This paper argues that (cardinal) numbers are originally given to us in the context ‘Fs exist n-wise’, and accordingly, numbers are certain manners or modes of existence, by addressing two objections both of which are due to Frege. First, the so-called Caesar objection will be answered by explaining exactly what kind of manner or mode numbers are. And then what we shall call the Functionality of Cardinality objection will be answered by establishing the fact that for any numbers m and (...) n, if there are exactly m Fs and also there are exactly n Fs, then m = n. (shrink)

I shall discuss some of the issues concerning a notorious doctrine of Frege that sentences are names of truth-values. I am interested in a problem raised by Kripke that the doctrine obscures the distinction between judgeable and unjudgeable contents. I shall present what I take to be Frege’s account of judgeable content: a proper expression of a judgeable content is susceptible to an analysis into a predicate and an argument-word, where a predicate is understood as a concept-word used to attribute (...) a certain property to the referent of the argument-word. In the light of this analysis, I shall argue that the doctrine does not obscure the distinction. The problem will also be discussed within the formal context of Grundgesetze. A new light will be shed on his rather peculiar conception of the symbol ‘ ${\boldsymbol \vdash}$’. (shrink)

This paper presents a new interpretation of Frege's context principle on which it applies primarily to singular terms for abstract objects but not necessarily to singular terms for ordinary objects.

Semantic theories based on a hierarchy of types have prominently been used to defend the possibility of unrestricted quantification. However, they also pose a prima facie problem for it: each quantifier ranges over at most one level of the hierarchy and is therefore not unrestricted. It is difficult to evaluate this problem without a principled account of what it is for a quantifier to be unrestricted. Drawing on an insight of Russell’s about the relationship between quantification and the structure of (...) predication, we offer such an account. We use this account to examine the problem in three different type-theoretic settings, which are increasingly permissive with respect to predication. We conclude that unrestricted quantification is available in all but the most permissive kind of type theory. (shrink)

This is a review of "Properties and Propositions: The Metaphysics of Higher-Order Logic" by Robert Trueman. Following an overview of the main themes of the book, I discuss the metaphysical presuppositions of Trueman's Fregean notation for predicate abstraction and evaluate his argument for strict typing.

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)

This paper uses the resources of higher-order logic to articulate a Fregean conception of predicate reference, and of word-world relations more generally, that is immune to the concept horse problem. The paper then addresses a prominent style of expressibility problem for views of broadly this kind, versions of which are due to Linnebo, Hale, and Wright.

Influenced by G. E. Moore, Russell broke with Idealism towards the end of 1898; but in later years he characterized his meeting Peano in August 1900 as ?the most important event? in ?the most important year in my intellectual life?. While Russell discovered his paradox during his post-Peano period, the question arises whether he was already committed, during his pre-Peano Moorean period, to assumptions from which his paradox may be derived. Peter Hylton has argued that the pre-Peano Russell was thus (...) vulnerable to (at least one version of) Russell's paradox and hence that the paradox exposes a pre-existing difficulty in Russell's Moorean philosophy. Contrary to Hylton, I argue that the Moorean Russell adhered to views which insulated him against the paradox. Further, I argue that Russell became vulnerable to his paradox as a result of changes in his Moorean position occasioned, first, by his acceptance of Cantor's theory of the transfinite, and, second, by his correspondence with Frege. I conclude with some general comments regarding Russell's acceptance of naïve set theory. (shrink)

Our linguistic communication is, in part, the exchange of truths. It is an empirical fact that in daily conversation we aim at truths, not falsehoods. This fact may lead us to assume that ordinary, assertion-based communication is the only possible communicative system for truth-apt information exchange, or at least has priority over any alternatives. This assumption is underwritten in three traditional doctrines: that assertion is a basic notion, in terms of which we define denial; that to predicate truth of a (...) sentence is to assert the content it expresses; and that one should, in the context of radical interpretation, try to maximize the truth of what foreigners believe or utter. However, I challenge this assumption via a thought experiment: imagine a language game in which everyone aims to exchange only falsehoods. I argue that information exchange is possible in this game, and so truth-guided communication and falsity-guided communication are conceptually on a par. As a consequence, we should reject the three doctrines, based as they are on the conceptual priority of assertion-based communication. (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.

