Despite the volume of discussion on the Liar Paradox recently, there is one stream of largely British thought on the matter which is hardly represented in the wider literature. This paper points out salient aspects of the history of this tradition, from its origin in forms of propositional quantification found in Ramsey, through to more precise symbolisations which have emerged more recently. But its purpose is to exposit, with respect to a number of contested cases, the ensuing results. Thus it (...) goes on to apply the analysis to several other well known paradoxes, including one rarely discussed, which reveals more fully the consequent consistency and completeness of natural language. (shrink)

This paper covers the history of the development of various epsilon calculi, and their applications, starting with the introduction of epsilon terms by Hilbert and Bernays. In particular it describes the Epsilon Substitution Method and the First and Second Epsilon Theorems, the original Epsilon Calculus of Bourbaki, several Intuitionistic Epsilon Calculi, and systems that have been constructed to incorporate epsilon terms in modal, and general intensional structures. Standard semantics for epsilon terms are discussed, with application to Arithmetic, and it is (...) shown how epsilon terms give distinctive theories of descriptions and identity, through providing complete individual terms for individuals, which are rigid across possible worlds. The Epsilon Calculus' problematic thereby extends that of the predicate calculus primarily through its applicability to anaphoric reference, both in extensional and also intensional constructions. There are higher-order applications, as well, some of which resolve paradoxes in contemporary logic through allowing for indeterminacy of reference. (shrink)

Prawitz proved a theorem, formalising ‘harmony’ in Natural Deduction systems, which showed that, corresponding to any deduction there is one to the same effect but in which no formula occurrence is both the consequence of an application of an introduction rule and major premise of an application of the related elimination rule. As Gentzen ordered the rules, certain rules in Classical Logic had to be excepted, but if we see the appropriate rules instead as rules for Contradiction, then we can (...) extend the theorem to the classical case. Properly arranged there is a thoroughgoing ‘harmony’, in the classical rules. Indeed, as we shall see, they are, all together, far more ‘harmonious’ in the general sense than has been commonly observed. As this paper will show, the appearance of disharmony has only arisen because of the illogical way in which natural deduction rules for Classical Logic have been presented. (shrink)

A paradox is generally a puzzling conclusion we seem to be driven towards by our reasoning, but which is highly counterintuitive, nevertheless. There are, amongst these, a large variety of paradoxes of a logical nature which have teased even professional logicians, in some cases for several millennia. But what are now sometimes isolated as 'the logical paradoxes' are a much less heterogeneous collection: they are a group of antinomies centered on the notion of self-reference, some of which were known in (...) Classical times, but most of which became particularly prominent in the early decades of last century. Quine distinguished amongst paradoxes such antinomies. He did so by first isolating the 'veridical' and 'falsidical' paradoxes, which, although puzzling riddles, turned out to be plainly true, or plainly false, after some inspection. In addition, however, there were paradoxes which 'produce a self-contradiction by accepted ways of reasoning', and which, Quine thought, established 'that some tacit and trusted pattern of reasoning must be made explicit, and henceforward be avoided or revised' (Quine 1966, p7). We will first look, more broadly, and historically, at several of the main conundrums of a logical nature which have proved difficult, some since antiquity, before concentrating later on the more recent troubles with paradoxes of self-reference. They will all be called 'logical paradoxes'. (shrink)

Do the laws of nature supervene on ordinary, non-nomic matters of fact? Lange's criticism of Humean supervenience (HS) plays a key role in his account of natural laws. Though we are sympathetic to his account, we remain unconvinced by his criticism. We focus on his thought experiment involving a world containing nothing but a lone proton and argue that it does not cast sufficient doubt on HS. In addition, we express some concern about locating the lawmakers in an ontology of (...) primitive subjunctive facts and suggest that a 'mixed' metaphysics to the lawmaker question might be attractive. (shrink)

C.S. Lewis’s ‘Argument from Desire’ is best summed up by his famous line, ‘If I find in myself a desire which no experience in this world can satisfy, the most probable explanation is that I was made for another world’. In short, unfulfilled ‘seemingly transcendent desires’ point to fulfilment in another realm. Lewis’s argument is fraught with disagreement, and subsequently, questions remain as to its efficacy as a theistic argument. In this essay, I will take a novel approach by using (...) Bayes’ theorem to assess the success of Lewis’s argument in support of theism over and against naturalism. As I will argue, a strength of this approach is that it allows me to largely bypass a significant area of disagreement within the literature, namely, whether these desires are best seen as natural or artificial. Additionally, I will argue for why these desires are the sort of good God would be interested in giving to persons. Then, I will proceed to outline what I take to be the best naturalistic accounts of these desires and outline some of the challenges these accounts face. Finally, I will conclude with plugging these results into Bayes’ theorem. (shrink)

Joe Campbell has identified an apparent flaw in van Inwagen’s Consequence Argument. It apparently derives a metaphysically necessary conclusion from what Campbell argues is a contingent premise: that the past is in some sense necessary. I criticise Campbell’s examples attempting to show that this is not the case (in the requisite sense) and suggest some directions along which an incompatibilist could reconstruct her argument so as to remain immune to Campbell’s worries.

