ABSTRACTFregeans hold that predicates denote things, albeit things different in kind from what singular terms denote. This leads to a familiar problem: it seems impossible to say what any given predicate denotes. One strategy for avoiding this problem reduces the Fregean position to form of nominalism. I develop an alternative strategy that lets the Fregean hold on to the view that predicate denote things by reconceiving the nature of singular denotation and of Fregean objects.

By a `denoting phrase' I mean a phrase such as any one of the following: a man, some man, any man, every man, all men, the present King of England, the present King of France, the center of mass of the solar system at the first instant of the twentieth century, the revolution of the earth round the sun, the revolution of the sun round the earth. Thus a phrase is denoting solely in virtue of its form. We may distinguish (...) three cases: (1) A phrase may be denoting, and yet not denote anything; e.g., `the present King of France'. (2) A phrase may denote one definite object; e.g., `the present King of England' denotes a certain man. (3) A phrase may denote ambiguously; e.g. `a man' denotes not many men, but an ambiguous man. The interpretation of such phrases is a matter of considerably difficulty; indeed, it is very hard to frame any theory not susceptible of formal refutation. All the difficulties with which I am acquainted are met, so far as I can discover, by the theory which I am about to explain. (shrink)

By a `denoting phrase' I mean a phrase such as any one of the following: a man, some man, any man, every man, all men, the present King of England, the present King of France, the center of mass of the solar system at the first instant of the twentieth century, the revolution of the earth round the sun, the revolution of the sun round the earth. Thus a phrase is denoting solely in virtue of its form. We may distinguish (...) three cases: (1) A phrase may be denoting, and yet not denote anything; e.g., `the present King of France'. (2) A phrase may denote one definite object; e.g., `the present King of England' denotes a certain man. (3) A phrase may denote ambiguously; e.g. `a man' denotes not many men, but an ambiguous man. The interpretation of such phrases is a matter of considerably difficulty; indeed, it is very hard to frame any theory not susceptible of formal refutation. All the difficulties with which I am acquainted are met, so far as I can discover, by the theory which I am about to explain. (shrink)

Copredication is the phenomenon whereby two or more predicates seem to require that their argument denotes different things. The denotation of words that copredicate has been broadly discussed. In this paper, I investigate the metaphysics behind this question. Thus, mereological theories of dot objects claim that these nouns denote complex entities; Asher (Lexical meaning in context, Cambridge University Press, 2011, https://doi.org/10.1017/CBO9780511793936) thinks that they denote bare particulars; and the Activation Package Theory contends that they stand for multiple denotations. According (...) to the Activation Package Theory, copredicative nouns stand for complex knowledge structures that offer a range of multiple potential denotations. In this paper, I claim that the Activation Package Theory contributes to solve some of the metaphysical questions that arise from copredication. (shrink)

We outline a class of term-languages for epistemic grounding inspired by Prawitz’s theory of grounds. We show how denotation functions can be defined over these languages, relating terms to proof-objects built up of constructive functions. We discuss certain properties that the languages may enjoy both individually and with respect to their expansions. Finally, we provide a ground-theoretic version of Prawitz’s completeness conjecture, and adapt to our framework a refutation of this conjecture due to Piecha and Schroeder-Heister.

Bertrand Russell’s _Principles of Mathematics_ (1903) gives rise to several interpretational challenges, especially concerning the theory of denoting concepts. Only relatively recently, for instance, has it been properly realised that Russell accepted denoting concepts that do not denote anything. Such empty denoting concepts are sometimes thought to enable Russell, whether he was aware of it or not, to avoid commitment to some of the problematic non-existent entities he seems to accept, such as the Homeric gods and chimeras. In this paper, (...) I argue first that the theory of denoting concepts in _Principles of __Mathematics_ has been generally misunderstood. According to the interpretation I defend, if a denoting concept shifts what a proposition is about, then the aggregate of the denoted terms will also be a constituent of the proposition. I then show that Russell therefore could not have avoided commitment to the Homeric gods and chimeras by appealing to empty denoting concepts. Finally, I develop what I think is the best understanding of the ontology of _Principles of __Mathematics_ by interpreting some difficult passages. (shrink)