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.

According to Aristotelian logic, in categorical logic, there are three kinds of judgements (qaḍīyya): affirmative, negative, and metathetic (ma‘dūla). Khūnajī, a famous Muslim logician in the 13th century, introduces a different judgement (or statement) entitled “affirmative judgement with the negative predicate” (mūjiba al-sāliba al-maḥmūl; henceforth, ANP judgement). Although in the Arabic language, formally, ANP judgement is similar to definite negative (sāliba muḥaṣṣala) and also metathetic judgements, the way of its construction is different from both of them and its truth conditions (...) are different from metathetic ones. From a modern logic viewpoint, ANP may indicate equality judgement; however, attributing it to Muslim logicians is questionable, although some of their wordings may implicitly show it. According to Ḥāʾirī, an Iranian contemporary philosopher and logician, the new judgement is supposed to solve some problems, especially logical explanation of the division of modalities into necessity, impossibility, and contingency (imkān khāṣṣ). However, Ṭabāṭabāʾī, another Iranian contemporary philosopher, disagrees with Ḥāʾirī and regards ANP judgement the same as an affirmative metathetic one. In this paper, while examining Ṭabāṭabāʾī’s and Ḥāʾirī’s reasons, by using some insights into modern logic, I will try to strengthen Ṭabāṭabāʾī’s views, although it may be confronted with some questions or deficiencies. (shrink)

The authors believe that the questions raised at the beginning of Frege’s On Sense and Reference – ‘Is [identity] a relation? A relation between objects, or between names or signs of objects?’ – set the course for a long-lasting but not at all satisfying discussion. For the disputants tend to advocate, either a ‘name-view’ of identity in a straightforward but rudimentary and logically untenable form, or else a version of an ‘object-view’ that makes all too light of the analysandum–analysans distinction (...) and hence is damned to analytical barrenness. In contrast, by unfolding the underlying idea of the original ‘name-view’, the authors offer three alternative and mutually compatible interpretations of identity that may best be characterized as the ‘name-based’, the ‘hybrid’ and the ‘sense-based’ variant of a ‘concept-view of identity’. At the same time, however, these interpretations may well be considered variants of a non-barren ‘object-view’. (shrink)

In “Function and Concept” and “On Concept and Object”, Frege argued that certain differences between dependent and independent meanings were inviolable and “founded deep in the nature of things” but, in those articles, he was not explicit about the actual consequences of violating such differences. However, since by creating a law that permitted one to pass from a concept to its extension, he himself mixed dependent and independent meanings, we are in a position to study some of the actual consequences (...) of his having done so. To make certain of Frege’s ideas about the inviolability of logical form more tangible, I describe a string of very interrelated consequences that his attempt to transform dependent meanings into independent meanings actually brought in its wake. (shrink)

In this article I contrast in two ways those conceptions of semantic theory deriving from Richard Montague's Intensional Logic (IL) and later developments with conceptions that stick pretty closely to a far weaker semantic apparatus for human first languages. IL is a higher-order language incorporating the simple theory of types. As such, it endows predicates with a reference. Its intensional features yield a conception of propositional identity (namely necessary equivalence) that has seemed to many to be too coarse to be (...) acceptable. In the most usual expositions, it takes the object of linguistic explication to be the sentence in a context, as in Kaplan, 1977. This last has led to recent speculations about 'shifted' contexts. IL may be contrasted with a more linguistically (representationally) bound conception of propositions and interpretation of their predicational and functional parts, and with the explication, not of sentences in contexts, but of potential utterances, relative to the antecedent referential intentions of their speakers. We may then advance, as an empirical hypothesis about all human languages, that contexts never shift, and propose that apparent counterexamples stem from the misconstrual of linguistically coded anaphoric relations, relations that are wanted independently anyway. Donald Davidson's posthumous volume Truth and Predication mounts a sustained criticism of the notion of predicate reference. This criticism is not decisive. However, it may put the ball in the other court, insofar as it asks for a justification of what IL takes as given. Elaborations of IL using structured propositions, recently defended in King, 2007, recognize the problem of predicate reference, and the correlative issue of the 'unity of the proposition'; but I do not see that they can do better than bite the bullet already bitten in IL. I agree with Frege's insight that full justification of predicate reference pushes the boundaries of natural language, and to that extent may not be found within the semantic (as opposed to general scientific) enterprise. (shrink)

