Number words seemingly function both as adjectives attributing cardinality properties to collections, as in Frege’s ‘Jupiter has four moons’, and as names referring to numbers, as in Frege’s ‘The number of Jupiter’s moons is four’. This leads to what Thomas Hofweber calls Frege’s Other Puzzle: How can number words function as modifiers and as singular terms if neither adjectives nor names can serve multiple semantic functions? Whereas most philosophers deny that one of these uses is genuine, (...) we instead argue that number words, like many related expressions, are polymorphic, having multiple uses whose meanings are systematically related via type shifting. (shrink)

In their recent article ‘Resolving Frege’s other Puzzle’ Eric Snyder, Richard Samuels, and Stewart Shapiro defend a semantic type-shifting solution to Frege’s other Puzzle and criticize my own cognitive type-shifting solution. In this article I respond to their criticism and in turn point to several problems with their preferred solution. In particular, I argue that they conflate semantic function and semantic value, and that their proposal is neither based on general semantic type-shifting principles (...) nor adequate to the data. (shrink)

Since their introduction by Partee and Rooth (1983) into linguistic theory, type shifting principles have been extensively employed in various linguistic domains, including nominal predicates (Partee 1987), kind denoting NPs (Chierchia 1998), interrogatives (Groenendijk and Stokhof 1989), scrambled definites (De Hoop and Van der Does 1998) and plurals (Winter 2001,2002). Most of the accounts that use type shifting principles employ them as ``last resort'' mechanisms, which apply only when other compositional mechanisms fail. This failure is often sloppily (...) referred to as type mismatch . The motivation for introducing type mismatch into the compositional mechanism is twofold: on the one hand it allows lexical items to be assigned the minimal types that are needed for describing their denotation; on the other hand, it has been argued that the ``last resort'' strategy of type shifting prevents derivation of undesired meanings. The first goal of this paper is to define a simple notion of type mismatch, which will rather closely follow Partee and Rooth's original proposal but will be expressed within more familiar terms of categorial semantics. After introducing this implementation of traditional type mismatch, it will be argued that in fact, it covers only one possible kind of trigger for type shifting principles. Partee and Rooth's notion of mismatch is ``external'' in that the type of an expression is changed only when it combines with another type to which it cannot compose using the ``normal'' compositional mechanism. It will be argued that, within an appropriate type system, another notion of mismatch is also useful. This is the kind of mismatch in which the semantic type of an expression does not match its syntactic category. Two such cases will be explored: mismatch between morpho-syntactic number (singular or plural) and semantic number (a denotation ranging over atoms or sets), and mismatch between syntactic category (noun, DP, adjective etc.) and semantic role (predicate, quantifier, predicate modifier etc.).. (shrink)

Students of classical Chinese philosophy are quite justly puzzled by the debates and paradoxes in the "School of Names" and the extant logico-semantic texts of the Later Mohists. The latter has received an incisive and extensive treatment in A. C. Graham's Later Mohist Logic, Ethics and Science. Thus far, no larger systematic work on Chinese logic and philosophy of language is available in English. Hansen's book is a good attempt to deal in the large scale with classical Chinese philosophy of (...) language. This book consists of five carefully written chapters. The first expounds a methodology which starts from the premise that interpretation is a theory--"an attempt to explain a text--to render it understandable. As such it is inescapably relative to the intended audience, and appropriately wedded to the critical, rational, logical evaluation procedures appropriate to other theories. The main evaluative features on which we have concentrated is the coherence of the theory." The text at issue is that ascribed to Kung-sun Lung discussed in chapter 5. In terms of its announced aim, it succeeds well in rendering a plausible though by no means uncontroversial explication of the text. The attempted explication is, however, mediated by a number of chapters which raise interesting philosophical issues that repay closer examination by students and philosophical scholars of Chinese philosophy of language. Chapter 2, for example, proposes a bold hypothesis on Chinese philosophy in terms of the logic of mass nouns. It is claimed that a "stuff-like ontology and semantics were implicitly operating as a background assumption behind pre-Han philosophy," and a negative corrollary: "an hypothesis that an abstract or mentalistic ontology and semantics of the type common to Western thinkers were not implicit assumptions behind pre-Han philosophy." For the reviewer, the negative thesis is highly plausible independently of the adequacy of the first. (shrink)

This is a book about sensory states and their apparent characteristics. It confronts a whole series of metaphysical and epistemological questions and presents an argument for type materialism: the view that sensory states are identical with the neural states with which they are correlated. According to type materialism, sensations are only possessed by human beings and members of related biological species; silicon-based androids cannot have sensations. The author rebuts several other rival theories, and explores a number of (...) important issues: the forms and limits of introspective awareness of sensations, the semantic properties of sensory concepts, knowledge of other minds, and unity of consciousness. The book is a significant contribution to the philosophy of mind, and has much to say to psychologists and cognitive scientists. (shrink)

In this paper, we outline and critically evaluate Thomas Hofweber’s solution to a semantic puzzle he calls Frege’s Other Puzzle. After sketching the Puzzle and two traditional responses to it—the Substantival Strategy and the Adjectival Strategy—we outline Hofweber’s proposed version of Adjectivalism. We argue that two key components—the syntactic and semantic components—of Hofweber’s analysis both suffer from serious empirical difficulties. Ultimately, this suggests that an altogether different solution to Frege’s Other Puzzle is required.

ABSTRACT In this paper, I argue that a number of influential Millian responses to Frege’s puzzle, which consist in denying that Frege’s data apply to natural languages, are not viable if logic is to play its role in legitimizing the logical appraisal of rational subjects. A notion of validity which does justice to the normativity of logic must make room for a distinction between valid inferences and enthymemes. I discuss the prospects of formal, relevant and manifest validity as (...) candidates for a notion which complies with this desideratum. Their success, or failure is argued to hang on the viability of a semantical account of de jure co-reference, which is in tension with standard Millian tenets. I conclude that these Millian theories face the following dilemma: either accept that there is no notion of logical validity which makes logic normative for reasoning, thus jeopardizing our well entrenched practices of rational appraisal; or accept that de jure co-reference is a real semantical relation. (shrink)

This paper provides a new approach to a family of outstanding logical and semantical puzzles, the most famous being Frege's puzzle. The three main reductionist theories of propositions (the possible-worlds theory, the propositional-function theory, the propositional-complex theory) are shown to be vulnerable to Benacerraf-style problems, difficulties involving modality, and other problems. The nonreductionist algebraic theory avoids these problems and allows us to identify the elusive nondescriptive, non-metalinguistic, necessary propositions responsible for the indicated family of puzzles. The algebraic approach is (...) also used to defend antiexistentialism against existentialist prejudices. The paper closes with a suggestion about how this theory of content might enable us to give purely semantic (as opposed to pragmatic) solutions to the puzzles based on a novel formulation of the principle of compositionality. (shrink)