There are logics where necessity is defined by means of a given identity connective: \ is a tautology). On the other hand, in many standard modal logics the concept of propositional identity \ can be defined by strict equivalence \}\). All these approaches to modality involve a principle that we call the Collapse Axiom : “There is only one necessary proposition.” In this paper, we consider a notion of PI which relies on the identity axioms of Suszko’s non-Fregean logic SCI. (...) Then S3 proves to be the smallest Lewis modal system where PI can be defined as SE. We extend S3 to a non-Fregean logic with propositional quantifiers such that necessity and PI are integrated as non-interdefinable concepts. CA is not valid and PI refines SE. Models are expansions of SCI-models. We show that SCI-models are Boolean prealgebras, and vice-versa. This associates non-Fregean logic with research on Hyperintensional Semantics. PI equals SE iff models are Boolean algebras and CA holds. A representation result establishes a connection to Fine’s approach to propositional quantifiers and shows that our theories are conservative extensions of S3–S5, respectively. If we exclude the Barcan formula and a related axiom, then the resulting systems are still complete w.r.t. a simpler denotational semantics. (shrink)

In line with the Principle of Uniform Solution, Graham Priest has challenged advocates like myself of the “multiple-meanings” solution to the paradoxes of truth and knowledge, due to the medieval logician Thomas Bradwardine, to extend this account to a similar solution to the paradoxes of denotation, such as Berry’s, König’s and Richard’s. I here rise to this challenge by showing how to adapt Bradwardine’s principles of truth and signification for propositions to corresponding principles of denotation and signification for (...) descriptive phrases, applying them to give a “multiple-meanings” solution to the denotational paradoxes. (shrink)

Discusses Russell's famous 1905 essay, ‘On Denoting’. It places it in the context of his overall philosophical views at the time, and assesses the changes that it brought about in those view.

Originally published in 1958. A study in the logical foundations of modern theoretical semantics, this book is concerned with notions of designation and consistency as well as denotation and truth. It presents several semantical theories, each of which with what were new concepts or treatments from the author. Talking at a time when semantical theory was gained great ground, this book also looks at the methodology of the sciences and the semantics of scientific language alongside analysis of meaning and (...) expression. It is influenced by the writings of Carnap, Church, Frege, Goodman, Quine, Russell and Tarski. (shrink)

Originally published in 1958. A study in the logical foundations of modern theoretical semantics, this book is concerned with notions of designation and consistency as well as denotation and truth. It presents several semantical theories, each of which with what were new concepts or treatments from the author. Talking at a time when semantical theory was gained great ground, this book also looks at the methodology of the sciences and the semantics of scientific language alongside analysis of meaning and (...) expression. It is influenced by the writings of Carnap, Church, Frege, Goodman, Quine, Russell and Tarski. (shrink)

Bertrand Russell introduced several novel ideas in his 1903 Principles of Mathematics that he later gave up and never went back to in his subsequent work. Two of these are the related notions of denoting concepts and classes as many. In this paper we reconstruct each of these notions in the framework of conceptual realism and connect them through a logic of names that encompasses both proper and common names, and among the latter, complex as well as simple common names. (...) Names, proper or common, and simple or complex, occur as parts of quantifier phrases, which in conceptual realism stand for referential concepts, i.e., cognitive capacities that inform our speech and mental acts with a referential nature and account for the intentionality, or directedness, of those acts. In Russell’s theory, quantifier phrases express denoting concepts (which do not include proper names). In conceptual realism, names, as well as predicates, can be nominalized and allowed to occur as "singular terms", i.e., as arguments of predicates. Occurring as a singular term, a name denotes, if it denotes at all, a class as many, where, as in Russell’s theory, a class as many of one object is identical with that one object, and a class as many of more than one object is a plurality, i.e., a plural object that we call a group. Also, as in Russell’s theory, there is no empty class as many. When nominalized, proper names function as "singular terms" just the way they do in so-called free logic. Leśniewski’s ontology, which is also called a logic of names can be completely interpreted within this conceptualist framework, and the well-known oddities of Leśniewski’s system are shown not to be odd at all when his system is so interpreted. Finally, we show how the pluralities, or groups, of the logic of classes as many can be used as the semantic basis of plural reference and predication. We explain in this way Russell’s "fundamental doctrine upon which all rests", i.e., "the doctrine that the subject of a proposition may be plural, and that such plural subjects are what is meant by classes [as many] which have more than one term" (Russell 1938, p. 517). (shrink)

