Jim Mackenzie; Wilson on Relativism and Teaching, Journal of Philosophy of Education, Volume 21, Issue 1, 30 May 2006, Pages 119–130, https://doi.org/10.1111/j.

Jim Mackenzie; Wilson on Relativism and Teaching, Journal of Philosophy of Education, Volume 21, Issue 1, 30 May 2006, Pages 119–130, https://doi.org/10.1111/j.

I finished my undergraduate degree at Monash University and joined Charles Hamblin’s seminar at the University of NSW in March, 1968. Phil Staines from the University of Newcastle joined at the same time, and Vic Dudman was an established member. Hamblin’s book Fallacies would be published in 1970, but the seminar discussions rarely concerned fallacies. This may have been because Hamblin had been working for so long and so closely with those ideas that he was now ready to turn elsewhere. (...) But I shall argue that the book was only part of a much broader program, other parts of which occupied us in the seminars. Hamblin never explicitly discussed the writing of Fallacies with me, and what follows is an attempt to explain how the book fitted into his overall project as a logician, drawn from his published works and from what I remember of his contributions to the seminar. (shrink)

The paper offers a new understanding of induction in the empirical sciences, one which assimilates it to induction in geometry rather than to statistical inference. To make the point a system of notions, essential to logically sound induction, is defined. Notable among them are arbitrary object and particular property. A second aim of the paper is to bring to light a largely neglected set of assumptions shared by both induction and deduction in the empirical sciences. This is made possible by (...) appealing to the logic of common nouns and applying it to the logic of natural-kind terms.This strategy yields a new insight into the concept of natural kinds. While the strategy reveals deep affinity between empirical induction and deduction it also reveals two problems peculiar to induction. This helps to explain the intuition that induction is the more problematic of the two. The paper does not set out ‘to solve the problem of induction’. 1The paper has benefited from the support and critical comments of several friends: Steven Davis, Kevin Dunbar, Anil Gupta, Michael Hallett, Ray Jackendoff and Storrs McCall. Two friends, however, deserve special thanks, Michael Makkai and Gonzalo Reyes. Many of the points made in the paper, otherwise unacknowledged, are due to their generosity and patience. In fact, the paper can be seen as an application of the logic of kinds on which Gonzalo Reyes has been working for several years. (shrink)

Is the assumption of a fundamental distinction between particulars and universals another unsupported dogma of metaphysics? F. P. Ramsey famously rejected the particular – universal distinction but neglected to consider the many different conceptions of the distinction that have been advanced. As a contribution to the piecemeal investigation of this issue three interrelated conceptions of the particular – universal distinction are examined: universals, by contrast to particulars, are unigrade; particulars are related to universals by an asymmetric tie of exemplification; universals (...) are incomplete whereas particulars are complete. It is argued that these conceptions are wanting in several respects. Sometimes they fail to mark a significant division amongst entities. Sometimes they make substantial demands upon the shape of reality; once these demands are understood aright it is no longer obvious that the distinction merits our acceptance. The case is made via a discussion of the possibility of multigrade universals. (shrink)

One version of the Julius Caesar problem arises when we demand assurance that expressions drawn from different theories or stretches of discourse refer to different things. The counter‐Caesar problem arises when assurance is demanded that expressions drawn from different theories. refer to the same thing. The Julio César problem generalises from the counter‐Caesar problem. It arises when we seek reassurance that expressions drawn from different languages refer to the same kind of things. If the Julio César problem is not resolved (...) then the Fregean account of numbers as objects is cast into doubt, the notion of number left relative to a language. Wright introduced this problem by asking whether there can be such a thing as ‘International Platonism’. After rejecting Hale's attempt to resolve it I argue that the threat posed by the Julio César problem diminishes – even though it cannot be made to logically disappear – once it is recognised that the radical interpretation of an unfamiliar language is inevitably holistic, the evidence available invariably defeasible and consequently Cartesian certainty about the significance of the utterances of a foreign tongue neither to be sought after nor attained. (shrink)