Are Fregean thoughts compositionally complex and composed of senses? We argue that, in Begriffsschrift, Frege took 'conceptual contents' to be unstructured, but that he quickly moved away from this position, holding just two years later that conceptual contents divide of themselves into 'function' and 'argument'. This second position is shown to be unstable, however, by Frege's famous substitution puzzle. For Frege, the crucial question the puzzle raises is why "The Morning Star is a planet" and "The Evening Star is a (...) planet" have different contents, but his second position predicts that they should have the same content. Frege's response to this antinomy is of course to distinguish sense from reference, but what has not previously been noticed is that this response also requires thoughts to be compositionally complex, composed of senses. That, however, raises the question just how thoughts are composed from senses. We reconstruct a Fregean answer, one that turns on an insistence that this question must be understood as semantic rather than metaphysical. It is not a question about the intrinsic nature of residents of the third realm but a question about how thoughts are expressed by sentences. (shrink)

It is widely assumed that Russell's problems with the unity of the proposition were recurring and insoluble within the framework of the logical theory of his Principles of Mathematics. By contrast, Frege's functional analysis of thoughts (grounded in a type-theoretic distinction between concepts and objects) is commonly assumed to provide a solution to the problem or, at least, a means of avoiding the difficulty altogether. The Fregean solution is unavailable to Russell because of his commitment to the thesis that there (...) is only one ultimate ontological category. This, combined with Russell's reification of propositions, ensures that he must hold concepts and objects to be of the same logical and ontological type. In this paper I argue that, while Frege's treatment of the unity of the proposition has immediate advantages over Russell's, a deeper consideration of the philosophical underpinnings and metaphysical consequences of the two approaches reveals that Frege's supposed solution is, in fact, far from satisfactory. Russell's repudiation of the Fregean position in the Principles is, I contend, convincing and Russell's own position, despite its problems, conforms to a greater extent than Frege's with common sense and, furthermore, with certain ideas which are central to our understanding of the origins of the analytical tradition. (shrink)

In Sein und Zeit Heidegger makes several claims about the nature of ‘assertion’ [Aussage]. These claims are of particular philosophical interest: they illustrate, for example, important points of contact and divergence between Heidegger's work and philosophical movements including Kantianism, the early Analytic tradition and contemporary pragmatism. This article provides a new assessment of one of these claims: that assertion is connected to a ‘present-at-hand’ ontology. I also indicate how my analysis sets the stage for a new reading of Heidegger's further (...) claim that assertion is an explanatorily derivative phenomenon. I begin with a loose overview of Heidegger's position and then develop a sharper formulation of the key premises. I go on to argue that existing treatments of the supposed link between assertion and the ‘present-at-hand’ are unsatisfactory, and advance a new, ‘methodological’, interpretation of that link. Finally, I sketch the implications of my interpretation for the further claim that assertion is explanatorily derivative. (shrink)

