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.     

The Logic of Analogy in the Law

This paper deals with two issues in the field of reasoning by analogy in the law. The one issue is whether there exists such a thing as analogous rule application, or whether there is only the ‘normal’ application of a broadened rule. It is argued that if rules, as the entities made by a legislator, are distinguished from generalised solutions for cases, the idea of analogous application of rules makes sense. It is also shown how the so-called ‘reason-based model of rule application’, in contrast to the traditional modus ponens or subsumption model, makes it easy to give a logical account of analogous rule application. The other issue is how to argue logically about whether two cases are sufficiently similar to adopt the outcome of the one case for the other case. Section 3 provides a general logical model to establish this. The model is based on the comparison of the reasons for and against a particular solution in the two cases.     

‘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.     

On the Quantitative Scalar or-Implicature

Two simple generalized conversational implicatures are investigated :(1) the quantitative scalar implicature associated with ‘or’, and (2) the ‘not-and’-implicature, which is the dual to (1). It is argued that it is more fruitful to consider these implicatures as rules of interpretation and to model them in an algebraic fashion than to consider them as nonmonotonic rules of inference and to model them in a proof-theoretic way.     

Truth and Assertability

Deflationists say that the equivalence between ‘p is true’ and p is all there is to the meaning of ‘true’. “Use” theories generally construe meaning as acceptance conditions. I argue: (i) there are certain obvious objections to a deflationary theory of truth so formulated; but (ii) they can be overcome if we employ a graded notion of use, i.e. a notion of assertability; but (iii) there appear to be certain further difficulties which cannot be overcome in this way.     

On Reduction Rules,Meaning-as-use,and Proof-theoretic Semantics

The intention here is that of giving a formal underpinning to the idea of ‘meaning-is-use’ which, even if based on proofs, it is rather different from proof-theoretic semantics as in the Dummett–Prawitz tradition. Instead, it is based on the idea that the meaning of logical constants are given by the explanation of immediate consequences, which in formalistic terms means the effect of elimination rules on the result of introduction rules, i.e. the so-called reduction rules. For that we suggest an extension to the Curry– Howard interpretation which draws on the idea of labelled deduction, and brings back Frege’s device of variable-abstraction to operate on the labels (i.e., proof-terms) alongside formulas of predicate logic. Presented by Heinrich Wansing     

How to Define Extrinsic Properties

There are, broadly, three sorts of account of intrinsicality: ‘self-sufficiency’, ‘essentiality’ and ‘pure qualitativeness’. I argue for the last of these, and urge that we take intrinsic properties of concrete objects to be all and only those shared by actual or possible duplicates, which only differ extrinsically. This approach gains support from Francescotti’s approach: defining ‘intrinsic’ in contradistinction to extrinsic properties which ‘consist in’ relations which rule out intrinsicality. I answer Weatherson’s criticisms of Francescotti, but, to answer criticisms of my own, I amend his account, proposing that possession of an extrinsic property consists in a relation to one or more actual or possible distinct concrete objects. Finally I indicate ways to avoid some apparent objections to this account.     

Blame Game Triangulation between Parents,Teachers and Children with Academic Problems

This cross-sectional survey on a sample of parent, teacher and child respondents (n = 195) elicited their perceptions on or about the ‘reasons/causes’ for academic problems in school students. A semi-structured ‘Demographic Data Sheet’ and another open ended exploratory ‘Causes of Academic Problems Interview Schedule’ (CAPIS) exclusively developed for this study was used. A classification of the ‘causes’ for academic problems into four categories by two independent observers revealed preponderance of ‘child-centered’ causes (N: 937), followed by ‘teacher-centered’ causes (N: 751), ‘parent-centered’ (N: 643) and ‘environment centered’ causes (N: 362). Analysis of trends show significant statistical differences in reported perceptions between the three respondents (p: < 0.04); with highest disparity between ‘teacher-centered’ causative perceptions (p: < 0.001). Concordance rates as measured by Cohen’s Kappa Coefficient is reflected by greater agreements on or about the reasons for academic problems between parent-teacher respondents (0.34) and least for child-teacher reports (−0.08). The results suggest an attitudinal triangulation on or about the reasons attributed for academic problems between parents, teachers and the children. This opens up the need for stepping up measures to de-triangulate or harmonize these varying inter personal perceptions for optimum benefit of such children.     