According to the species of neo‐logicism advanced by Hale and Wright, mathematical knowledge is essentially logical knowledge. Their view is found to be best understood as a set of related though independent theses: (1) neo‐fregeanism—a general conception of the relation between language and reality; (2) the method of abstraction—a particular method for introducing concepts into language; (3) the scope of logic—second‐order logic is logic. The criticisms of Boolos, Dummett, Field and Quine (amongst others) of these theses are explicated and assessed. (...) The issues discussed include reductionism, rejectionism, the Julius Caesar problem, the Bad Company objections, and the charge that second‐order logic is set theory in disguise.The irresistible metaphor is that pure abstract objects […] are no more than shadows cast by the syntax of our discourse. And the aptness of the metaphor is enhanced by the reflection that shadows are, after their own fashion, real. (Crispin Wright [1992], p. 181–2)But I feel conscious that many a reader will scarcely recognise in the shadowy forms which I bring before him his numbers which all his life long have accompanied him as faithful and familiar friends; (Richard Dedekind [1963], p. 33)1 Introduction2 Logical‐historical preliminaries3 The linguistic turn4 Reductionism5 Rejectionism6 The ‘Julius Caesar’ problem7 Second‐order logic8 Bad company objections9 Conclusion. (shrink)

Logic is usually thought to concern itself only with features that sentences and arguments possess in virtue of their logical structures or forms. The logical form of a sentence or argument is determined by its syntactic or semantic structure and by the placement of certain expressions called “logical constants.”[1] Thus, for example, the sentences Every boy loves some girl. and Some boy loves every girl. are thought to differ in logical form, even though they share a common syntactic and semantic (...) structure, because they differ in the placement of the logical constants “every” and “some”. By contrast, the sentences Every girl loves some boy. and Every boy loves some girl. are thought to have the same logical form, because “girl” and “boy” are not logical constants. Thus, in order to settle questions about logical form, and ultimately about which arguments are logically valid and which sentences logically true, we must distinguish the “logical constants” of a language from its nonlogical expressions. (shrink)

Frege introduced the notion of pragmatic force as what distinguishes statements from questions. This distinction was elaborated by Wittgenstein in his later works, and systematised as an account of different kinds of speech acts in formal dialogue theory by Hamblin. It lies at the heart of the inferential semantics more recently developed by Brandom. The present paper attempts to sketch some of the relations between these developments.

In his recent paper, Winch attacks a group of theories he calls cognitivism. These theories agree in holding that ‘the ability to think, both consciously and subconsciously, amounts to an ability to internally manipulate symbolic representations of that which we think about.The relevance of this attack to education is that ‘Cognitivism’ supplies plausible‐looking reasons for thinking that learning can take place without instruction, practice, memorisation or training and its prestige as a theory of learning devalues those activities within education.Its rejection (...) should therefore lead us to re‐examine our need for explicit teacher‐oriented pedagogies’.Cognitivism has led to an emphasis on autonomous learning and a consequent devaluing of the role of overt teaching, ‘the active transmission of knowledge and technique by an authoritative figure’. (shrink)

Jim Mackenzie; Authority, Journal of Philosophy of Education, Volume 22, Issue 1, 30 May 2006, Pages 57–65, https://doi.org/10.1111/j.1467-9752.1988.tb00177.x.

Is linguistic understanding a form of knowledge? I clarify the question and then consider two natural forms a positive answer might take. I argue that, although some recent arguments fail to decide the issue, neither positive answer should be accepted. The aim is not yet to foreclose on the view that linguistic understanding is a form of knowledge, but to develop desiderata on a satisfactory successor to the two natural views rejected here.