In the paper, I discuss a possibility of defending the Direct Reference theory from its most dangerous threaten which is the notorious Frege's puzzle. I discuss two possible ways of doing that. First is based on King's theory of propositions as facts. I show that tools provided by King's theory are not enough to solve the puzzle. More promising is a method supported by new Soames's theory of propositions as cognitive event-types. I try to show that this framework allows us (...) to develop a satisfying solution of the puzzle, which focuses​ on the notion of the cognitive value of the sentence. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:167. ON McRAE' S HUME Professor McRae's interesting paper may be rather naturally divided into two parts. In the first part he explains what he takes Hume's account of time to be; in the second he advances the bold thesis that Hume's account of time, or perhaps of duration, provides a basis or foundation for his more widely discussed remarks on identity, substance, the self, the necessary connections. In (...) what follows I first reconstruct Professor McRae' s paper, and then I raise some problems, perhaps puzzles, about Hume's view on duration, time and fictions. According to McRae, some philosophers (Descartes, Spinoza, Leibniz) distinguish between time and duration, both of which are taken to be perfectly legitimate notions. Hume, by contrast, takes time and duration to be the same, viz., a succession of moments. What philosophers and the vulgar call 'duration' is something quite different, namely a single unbroken stretch of time which is not composed of successive parts. Of duration taken in this latter way, McRae says, Hume has four things to say, all of them negative: (1) we have no idea of duration; (2) no object has duration; (3) there is no such thing as duration; and (4) duration is a fiction. Properly understood as a succession of moments, however, time certainly exists and is thus not a fiction. Moreover, we have the or at least an idea of time, despite the fact that it is obtained without derivation from a precedent impression. And, while no object can be said to have time, Hume will nonetheless allow that objects exist at certain times and perhaps across a time span. In the second part of his paper, Professor McRae distinguishes two types of Humean fictions. The first arises when one idea is confused with another and mis-applied to some object. The second arises when the imagination creates an "idea" in the attempt to resolve a 168. contradiction which comes up when the first fiction is applied to an object. What I have called McRae' s "bold thesis" in the second part of his paper can now be stated. Duration, or the putative idea thereof, is a fiction of the first type, one that is attributed to what Hume calls "steadfast objects." However, such an object can be considered in two ways. One might consider the object at two stages of this duration and, McRae says, "...this will give us the idea of number" (p. 126); or, one might consider in turn a series of objects, each of them supposedly "steadfast," all along supposing that though time is changing, the objects are not, and "...in this way- we get the idea of unity" (Ibid.). But no object is both a unity and a multiplicity. So, to reconcile these conflicting considerations, the "idea" or fiction of identity is invented. As McRae says: "The idea of identity is a pure product of the imagination invented to mediate between unity and number" (Ibid. ). This invented "idea" is then mis-applied (a fiction of type one) to interrupted appearances of an object. To reconcile the supposed identity of an object with successive appearances of it, the fiction of substance is invented. Quoting both McRae and Hume, In order to reconcile the contradiction between identity and diversity, the imagination is apt to feign something unknown and invisible, which it supposes to continue the same under all these variations ; 2 and this unintelligible something it calls a substance... (p. 128). Related needs to resolve contradictions, on McRae' s account, lead to the fictions of the self (p. 128) and of necessary connections (p. 130), though the latter fiction is of type one. Hence, McRae' s "bold thesis" amounts to this: Duration is a fiction. In the attempt to apply this fiction, one is led to, logically led to, most, if not all, of the other famous Humean fictions. And, if we allow that there are mental acts, for Hume, as well as impressions and ideas, "...then a fictitious duration will be attributed to 169. objects and by a progressive compounding of fictitious mental actions will give the world the ontological structure which it has for the vulgar belief we all share. It... (shrink)

The standard argument for the existence of distinctively mathematical objects like numbers has two main premises: some mathematical claims are true, and the truth of those claims requires the existence of distinctively mathematical objects. Most nominalists deny. Those who deny typically reject Quine’s criterion of ontological commitment. I target a different assumption in a standard type of semantic argument for. Benacerraf’s semantic argument, for example, relies on the claim that two sentences, one about numbers and the other about (...) cities, have the same grammatical form. He makes this claim on the grounds that the two sentences are superficially similar. I argue that these grounds are not sufficient. Other sentences with the same superficial form appear to have different grammatical forms. I offer two plausible interpretations of Benacerraf’s number sentence that make use of plural quantification. These interpretations appear not to incur ontological commitments to distinctively mathematical objects, even assuming Quine’s criterion. Such interpretations open a new, plural strategy for the mathematical nominalist. (shrink)

Frege's theory of indirect contexts and the shift of sense and reference in these contexts has puzzled many. What can the hierarchy of indirect senses, doubly indirect senses, and so on, be? Donald Davidson gave a well-known 'unlearnability' argument against Frege's theory. The present paper argues that the key to Frege's theory lies in the fact that whenever a reference is specified (even though many senses determine a single reference), it is specified in a particular way, so that giving a (...) reference implies giving a sense; and that one must be 'acquainted' with the sense. It is argued that an indirect sense must be 'immediately revelatory' of its reference. General principles for Frege's doctrine of sense and reference are sated, for both direct and indirect quotation, to be understood iteratively. I also discuss Frege's doctrine of tensed and first person statements in the light of my analysis. The views of various other authors are examined. The conclusion is to ascribe to Frege an implicit doctrine of acquaintance similar to that of Russell. (shrink)

This paper investigates a certain puzzling argument concerning number expressions and their meanings, the Easy Argument for Numbers. After finding faults with previous views, I offer a new take on what’s ultimately wrong with the Argument: it equivocates. I develop a semantics for number expressions which relates various of their uses, including those relevant to the Easy Argument, via type-shifting. By marrying Romero ’s :687–737, 2005) analysis of specificational clauses with Scontras ’ semantics for Degree Nouns, I (...) show how to extend Landman ’s Adjectival Theory to numerical specificational clauses. The resulting semantics can explain various contrasts observed by Moltmann, but only if Scontras’ contention that degrees and numbers are sortally distinct is correct. At the same time, the Easy Argument can establish its intended conclusion only if numbers and degrees are mistakenly assumed to be identical. (shrink)