Information and communication technology (ICT) initiatives at the university of fort hare: Cure or plague?

Conclusion This paper set out to provide a skeptical perspective to the view that IT has the potential to bring people into the global community. While not doubting the merits of IT’s capabilities it proposed that such claims be qualified in view of disparities in the distribution of wealth between nations and between peoples. It focused attention on the plight of students at the University of Fort Hare, in the Eastern Cape, which is the poorest of South Africa’s nine provinces. It argued instead that IT has the likelihood of accentuating instead of bridging existing inequalities in wealth between countries and between peoples. It contended that not‘everybody’ is predisposed to becoming a role player in the global agenda given that access to IT and online facilities is stratified by income. This, the paper posited, is most likely to exacerbate the "global digital divide"—the growing disparity in wealth between countries of the North and the South, and between peoples, the information "haves" and "have-nots". The U.S.’s 1999 expenditure on IT, which stood at $762 as opposed to South Africa’s expenditure in the same year, which was $10.6, illustrates the "divide". But while on the surface the University of Fort Hare’s situation seemed very gloomy, the paper outlined positive, but modest initiatives not only to provide access to IT and online facilities, but also to quip staff and students with requisite skills to enable them to be role players in the global agenda. He serves on the Editorial Committee of the South African Journal of Higher Education as Senior Consultant Editor, and is the Head of the Department of Foundations of Education at Fort Hare.     

Three-and-a-half folk concepts of intentional action

Fiery Cushman and Alfred Mele recently proposed a ‘two-and-a-half rules’ theory of folk intentionality. They suggested that laypersons attribute intentionality employing: one rule based on desire, one based on belief, and another principle based on moral judgment, which may either reflect a folk concept (and so count as a third rule) or a bias (and so not count as a rule proper) and which they provisionally count as ‘half a rule’. In this article, I discuss some cases in which an agent is judged as having neither belief nor desire to bring about an action, and yet laypersons find the agent’s action to be intentional. Many lay responses apparently follow a rule, but many other seem biased. The contribution of this study is two-fold: by addressing actions performed without desire or belief, it expands Mele and Cushman’s account; it also helps discriminate between a two-rules and a three-rules theory. As a conclusion, I argue in favor of a three-and-a-half concepts theory.     

Intensional Specifications of Truth-Conditions: ‘Because’, ‘In Virtue of’, and ‘Made True By…’

Although a number of truth theorists have claimed that a deflationary theory of ‘is true’ needs nothing more than the uniform implication of instances of the theorem ‘the proposition that p is true if and only if p’, reflection shows that this is inadequate. If deflationists can’t support the instances when replacing the biconditional with ‘because’, then their view is in peril. Deflationists sometimes acknowledge this by addressing, occasionally attempting to deflate, ‘because’ and ‘in virtue of’ formulas and their close relatives. I examine what I take to be the most promising deflationist moves in this direction and argue that they fail.     

The Quantitative/Qualitative Watershed for Rules of Uncertain Inference

We chart the ways in which closure properties of consequence relations for uncertain inference take on different forms according to whether the relations are generated in a quantitative or a qualitative manner. Among the main themes are: the identification of watershed conditions between probabilistically and qualitatively sound rules; failsafe and classicality transforms of qualitatively sound rules; non-Horn conditions satisfied by probabilistic consequence; representation and completeness problems; and threshold-sensitive conditions such as ‘preface’ and ‘lottery’ rules. Special Issue Formal Epistemology I. Edited by Branden Fitelson     

Temporal Parts and Time Travel

This paper argues that, in light of certain scenarios involving time travel, Sider’s definition of ‘instantaneous temporal part’ cannot be accepted in conjunction with a semantic thesis that perdurantists often assume. I examine a rejoinder from Sider, as well as Thomson’s alternative definition of ‘instantaneous temporal part’, and show how neither helps. Given this, we should give up on the perdurantist semantic thesis. I end by recommending that, once we no longer accept such semantics, we should accept a new set of definitions, which are superior in certain respects to Sider’s original set.     