This paper develops a novel theory of abstraction—what we call collective abstraction. The theory solves a notorious problem for noneliminative structuralism. The noneliminative structuralist holds that in addition to various isomorphic systems there is a pure structure that can be abstracted from each of these systems; but existing accounts of abstraction fail for nonrigid systems like the complex numbers. The problem with the existing accounts is that they attempt to define a unique abstraction operation. The theory of collective abstraction instead (...) simultaneously defines a collection of distinct abstraction operations, each of which maps a system to its corresponding pure structure. The theory is precisely formulated in an essentialist language. This allows us to throw new light on the question to what extent structuralists are committed to symmetric dependence. Finally, we apply the theory of collective abstraction to solve a problem about converse relations. (shrink)

I articulate and defend a necessary and sufficient condition for predication. The condition is that a term or term-occurrence stands in the relation of ascription to its designatum, ascription being a fundamental semantic relation that differs from reference. This view has dramatically different semantic consequences from its alternatives. After outlining the alternatives, I draw out these consequences and show how they favour the ascription view. I then develop the view and elicit a number of its virtues.

This paper proposes an Interface Transparency Thesis concerning how linguistic meanings are related to the cognitive systems that are used to evaluate sentences for truth/falsity: a declarative sentence S is semantically associated with a canonical procedure for determining whether S is true; while this procedure need not be used as a verification strategy, competent speakers are biased towards strategies that directly reflect canonical specifications of truth conditions. Evidence in favor of this hypothesis comes from a psycholinguistic experiment examining adult judgments (...) concerning ‘Most of the dots are blue’. This sentence is true if and only if the number of blue dots exceeds the number of nonblue dots. But this leaves unsettled, e.g., how the second cardinality is specified for purposes of understanding and/or verification: via the nonblue things, given a restriction to the dots, as in ‘|{x: Dot(x) & ~Blue(x)}|’; via the blue things, given the same restriction, and subtraction from the number of dots, as in ‘|{x: Dot(x)}| – |{x: Dot(x) & Blue(x)}|’; or in some other way. Psycholinguistic evidence and psychophysical modeling support the second hypothesis. (shrink)

According to Rosenthal’s Higher-Order Thought (HOT) theory of consciousness, first-order mental states become conscious only when they are targeted by HOTs that necessarily represent the states as belonging to self. On this view a state represented as belonging to someone distinct from self could not be a conscious state. Rosenthal develops this view in terms of what he calls the ‘thin immunity principle’ (TIP). According to TIP, when I experience a conscious state, I cannot be wrong about whether it is (...) I who I think is in that state. We first suggest that TIP is a direct consequence of the HOT theory. Next we argue that somatoparaphrenia—a pathology in which sensations are sometimes represented as belonging to other people—shows that TIP can be violated. This violation of TIP in turn shows that the HOT theory’s claim that conscious states are necessarily represented as belonging to self is in error. Rosenthal’s attempt to account for pathological cases is found to be inadequate when applied to somatoparaphrenia, and other possible defenses are also shown to be incapable of preserving TIP. We further conclude by suggesting that the HOT theory’s failing in this regard is not a failing that is peculiar to this theory of consciousness. (shrink)

What we can call asymmetric disagreement occurs when one agent is in disagreement with another, but not vice-versa. In this paper, I give an example of and develop a framework for understanding this phenomenon. One pivotal feature of my example is that one of the agents in the scenario has a belief about what might be the case—a might-belief. I show that a traditional account of might-beliefs and disagreement cannot explain the initially surprising phenomenon of asymmetric disagreement. In order to (...) provide an explanation, I develop a dynamic account of might-beliefs and a corresponding account of disagreement. I close by exploring a choice point for our account—showing that the simple dynamic account has some controversial (though, perhaps, true) consequences. I explore how revisionary notions of validity, inconsistency, and disagreement can allow us to avoid these consequences if we wish. (shrink)

Moral Expressivists typically concede that, in some minimal sense, moral sentences are truth-apt but claim that in some more robust sense they are not. The Immodest Disciplined Syntacticist, a species of minimalist about truth, raises a doubt as to whether this contrast can be made out. I here address this challenge by motivating and describing a distinction between reducibly and irreducibly truth-apt sentences. In the light of this distinction the Disciplined Syntacticist must either adopt a more modest version of his (...) theory, friendlier to Expressivism, or substantially modify it, abandoning one of its central conditions on truth-aptness. One natural and promising such modification, the Pure Discipline View, is described and its implications for an understanding of Expressivism briefly discussed. (shrink)

