Experiments are described, using electroencephalography (EEG) and simple tests of performance, which support the hypothesis that collapse of a quantum field is of importance to the functioning of the brain. The theoretical basis of our experiments is derived from Penrose (1989) who suggested that conscious decision-making is a manifestation of the outcome of quantum computation in the brain involving collapse of some relevant wave function. He also proposed that collapse of any wave function depends on a gravitational criterion. As different (...) brain areas are known to subserve different functions, we argue that `Penrose collapse' must occur in a particular brain area when performing a task that uses it. Further, taking an EEG from the area should amplify the gravitational prerequisite for collapse, so affecting task performance. There are no non-quantum theories which could lead one to expect that taking an EEG could directly affect task performance by subjects. The results of both pilot and main experiments indicated that task performance was indeed influenced by taking an EEG from relevant brain areas. Control experiments suggested that the influence was quantum mechanical in origin, and was not due to any experimental artefact. The results are statistically significant and merit attempts at replication in an independent laboratory, preferably with more sophisticated equipment than was available to us. (shrink)

The history of Athenian relations with Sicily in the fifth century is beset with difficulties; and no part of it, perhaps, is more obscure than the story of what is commonly known as the First Sicilian Expedition, which set sail from Athens in the late summer of 427 under Laches, and was reinforced under Pythodorus, Sophocles and Eurymedon in the winter of 426.

The paper presents and applies Hilbert's Epsilon Calculus, first describing its standard proof theory, and giving it an intensional semantics. These are contrasted with the proof theory of Fregean Predicate Logic, and the traditional (extensional) choice function semantics for the calculus. The semantics provided show that epsilon terms are referring terms in Donnellan's sense, enabling the symbolisation and validation of argument forms involving E-type pronouns, both in extensional and intensional contexts. By providing for transparency in intensional constructions they support a (...) Model Conceptualism to contrast with traditional intensional logic's Modal Realism. But epsilon-terms also symbolise fictions, and through their difference from iota terms enable the solution of a number of outstanding puzzles about Direct Reference and de re beliefs. (shrink)

Recovers some of the value in the Wittgensteinian period of philosophy, using certain logical systems: Prior's theory of operators and Hilbert's epsilon calculus. This work applies, discursively, the previous largely technical results published in Prolegomena to Formal Logic (Aldershot, Gower 1989) and Intensional Logic (Aldershot, Ashgate 1994) to resolve matters of current interest in philosophy, logic and linguistics - notably attacking a variety of realisms found in comtemporary cognitive science and the philosophy of mathematics.

Fregean logic has difficulty with certain arguments in which there is cross-reference between premises and conclusion. In this paper I describe a method of handling arguments of the troublesome kind: It involves replacing standard quantifiers with explicit existential statements, and turns standard logic into a free one. A validation procedure is provided for the logic.

Two uses of ‘if are discussed which do not involve conditions. The first is illustrated in the example ‘If he's here, I don't see him’, the second in ‘He's not a dunce, if a trifle stupid’. A third non‐conditional use, cognate with the first is also mentioned: it would be illustrated in the example ‘If he's a Dutchman, I'll eat my hat’. It is argued that recent attempts to formulate a logic of conditionals have distorted our understanding of ‘if, by (...) ignoring these uses, sometimes deliberately. Specifically, as a result, many arguments involving ‘if have been misjudged as invalid, because the expectation has been that ‘if expresses a condition. It is suggested that the traditional analysis of ‘necessary and sufficient conditions’ in terms of ‘if and only if, is partly to blame for these misunderstandings. And the proper understanding of ‘if’ which emerges shows it is quite fully captured in the propositional calculus. (shrink)

SummaryThis paper firms up previous arguments for referential transparency in intensional constructions by providing conclusive proofs of this, both formal and informal. Centrally the paper uses epsilon terms to symbolise referring expressions, and so it obtains the rigid designators needed to allow the same object to be referred to in all worlds and minds. The details of several contrary ideas are examined to reinforce the claim that they are incorrect. But also certain world‐dependent or mind‐dependent objects are identified, using epsilon (...) terms, to give an understanding of what might have caused the historical belief in referential opacity. (shrink)

Concepts of stability and symmetry in irreversible thermodynamics are developed through the analysis of system energy flows. The excess power function, derived from a local energy conservation equation, is shown to yield necessary and sufficient stability criteria for linear and nonlinear irreversible processes. In the absence of symmetry-destroying external forces, the linear range may be characterized by a set of phenomenological coefficient symmetries relating coupled forces and displacements, velocities, and accelerations, whereas rotational phenomena in nonlinear processes may be characterized by (...) skew-symmetric components of the phenomenological coefficients. A physical interpretation of the nature of the skew-symmetric parts is given and the variational principle of minimum dissipation of energy is related to a stability criterion. (shrink)

Like the author's first work, this text again develops two advanced logical systems: the formalization of intensional constructions initiated by Arthur Prior, and the refinement of predicate logic instituted by David Hilbert. This book is more historical than the first, but the emphasis is still on the application of the two systems to problems in analytical metaphysics. The natures of provability and possibility are studied further, as well as the natures of opacity and intensional objects.

I have become more convinced, over the years, by the truth of Wittgenstein’s characterisation of philosophy as arising through misconceptions of grammar. Such a misconception of grammar characterises a very popular approach to indexicality which has been current since the 1970s, stemming from the work of Casteñeda, and Kaplan. Gareth Evans was inclined to allow, for instance, that one could say ‘“To the left (I am hot)” is true, as uttered by x at t iff there is someone moderately near (...) to the left of x such that, if he were to utter the sentence “I am hot” at t, what he would thereby say is true’ (Evans 1985: 358). But not only does this disturb the proper relation between direct and indirect speech, it continues a Fregean tradition which these very cases show to be quite mistaken about the logic of intensions. In this paper, however, I want primarily to point out how this misconception of grammar has distorted our view of people. For some of the above thinkers have tried to make out that human motivation is related to the possession of a certain category of indexical belief, by Lewis called ‘de se beliefs’. I shall look here at how the matter arises in Hugh Mellor’s work on Time. In connection with Time, indexicality arises in McTaggart’s ‘A-series’, and Mellor treats this indexicality in parallel with Evans’ language. First, therefore, I aim to show how Mellor’s discussion of Time grammatically misconceives the situation, and leads to a misrepresentation of the motivation of human action. But a larger conclusion about Fregean intensions is also then immediately available. (shrink)

It seems surprising that this text—or others similar— has been accepted without any serious search for a more meaningful alternative. Even if it be thought that Euripides was capable of adding , in an unusual sense producing an awkward tautology, to , surely this should only be accepted in the absence ofa more credible emendation which departs no further from the manuscripts? Is there such an alternative? In the corresponding last line of the strophe we have : the first syllable (...) of is doubtful; there seems to be no convincing metrical objection to its being a long syllable here. This atonce suggests the maintenance of the manuscripts' to maintain the metrical balance. (shrink)