Prior's puzzle is a puzzle about the substitution of certain putatively synonymous or coreferential expressions in sentences. Prior's puzzle is important, because a satisfactory solution to it should constitute a crucial part of an adequate semantic theory for both proposition-embedding expressions and attitudinal verbs. I argue that two recent solutions to this puzzle are unsatisfactory. They either focus on the meaning of attitudinal verbs or content nouns. I propose a solution relying on a recent analysis of that-clauses in linguistics. Our (...) solution is superior, as it not only avoids the problems faced by previous solutions, but it also brings developments in linguistics in line to solve an old puzzle in philosophy. (shrink)

The nosological diagnosis is a particular type of nontheoretical diagnosis consisting of identifying the disease that afflicts the patient without explaining the underlying etiopathological mechanisms. Its origins are within the essentialist point of view on the nature of diseases, which dates back at least to 18th-century taxonomy studies. In this article, we propose a model of nosological diagnosis as a two-phase process composed of the categorization of inductive inferences and argumentations by analogy. In the inductive phase, disease entities are identified (...) by means of typicality-based categorization processes, and meaningful clinical samples are learned ; in the subsequent phase, those samples are used as the bases of argumentations by analogy to obtain a diagnosis for a given patient. This model extends the prototype resemblance theory of disease including also the exemplar theory proposed in cognitive science and, moreover, it frames the clinical activity of nosological diagnosis and how it can be explained within the theory of argumentation. According to it, diagnosis based on the recognition of a typical syndrome is explained in terms of the prototype theory of categorization and the antisymmetrical argumentation by analogy, while diagnosis based on a comparison with a previous clinical case is explained by the exemplar theory of categorization and by the symmetrical argumentation by analogy. (shrink)

Philosophers of action and perception have reached a consensus: the term ‘intentionality’ has significantly different senses in their respective fields. But Anscombe argues that these distinct senses are analogically united in such a way that one cannot understand the concept if one focuses exclusively on its use in one’s preferred philosophical sub-discipline. She highlights three salient points of analogy: (i) intentional objects are given by expressions that employ a “description under which;” (ii) intentional descriptions are typically vague and indeterminate; and (...) (iii) intentional descriptions may be false. I explore these three features as they apply to both perception and action and defend Anscombe’s view that the analogical concept of intentionality is a grammatical concept. That is, there are two distinctive linguistic/social practices that involve, respectively, a special sense of the question ‘Why?’ and a special sense of the question ‘What?’ To competently ask and answer the questions that constitute these practices not only reflects, but also conveys a grammatical understanding of intentionality’s basic, formal structure. (shrink)

In his Tractatus Logico-Philosophicus, Wittgenstein conveyed the idea that ethics cannot be located in an object or self-standing subject matter of propositional discourse, true or false. At the same time, he took his work to have an eminently ethical purpose, and his attitude was not that of the emotivist. The trajectory of this conception of the normativity of philosophy as it developed in his subsequent thought is traced. It is explained that and how the notion of a ‘form of life’ (...) (Lebensform) emerged only in his later thought, in 1937, earmarking a significant step forward in his philosophical method. We argue that the concept of Lebensform represents a way of domesticating logic itself, the very idea of a claim or reason, supplementing the idea of a ‘language game’, which it deepens. Lebensform is contrasted with the phenomenologists’ Lebenswelt through a reading of the notions of ‘I’, ‘world’ and ‘self’ as they were treated in the Tractatus, The Blue and Brown Books and Philosophical Investigations. Finally, the notion of Lebensform is shown to have replaced the notion of culture (Kultur) in Philosophical Investigations. Wittgenstein’s spring 1937 ‘domestication’ of the nature of logic is shown to have been fully consonant with the idea that he was influenced by his reading Alan Turing’s 1936/1937 paper, ‘On computable numbers, with an application to the Entscheidungsproblem’. (shrink)