ABSTRACT. Fodor characterizes concepts as consisting of two dimensions: one is content, which is purely denotational/broad, the other the Mentalese vehicle bearing that content, which Fodor calls the Mode of Presentation (MOP), understood "syntactically." I argue that, so understood, concepts are not interpersonally sharable; so Fodor's own account violates what he calls the Publicity Constraint in his (1998) book. Furthermore, I argue that Fodor's non-semantic, or "syntactic," solution to Frege cases succumbs to the problem of providing interpersonally applicable functional (...) roles for MOPs. This is a serious problem because Fodor himself has argued extensively that if Fregean senses or meanings are understood as functional/conceptual roles, then they can't be public, since, according to Fodor, there are no interpersonally applicable functional roles in the relevant senses. I elaborate on these relevant senses in the paper. (shrink)

‘The following sentence is true only if numbers exist: The number of planets is eight. It is true; hence, numbers exist.’ So runs a familiar argument for realism about mathematical objects. But this argument relies on a controversial semantic thesis: that ‘The number of planets’ and ‘eight’ are singular terms standing for the number eight, and the copula expresses identity. This is the ‘Fregean analysis’.I show that the Fregean analysis is false by providing an analysis of sentences such as that (...) best explains the available linguistic data, and according to which no terms in purport to stand for numbers. (shrink)

Abstract Though it has been claimed that Frege's commitment to expressions in indirect contexts not having their customary senses commits him to an infinite number of semantic primitives, Terrence Parsons has argued that Frege's explicit commitments are compatible with a two-level theory of senses. In this paper, we argue Frege is committed to some principles Parsons has overlooked, and, from these and other principles to which Frege is committed, give a proof that he is indeed committed to an infinite (...) number of semantic primitives?an intolerable result. (shrink)

The traditional understanding of abstraction operates on the basis of the assumption that only entities are subject to thought processes in which particulars are disregarded and commonalities are lifted out (the so-called method of genus proximum and differentia specifica). On this basis Frege criticized the notion of abstraction and convincingly argued that (this kind of) “entitary- directed” abstraction can never provide us with any numbers. However, Frege did not consider the alternative of “property- abstraction.” In this article an argument for (...) this alternative kind of abstraction is formulated by introducing a notion of the “modal universality” of the arithmetical and by developing it in terms of the distinction between type-laws (laws for entities – applicable to a limited class of entities) and modal laws (obtaining for every possible entity without any restriction). In order to substantiate this argument a case is made for the acceptance of an ontic foundation for the arithmetical (and other modes or functions of reality – with special reference to Cassirer, Bernays, Gödel and Wang), which, in the final section, serves to give an ontological account of (i) the connections between the arithmetical and other aspects of reality and (ii) the applicabality of arithmetic. In the course of the argument the impasse of logicism is briefly highlighted, while a few remarks are made with regard to the logical subject- object relation in connection with Frege's view that number attaches to a concept. S. Afr. J. Philos. Vol.22(1) 2003: 63-80. (shrink)

This is the 1991 (2nd) edition of the 1986 book (MIT Press), considered to be the classic defense of Millianism. The nature of the information content of declarative sentences is a central topic in the philosophy of language. The natural view that a sentence like "John loves Mary" contains information in which two individuals occur as constituents is termed the naive theory, and is one that has been abandoned by most contemporary scholars. This theory was refuted originally by philosopher Gottlob (...) Frege. His argument that the naive theory did not work is termed Frege's puzzle, and his rival account of information content is termed the orthodox theory. In this detailed study, Nathan Salmon defends a version of the naive theory and presents a proposal for its extension that provides a better picture of information content than the orthodox theory gives. He argues that a great deal of what has generally been taken for granted in the philosophy of language over the past few decades is either mistaken or unsupported, and consequently, much current research is focused on the wrong set of questions. Salmon dissolves Frege's puzzle as it is usually formulated and demonstrates how it can be reconstructed and strengthened to yield a more powerful objection to the naive theory. He then defends the naive theory against the new Frege puzzle by presenting an idea that yields both a surprisingly rich and powerful extension of the naive theory and a better picture of information content than that of the original orthodox theory. Nathan Salmon is Professor of Philosophy, University of California at Santa Barbara. (shrink)

Departing from the dominant theories of Frege, Russell and Mill, Kit Fine has sketched a novel solution to Frege’s puzzle in his book Semantic Relationism. In this article, I briefly discuss the puzzle in its various forms and the attempted solutions of Frege and Russell. I then explicate the essential features of the new theory and critically appraise the mechanism suggested by Fine to solve the puzzle. I show that Semantic Relationism fails to address the concerns raised in the (...) puzzle. (shrink)

Saul Kripke's puzzle about belief demonstrates the lack of soundness of the traditional argument for the Fregean fundamental principle that the sentences 'S believes that a is F' and 'S believes that b is F' can differ in truth value even if a = b. This principle is a crucial premise in the traditional Fregean argument for the existence of semantically relevant senses, individuative elements of beliefs that are sensitive to our varying conceptions of what the beliefs are about. Joseph (...) Owens has offered a new argument for this fundamental principle, one that is not subject to Kripke's criticisms. I argue that even though Owens' argument avoids Kripke's criticisms, it has other flaws. (shrink)

In a series of recent works, Kit Fine, 605–631, 2003, 2007) has sketched a novel solution to Frege’s puzzle. Radically departing from previous solutions, Fine argues that Frege’s puzzle forces us to reject compositionality. In this paper we first provide an explicit formalization of the relational semantics for first-order logic suggested, but only briefly sketched, by Fine. We then show why the relational semantics alone is technically inadequate, forcing Fine to enrich the syntax with a coordination (...) schema. Given this enrichment, we argue, that that the semantics is compositional. We then examine the deep consequences of this result for Fine’s proposed solution to Frege’s puzzle. We argue that Fine has mis-diagnosed his own solution–his attempted solution does not deny compositionality. The correct characterization of Fine’s solution fits him more comfortably among familiar solutions to the puzzle. (shrink)

The paper deals with the general peculiarities of numerals. Cases where the sense of numeral cannot simply be explained by the idea of counting, of number, or of order are considered. Special types of texts folklore on the one band, propaganda on the other hand - are analyzed. For the latter the examples from two Soviet central official newspapers - Pravda and lzvestija of May 1986 have been chosen. These texts partially reflect common stylistic features of Soviet propagandistic discourse (...) of the "period of stagnation"; their specificity is caused by the special situation, which obtained in the country in those days - the catastrophe in the atomic power station in Chemobyl. It is claimed that all the considered examples reflect several aspects of meaning of numerals contained in their general semantics. Thus, the development of the evaluative meaning is explained by the semantics of degree contained in the numerals. These data contribute to Frege's idea of relativity of number, but from another, purely linguistic, point of view. (shrink)

