ABSTRACT Is it possible to effect singular reference to mathematical objects in the abstractionist framework? I will argue that even if mathematical expressions pass the relevant syntactic and inferential tests to qualify as singular terms, that does not mean that their semantic function is to refer to a particular object. I will defend two arguments leading to this claim: the permutation argument for the referential indeterminacy of mathematical terms, and the argument from the semantic idleness of the terms introduced by (...) abstraction principles. (shrink)

This paper explores a pair of puzzling and controversial topics in the history of late nineteenth-century philosophy: the psychologism debates, and the nature of neo-Kantianism. Each is sufficientl...

It is a commonplace that Frege thought ordinary language to be seriously defective. Yet his remarks about ordinary language are not always unflattering. Comparing the relation between his formal language and ordinary language to the relation between the microscope and the eye, Frege remarked: ‘[the eye], because of the range of its applicability and because of the ease with which it can adapt itself to the most varied circumstances, has a great superiority over the microscope’. The point, of course, is (...) that, for Frege, the deficiencies of ordinary language arise in connection with the scientific endeavour: ordinary language is not an acceptable medium in which to pursue truth. As he goes on to observe: ‘… viewed as an optical instrument [the eye] reveals many imperfections … as soon as scientific purposes place strong requirements upon sharpness of resolution, the eye proves to be inadequate. On the other hand, the microscope is perfectly suited for just such purposes’. (shrink)

What characterizes indexical thinking is the fact that the modes of presentation through which one thinks of objects are context-bound and perspectival. Such modes of presentation, I claim, are mental files presupposing that we stand in certain relations to the reference : the role of the file is to store information one can gain in virtue of standing in that relation to the object. This raises the communication problem, first raised by Frege : if indexical thoughts are context-bound and relation-based, (...) how is it possible to communicate them to those who are not in the same context and do not stand in the right relations to the object? Following Frege, I argue that the solution comes from an important distinction between linguistic and psychological modes of presentation. Psychological modes of presentation are mental files. They are perspectival and context-bound. But linguistic modes of presentation are fixed by the conventions of the language and they are shared by the language users. They are public and serve to coordinate mental files in communication by constraining them to contain the piece of information they encode. In this way communication takes place even though the indexical thoughts entertained by the speaker are, in some sense, private and cannot be shared by the audience. (shrink)

This paper develops a criterion for sameness of Fregean senses. I consider three criteria: logical equivalence, intensional isomorphism, and epistemic equipollence. I reject the first two and argue for a version of the third.

Alvin Plantinga gave a reductio of the conjunction of the following three theses: Existentialism (the view that, e.g., the proposition that Socrates exists can't exist unless Socrates does), Serious Actualism (the view that nothing can have a property at a world without existing at that world) and Contingency (the view that some objects, like Socrates, exist only contingently). I sketch a view of truth at a world which enables the Existentialist to resist Plantinga's argument without giving up either Serious Actualism (...) or Contingency. (shrink)

This paper challenges a standard interpretation according to which Frege’s conception of logic (early and late) is at odds with the contemporary one, because on the latter’s view logic is formal, while on Frege’s view it is not, given that logic’s subject matter is reality’s most general features. I argue that Frege – in Begriffsschrift – retained the idea that logic is formal; Frege sees logic as providing the ‘logical cement’ that ties up together the contentful concepts of specific sciences, (...) not the most general truths. Finally, I discuss how Frege conceives of the application of Begriffsschrift, and of its status as a ‘lingua characteristica’. (shrink)

Bertrand Russell’s 1906 article ‘The Theory of Implication’ contains an algebraic weak completeness proof for classical propositional logic. Russell did not present it as such. We give an exposition of the proof and investigate Russell’s view of what he was about, whether he could have appreciated the proof for what it is, and why there is no parallel of the proof in Principia Mathematica.

