We present a full completeness theorem for the multiplicative fragment of a variant of noncommutative linear logic, Yetter's cyclic linear logic (CyLL). The semantics is obtained by interpreting proofs as dinatural transformations on a category of topological vector spaces, these transformations being equivariant under certain actions of a noncocommutative Hopf algebra called the shuffie algebra. Multiplicative sequents are assigned a vector space of such dinaturals, and we show that this space has as a basis the denotations of cut-free proofs in (...) CyLL + MIX. This can be viewed as a fully faithful representation of a free *-autonomous category, canonically enriched over vector spaces. This paper is a natural extension of the authors' previous work, "Linear Lauchli Semantics", where a similar theorem is obtained for the commutative logic MLL + MIX. In that paper, we interpret proofs as dinaturals which are invariant under certain actions of the additive group of integers. Here we also present a simplification of that work by showing that the invariance criterion is actually a consequence of dinaturality. The passage from groups to Hopf algebras in this paper corresponds to the passage from commutative to noncommutative logic. However, in our noncommutative setting, one must still keep the invariance condition on dinaturals. (shrink)

Historical materialism I take to be the view expressed in the well-known Preface to the Critique of Political Economy (1859) and exemplified in Capital and in many other writings by Marx and by Marxists. I shall begin with a few introductory remarks, next sketch in the theory, and finally contend that, despite real attractions, it too far limits the scope of legitimate historical enquiry to be ultimately acceptable.

Historical materialism I take to be the view expressed in the well-known Preface to the Critique of Political Economy and exemplified in Capital and in many other writings by Marx and by Marxists. I shall begin with a few introductory remarks, next sketch in the theory, and finally contend that, despite real attractions, it too far limits the scope of legitimate historical enquiry to be ultimately acceptable.

There is probably no student of modern philosophy, and certainly no listener to the Third Programme, who has never received the warning that he must on no account deduce an “ought” from an “is.” This prohibition, it is claimed, is securely based in established and unchallengeable principles of logic. Professor Flew was speaking for many others when he said, in the course of a broadcast entitled “Problems of Perspectives”, “I think it is very important indeed to make as clear as (...) we can and to underline with all possible emphasis that this is a point of inexorable logic”. And Professor Popper, to take but one other example, has expressed himself no less trenchantly: “Perhaps the simplest and most important point about ethics is purely logical, I mean the impossibility to derive nontautological ethical rules—imperatives, principles of policy, aims or however we may describe them—from statements of fact”—a view that is fully endorsed by Mr. Hare in his Language of Morals. (shrink)