Harmonising natural deduction

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.     

Directionality and temporal factors in conditional reasoning

An experiment is reported which tests psycholinguistic hypotheses about conditional rules of the form ‘If p then q’ (IT) and ‘p only if q’ (OI). It is postulated that each rule has a ‘directionality’ determined by linguistic usage which is ‘forwards’ for IT rules and ‘backwards’ for OI rules. It is further suggested that where temporal relations exist between the events denoted by p and q, the rules will be understood and processed more rapidly if the directionality of the rule is congruent with the temporal order. The results supported these hypotheses and provide a useful replication and extension of previous work.     

Liberalism,Abstract Individualism,and the Problem of Particular Obligations

In the following I take issue with the allegation that liberalism must inevitably be guilty of ‘abstract individualism’. I treat Michael Sandel’s well-known claim that there are ‘loyalties and convictions whose moral force consists partly in the fact that living by them is inseparable from understanding ourselves as the particular persons we are’ as representative of this widely held view. Specifically, I argue: (i) that Sandel’s account of the manner in which ‘constitutive’ loyalties function as reasons for action presupposes the possibility of there being (what I call) ‘underivable particular obligations’, but that such obligations are, in fact, a logical impossibility; and (ii) that Sandel’s account of the self as necessarily ‘encumbered’ presupposes an account of personal identity which confuses identification with definition, and which is, therefore, fundamentally flawed. For their constructive and insightful comments on an earlier draft of this paper, I owe a special debt of gratitude to the following: Clare Chambers, Roger Crisp, Cécile Fabre, Paul Kelly, David Lloyd-Thomas. Thanks also go to Res Publica’s two anonymous referees.     

Scalar implicature and contrastive explanation

I argue for a subsumption of any version of Grice’s first quantity maxim posited to underlie scalar implicature, by developing the idea of implicature recovery as a kind of explanatory inference, as e.g. in science. I take the applicable model to be contrastive explanation, while following van Fraassen’s analysis of explanation as an answer to a why-question. A scalar implicature is embedded in such an answer, one that meets two probabilistic constraints: the probability of the answer, and ‘favoring’. I argue that besides having application at large, outside of linguistic interpretation, these constraints largely account not only for implicatures based on strength order, logical and otherwise, but also for unordered cases. I thus suggest that Grice’s maxim and its descendants are expressions of general explanatory constraints, as they happen to be manifested in this particular explanatory task. I conclude by briefly discussing how I accordingly view Grice’s system outside of scalar implicature.     

Traditional Logic,Modern Logic and Natural Language

In a recent paper Johan van Benthem reviews earlier work done by himself and colleagues on ‘natural logic’. His paper makes a number of challenging comments on the relationships between traditional logic, modern logic and natural logic. I respond to his challenge, by drawing what I think are the most significant lines dividing traditional logic from modern. The leading difference is in the way logic is expected to be used for checking arguments. For traditionals the checking is local, i.e. separately for each inference step. Between inference steps, several kinds of paraphrasing are allowed. Today we formalise globally: we choose a symbolisation that works for the entire argument, and thus we eliminate intuitive steps and changes of viewpoint during the argument. Frege and Peano recast the logical rules so as to make this possible. I comment also on the traditional assumption that logical processing takes place at the top syntactic level, and I question Johan’s view that natural logic is ‘natural’.     

Actuality, Necessity, and Logical Truth

The traditional view that all logical truths are metaphysically necessary has come under attack in recent years. The contrary claim is prominent in David Kaplan’s work on demonstratives, and Edward Zalta has argued that logical truths that are not necessary appear in modal languages supplemented only with some device for making reference to the actual world (and thus independently of whether demonstratives like ‘I’, ‘here’, and ‘now’ are present). If this latter claim can be sustained, it strikes close to the heart of the traditional view. I begin this paper by discussing and refuting Zalta’s argument in the context of a language for propositional modal logic with an actuality connective (section 1). This involves showing that his argument in favor of real world validity his preferred explication of logical truth, is fallacious. Next (section 2) I argue for an alternative explication of logical truth called general validity. Since the rule of necessitation preserves general validity, the argument of section 2 provides a reason for affirming the traditional view. Finally (section 3) I show that the intuitive idea behind the discredited notion of real world validity finds legitimate expression in an object language connective for deep necessity. Earlier versions of this paper were read at the universities of Graz, Maribor, and Salzburg, and at a workshop on the philosophy of logic at the National Autonomous University of Mexico (UNAM) in Mexico City. My thanks to those present at these events for many helpful suggestions. Thanks are also due to an anonymous referee for Philosophical Studies.     