The paper sets out to offer an alternative to the function/argument approach to the most essential aspects of natural language meanings. That is, we question the assumption that semantic completeness (of, e.g., propositions) or incompleteness (of, e.g., predicates) exactly replicate the corresponding grammatical concepts (of, e.g., sentences and verbs, respectively). We argue that even if one gives up this assumption, it is still possible to keep the compositionality of the semantic interpretation of simple predicate/argument structures. In our opinion, compositionality presupposes (...) that we are able to compare arbitrary meanings in term of information content. This is why our proposal relies on an ‘intrinsically’ type free algebraic semantic theory. The basic entities in our models are neither individuals, nor eventualities, nor their properties, but ‘pieces of evidence’ for believing in the ‘truth’ or ‘existence’ or ‘identity’ of any kind of phenomenon. Our formal language contains a single binary non-associative constructor used for creating structured complex terms representing arbitrary phenomena. We give a finite Hilbert-style axiomatisation and a decision algorithm for the entailment problem of the suggested system. (shrink)

The problem, or cluster of problems, of the unity of the proposition, along with the cluster of problems that tend to go under the name of Bradley’s regress, has recently again become a going concern for philosophers, after having for some time been regarded as primarily of historical interest. In this paper, I distinguish between the different problems that tend to be brought up under the heading of the unity of the proposition, and between different related regress arguments. I present (...) my favored solutions to these problems. (shrink)

Scholars often assert that Plato and Aristotle share the view that discursive thought is internal speech. However, there has been little work to clarify or substantiate this reading. In this paper I show Plato and Aristotle share some core commitments about the relationship of thought and speech, but cash out TIS in different ways. Plato and Aristotle both hold that discursive thinking is a process that moves from a set of doxastic states to a final doxastic state. The resulting judgments (...) can be true or false. Norms govern these final judgments and, in virtue of that, they govern the process that arrives at those judgments. The principal norm is consistency. However, the philosophers differ on the source of this norm. For Plato, persuasiveness and accuracy ground non-contradiction because internal speech is dialogical. For Aristotle, the Principle of Non-Contradiction grounds a Doxastic Thesis that no judgment can contradict itself. For Aristotle, metaphysics grounds non-contradiction because internal speech is monological. (shrink)

For Wittgenstein, as Cora Diamond interprets him in the essays collected in her recent The Realistic Spirit , there are no logical truths, and a host of other linguistic constructions, such as ‘A is an object’ are, contrary to appearances, nonsensical. In what follows, after outlining Diamond's account I argue that the position she ascribes to Wittgenstein is incoherent. I also reject some possible responses to this charge, among them an appeal to the distinction between what can be said and (...) what can only be shown. (shrink)

Whether one is reading Wittgenstein's Tractatus or his later writings, one must be struck by his insistence that he is not putting forward philosophical doctrines or theses; or by his suggestion that it cannot be done, that it is only through some confusion one is in about what one is doing that one could take oneself to be putting forward philosophical doctrines or theses at all. I think that there is almost nothing in Wittgenstein which is of value and which (...) can be grasped if it is pulled away from that view of philosophy. But that view of philosophy is itself something that has to be seen first in the Tractatus if it is to be understood in its later forms, and in the Tractatus it is inseparable from what is central there, the distinction between what can be said and what can only be shown. (shrink)

Frege's attempt to provide a foundation for the possibility of language and communication, like Kant's attempt to provide a foundation for the possibility of knowledge, fails to provide us with something absolute and foundational in a fixed sense. However, both these philosophers succeed in showing something about necessity that can be preserved independently of their absolutisms. Part III of this paper will provide reasons for accepting this thesis, while Parts I and II will provide an expository background on Frege's view (...) in preparation for supporting the thesis. (shrink)

Jonathan Lowe argues that metaphysics should be restored to a central position in philosophy, as the most fundamental form of rational inquiry, whose findings underpin those of all other disciplines. He portrays metaphysics as charting the possibilities of existence, by idetifying the categories of being and the relations of ontological dependency between entities of different categories. He proceeds to set out a unified and original metaphysical system: he defends a substance ontology, according to which the existence of the world s (...) one world in time depends upon the existence of persisting things which retain their identity over time and through processes of qualitative change. And he contends that even necessary beings, such as the abstract objects of mathematics, depend ultimately for their existence upon there being a concrete world of enduring substances. Within his system of metaphysics Lowe seeks to answer many of the deepest and most challenging questions in philosophy. (shrink)