In many papers dealing with the stylistic features of legal texts, metaphor is highlighted as a stylistic figure often used in the language of law. On a daily basis we can witness the frequent use of metaphoric collocations like soft laws, hard laws, silent partner, hedge funds, etc. In this paper, the author analyses the use of denotations for colours as constituent parts of metaphoric collocations in the language of law. The analysis is conducted by using a comparative approach to (...) examples extracted by means of computer technology from international bills and conventions available online. In the main part of the paper, examples are classified by using a colour denotation as the main criterion for the classification. After that, the examples are compared with corresponding expressions used in German and Croatian. Taking into account the main principle of the Skopos translation theory that differences between cultures strongly influence the translation process, the hypothesis of this research is that in many cases there will be no lexical equivalence between collocations with colour denotation in three languages. Due to the fact that international bills and conventions build the corpus of the research, and that the English language has become the lingua franca of international communication, it can be expected that some metaphoric terms and collocations would be literally translated from English. Conclusions drawn from the comparative analysis of legal collocations containing denotations for colours can be interesting to lawyers and LSP teachers in the field of law. In this sense, results of the research can contribute to motivational aspects of teaching Legal English and Legal German. (shrink)

The two theories of verbal cognition, namely abhihitānvaya and anvitābhidhāna, first put forth by the Bhāṭṭa and Prābhākara Mīmāṃsakas respectively in the second half of the first millennium C.E., can be considered as being foundational as all subsequent thinkers of the Sanskritic intellectual tradition engaged with and elaborated upon these while debating the nature of language and meaning. In this paper, I focus on the first chapter of Śālikanātha’s Vākyārthamātṛkā and outline the process of anvitābhidhāna described therein. Śālikanātha explains this (...) as comprising three steps, and thereafter discusses each of these three to elaborate upon and philosophically defend this conception of how one cognizes sentential meaning. The aim of this paper is to present Śālikanātha’s three-step model, and thus demonstrate especially the distinct conception of abhidhāna for the Prābhākara Mīmāṃsakas as complex and chronologically extended as contrasted with the Bhāṭṭa conception of abhidhāna as non-complex and instantaneous. Such an understanding of the disparate semantic contents with which the Bhāṭṭas and Prābhākaras use the identical term abhidhāna is crucial for any correct study of their respective doctrines. (shrink)

In a recent article, Michael Kremer revisits Russell's "Gray's Elegy" argument—the argument in "On Denoting" in which Russell rejects "the whole distinction of meaning and denotation". Kremer argues that the Gray's Elegy argument is directed not at Frege's distinction between Sinn and Bedeutung but rather at Russell's own theory of "denoting concepts" in his earlier Principles of Mathematics. Furthermore, and more originally, Kremer argues that Russell's views of acquaintance play a central role in the argument. For Kremer, it is (...) because Frege does not share Russell's views of acquaintance that the Gray's Elegy argument succeeds against Russell's own earlier theory but not against Frege's position. (shrink)

By a `denoting phrase' I mean a phrase such as any one of the following: a man, some man, any man, every man, all men, the present King of England, the presenting King of France, the center of mass of the solar system at the first instant of the twentieth century, the revolution of the earth round the sun, the revolution of the sun round the earth. Thus a phrase is denoting solely in virtue of its..

In a recent article, Michael Kremer revisits Russell's "Gray's Elegy" argument—the argument in "On Denoting" in which Russell rejects "the whole distinction of meaning and denotation". Kremer argues that the Gray's Elegy argument is directed not at Frege's distinction between Sinn and Bedeutung but rather at Russell's own theory of "denoting concepts" in his earlier Principles of Mathematics. Furthermore, and more originally, Kremer argues that Russell's views of acquaintance play a central role in the argument. For Kremer, it is (...) because Frege does not share Russell's views of acquaintance that the Gray's Elegy argument succeeds against Russell's own earlier theory but not against Frege's position. (shrink)

In "the principles of mathematics" russell accepts (a) that word meaning (e.G., That 'fido' means fido) is irrelevant to logic and (b) that such sentences as 'all men are mortal' do not express quantified propositions but are about things (in this case, The class of men). If we note these confusions, And also that (b), Though not (a) has been abandoned by 'on denoting', We see what denoting is and how russell relates to frege on sinn and bedautung.

The terms denotation and reference are commonly used as synonyms. A more fine-grained analysis of natural language as offered by TIL shows that we can distinguish these terms in the case of empirical expressions. The latter are shown to denote non-trivial intensions while their reference is the value of these intensions in the actual world.