Moral Expressivists typically concede that, in someminimalsense, moral sentences are truth‐apt but claim that in some morerobustsense they are not. TheImmodest Disciplined Syntacticist, a species of minimalist about truth, raises a doubt as to whether this contrast can be made out. I here address this challenge by motivating and describing a distinction betweenreduciblyandirreduciblytruth‐apt sentences. In the light of this distinction the Disciplined Syntacticist must either adopt a moremodestversion of his theory, friendlier to Expressivism, or substantially modify it, abandoning one of (...) its central conditions on truth‐aptness. One natural and promising such modification, thePure Discipline View, is described and its implications for an understanding of Expressivism briefly discussed. (shrink)

Most philosophers seem to be under a misleading impression about the difference between ‘and’ and ‘but’. They hold that they are truth-functional equivalents but that ‘but’ adds a Gricean ‘conventional implicature’ to ‘and’. Frege thought that the implicature attached to ‘but’ was that the second clause is unlikely given the first; others have simply said they express a contrast between the two. Though the second formulation may seem more general, in practice writers seem to agree with Frege's idea. The present (...) note will argue against this conventional view. Indeed, ‘and’ and ‘but’ may both convey conflicting implicatures; and the traditional characterization of the implicature of ‘but’ is outright mistaken, or at least misleading. (shrink)

It is well known that Frege was an extensionalist, in the following sense: he held that the truth-value of a sentence is always a function only of the references of its parts. One consequence of this view is that expressions occurring in certain linguistic contexts – for example, the that-clauses of propositional attitude ascriptions – do not have their usual references, but refer instead to what are usually their senses. But although a number of philosophers have objected to this result, (...) no one has yet attempted to see what happens to Frege's views – and, in particular, to his theory of sense and reference – if his extensionalism is abandoned while his other views are maintained. This paper thus does two things. First, it clears the way for such an attempt, by arguing that recent defences of Frege's extensionalism – by Tyler Burge, Saul Kripke, Terence Parsons and Christopher Peacocke – fall short. Second, it sketches a positive proposal for a non-extensionalist application of Frege's theory of sense and reference to sentences of indirect discourse and ascriptions of propositional attitude. (shrink)

In his Naming and Necessity, Saul Kripke puts forth a series of arguments against theories of proper names he calls Frege-Russell theories. As the title reveals, Kripke takes Gottlob Frege's theory of sense and Bedeutung to be a good representative of these theories. In this essay, I characterize how Frege might have answered Kripke. I agree with Kripke that presumably Frege thought that the sense of a proper name is the same as some definite description. I, however, question his assumption (...) that Frege's theory of proper names was a theory of meaning as he uses the term. I go even further and suggest that it is not so obvious that Frege thought, at least always, that the role of the concept of sense in his theory is a semantic concept at all. This constitutes the heart of my reconstruction of Frege's answer. I argue that this, together with Frege's conception of natural languages, would have allowed him to hold that the sense of a proper name may sometimes be the same as the sense of an indefinite or even a wrong description. This makes Frege's theory immune to Kripke's counter-arguments. (shrink)

A response to critics, Douglas Patterson and Mark Textor, on Künne's modest theory of truth in *Conceptions of Truth*.

I offer an analysis of the sentence "the concept horse is a concept". It will be argued that the grammatical subject of this sentence, "the concept horse", indeed refers to a concept, and not to an object, as Frege once held. The argument is based on a criterion of proper-namehood according to which an expression is a proper name if it is so rendered in Frege's ideography. The predicate "is a concept", on the other hand, should not be thought of (...) as referring to a function. It will be argued that the analysis of sentences of the form "C is a concept" requires the introduction of a new form of statement. Such statements are not to be thought of as having function--argument form, but rather the structure subject--copula--predicate. (shrink)