Barry Schein proposes combining a second-order treatment of plurals with DonaldDavidson's suggestion that there are positions for reference to events in ordinary predicates inorder to account for several of the more puzzling features of ...

Acceptance of Humean Supervenience and thereductive Humean analyses that entail it leadsto a litany of inadequately explained conflictswith our intuitions regarding laws andpossibilities. However, the non-reductiveHumeanism developed here, on which law claimsare understood as normative rather than factstating, can accommodate those intuitions. Rational constraints on such norms provide aset of consistency relations that ground asemantics formulated in terms offactual-normative worlds, solving theFrege-Geach problem of construing unassertedcontexts. This set of factual-normative worldsincludes exactly the intuitive sets ofnomologically possible worlds associated witheach possible (...) set of laws. The extension ofthe semantics to counterfactual and subjunctiveconditionals is sketched. Potential objectionsinvolving subjectivity, mind-dependence, andnon-factuality are discussed. (shrink)

This article considers the implications for film analysis of the presence or absence of a manual crank. More specifically, it looks at the 16 mm Time and Motion Study Projector as used in behavioral research in the 1960s and 1970s. The controversial concept of ‘interactional synchrony’, or the dance-like coordination of people in conversation, emerged from the use of this hand-turned projector. William S. Condon developed the concept along with the technique of microanalysis. Starting with the projector manufactured by Bell (...) & Howell, he made numerous improvements to facilitate observation—‘sweeping’ over segments of very short duration to discover the rhythmic synchrony of all filmed participants. It led him to a theory of ‘process’ in communication, and in the reception of speech in particular. People always ‘danced’ to the tune of their own voice, and their listeners ‘danced’ to the tune of the speaker—at intervals of one-sixth or one-eighth of a second. This also led Condon to an epistemology of discovery derived partly from philosophy but mostly from his machinery. The universe, he said, is a ‘continuum of order’ whose structures are preserved through translations of order: of thought into speech, speech into vibrations, vibrations into neurons, and back into behavior. The only exceptions are people with disabilities, like the autistics Condon studied from the 1970s onward. But the very distinction of normal and pathological was epiphenomenal to his scanning technique; it was rooted in material and formal qualities of film and of the projector whose crank he turned often. (shrink)

Review of extant research on the corporate environmental performance (CEP) and corporate financial performance (CFP) link generally demonstrates a positive relationship. However, some arguments and empirical results have demonstrated otherwise. As a result, researchers have called for a contingency approach to this research stream, which moves beyond the basic question “does it pay to be green?” and instead asks “when does it pay to be green?” In answering this call, we provide a meta-analytic review of CEP–CFP literature in which we (...) identify potential moderators to the CEP–CFP relationship including environmental performance type (e.g., reactive vs. proactive performance), firm characteristics (e.g., large vs. small firms), and methodological issues (e.g., self-report measures). By analyzing these contingencies, this study attempts to provide a basis on which to draw conclusions regarding some inconsistencies and debates in the CEP–CFP research. Some of the results of the moderator analysis suggest that small firms benefit from environmental performance as much or more than large firms, US firms seem to benefit more than international counterparts, and environmental performance seems to have the strongest influence on market-measures of financial performance. (shrink)

Whether we're buying a pair of jeans, ordering a cup of coffee, selecting a long-distance carrier, applying to college, choosing a doctor, or setting up a 401(k), everyday decisions ; both big and small ; have become increasingly complex due to the overwhelming abundance of choice with which we are presented. As Americans, we assume that more choice means better options and greater satisfaction. But beware of excessive choice: choice overload can make you question the decisions you make before you (...) even make them, it can set you up for unrealistically high expectations, and it can make you blame yourself for any and all failures. In the long run, this can lead to decision-making paralysis, anxiety, and perpetual stress. And, in a culture that tells us that there is no excuse for falling short of perfection when your options are limitless, too much choice can lead to clinical depression. In The Paradox of Choice, Barry Schwartz explains at what point choice ; the hallmark of individual freedom and self-determination that we so cherish ; becomes detrimental to our psychological and emotional well-being. In accessible, engaging, and anecdotal prose, Schwartz shows how the dramatic explosion in choice ; from the mundane to the profound challenges of balancing career, family, and individual needs ; has paradoxically become a problem instead of a solution. Schwartz also shows how our obsession with choice encourages us to seek that which makes us feel worse. By synthesizing current research in the social sciences, Schwartz makes the counter intuitive case that eliminating choices can greatly reduce the stress, anxiety, and busyness of our lives. He offers eleven practical steps on how to limit choices to a manageable number, have the discipline to focus on those that are important and ignore the rest, and ultimately derive greater satisfaction from the choices you have to make."--provided by publisher. (shrink)