This paper examines some aspects of Strawson’s conception of descriptive metaphysics, as it is developed in Individuals. Descriptive metaphysics sets out to describe ”the actual structure of our thought about the world”. Three specific problems for this project are discussed. First, isn’t the description of our actual thought about the world mainly an empirical task? Second, how determinate and consistent is the stuff we find, how determinate and consistent is our conceptual scheme? Third, who are “we” here? Answers to these (...) sets of questions are mainly negative in spirit. But all this will probably not mean that there will be no place for metaphysics, descriptive or revisionary, as a subject. The whole enterprise is perhaps more fraught with difficulties than Strawson thought, however. (shrink)

The central premise of Michael Dummett's global argument for anti-realism is the thesis that a speaker's grasp of the meaning of a declarative, indexical-free sentence must be manifested in her uses of that sentence. This enigmatic thesis has been the subject of a great deal of discussion, and something of a consensus has emerged about its content and justification. The received view is that the manifestation thesis expresses a behaviorist and reductive theory of meaning, essentially in agreement with Quine's view (...) of language, and motivated by worries about the epistemology of communication. In the present paper I begin by arguing that this standard interpretation of the manifestation thesis is neither particularly faithful to Dummett's writings nor philosophically compelling. I then continue by reconstructing, from Dummett's texts, an account of the manifestation thesis, and of its justification, that differ sharply from the received view. On my reading, the thesis is motivated not epistemologically, but conceptually. I argue that connections among our conceptions of meaning, assertion, and justification lead to a conclusion about the metaphysics of meaning: we cannot form a clearly coherent conception of how two speakers can attach different meanings to a sentence without at the same time differing in what they count as justifying assertions made with that sentence. I conclude with some suggestions about how Dummett's argument for global anti-realism should be understood, given my account of the manifestation thesis. (shrink)

The dominant topic of this study pertains to the relationship between the possession of properties on the part of linguistic items, such as words, concatenations of words or sentences, and the possibility of truly ascribing those properties to the concerned units. It can be verified that among the qualities which linguistic expressions can exhibit there are some which could be correctly attributed to them only by employing items which differ from the pertinent expressions. As various properties exist which exhibit this (...) particular feature the question how different phenomena of the impossibility of self-ascription are related to each other attains relevance. There is evidence to the effect that the existence of linguistic qualities exemplifying the pertinent peculiarity has been realized even in some non-Western philosophical tradition. For that reason the present investigation possesses both historical and problem-oriented ingredients. On the one hand the goal is pursued to substantiate the claim that the phenomenon of impossibility of self-ascription has been recognized in a non-Western tradition, at least with respect to particular linguistic properties. This task is performed by an analysis of a textual segment within a work which has been written in the tradition of linguistic philosophy in India, presumably in the fifth or sixth century AD, and by an attempt to demonstrate that a most coherent argumentative structure can be distilled from the textual segment supposing that it concerns the topic of impossibility of self-ascription with respect to semantic functions. On the other hand the question of how the impossibility of self-ascription regarding particular semantic functions is connected with problems of self-ascription regarding lack of truth constitutes a major concern of the study. It is contended that the latter phenomenon involves specific aspects and that accordingly the thesis insinuated by some scholars that the investigated text could provide a basis for the solution of truth-paradoxes is unwarranted. In view of the fact that the supposition that self-ascriptions of lack of truth always lack the property of expressing a truth is not self-evident it has been endeavoured to support the plausibility of this tenet and to show that this stance need not lead to inconsistencies, if it were assumed that only a particular type of content differing from a linguistically expressed content exhibits the qualities of being definitely true or untrue and of always complying with ‘classical’ inference-rules — in particular modus ponendo ponens and reductio ad absurdum — as well as with a principle according to which a linguistic unit expresses a truth exactly if its content is true. A contention is that the postulation of this type of content need not be made merely ad hoc. The envisaged position implies that the existence of indexical elements is by no means the only factor preventing that linguistic synonymy guarantees identity of truth value and that even linguistic items without deictic ingredients can be simultaneously linked to various types of content. As the investigations also refer to other phenomena suggesting that being simultaneously related to a multitude of contents is not an uncommon feature of linguistic expressions they touch on questions of interpretation and translation and thereby affect some general issues of the humanities. (shrink)