The aim of this paper is to motivate and defend a conventional approach to assertion and other illocutionary acts. Such an approach takes assertions, questions and orders to be moves within an essentially rule-governed activity similar to a game. The most controversial aspect of a conventional account of assertion is that according to it, for classifying an utterance as an assertion, question or command, “it is irrelevant what intentions the person speaking may have had” (Dummett 1973, p. 302). I understand (...) this to mean that it is irrelevant for the issue of whether an utterance is an assertion whether the utterer has certain communicative intentions, such as the intention to utter something true, the intention to get one’s audience to believe (that one believes) what one has asserted etc. Just as one can commit a foul in football without meaning to do so, one can make an assertion, issue a command or ask a question without meaning to do so. The rules of football specify that a certain form of conduct (tackling an opponent in a certain way), carried out under certain general conditions (being a member of a team engaged in a game of football) counts as committing a foul. Similarly, I claim, the rules of language specify that a certain form of conduct (uttering an assertoric sentence), carried out under certain general conditions (being a member of a speech community engaged in a conversation) counts as making an assertion. (shrink)

ABSTRACT. The received picture of linguistic communication understands communication as the transmission of information from speaker's head to hearer's head. This picture is in conflict with the attractive Lewisian view of belief as self-location, which is motivated by de se attitudes – first-personal attitudes about oneself – as well as attitudes about subjective matters such as personal taste. In this paper, I provide a solution to the conflict that reconciles these views. I argue for an account of mental attitudes and (...) communication on which mental content and speech act content is understood as sets of multicentered worlds – roughly, possible worlds ‘centered’ on a sequence of individuals at a time. I develop a Stalnakerian model of communication based on multicentered worlds content, and I provide a suitable semantics for personal pronouns and predicates of personal taste. The resulting picture is one on which the point of conversation is the coordination of individual perspectives. (shrink)

This paper criticizes the circularity reading of Frege's argument for the indefinability of truth. According to this reading, Frege is appealing to a sort of circularity in the argument. I argue that the circularity reading is interpretatively incorrect, or makes Frege's argument a non‐starter.

In this paper I present how the normative inferentialist can make the distinction between sentence meaning and content of the utterance. The inferentialist can understand sentence meaning as a role conferred to that sentence by the rules governing inferential transitions and content of the utterance as just a part of sentence meaning. I attempt to show how such a framework can account for prominent scenarios presented by contextualists as a challenge to semantic minimalism/literalism. I argue that inferentialism can address contextualist (...) challenges in a simple and effective manner by understanding sentence meaning as broad, but invariant. (shrink)

Abstract objects are standardly taken to be causally inert, however principled arguments for this claim are rarely given. As a result, a number of recent authors have claimed that abstract objects are causally efficacious. These authors take abstracta to be temporally located in order to enter into causal relations but lack a spatial location. In this paper, I argue that such a position is untenable by showing first that causation requires its relata to have a temporal location, but second, that (...) if an entity is temporally located then it is spatiotemporally located since this follows from the theory of Relativity. Since abstract objects lack a spatiotemporal location, then if something is causally efficacious, it is not abstract. (shrink)

On a representationalist view, conceptual engineering is the practice of changing the extensions and intensions of the devices we use to speak and think. But if this view holds true, conceptual engineering has a bad rationale. Extensions and intensions are not the sorts of things that are better or worse as such. A representationalist account of conceptual engineering thus falls prey to the objection that the practice has a bad rationale. To account for the assumption that conceptual engineering is worthwhile, (...) we propose to view what is being engineered as inferential devices, as opposed to representational devices. The objective is not to establish that being or having an inferential role is all there is to meaning or conceptual content. Rather, our agenda is to recommend a shift of focus from the representational features of content to the inferential features of content for the purposes of doing and thinking about conceptual engineering. Inferentialism about conceptual engineering makes better sense of the practice than a representationalist approach: In addition to accounting for the rationality of engaging in conceptual engineering, inferentialism provides a sound interpretation of what is at stake in concrete examples of conceptual engineering. (shrink)