‘That’-Clauses and Non-nominal Quantification

This paper argues that ‘that’-clauses are not singular terms (without denying that their semantical values are propositions). In its first part, three arguments are presented to support the thesis, two of which are defended against recent criticism. The two good arguments are based on the observation that substitution of ‘the proposition that p’ for ‘that p’ may result in ungrammaticality. The second part of the paper is devoted to a refutation of the main argument for the claim that ‘that’-clauses are singular terms, namely that this claim is needed in order to account for the possibility of quantification into ‘that’-clause position. It is shown that not all quantification in natural languages is quantification into the position of singular terms, but that there is also so-called ‘non-nominal quantification’. A formal analysis of non-nominal quantification is given, and it is argued that quantification into ‘that’-clause position can be treated as another kind non-nominal quantification.     

On the Mind Dependence of Truth

The claim that truth is mind dependent has some initial plausibility only if truth bearers are taken to be mind dependent entities such as beliefs or statements. Even on that assumption, however, the claim is not uncontroversial. If it is spelled out as the thesis that “in a world devoid of mind nothing would be true”, then everything depends on how the phrase ‘true in world w’ is interpreted. If ‘A is true in w’ is interpreted as ‘A is true of w’ (i.e. ‘w satisfies A’s truth conditions’, the claim need not be true. If on the other hand it is interpreted as ‘A is true of w and exists in w’ then the claim is trivially true, though devoid of any antirealistic efficacy. Philosophers like Heidegger and Rorty, who hold that truth is mind dependent but reality is not, must regard such principles as “A if and only if it is true that A” as only contingently true, which may be a good reason to reject the mind dependence of truth anyway.     

Irrelevance: Strengthening the Bayesian requirements

Bayesians standardly identify irrelevance with probabilistic irrelevance. However, there are cases where e is probabilistically irrelevant to h but intuitively e is relevant to h. For instance, ‘Die A came up 1 and die B came up 1, 3, 5 or 6’ is probabilistically irrelevant to ‘Die A came up odd and die B came up even’, yet, intuitively, it is not, irrelevant to that claim, in the sense that ‘Sydney has a harbour Bridge’ is irrelevant to it. In the context of decision making this notion of irrelevance combined with such rules as ‘Do not expend resources on irrelevant evidence’ leads to bad results. A stronger notion of irrelevance fitting our intuitions and the contexts of decision making is proposed: e is irrelevant to h if and only if every part of e is probabilistically irrelevant to every part of h. However, we need to take care in determining what counts as part of a statement.     

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’.     

Chomsky On The ‘Ordinary Language’ View Of Language

There is a common-sense view of language, which is held by Wittgenstein, Strawson Dummett, Searle, Putnam, Lewis, Wiggins, and others. According to this view a language consists of conventions, it is rule-governed, rules are conventionalised, a language is learnt, there are general learning mechanisms in the brain, and so on. I shall call this view the ‘ordinary language’ view of language. Chomsky’s attitude towards this view of language has been rather negative, and his rejection of it is a major motivation for the development of his own theory. In this paper I shall review Chomsky’s long-standing criticisms. I shall show that (1)Chomsky’s argument does not constitute a dismissal of the ‘ordinarylanguage’ view of language, (2) Chomsky’s conclusions about language do not follow from his argument, and (3) the ‘ordinary language’ view actually points to a promising way for us to understand the true nature of language and mind. This revised version was published online in August 2006 with corrections to the Cover Date.