According to Frege, we need a criterion for recognising when different sentences express the same thought to make progress in logic. He himself hedged his own equipollence criterion with a number of provisos. In the literature on Frege, little attention has been paid to the problems these provisos raise. In this paper, I will argue that Fregeans have ignored these provisos at their peril. For without these provisos, Frege’s criterion yields wrong results; but with the provisos in place, it is (...) of no use for Frege’s purposes. This is connected to what Frege took to be the ‘greatest difficulty for philosophy’: natural language sentences don’t just express thoughts; they convey evaluations and communicative hints. Because of this, Frege’s recognition criterion for thoughts cannot be applied to them and we cannot make logical progress by ‘recognising a thought in different linguistic guises’. (shrink)

I argue that maps do not feature predication, as analyzed by Frege and Tarski. I take as my foil (Casati and Varzi, Parts and places, 1999), which attributes predication to maps. I argue that the details of Casati and Varzi’s own semantics militate against this attribution. Casati and Varzi emphasize what I call the Absence Intuition: if a marker representing some property (such as mountainous terrain) appears on a map, then absence of that marker from a map coordinate signifies absence (...) of the corresponding property from the corresponding location. Predication elicits nothing like the Absence Intuition. “F(a)” does not, in general, signify that objects other than a lack property F. On the basis of this asymmetry, I argue that attaching a marker to map coordinates is a different mode of semantic composition than attaching a predicate to a singular term. (shrink)

In this paper, I critically discuss Frege’s philosophy of geometry with special emphasis on his position in The Foundations of Arithmetic of 1884. In Sect. 2, I argue that that what Frege calls faculty of intuition in his dissertation is probably meant to refer to a capacity of visualizing geometrical configurations structurally in a way which is essentially the same for most Western educated human beings. I further suggest that according to his Habilitationsschrift it is through spatial intuition that we (...) come to know the axioms of Euclidean geometry. In Sect. 3, I argue that Frege seems right in claiming in The Foundations, §14 that the synthetic nature of the Euclidean axioms follows from the fact that they are independent of one another and of the primitive laws of logic. If the former were dependent on the latter, they would be analytic in Frege’s sense of analyticity. But then they would not be independent of one another and due to their mutual provability would lose their status as axioms of Euclidean geometry, since according to Frege an axiom of a theory T is per definitionen unprovable in T. I further argue that only by invoking pure spatial intuition can Frege “explain” the epistemological status of the axioms of Euclidean geometry completely: their synthetic a priori nature. Finally, I argue that his view about independence in The Foundations, §14 seems to clash with his conception of independence in his mature period. In Sect. 4, I scrutinize Frege’s somewhat vague, but unduly neglected remarks in The Foundations, §26 on space, spatial intuition and the axioms of Euclidean geometry. I argue that for the sake of coherence Frege should have said unambiguously that space is objective, that it is independedent not only of our spatial intuition, but of our mental life altogether including our judgements about space, instead of encouraging the possible conjecture that in his view it contains an objective and a subjective component. I further argue that for Frege the objectivity of both space and the axioms of Euclidean geometry manifests itself in our universal and compulsory acknowledgement of the Euclidean axioms as true. I conclude Sect. 4 by arguing that there is a conflict between the subjectivity of our spatial intuitions as stressed in The Foundations, §26 and Frege’s thesis in his dissertation that the axioms of Euclidean geometry derive their validity from the nature of our faculty of intuition. To resolve this conflict, I propose that in the light of his avowed realism in The Foundations Frege could have replaced his early thesis by saying that although we come to know the axioms of Euclidean geometry through spatial intuition and are justified in acknowledging them as true on the basis of geometrical intuition, their truth is independent not only of the nature of our faculty of intuition and singular acts of intuition, but of our mental processes and activities in general, including the inner mental act of judging. In Sect. 5, I argue that Frege most likely did not adopt Kant’s method of acquiring geometrical knowledge via the ostensive construction of concepts in spatial intuition. In contrast to Kant, Frege holds that the axioms of three-dimensional Euclidean geometry express state of affairs about space obtaining independently of our spatial intuition. In Sect. 6, I conclude with a summarized assessment of Frege’s philosophy of geometry. (shrink)