A constant of Frege’s writing is his rejection of indeterminate predicates as found in natural language. This paper follows Frege’s remarks on vagueness from the early "Begriffsschrift” to his mature works, drawing brief parallels with the main contemporary theories of vagueness. I critically examine Frege’s arguments for the inconsistency of natural language and argue that the inability to accommodate vagueness in his mature ontology is mainly due to heuristic rules of thumb which Frege took as essential, not to a deep (...) problem in his fundamental apparatus. (shrink)

Prolegomena It is fitting to begin this book on intuitionistic type theory by putting the subject matter into perspective. The purpose of this chapter is to ...

Modality and Anti-Metaphysics critically examines the most prominent approaches to modality among analytic philosophers in the twentieth century, including essentialism. Defending both the project of metaphysics and the essentialist position that metaphysical modality is conceptually and ontologically primitive, Stephen McLeod argues that the logical positivists did not succeed in banishing metaphysical modality from their own theoretical apparatus and he offers an original defence of metaphysics against their advocacy of its elimination. -/- Seeking to assuage the sceptical worries which underlie modal (...) anti-realism, McLeod provides an original contribution to essentialist epistemology, engaging with current debates about modality and suggesting that standard essentialist approaches to some issues in the philosophies of logic and language require revision. -/- This book offers valuable insights to professional philosophers, postgraduates and advanced undergraduates interested in metaphysics, philosophy of logic or the history of twentieth-century analytic philosophy. (shrink)

Joan Weiner (2007) has argued that Frege’s definitions of numbers are linguistic stipulations, with no content-preserving or ontological point: they don’t capture any determinate content of numerals, as they have none, and don’t present numbers as preexisting objects. I show that this view is based on exegetical and systematic errors. First, Idemonstrate that Weiner misrepresents the Fregean notions of ‘Foundations-content’, sense, reference, and truth. I then consider the role of definitions, demonstrating that they cannot be mere linguistic stipulations, since they (...) have a content-preserving, ontological point, and a decompositional aspect; Frege’s project of logical analysis and systematisation makes no sense without definitions so understood. The pivotal ontological role of elucidations is also explained. Next, three aspects of definition are distinguished, the informal versus the formal aspect, and the aspect of definition achieved through the entire process of systematisation, which encompasses the previous two and is little discussed in the literature. It is suggested that these insights can contribute to resolving some of the puzzles concerning the tension between the epistemological aim of logicism and Frege’s presentation of definitions as arbitrary conventions. Finally, I stress the interdependence between the epistemological and ontological aspects of Frege’s project of defining number. (shrink)

Bertrand Russell: Logic For Russell, Aristotelian syllogistic inference does not do justice to the subject of logic. This is surely not surprising. It may well be something of a surprise, however, to learn that in Russell’s view neither Boolean algebra nor modern quantification theory do justice to the subject. For Russell, logic is a synthetic … Continue reading Russell: Logic →.

This dissertation is about the structure of thought. Following Gottlob Frege, I define a thought as the sort of content relevant to determining whether an assertion is true or false. The historical component of the dissertation involves interpreting Frege’s actual views on the structure of thought. I argue that Frege did not think that a thought has a unique decomposition into its component senses, but rather the same thought can be decomposed into senses in a variety of distinct ways. I (...) extend Frege’s position and use it to develop an account of the hierarchy of senses, the senses expressed by indexicals and demonstratives, and the distinction between logical and non-logical structure. I also discuss various connections with the nature of meta-representation, our capacity for reflective judgment, some aspects of the structure of conscious experience, the way we perceive regions of space and durations of time, and our conscious awareness of our own perceptions and events of thinking. (shrink)

This entry introduces the reader to the main ideas in Frege's philosophy of logic, mathematics, and language.