‘Why Is There Something Rather Than Nothing?’ The Big Question

‘Good’ is nothing specific but is transcendentally or generally applied over specific, and specified, ‘categories’. These ‘categories’ may be seen—at least for the purposes of this note—as under Platonic Forms. The rule that instances under a category or form need a Form to be under is valid. It may be tautological: but this is OK for rules. Not being specific, however, ‘good’ neither needs nor can have a specifying Form. So, on these grounds, the Form of the Good is otious. Any rule of the kind, ‘Everything needs a Form, so good needs a Form of the Good’ is mistaken, in that good is not a kind, but a transcendental. To give a Form to the transcendental ‘good’ is a mistake: it is a Rylian category mistake. And the Form of the Good either does no work, or works unprofitably in any but an aesthetic sense.     

What is Wrong with Rational Suicide

Recently, the ‘right to die’ became a major social issue. Few agree suicide is a right tout court. Even those who believe suicide (‘regular’, passive, or physician-assisted) is sometimes morally permissible usually require that a suicide be ‘rational suicide’: instrumentally rational, autonomous, due to stable goals, not due to mental illness, etc. We argue that there are some perfectly ‘rational suicides’ that are, nevertheless, bad mistakes. The concentration on the rationality of the suicide instead of on whether it is a mistake may lead to permitting suicides that should be forbidden.     

Teaching and Truthfulness

Some tendencies in modern education—the stress on ‘performativity’, for instance, and ‘celebration of difference’—threaten the value traditionally placed on truthful teaching. In this paper, truthfulness is mainly understood, following Bernard Williams, as a disposition to ‘Accuracy’ and ‘Sincerity’—hence as a virtue. It is to be distinguished from truth (a property of beliefs), and current debates about the nature of truth are not relevant to the issue of the value of truthfulness. This issue devolves into the question of whether truthfulness is a distinctive virtue of teachers, which they have a special obligation to exercise in the face of competing aims. This paper defends the idea of distinctive professional duties and considers two conceptions of teaching which ascribe a central place to truthfulness. The first conceives of teaching as a personal relationship within which trust, and hence, it is claimed, truthfulness, are paramount. This claim is challenged, and the paper concludes by sympathetically considering a second conception of teaching, articulated by Oakeshott and Heidegger. In this conception, teaching is a ‘releasement’ from ‘the daily flux’ of pupils’ lives through a truthful initiation into the alternatives to this ‘daily flux’ found within ‘the civilized inheritance of mankind’.     

Against the possibility of historical evidence for miracles

In his bookThe Concept of Miracle and his paper ‘For the Possibility of Miracles’ Swinburne claims that there are no logical difficulties in supposing that there could be strong historical evidence for the occurrence of miracles. This claim is based on three assertions; two of which I demonstrate are only true contingently. In this paper I identify several logical difficulties regarding the possibility of attaining historical evidence for the occurrence of miracles. On the strength of these logical difficulties I hope to demonstrate that there is sufficient reason to doubt Swinburne’s central claim.     

Statues and Lumps: A Strange Coincidence?

Puzzles about persistence and change through time, i.e., about identity across time, have foundered on confusion about what it is for ‘two things’ to be have ‘the same thing’ at a time. This is most directly seen in the dispute over whether material objects can occupy exactly the same place at the same time. This paper defends the possibility of such coincidence against several arguments to the contrary. Distinguishing a temporally relative from an absolute sense of ‘the same’, we see that the intuition, ‘this is only one thing’, and the dictum, ‘two things cannot occupy the same place at the same time’, are individuating things at a time rather than absolutely and are therefore compatible with coincidence. Several other objections philosophers have raised ride on this same ambiguity. Burke, originating what has become the most popular objection to coincidence, argues that if coincidence is possible there would be no explanation of how objects that are qualitatively the same at a time could belong to different sorts. But we can explain an object’s sort by appealing to its properties at other times. Burke’s argument to the contrary equivocates on different notions of ‘cross-time identity’ and ‘the statue’. From a largely negative series of arguments emerges a positive picture of what it means to say multiple things coincide and of why an object’s historical properties explain its sort rather than vice versa – in short, of how coincidence is possible.     