A tempting solution to problems of semantic vagueness and to the Liar Paradox is an appeal to truth-value gaps. It is tempting to say, for example, that, where Harry is a borderline case of bald, the sentenceHarry is baldis neither true nor false: it is in the ‘gap’ between these two values, and perhaps deserves a third truth-value. Similarly with the Liar Paradox. Consider the following Liar sentence: is false.That is, sentence says of itself that it is false. If we (...) accept the Tarskian schema S is true iff pwhere ‘S’ is a name of a sentence ‘p,’ we are led into paradox. Both the assumption that is true, and the assumption that is false lead us, via, to is true if and only if is false.Given this result, a natural reaction is to place in a ‘gap’ between true and false. (shrink)

The form of the sentence, as it is understood in contemporary semantics and linguistics, is functional. This paper interprets the metaphors in which Frege shows what the functional sentence means, arguing that Frege's sentence is neither an adequate translation of natural language nor of use in feminist theorizing.

One of Kripke's fundamental objections to descriptivism was that the theory misclassifies certain _a posteriori_ propositions expressed by sentences involving names as _a priori_. Though nowadays very few philosophers would endorse a descriptivism of the sort that Kripke criticized, many find two-dimensional semantics attractive as a kind of successor theory. Because two-dimensionalism needn't be a form of descriptivism, it is not open to the epistemic argument as formulated by Kripke; but the most promising versions of two-dimensionalism are open to a (...) close relative of that argument. (shrink)

In this article, I maintain that Habermas, in his critical essay on Brandom included inTruth and Justification(2003), reduces communication to its narrowly dialogical form, and in doing so tends to ignore the fact that the discursive process is, above all, for Brandom, the product of a shared coordination of different individual perspectives contributing to advancing the game of giving and asking one another for reasons. On the one hand, I propose to carry out a critical analysis of Habermas’ position and, (...) on the other hand, to do justice to Brandom by emphasizing the specificity of the discursive communicative process. (shrink)

One of Kripke's fundamental objections to descriptivism was that the theory misclassifies certain a posteriori propositions expressed by sentences involving names as a priori. Though nowadays very few philosophers would endorse a descriptivism of the sort that Kripke criticized, many find two-dimensional semantics attractive as a kind of successor theory. Because two-dimensionalism needn't be a form of descriptivism, it is not open to the epistemic argument as formulated by Kripke; but the most promising versions of two-dimensionalism are open to a (...) close relative of that argument. (shrink)

In several works, Frege argues that content is objective (i.e., thethoughts we entertain and communicate, and the senses of which theyare composed, are public, not private, property). There are, however,some remarks in the Fregean corpus that are in tension with this view.This paper is centered on an investigation of the most notorious andextreme such passage: the `Dr. Lauben example, from Frege (1918). Aprincipal aim is to attain more clarity on the evident tension withinFreges views on content, between this dominant objectivism (...) and someelements that seem to run counter to it, via developing an understandingof the `Dr. Lauben example. Then I will argue that this interpretation goes some way toward undermining some prevalent contemporary viewsabout language. Based on the advice of Dr. Lauben, I will argue againsta certain understanding of the causal-historical theory of reference –more specifically, of the phenomenon of deferential uses of linguisticexpressions – upon which these views are premised, and I will drawout some morals that pertain to individualism and competence. (shrink)

A discussion of Frege's views concerning the meaning of 'I' and his distinction between the 'I' of soliloquy and the 'I' of conversation.