The paper illustrates how organic chemists dramatically altered their practices in the middle part of the twentieth century through the adoption of analytical instrumentation — such as ultraviolet and infrared absorption spectroscopy and nuclear magnetic resonance spectroscopy — through which the difficult process of structure determination for small molecules became routine. Changes in practice were manifested in two ways: in the use of these instruments in the development of ‘rule-based’ theories; and in an increased focus on synthesis, at the expense (...) of chemical analysis. These rule-based theories took the form of generalizations relating structure to chemical and physical properties, as measured by instrumentation. This ‘Instrumental Revolution’ in organic chemistry was two-fold: encompassing an embrace of new tools that provided unprecedented access to structures, and a new way of thinking about molecules and their reactivity in terms of shape and structure. These practices suggest the possibility of a change in the ontological status of chemical structures, brought about by the regular use of instruments. The career of Robert Burns Woodward provides the central historical examples for the paper. Woodward was an organic chemist at Harvard from 1937 until the time of his death. In 1965, he won the Nobel Prize in Chemistry. (shrink)

Jean-Paul Sartre, in describing the realization of his freedom, was often inclined to say mysterious things like ‘I am what I am not’, ‘I am not what I am’ (‘as I am already what I will be …, I am the self which I will be, in the mode of not being it’, ‘I make myself not to be the past … which I am’.) He was therefore plainly contradicting himself, but was this merely a playful literary figure (paradox), or (...) was he really being incoherent? By the latter judgment I do not mean to reject his statements entirely (like many of his Anglo-Saxon contemporaries); for I believe there is an intimate link between contradiction and freedom, as I shall explain in this paper. But a minor thing we must first have out of the way is the suggestion that Sartre's language was just a rhetorical trope, designed merely to express some banal platitude in a bemusing way: ‘I am not yet what I will be’, ‘I am no longer what I was’ are sane and sensible, for instance, but cannot be the meant content of Sartre's sayings, since, while they would indeed describe the reform of some character, they would be appropriate only before or after some metamorphosis, not, as Sartre clearly intended, in the midst of some process of riddance and conversion, whether radical or otherwise. Yet, in the turmoil of such a change, ‘I am not what I am’ (or the everyday ‘I am not myself’) still, surely, cannot be true, and if that is the case, Sartre must be being inocherent, and therefore, obfuscating and deliberately obscure, and hence, it seems, must properly be rejected by all right and clear thinking men. (shrink)

In a previous issue of Philosophical Investigations Professor Radford provides a counterexample to the equation1: a word is on the tip of a man's tongue IFF (a) he can recognize the word and (b1) he believes he may be able to produce It (fairly soon).

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)

One of the claims made for C. S. Peirce's existential graphs has been that they are a deductively complete formulation of first-order logic with identity. As Peirce presented them, this is true only for certain versions of first-order logic :those which do not include terms for individuals. I amend Peirce's rules here, showing, in particular, how they are capable of demonstrating that, for instance, ?Jack is in the kitchen? contradicts ?Jack is not in the kitchen?

Routley?s Formula says, for instance, that if it is believed there is a man then there is something which is believed to be a man. In this paper I defend the formula; first directly, but then by looking at work by Gensler and Hintikka against it, and at the original work of Routley, Meyer and Goddard for it. The argument ultimately reduces to a central point about the extensionality of objects in Routley, Meyer and Goddard?s intensional system, i.e. in its (...) formulation of transparency. (shrink)

Wittgenstein's Remarks on the Foundations of Mathematics was poorly received by the critics when it was first published, and only a few sympathetic commentators have made much of it since then. The book has not had a great success, because the majority of people interested in the philosophy of mathematics these days have a quite different approach to the subject from Wittgenstein. But not only that, they have a quite different logic from Wittgenstein. I believe one of the main sources (...) of the antipathy felt towards the Remarks lies in the foreignness of the logic Wittgenstein develops there. I hope, in what follows, to make that logic more understandable, and with it the philosophy of mathematics it supports. (shrink)