While Russell’s concerns in developing the theory of descriptions were primarily with his foundation of logic, he was aware of the epistemological uses of both the theory of denoting concepts and the 1905 theory of deWnite descriptions. At the end of “On Denoting” he suggests that the principle of acquaintance is a “result” of the new theory of denoting. In this paper I examine the relation between the theory of descriptions and the principle of acquaintance, and I reject two suggestions, (...) one that Russell’s view commits him to the position that quantiWers range only over objects of acquaintance, the other that the principle of acquaintance plays a crucial role in the Gray’s Elegy argument. Russell’s earlier theory of denoting concepts went hand in hand with the principle of acquaintance, as Russell made clear in his “Points about Denoting”. So the principle of acquaintance was neither a motivator for the new account nor a special consequence of it. The new account of “On Denoting”, while dispensing with denoting concepts, preserved the connection that the older de-. (shrink)

The Transparent Intensional Logic explicates the meaning of a linguistic expression as a construction. The construction is a hyperintensional entity. It is characterised as instructions for a „calculation“ of a concrete value. In the terminology of Pavel Tichy a linguistic expression denotes its meaning , which construes the signification of the expression. If the signification is an intension, we can call it a reference of the expression. In several semantic conceptions the question of the denotation and of the reference (...) are not treated equally. The terminological chaos can be resolved in a specific way thanks to „fine-grained“ character of the logical analysis offered by TIL. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:_Russell_ journal (home office): E:CPBRRUSSJOURTYPE2602\REVIEWS.262 : 2007-01-24 01:12 eviews THE DENOTING CENTURY, 1 19 90 05 5– –2 20 00 05 5 Michael Scanlan Philosophy / Oregon State U. Corvallis, or 97331, usa [email protected] Guido Imaguire and Bernard Linsky, eds. On Denoting: 1905–2005. Munich: Philosophia Verlag, 2005. Pp. 451. 98.00. isbn 3-88405-091-5. his anniversary collection of papers connected with Russell’s 1905 publiTcation of “On Denoting” reflects both the almost (...) mythic status that paper has achieved in analytic philosophy and the quite variegated nature of the significance that philosophers have seen in it. The papers in this collection break down roughly into two sorts. There are those which take a historical approach and attempt to explicate various aspects of the content of the OD article. The other sort might be labelled “application” papers in which Russell’s analysis in OD is seen as a tool or a model for subsequent philosophical work, in the spirit of Ramsey’s much quoted “paradigm of philosophy” remark. The volume opens with a reprint of the OD text with pagination indicated for the original Mind printing, for the text in Collected Papers 4 and for the widely referenced Logic and Knowledge Russell collection edited by R. C. Marsh. The Mind and Papers texts use the American convention of single quotation marks within double quotation marks. The Marsh edition (and the text given here) uses the inverse British convention. Readers need to be aware that paper authors here, and elsewhere, vary in which text they cite. The end of the volume has a comprehensive 21-page bibliography of the secondary literature. In between there are thirteen papers. I will be rather brief with the “application” papers, since I believe that Russell readers will tend to favour the more historically oriented papers. Some of the application papers wander quite far afield from Russell’s treatment of definite descriptions. For instance the paper by Thomas Mormann on “Description, Construction and Representation from Russell and Carnap to Stone” takes off from Russell’s assertion that his theory of descriptions was an early version of his subsequent interest in substituting “constructions” for “inferred entities” such as space-time points. The paper is almost exclusively a (worthwhile and mathematically astute) analysis of Russell’s efforts along these lines in Our russell: the Journal of Bertrand Russell Studies n.s. 26 (winter 2006–07): 167–90 The Bertrand Russell Research Centre, McMaster U. issn 0036-01631 _Russell_ journal (home office): E:CPBRRUSSJOURTYPE2602\REVIEWS.262 : 2007-01-24 01:12 168 Reviews Knowledge of the External World and The Analysis of Matter. The author argues that Russell’s constructions did not actually achieve the effects he wanted, but that (curiously) they can be properly developed within the later framework of topological spaces developed by Marshall Stone in 1937. The paper by Guido Imaguire, “Theory of Descriptions and Inferential Semantics”, explicitly eschews an “exegetical” approach and allies itself with a “systematical approach, in which one analyses possible new features and extensions of the proposed theory” (p. 397). The extension considered here is to “inferential semantics”, especially that of Robert Brandom. The spirit of this approach is to take the semantics of a language to be determined by the set of allowed inferences within that language. Imaguire takes as an essential lesson of Russell’s theory of descriptions that definite descriptions and proper names cannot be treated as singular terms of a language in the same manner. He goes on to argue for a criterion for distinguishing proper names from definite descriptions based on inferences allowed between sentences containing them, and he takes this distinction to argue for a modification of Brandom’s treatment of singular terms in his inferential semantics. Elena Tatievskaya’s paper on “Russell’s Theory of Descriptions and Wittgenstein on Internal Properties of Propositions” is another paper that is mainly about something other than Russell and his theory of descriptions. It is a very detailed study of Wittgenstein’s attempt to make good on his claim that the logical symbols of propositional logic notation, such as v and ~, do not correspond to “logical” components of propositions (Tractatus... (shrink)