Our starting point is Michael Luntley's falsificationist semantics for the logical connectives and quantifiers: the details of his account are criticised but we provide an alternative falsificationist semantics that yields intuitionist logic, as Luntley surmises such a semantics ought. Next an account of the logical connectives and quantifiers that combines verificationist and falsificationist perspectives is proposed and evaluated. While the logic is again intuitionist there is, somewhat surprisingly, an unavoidable asymmetry between the verification and falsification conditions for negation, the conditional, (...) and the universal quantifier. Lastly we are lead to a novel characterization of realism. (shrink)

The restricted semantic ellipsis hypothesis, we have argued, is committed to an enormous number of multiply ambiguous expressions, the introduction of which gains us no extra explanatory power. We should, therefore, reject it. We should also spurn the original version since: (a) it entails the restricted version and (b) it incorrectly declares that, whenever a speaker makes an assertion by uttering an unembedded word or phrase, the expression uttered has illocutionary force.Once rejected, the semantic ellipsis hypothesis cannot account for the (...) many exceptions to the syntactic ellipsis hypothesis. So, we can safely infer that the Claim is true.(1)The Claim: Speakers can make assertions by uttering ordinary, unembedded, words and phrases.To the degree that the Claim reallyis in tension with the primacy of sentences (i.e., the view that (a) only sentences can be used to make assertions and (b) only sentences are meaningful in isolation) this doctrine must also be rejected. (shrink)

Around the turn of the century, Poincare and Hilbert each published an account of geometry that took the discipline to be an implicit definition of its concepts. The terms ‘point’, ‘line’, and ‘plane’ can be applied to any system of objects that satisfies the axioms. Each mathematician found spirited opposition from a different logicist—Russell against Poincare' and Frege against Hilbert— who maintained the dying view that geometry essentially concerns space or spatial intuition. The debates illustrate the emerging idea of mathematics (...) as the science of structure. The article closes with some remarks on structuralist and nonstructuralist themes in Frege's own development of arithmetic. (shrink)

Hector‐Neri Castaüeda claimed in several papers that a proposition expressed by an indexical sentence (in a context of utterance) can be re‐expressed by means of an oratio obliqua clause (in a sentential context) that contains a quasi‐indicator. Robert M. Adams and Rogers Albritton have presented a counter‐argument that is accepted by Castaüeda himself. I will argue that the Adams/Albritton argument is not convincing: The argument uses several assumptions which could be disputed. The paper tries to develop a more direct argument (...) against Castaüeda's central claim. If Castaüeda's thesis is false, what then is achieved by quasi‐indexicals in oratio ubliqua? Adams and Castaüeda answer this question with a picture: the quasi‐indexical clause portrays an indexical proposition. I use Perry's idea that quasi‐indicators could be seen as expressions that bind special sense variables to give a less metaphorical account of the functioning of quasi‐indicators. Finally. I explore the consequences of this account for iterated knowledge‐ascriptions with quasi‐indicators and for truth‐conditional theories of meaning. (shrink)

The paper suggests a way of viewing the two Fregean principles of compositionality and contextuality as working together in the enterprise of interpretation. A third Fregean theme, that of elucidation (more precisely, the elucidation of primitive, undefinable terms of logic, mathematics and metamathematics) secures a place for some version of the context principle in Frege's later writings. When thinking about the functioning of elucidations, Frege acknowledges a principle of charitable interpretation. I argue that there is a deep connection between the (...) three themes, and that not only compositionality and contextuality, but also charity is a genuinely Fregean theme. -/- Context. Interpretation. Linguistics. Logic. Meaning. Word. (shrink)

A widely held view about Fregean Sense has it that the determination of a sign's referent by the sign's sense is achieved viasatisfaction: the sense specifies a condition (or set of conditions) and the referent is that entity, if any, which uniquely satisfies that (set of) condition(s). This is usually held in conjunction with the claim that the sense is existentially and qualitatively independent of the referent: if the referent did not exist, or did not uniquely satisfy the sense, the (...) sense would still exist and would still specify the same condition(s) that it actually does (and might determine a different referent than its actual one). Proponents of this view give several reasons for holding it. I describe these reasons and argue that they are not convincing. More generally, I try to show that the notion of satisfaction has no useful application within Frege's system. I then suggest an alternative account of the determination of a referent by a sense that I think is truer to Frege and more illuminating. Compared to the satisfaction view, my account construes determination as a more naturalistic and epistemically real relation between speakers and things in the world. (shrink)