The aim of this paper is to present a constructive solution to Frege's puzzle (largely limited to the mathematical context) based on type theory. Two ways in which an equality statement may be said to have cognitive significance are distinguished. One concerns the mode of presentation of the equality, the other its mode of proof. Frege's distinction between sense and reference, which emphasizes the former aspect, cannot adequately explain the cognitive significance of equality statements unless a clear identity (...) criterion for senses is provided. It is argued that providing a solution based on proofs is more satisfactory from the standpoint of constructive semantics. (shrink)

Gottlob Frege’s Grundgesetze der Arithmetik (Basic Laws of Arithmetic, Vol. I/II; 1893/1903) is a modern classic. Since the 1930s it has belonged to an exclusive class of only eleven works in the history of symbolic logic, which contain the ‘first appearance of a new idea of fundamental importance’ [Church, 1936, p. 122], and its author is the only one whose other major works — Begriffsschrift (1879) and Die Grundlagen der Arithmetik (1884) — also belong to this distinguished group. (...) Together with the seminal paper ‘Über Sinn und Bedeutung’ these three monographs represent the essential contributions to one of the most fascinating foundational projects in mathematics, then and now. For decades Frege struggled with the question, ‘how are we to apprehend logical objects, in particular, the numbers? What justifies us in acknowledging numbers as objects?’ [Frege, 2013, ‘Afterword’, p. 265]. His favourite answer, for a long time, was that arithmetic is a complex branch of logic. But since there is no logicism without logic, Frege started in Begriffsschrift with the invention of a nearly perfect formalization of higher-order classical predicate logic. To discover how far we can get in arithmetic by analytic means alone, it was even necessary to clarify the semantic character of the concept of number. This was done in a marvellous way by Frege five years later, in Grundlagen. The next step was nothing less than the complete execution of his logicist project, a monumental undertaking; and it is well known that here Frege failed, due to Russell’s derivation of the antinomy in 1902. But, despite the contradiction, Grundgesetze contains Frege’s legacy to logicism, which became more and more attractive. (shrink)

Here we present what we believe is a novel account of what languages are, along with an axiomatically rich representation of languages and language-related data that is based on this account. We propose an account of languages as aggregates of dispositions distributed across aggregates of persons, and in doing so we address linguistic competences and the processes that realize them. This paves the way for representing additional types of language-related entities. Like demographic data of other sorts, data about languages (...) may be of use to researchers in a number of areas, including biomedical research. Data on the languages used in clinical encounters are typically included in medical records, and capture an important factor in patient-provider interactions. Like many types of patient and demographic data, data on a person’s preferred and primary languages are organized in different ways by different systems. This can be a barrier to data integration. We believe that a robust framework for representing language in general and preferred and primary language in particular – which has been lacking in ontologies thus far – can promote more successful integration of language-related data from disparate data sources. (shrink)

This paper has three main goals. First, to motivate a puzzle about how ignorance-expressing terms like maybe and if interact: they iterate, and when they do they exhibit scopelessness. Second, to argue that there is an ambiguity in our theoretical toolbox, and that exposing that opens the door to a solution to the puzzle. And third, to explore the reach of that solution. Along the way, the paper highlights a number of pleasing properties of two elegant semantic theories, explores some (...) meta-theoretic properties of dynamic notions of meaning, dips its toe into some hazardous waters, and offers characterization theorems for the space of meanings an indicative conditional can have. (shrink)

So-called 'Frege cases' pose a challenge for anyone who would hope to treat the contents of beliefs (and similar mental states) as Russellian propositions: It is then impossible to explain people's behavior in Frege cases without invoking non-intentional features of their mental states, and doing that seems to undermine the intentionality of psychological explanation. In the present paper, I develop this sort of objection in what seems to me to be its strongest form, but then offer a response to it. (...) I grant that psychological explanation must invoke non-intentional features of mental states, but it is of crucial importance which such features must be referenced. -/- It emerges from a careful reading of Frege's own view that we need only invoke what I call 'formal' relations between mental states. I then claim that referencing such 'formal' relations within psychological explanation does not undermine its intentionality in the way that invoking, say, neurological features would. The central worry about this view is that either (a) 'formal' relations bring narrow content in through back door or (b) 'formal' relations end up doing all the explanatory work. Various forms of each worry are discussed. The crucial point, ultimately, is that the present strategy for responding to Frege cases is not available either to the 'psycho-Fregean', who would identify the content of a belief with its truth-value, nor even to someone who would identify the content of a belief with a set of possible worlds. It requires the sort of rich semantic structure that is distinctive of Russellian propositions. There is therefore no reason to suppose that the invocation of 'formal' relations threatens to deprive content of any work to do. (shrink)

Many philosophers have argued or taken for granted that Frege's puzzle has little or nothing to do with identity statements. I show that this is wrong, arguing that the puzzle can only be motivated relative to a thinker's beliefs about the identity or distinctness of the relevant object. The result is important, as it suggests that the puzzle can be solved, not by a semantic theory of names or referring expressions as such, but simply by a theory of identity statements. (...) To show this, I sketch a framework for developing solutions of this sort. I also consider how this result could be implemented by two influential solutions to Frege's puzzle, Perry's referential-reflexivism and Fine's semantic relationism. (shrink)

Frege begins Die Grundlagen der Arithmetik, the work that introduces the project which was to occupy him for most of his professional career, with the question, 'What is the number one?' It is a question to which even mathematicians, he says, have no satisfactory answer. And given this scandalous situation, he adds, there is small hope that we shall be able to say what number is. Frege intends to rectify the situation by providing definitions of the number one and the (...) concept of number. But what, exactly, is required of a definition? Surely it will not do to stipulate that the number one is Julius Caesar - that would change the subject. It seems reasonable to suppose that an acceptable definition must be a true statement containing a description that picks out the object to which the numeral '1' already refers. And, similarly, that an acceptable definition of the concept of number must contain a description that picks out precisely those objects that are numbers - those objects to which our numerals refer. Yet, while Frege writes a great deal about what criteria his definitions must satisfy, the above criteria are not among those he mentions. Nor does he attempt to convince us that his definitions of '1' and the other numerals are correct by arguing that these definitions pick out objects to which these numerals have always referred. Yet, while Frege writes a great deal about what criteria his definitions must satisfy, the above criteria are not among those he mentions. Nor does he attempt to convince us that his definitions of ‘1’ and the other numerals are correct by arguing that these definitions pick out objects to which these numerals have always referred. There is, as we shall see shortly, a great deal of evidence that Frege’s definitions are not intended to pick out objects to which our numerals already refer. But if this is so, how can these definitions teach us anything about our science of arithmetic? And what criteria must these definitions satisfy? To answer these questions, we need to understand what it is that Frege thinks we need to learn about the science of arithmetic. (shrink)

Frege's puzzle is a fundamental challenge for accounts of mental and linguistic representation. This piece surveys a family of recent approaches to the puzzle that posit representational relations. I identify the central commitments of relational approaches and present several arguments for them. I also distinguish two kinds of relationism—semantic relationism and formal relationism—corresponding to two conceptions of representational relations. I briefly discuss the consequences of relational approaches for foundational questions about propositional attitudes, intentional explanation, and compositionality.