This paper explores the impact of quantification into predicate position on the metaphysics of properties, arguing that two familiar debates about properties are fundamentally altered by recasting them in a second-order setting. Two theories of properties are outlined, differing over whether the existence of properties is expressed using first-order or second-order quantifiers. It is argued that the second-order theory: provides good reason to regard debate about the locations of properties as contentless; resolves debate about whether properties are particulars or universals (...) in favour of universals. (shrink)

When do data provide good evidence for a hypothesis, evidence that warrants an inference to the hypothesis? Standard answers either reject the legitimacy of induction or else allow warranted inference from data to hypothesis when there are suitable relationships between and among the data and hypotheses. The severity account rejects all of these, maintaining instead that the good evidence relation concerns not only relations between data and hypotheses but also the methods for obtaining the data and the sensitivity of these (...) methods to detecting falsehood. So, for example, the severity account allows two rival hypotheses to fit the data equally well, even to the point of having the same prior and posterior probabilities relative to those data, while the data nonetheless favour one hypothesis over the other by virtue of those data providing a severe test of one hypothesis and not the other. The contributions to Error and Inference variously trace the genesis of the severity account from statistics-oriented sciences, elaborate upon the account’s details, apply the account to various philosophical issues, and offer challenges to the account’s adequacy and replies to major criticisms. The editors have developed the severity account in detail elsewhere, and this anthology is an effort …. (shrink)

ABSTRACT Frege characterizes judgement as the acknowledgement of the truth of a thought, appearing thereby to rule out false judgement. First in this paper I explain Frege’s characterization so that it does not have this consequence. Frege is not saying that for a subject S to judge that p is for S to acknowledge the truth of the thought that p. Rather, he is articulating judgement’s nature within self-consciousness. From within, to judge means to acknowledge a truth. Second, I suggest (...) that this articulation is centrally operative in Frege’s argument for the indefinability of truth. As Frege argues, it follows from judgement’s self-consciousness that truth is indefinable. (shrink)

Donnellan famously argued that while one can fix the reference of a name with a definite description, one cannot thereby have a de re belief about the named object. All that is generated is meta-linguistic knowledge that the sentence “If there is a unique F, then N is F” is true. Donnellan’s argument and the sceptical position are extremely influential. This article aims to show that Donnellan’s argument is unsound, and that the Millian who embraces Donnellan’s scepticism that the reference-fixer (...) cannot secure the relevant de re belief faces a serious problem: Millianism about names plus scepticism about the reference-fixer’s de re belief conflicts with what seems to be an analytical thesis about the relationship between semantic content and understanding. The upshot is that the Millian has good reason to seek an alternative to scepticism. (shrink)

General-elimination harmony articulates Gentzen’s idea that the elimination-rules are justified if they infer from an assertion no more than can already be inferred from the grounds for making it. Dummett described the rules as not only harmonious but stable if the E-rules allow one to infer no more and no less than the I-rules justify. Pfenning and Davies call the rules locally complete if the E-rules are strong enough to allow one to infer the original judgement. A method is given (...) of generating harmonious general-elimination rules from a collection of I-rules. We show that the general-elimination rules satisfy Pfenning and Davies’ test for local completeness, but question whether that is enough to show that they are stable. Alternative conditions for stability are considered, including equivalence between the introduction- and elimination-meanings of a connective, and recovery of the grounds for assertion, finally generalizing the notion of local completeness to capture Dummett’s notion of stability satisfactorily. We show that the general-elimination rules meet the last of these conditions, and so are indeed not only harmonious but also stable. (shrink)

There are different ways we use the expressions “extension” and “intension”. I specify in the first part of this paper two basic senses of this distinction, and try to show that the old metaphysical sense, by means of particular instance vs. universal, is more fundamental than the contemporary sense by means of substitutivity. In the second part, I argue that logic in general is essentially intensional, not only because logic is a rule-guided activity, but because even the extensional definition of (...) a logic system presupposes an intensional notion of logical consequence. DOI:10.5007/1808-1711.2010v14n1p111. (shrink)