How is God-talk logically possible? A sketch for an argument on the logic of ‘God’

In this paper I want to argue for the optimal way to characterise the logical and semantical behaviour of the singular term ‘God’ used in religious language. The relevance of this enterprise to logical theory is the main focus as well. Doing this presupposes to outline the two rivaling approaches of well-definition of singular terms: Kripke’s (“rigid designators”) and Hintikka’s (“world-lines”). ‘God’ as a “rigid designator” is purified from all real-life-language-games of identification and only spells out a metaphysical tag, which favours the view of “anything goes”. Instead, ‘God’ as a “world-line,” plus two ways of quantification, is much more flexible to theological traditions, teachings of the church, religious practices and personal feelings. Thus, it provides a sufficiently well-defined singular term for the purposes of logical theory. The whole sketch is based on Jaakko Hintikka’s logical ideas, mainly on his responses to different authors in PJH. I have systematically omitted direct references to his texts because I have modified considerably his ideas for my own purposes.     

Listening to Dialogue

In accordance with Progressivism, Matthew Lipman, introduced an educational model for renewal and change by means of the child. With his Philosophy for Children programme he wished to offer an alternative for the intellectualistic oriented education which silenced children. The answer to the search for freedom and change, Lipman finds in the symbioses between ‘Philosophy’ and ‘Children’. Philosophy expressed in critical thinking and communication, was the basis to emancipate the child from the oppression of the adult and to cause change. According to Lipman the main purpose of philosophy is to free every individual from determination. This plea is being elaborated by dialogue. The main issue of our paper concerns the question whether Lipman’s alternative ‘Philosophy for Children’ can fulfil the promise of change and freedom. To answer this question we will investigate thoroughly where dialogue and change in Philosophy for Children stand for. Finally we will propose another perspective of dialogue. A dialogue stressed on listening. Listening to how the world appears to us and how we appear to ourselves. Nancy Vansieleghem is working on a Ph.D. in Philosophy of Education at the Department of Education at the University of Gent, Belgium. Her main area of research is philosophy of dialogue and public space.     

Space Cannot Be Cut—Why Self-Identity Naturally Includes Neighbourhood

Psychology is not alone in its struggle with conceptualizing the dynamic relationship between space and individual or collective identity. This general epistemological issue haunts biology where it has a specific focus in evolutionary arguments. It arises because of the incompatibility between definitive logical systems of ‘contradiction or unity’, which can only apply to inert material systems, and natural evolutionary processes of cumulative energetic transformation. This incompatibility makes any attempt to apply definitive logic to evolutionary change unrealistic and paradoxical. It is important to recognise, because discrete perceptions of self and group, based on the supposition that any distinguishable identity can be completely cut free, as an ‘independent singleness’, from the space it inescapably includes and is included in, are a profound but unnecessary source of psychological, social and environmental conflict. These perceptions underlie Darwin’s definition of ‘natural selection’ as ‘the preservation of favoured races in the struggle for life’. They result in precedence being given to striving for homogeneous supremacy, through the competitive suppression of others, instead of seeking sustainable, co-creative evolutionary relationship in spatially and temporally heterogeneous communities. Here, I show how ‘natural inclusion’, a new, post-dialectic understanding of evolutionary process, becomes possible through recognising space as a limitless, indivisible, receptive (non-resistive) ‘intangible presence’ vital for movement and communication, not as empty distance between one tangible thing and another. The fluid boundary logic of natural inclusion as the co-creative, fluid dynamic transformation of all through all in receptive spatial context, allows all form to be understood as flow-form, distinctive but dynamically continuous, not singularly discrete. This simple move from regarding space and boundaries as sources of discontinuity and discrete definition to sources of continuity and dynamic distinction correspondingly enables self-identity to be understood as a dynamic inclusion of neighbourhood, through the inclusion of space throughout and beyond all natural figural forms as configurations of energy. Fully to appreciate and communicate the significance of this move, it is necessary to widen the linguistic, mathematical and imaginative remit of conventional scientific argument and explication so as to include more poetic, fluid and artistic forms of expression.     

My beliefs about your beliefs: a case study in theory of mind and epistemic logic

We model three examples of beliefs that agents may have about other agents’ beliefs, and provide motivation for this conceptualization from the theory of mind literature. We assume a modal logical framework for modelling degrees of belief by partially ordered preference relations. In this setting, we describe that agents believe that other agents do not distinguish among their beliefs (‘no preferences’), that agents believe that the beliefs of other agents are in part as their own (‘my preferences’), and the special case that agents believe that the beliefs of other agents are exactly as their own (‘preference refinement’). This multi-agent belief interaction is frame characterizable. We provide examples for introspective agents. We investigate which of these forms of belief interaction are preserved under three common forms of belief revision.