Frege puzzles exploit cognitive differences between co-referential terms. Traditionally, they were handled by some version of Frege’s distinction between sense and reference, which avoided disruptive consequences for epistemology. However, the Fregean programme did not live up to its original promise, and was undermined by the development of theories of direct reference; for semantic purposes, its prospects now look dim. In particular, well-known analogues of Frege puzzles concern pairs of uncontentious synonyms; attempts to deal with them by distinguishing idiolects or (...) postulating ‘narrow contents’ or elaborate forms of context-sensitivity are inadequate or semantically implausible. Although ascriptions of knowledge, belief, and other attitudes are ubiquitous in epistemology, epistemologists have not properly come to terms with the surprising consequences of anti-Fregean semantic accounts of attitude ascriptions. In ‘A Puzzle about Belief ’, Saul Kripke shows that natural-seeming disquotational principles for ascribing belief lead to apparently unacceptable consequences, including outright contradictions, in problem cases. Such disquotation principles, I argue, are best regarded not as conceptual connections but just as heuristics in the psychological sense, quick and easy ways of assessing belief ascriptions, usually accurate under normal conditions but far from 100% reliable. I discuss similar heuristics for ascribing knowledge and other attitudes. That the principles have a merely heuristic status need not be pre-theoretically manifest to their users. This view vindicates Kripke’s conclusion that it would be wrong-headed to draw semantic conclusions from Frege puzzles. I discuss the epistemological consequences of an anti-Fregean approach to Frege puzzles, including for Kripke’s cases of the contingent a priori and the necessary a posteriori, but also for evidence, for epistemic modalities, and for epistemic and subjective conceptions of probability. Anna Mahtani’s recent identification of Frege puzzles for the ex ante Pareto Principle as used in welfare economics provides an interesting example. I suggest a model-building methodology as the most promising way of handling at least some of the difficulties. A final issue is the choice between different anti-Fregean approaches to semantics, from very coarse-grained intensional approaches on which sentences express functions from possible worlds to truth-values to more fine-grained hyperintensional approaches on which sentences express functions from possible or impossible worlds to truth-values or else Russellian structured propositions. Some of the hyperintensional theories violate semantic compositionality. More generally, since our attitude ascriptions rely on heuristics, they should be expected to exhibit some level of error; although hyperintensional approaches may be able slightly to reduce the level of postulated error, they do so at the cost of vastly increased theoretical complexity, and so have weak explanatory power. Methodologically, a simple intensional approach does better. (shrink)

A new class of program-oriented logical formalisms is investigated – renominative logics with extended renominations, equality predicates, and predicate complement composition. Composition algebras and languages of such logics are described; their semantic properties are investigated. For these logics, a number of logical consequence relations are proposed and investigated, in particular, the logical consequence relations with undefinedness conditions. Properties of these relations form the semantic basis for further construction of sequent-type calculi for the proposed logics.

Objectives: Medical decision support and other intelligent applications in the life sciences depend on increasing amounts of digital information. Knowledge bases as well as formal ontologies are being used to organize biomedical knowledge and data. However, these two kinds of artefacts are not always clearly distinguished. Whereas the popular RDF(S) standard provides an intuitive triple-based representation, it is semantically weak. Description logics based ontology languages like OWL-DL carry a clear-cut semantics, but they are computationally expensive, and they are (...) often misinterpreted to encode all kinds of statements, including those which are not ontological. Method: We distinguish four kinds of statements needed to comprehensively represent domain knowledge: universal statements, terminological statements, statements about particulars and contingent statements. We argue that the task of formal ontologies is solely to represent universal statements, while the non-ontological kinds of statements can nevertheless be connected with ontological representations. To illustrate these four types of representations, we use a running example from parasitology. Results: We finally formulate recommendations for semantically adequate ontologies that can efficiently be used as a stable framework for more context-dependent biomedical knowledge representation and reasoning applications like clinical decision support systems. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Scale Theory: A Nondisciplinary Inquiry by Joshua DiCaglioS. Scott GrahamScale Theory: A Nondisciplinary Inquiry. By Joshua DiCaglio. Minneapolis: University of Minnesota Press, 2021. 349 pp. Paperback: $30.00. ISBN: 978-1-5179-1207-9.Scale Theory embodies its title in every possible way. It offers both a deep dive into and a 10,000-foot view of scale, scalar thinking, and the role of scale in scientific inquiry. The subtitle, A Nondisciplinary Inquiry, is no less (...) apt. Author Joshua DiCaglio blends insights from rhetoric, philosophy, literary studies, and mysticism to create a novel account of scalar thinking. In so doing, he weaves together detailed thought experiments, the work of Gregory Bateson, and Philip K. Dick's account of an extraterrestrial communication he received while under the influence of anesthesia. Provocatively, Scale Theory treats these diverse intellectual resources as coequal contributors to an emerging theory of scale and scalar thinking. Within this nondisciplinary framework, the book is devoted to advancing two primary theses: (1) Notions of scale are undertheorized in science studies and related strands of new materialisms; and (2) Proper attention to questions of scale within these theoretical traditions should prompt a more thoughtful reconsideration of the merits of mystic holism. Ultimately, Scale Theory makes a compelling case for the first thesis and advances inquiry usefully in this area. With respect to the second thesis, DiCaglio refers to a certain academic "allergy" to holism (99), and I must confess I share this allergy. That said, I assume readers already predisposed favorably toward mystic holism are likely to find Scale Theory's attention to the second thesis thoughtful and engaging.Scale Theory is organized into three distinct parts. Part 1, "Algorithms for a Theory of Scale," presents three interrelated thought experiments that call upon readers to imagine themselves at various distances and vantage points with respect to several objects of interest. Part 1 is stylistically [End Page 388] Wittgensteinian. Like the Tractatus-Logico Philosophicus (Wittgenstein 2013) or Latour's "Irreductions," (1993), the thought experiments unfold as a series of numbered and nested propositions, each postulating or interrogating an emerging concept in DiCaglio's theory of scale. Part 2, "Configurations for a Theory of Scale," returns the reader to more familiar styles of prose, providing a sort of review of the relevant literature and its relationship to the insights of the thought experiments. Finally, part 3, "Rhetorical Technologies for a Theory of Scale," reflects on the twin marginalizations of rhetoric and mysticism in mainstream Western academia and argues for a new embrace of disembodied inquiry.The aforementioned thought experiments of part 1 outline DiCaglio's theories of scale, scalar thinking, and scalar analysis. The discussion makes extensive use of visual and cinematic metaphors to aid the reader's consideration of scalar questions. Ultimately, DiCaglio posits that scale is a function of the relationship between the "'being' of phenomena" and "the one who is measuring" (8). He argues, therefore, that "scale functions at a level above ontology and epistemology: scale is a means of orienting yourself both to experience and the being of things" (8). In making this argument, Scale Theory reflects on a range of scientific practices that require gradients of scale. Microscopy, telescopy, and simulations all provide scientists with tools to escape the mundane scales of embodied human experience. DiCaglio argues that "science must always find itself grouping things together, speaking of species, types, systems, and so on which exist on a different logical type than the individual encounters that make up these groups" (41). The taxonomic activities of scientific practice require shifts in scale to account for kingdoms, phyla, orders, genera, species, and all manner of nonbiological analogs.Within this framework, scale functions as a sort of meta-ontology that allows objects to be provisionally identified and delineated. Echoing Bateson, DiCaglio argues thatIn order for any thing to be said to exist whatsoever, a differential must exist out of which a difference can be discerned. Every differential occurs on some scale at which a fluctuation or movement is able to make a difference. If one goes to a smaller scale, any given differential is no longer able to be used to register a difference.(51... (shrink)