It is widely recognized that Frege's systematic conception of science has a major impact on his work. I argue that central to this conception and its impact is Frege's Simplicity Requirement that a scientific system must have as few primitive truths as possible. Frege states this requirement often, justifies it in several ways, and appeals to it to motivate important aspects of his broader views. Acknowledging its central role illuminates several aspects of his work in new ways, including his treatment (...) of truth values, logical concepts, and the dependence relations that induce a ‘natural order’ of truths. (shrink)

Why does Frege claim that logical axioms are ‘self‐evident,’ to be recognized as true ‘independently of other truths,’ and then offer arguments for those axioms? I argue that he thinks the arguments provide us with the justification that we need for accepting the axioms and that this is compatible with his remarks about self‐evidence. This compatibility depends on philosophical considerations connected with the ‘critical method’: an interesting approach to the justification of axioms endorsed by leading philosophers at the time.

Frege held that the result of applying a predicate to names lacks reference if any of the names lack reference. We defend the principle against a number of plausible objections. We put forth an account of consequence for a first-order language with identity in which the principle holds.

Atomism denies that complexes exist. Common-sense metaphysics may posit masses, composite individuals and sets, but atomism says there are only simples. In a singularist logic, it is difficult to make a plausible case for atomism. But we should accept plural logic, and then atomism can paraphrase away apparent reference to complexes. The paraphrases require unfamiliar plural universals, but these are of independent interest; for example, we can identify numbers and sets with plural universals. The atomist paraphrases would fail if plurals (...) presuppose complexes: but an Appendix shows that reference to complexes is not required in the semantics of plurals. (shrink)

§1. Introduction. I dedicate this essay to the two-dozen-odd people whose refutations of Cantor's diagonal argument have come to me either as referee or as editor in the last twenty years or so. Sadly these submissions were all quite unpublishable; I sent them back with what I hope were helpful comments. A few years ago it occurred to me to wonder why so many people devote so much energy to refuting this harmless little argument—what had it done to make them (...) angry with it? So I started to keep notes of these papers, in the hope that some pattern would emerge.These pages report the results. They might be useful for editors faced with similar problem papers, or even for the authors of the papers themselves. But the main message to reach me is that there are several points of basic elementary logic that we usually teach and explain very badly, or not at all.In 1995 an engineer named William Dilworth, who had published a refutation of Cantor's argument in the Transactions of the Wisconsin Academy of Sciences, Arts and Letters, sued for libel a mathematician named Underwood Dudley who had called him a crank. (shrink)

Sentences in context have semantic contents determined by a range of factors both internal and external to speakers. I argue against the thesis that semantic content is transparent to speakers in the sense of being immediately accessible to speakers in virtue of their linguistic competence.

Views that treat the contents of sentences as structured, Russellian propositions face a problem with empty names. It seems that those sorts of things cannot be the contents of sentences containing such names. I motivate and defend a solution to the problem according to which a sentence may have a singular proposition as its content at one time, and a nonsingular one at another. When the name is empty the content is a nonsingular Russellian structured proposition; when the name is (...) not empty the content is a singular Russellian structured proposition. (shrink)

§1. Introduction. I dedicate this essay to the two-dozen-odd people whose refutations of Cantor's diagonal argument have come to me either as referee or as editor in the last twenty years or so. Sadly these submissions were all quite unpublishable; I sent them back with what I hope were helpful comments. A few years ago it occurred to me to wonder why so many people devote so much energy to refuting this harmless little argument—what had it done to make them (...) angry with it? So I started to keep notes of these papers, in the hope that some pattern would emerge.These pages report the results. They might be useful for editors faced with similar problem papers, or even for the authors of the papers themselves. But the main message to reach me is that there are several points of basic elementary logic that we usually teach and explain very badly, or not at all.In 1995 an engineer named William Dilworth, who had published a refutation of Cantor's argument in the Transactions of the Wisconsin Academy of Sciences, Arts and Letters, sued for libel a mathematician named Underwood Dudley who had called him a crank. (shrink)