This article provides a theoretical critique from a particular ‘ideal type’ ethical perspective of professional codes in general and the United Kingdom Central Council for Nursing, Midwifery and Health Visiting (UKCC) Code of professional conduct (reprinted on pp. 77-78) in particular. Having outlined a specific ‘ideal type’ of what ethically informed and aware practice may be, the article examines the extent to which professional codes may be likely to elicit and engender such practice. Because of their terminological inexactitudes (...) and confusions, their arbitrary values and principles, their lack of helpful ethical guidance, and their exclusion of ordinary moral experience, a number of contemporary professional codes in health and social care can be arraigned as ethically inadequate. The UKCC Code of professional conduct embodies many of these flaws, and others besides. Some of its weaknesses in this respect are anatomized before some tentative suggestions are offered for the reform of codes and the engendering of greater ethical awareness among professionals in the light of greater public ethical concerns and values. (shrink)

Turing’s paper on computable numbers has played its role in underpinning different perspectives on the world of information. On the one hand, it encourages a digital ontology, with a perceived flatness of computational structure comprehensively hosting causality at the physical level and beyond. On the other, it can give an insight into the way in which higher order information arises and leads to loss of computational control—while demonstrating how the control can be re-established, in special circumstances, via suitable (...) class='Hi'>type reductions. We examine the classical computational framework more closely than is usual, drawing out lessons for the wider application of information–theoretical approaches to characterizing the real world. The problem which arises across a range of contexts is the characterizing of the balance of power between the complexity of informational structure and the means available to bring this information back into the computational fold. We proceed via appropriate mathematical modelling to a more coherent view of the computational structure of information, relevant to a wide spectrum of areas of investigation. (shrink)

This article concerns the ongoing neo-logicist program in the philosophy of mathematics. The enterprise began life, in something close to its present form, with Crispin Wright’s seminal [1983]. It was bolstered when Bob Hale [1987] joined the fray on Wright’s behalf and it continues through many extensions, objections, and replies to objections . The overall plan is to develop branches of established mathematics using abstraction principles in the form: Formula where a and b are variables of a given type (...) , Σ is a higher-order operator denoting a function from items of the given type to objects in the range of the first-order variables, and E is an equivalence relation over items of the given type. In what follows, I will sometimes omit the initial quantifiers.Frege [1884, 1893] himself employed three abstraction principles. One of them, used for illustration, comes from geometry: "The direction of l1 is identical to the direction of l2 if and only if l1 is parallel to l2."Call this the direction principle. The second was dubbed N= in [Wright, 1983] and is now called Hume’s principle: Formula where F≈G is an abbreviation of the second-order statement that there is a one-to-one relation mapping the F’s onto the G’s. In words, states that the number of F is identical to the number of G if and only if F is equinumerous with G. Unlike the direction-principle, the relevant variables, F, G here are second-order. Georg Cantor …. (shrink)

The number of women living with HIV/AIDS is increasing worldwide, and there is an urgent public health need to develop new user-initiated HIV prevention methods, including microbicides. Although funding for microbicide development has increased since 2000, financial support is provided predominantly by governmental agencies and private foundations. Many donors, including the US Agency for International Development (USAID) and the US National Institutes of Health (NIH), have policies that restrict how research funds may be used. Among these are the now-rescinded Mexico (...) City Policy, elements of the US Foreign Assistance Act, and restrictions on non-study-related care. The effect of these restrictions on the design and conduct of clinical research is poorly understood. As part of a recent mapping exercise conducted by the Global Campaign for Microbicides, we reviewed the impact of donor restrictions on seven HIV prevention trials. We found considerable confusion within the HIV prevention field as to whether and how Mexico City and other policies affect the use of research funds. We also found that these donor-imposed policies limited the level of care provided to trial participants and the types of capacity building projects undertaken. (shrink)

The aim of this paper is to give a detailed reconstruction of Frege's solution to his puzzle about the cognitive function of truth, which is this: On the one hand, the concept of truth seems to play an essential role in acquiring knowledge because the transition from the mere hypothetical assumption that p to the acknowledgement of its truth is a crucial step in acquiring the knowledge that p, while, on the other hand, this concept seems to be completely (...) redundant because the sense of the word 'true' does not make any essential contribution to the senses of the sentences in which it occurs. (shrink)

BackgroundPublic awareness and engagement are among the main prerequisites for protecting the rights of research participants and for successful and sustainable functioning of research biobanks. The aim of our study was to analyse public awareness and attitudes towards research biobanks in Latvia, and to compare these data with the results of the 2010 Eurobarometer study. We also analysed the influence of awareness and attitudes towards biobanks on willingness to participate in biobank studies and on preferred type of informed consent.MethodsWe (...) developed a 12-question survey repeating seven questions about biobanks from the 2010 Eurobarometer questionnaire and adding five others. After describing the study variables, we performed a two-stage analysis of the results. In the first stage we analysed differences between the answers from 2010 and 2019 and conducted univariate analyses of relationships among particular variables, and between those variables and the socio-demographic characteristics of participants. In the second stage we investigated multivariable associations of willingness to participate and type of consent with awareness, trust and the socio-economic characteristics of participants.ResultsAccording to our study, the general public in Latvia is still not well informed about research biobanks. Fewer respondents have heard about research biobanks than in 2010. At the same time, the number of respondents who are willing to donate biological samples and personal data to a biobank has increased, e.g. the number of respondents who would definitely or probably be willing to provide information about themselves has increased from 25.8.% to 40.7 since 2010. Overall, concerns about the donation of different types of biological samples and data to a biobank have slightly decreased.ConclusionsPublic awareness about biobanks is important for their sustainability. It needs to be increased not only by traditional methods of informing the public, but also by more innovative and participatory approaches, e.g. by citizen science projects. There is a need to strengthen the public visibility and trustworthiness of ethics committees in Latvia in the field of biobanking. (shrink)

Mandarin Chinese exhibits two paradigms of conditionals with indefinite wh-words that have the semantics of donkey sentences, represented by ‘bare conditionals’ on the one hand and ruguo- and dou-conditionals on the other. The bare conditionals require multiple occurrences of wh-words, disallowing the use of overt or covert anaphoric elements in the consequent clause, whereas the ruguo- and dou-conditionals present a completely opposite pattern. We argue that the bare conditionals are cases of unselective binding par excellence (Heim 1982, Kamp (...) 1981) while the ruguo- and dou-conditionals are most naturally accounted for with the traditional E-type pronoun strategy of Evans (1980). We thus argue partly for a return to the E-type strategy (along with Heim 1990) but maintain the need for unselective binding in UG (cf. Kratzer 1989, Chierchia 1992). It is further shown that these two paradigms do not differ with respect to the proportion problem and the distribution of symmetric and asymmetric readings of Kadmon (1987), though they differ with respect to ∀ and ∃ readings (discussed in Chierchia 1992) in a non-trivial way that provides further support for the proposed approach. Finally, evidence is given that the bare conditionals should be kept apart from correlative constructions in languages like Hindi, and treated differently from the latter. (shrink)

This paper will critically examine two solutions to Frege’s puzzle: the Millian-Russellian solution proposed by Salmon and Braun, which invokes non-semantic modes of presentation (guises, ways of believing or the like); and Fine’s relationalist solution, which appeals to semantic coordination. Special attention will be devoted to discussing the conception of modes of presentation as mental files and to elucidating the nature of coordination. A third solution to Frege’s puzzle will be explored which, like Salmon’s and Braun’s, adopts the (...) Millian-Russellian semantics but, like Fine’s, involves coordination instead of modes of presentation; however, coordination will not be conceived as a semantic relation but as a cognitive and subjective relation, which provides no contribution to semantic content. This novel Millian-Russellian account involving cognitive coordination will be labelled cognitive relationism. (shrink)

Corcoran, John. 2005. Meanings of word: type-occurrence-token. Bulletin of Symbolic Logic 11(2005) 117. -/- Once we are aware of the various senses of ‘word’, we realize that self-referential statements use ambiguous sentences. If a statement is made using the sentence ‘this is a pronoun’, is the speaker referring to an interpreted string, a string-type, a string-occurrence, a string-token, or what? The listeners can wonder “this what?”. -/- John Corcoran, Meanings of word: type-occurrence-token Philosophy, University at Buffalo, Buffalo, (...) NY 14260-4150 E-mail: [email protected] The four-letter written-English expression ‘word’, which plays important roles in applications and expositions of logic and philosophy of logic, is ambiguous (multisense, or polysemic) in that it has multiple normal meanings (senses, or definitions). Several of its meanings are vague (imprecise, or indefinite) in that they admit of borderline (marginal, or fringe) cases. This paper juxtaposes, distinguishes, and analyses several senses of ‘word’ focusing on a constellation of senses analogous to constellations of senses of other expression words such as ‘expression’, ‘symbol’, ‘character’, ‘letter’, ‘term’, ‘phrase’, ‘formula’, ‘sentence’, ‘derivation’, ‘paragraph’, and ‘discourse’. Consider, e.g., the word ‘letter’. In one sense there are exactly twenty-six letters (letter-types or ideal letters) in the English alphabet and there are exactly four letters in the word ‘letter’. In another sense, there are exactly six letters (letter-repetitions or letter-occurrences) in the word-type ‘letter’. In yet another sense, every new inscription (act of writing or printing) of ‘letter’ brings into existence six new letters (letter-tokens or ink-letters) and one new word that had not previously existed. The number of letter-occurrences (occurrences of a letter-type) in a given word-type is the same as the number of letter-tokens (tokens of a letter-type) in a single token of the given word. Many logicians fail to distinguish “token” from “occurrence” and a few actually confuse the two concepts. Epistemological and ontological problems concerning word-types, word-occurrences, and word-tokens are described in philosophically neutral terms. This paper presents a theoretical framework of concepts and principles concerning logicography, including use of English in logic. The framework is applied to analytical exposition and critical evaluation of classic passages in the works of philosophers and logicians including Boole, Peirce, Frege, Russell, Tarski, Church and Quine. This paper is intended as a philosophical sequel to Corcoran et al. “String Theory”, Journal of Symbolic Logic 39(1974) 625-637. https://www.academia.edu/s/cdfa6c854e?source=link -/- . (shrink)

In Latin Hexameter Verse, his 1903 manual for composers of Latin hexameters which is still useful as a guide to Vergil's metrical and prosodic practices, S. E. Winbolt states that a hexameter ‘must not end with an adjective preceded by a noun with a similar short ending, e.g.…flumina nota’ unless the adjective is emphatic, ‘i.e. strongly distinctive, predicative or antithetical’. Whether or not his distinction between emphatic and non-emphatic adjectives in this position is wholly workable , Winbolt here rightly detects (...) a strong tendency in Vergil and other Latin poets towards avoiding endings of this general kind, which we can conveniently call the ‘Discordia taetra’ type after one of its earliest and best-known instances in the Annales of Ennius . The rarity of this type of line-ending is clear in Vergil; there are only 16 examples, regardless of whether the adjective is emphatic or not, in the 9890 lines of the Aeneid. Such a select and easily-defined phenomenon might prove a yardstick of some interest in the history of the Latin hexameter, for it seems to raise a number of questions to which the answers would be significant and useful. Is this type of ending avoided equally by all poets? Is there an increasing tendency to avoid it as time goes on? Is it associated with any particular genres of hexameter poetry? Do poets tend to use in it the same words or phrases as their predecessors? To discover the answers, this article will look at the ‘Discordia taetra’ phenomenon in Latin hexameter poetry, defining it as the instance where a noun ending in a short vowel is immediately succeeded by an adjective of similar ending and in agreement at the end of the hexameter, and where such a noun is not a substantivised adjective and such an adjective is neither predicative nor a participle. (shrink)

In the article, the semantics of image text in media discourse is reviewed. The authors describe the growing influence of media on society as well as its means in formation of the certain opinion on events or stereotyping in one single social group. They draw attention to the process of globalization typical for modern society and emphasize that the potential of media is turned to unification of society, presentation of common standards, values and all humankind’s fashion. The authors of (...) the article are concerned with the problem of ethnical identity and the need to develop and promote the image of different ethnic groups. One of the tools for creating an image is an image text. In image text, the information is presented in a way that the audience perceives all events and persons mentioned in it positively. The significant quality of the image text is an estimated lexicon. There are several types of such material, for example: note, interview, report, biography etc. In addition, the authors of the article explore the image texts based on the materials published in mass media of the Republic of Buryatia. These materials make the positive image of Buryats, representing the smallest ethnic group of Baikal Region. In conclusion, the authors note that the media discourse of the image texts have considerable influence on the objective reality and human behavior. Taking into consideration the experience of using the image texts in politics, business, and other spheres of human activities, they can become one of effective means of development the image of ethnic group. (shrink)

BACKGROUND -/- The need for detailed description and modeling of cells drives the continuous generation of large and diverse datasets. Unfortunately, there exists no systematic and comprehensive way to organize these datasets and their information. CELDA (Cell: Expression, Localization, Development, Anatomy) is a novel ontology for the association of primary experimental data and derived knowledge to various types of cells of organisms. -/- RESULTS -/- CELDA is a structure that can help to categorize cell types based on species, anatomical localization, (...) subcellular structures, developmental stages and origin. It targets cells in vitro as well as in vivo. Instead of developing a novel ontology from scratch, we carefully designed CELDA in such a way that existing ontologies were integrated as much as possible, and only minimal extensions were performed to cover those classes and areas not present in any existing model. Currently, ten existing ontologies and models are linked to CELDA through the top-level ontology BioTop. Together with 15.439 newly created classes, CELDA contains more than 196.000 classes and 233.670 relationship axioms. CELDA is primarily used as a representational framework for modeling, analyzing and comparing cells within and across species in CellFinder, a web based data repository on cells (http://cellfinder.org). -/- CONCLUSIONS -/- CELDA can semantically link diverse types of information about cell types. It has been integrated within the research platform CellFinder, where it exemplarily relates cell types from liver and kidney during development on the one hand and anatomical locations in humans on the other, integrating information on all spatial and temporal stages. CELDA is available from the CellFinder website: http://cellfinder.org/about/ontology. (shrink)

In this paper, I argue that a number of recent Russell interpreters, including Evans, Davidson, Campbell, and Proops, mistakenly attribute to Russell what I call ‘the received view of acquaintance’: the view that acquaintance safeguards us from misidentifying the objects of our acquaintance. I contend that Russell’s discussions of phenomenal continua cases show that he does not accept the received view of acquaintance. I also show that the possibility of misidentifying the objects of acquaintance should be unsurprising given underappreciated aspects (...) of Russell’s overall theory of knowledge and acquaintance. Finally, I consider the radical impact that Russell’s actual views on acquaintance have for our understanding of his well-known George IV case in ‘On Denoting’. In particular, I argue that Russell’s treatment of the George IV case is not a one-size-fits-all solution to Frege’s Puzzle and provides no support for the received view of acquaintance. (shrink)

Frege's main contributions to logic and the philosophy of mathematics are, on the one hand, his introduction of modern relational and quantificational logic and, on the other, his analysis of the concept of number. My focus in this paper will be on the latter, although the two are closely related, of course, in ways that will also play a role. More specifically, I will discuss Frege's logicist reconceptualization of the natural numbers with the goal of clarifying two aspects: the (...) motivations for its core ideas; the step-by-step development of these ideas, from Begriffsschrift through Die Grundlagen der Arithmetik and Grundgesetze der Arithmetik to Frege's very last writings, indeed even beyond those, to a number of recent "neo-Fregean" proposals for how to update them. One main development, or break, in Frege's views occurred after he was informed of Russell's antinomy. His attempt to come to terms with this antinomy has found some attention in the literature already. It has seldom been analyzed in connection with earlier changes in his views, however, partly because those changes themselves have been largely ignored. Nor has it been discussed much in connection with Frege's basic motivations, as formed in reaction to earlier positions. Doing both in this paper will not only shed new light on his response to Russell's antinomy, but also on other aspects of his views. In addition, it will provide us with a framework for comparing recent updates of these views, thus for assessing the remaining attraction of Frege's general approach. I will proceed as follows: In the first part of the paper (§1.1 and §1.2), I will consider the relationship of Frege's conception of the natural numbers to earlier conceptions, in particular to what I will call the "pluralities conception", thus bringing into sharper focus his core ideas and their motivations. In the next part (§2.1 and §2.2), I will trace the order in which these ideas come up in Frege's writings, as well as the ways in which his position gets modified along the way, both before and after Russell's antinomy.. (shrink)

The vision of natural kinds that is most common in the modern philosophy of biology, particularly with respect to the question whether species and other taxa are natural kinds, is based on a revision of the notion by Mill in A System of Logic. However, there was another conception that Whewell had previously captured well, which taxonomists have always employed, of kinds as being types that need not have necessary and sufficient characters and properties, or essences. These competing views (...) employ different approaches to scientific methodologies: Mill’s class-kinds are not formed by induction but by deduction, while Whewell’s type-kinds are inductive. More recently, phylogenetic kinds (clades, or monophyletic-kinds) are inductively projectible, and escape Mill’s strictures. Mill’s version represents a shift in the notions of kinds from the biological to the physical sciences. (shrink)