The widely held assumption about what motivated On Denoting is irreconcilable with Russell's position shortly beforehand; but discarding it leaves one with a carefully worked out solution whose problem is missing. The real motivation is to be found in a notoriously obscure passage in OD, in which Russell exposes a decisive (though easily overlooked) flaw in his former theory of denoting; a flaw which also cripples Frege's theory of sense and reference. A comprehensive account of this passage is the chief (...) concern of the present paper. Recognizing the critical role of this argument of Russell's leads to a more credible account of his argumentation in that essay. It also suggests that the fundamental standpoint underlyingThe Principles of Mathematics remains intact. In this light, the appropriation of OD to the philosophy of language may be misguided. (shrink)

This paper continues the discussion of the theory of eliminative materialism. The argument of the paper is that there is a simple principle about denotation--Called "the principle of the use of inter-Denoting terms"--Which can be seen to be clearly and necessarily true, And also to be inconsistent with the theory of eliminative materialism.

Russell's theory of descriptions has recently come under attack as being trivial and circular--Specifically, That it predicates uniqueness of definite descriptions only after identifying those descriptions as phrases analysable via the uniqueness criterion in the first place. It is shown that this criticism is quite off target. The confusion results largely from failure to distinguish the class of denoting phrases from its sub-Set, Definite descriptions. A few reminders are issued in hopes of facilitating the study and teaching of the theory (...) which will probably be remembered as russell's greatest contribution to philosophy. (shrink)

This chapter contains sections titled: The Philosophical Tale.

Focusing on the simple demonstrative ‘that’ and demonstrative expressions of the form ‘that F,’ this paper reviews four accounts of what determines the denotations of demonstratives—the description theory, according to which the work is done by a proper definite description associated with the demonstrative; the causal theory, according to which it is done by a non-deviant causal chain connecting the object and the demonstrative; the demonstration theory, according to which it is done by a demonstration accompanying the demonstrative; and the (...) mental reference theory, according to which it is done by the mental act of reference that the demonstrative expresses—and it offers evidence of the superiority of the mental reference theory. (shrink)

Part 1 sets out the logical/semantical background to ‘On Denoting’, including an exposition of Russell's views in Principles of Mathematics, the role and justification of Frege's notorious Axiom V, and speculation about how the search for a solution to the Contradiction might have motivated a new treatment of denoting. Part 2 consists primarily of an extended analysis of Russell's views on knowledge by acquaintance and knowledge by description, in which I try to show that the discomfiture between Russell's semantical and (...) epistemological commitments begins as far back as 1903. I close with a non-Russellian critique of Russell's views on how we are able to make use of linguistic representations in thought and with the suggestion that a theory of comprehension is needed to supplement semantic theory. (shrink)

Introduction By the late fifth century BCE Panini had composed the Astadhyayi, consisting of nearly 4000 rules giving a precise and fairly complete ...

The aim of the thesis is twofold. Firstly, it is argued that Frege's theory of meaning and denotation is the first successful non-psychologistic response to what has been called 'the puzzle of identity' and that, where Frege's theory differs most significantly from the theory of meaning and denotation developed by Russell in The Principles of Mathematics and in his unpublished manuscripts on logic of 1903-1905, Russell was right. Secondly, it is shown that Russell was again right when he (...) claimed that the central argument of 'On Denoting' completely discredits both his own and Frege's theory of meaning and denotation. An interpretation of the relevant passage of 'On Denoting' is put forward. The discussion makes evident that it is virtually impossible to disentangle that argument if one ignores his unpublished work on the topic. (shrink)

The question of the origin of polyadic expressivity is explored and the results are brought to bear on Bertrand Russell's 1903 theory of denoting concepts, which is the main object of criticism in his 1905 "On Denoting". It is shown that, appearances to the contrary notwithstanding, the background ontology of the earlier theory of denoting enables the full-blown expressive power of first-order polyadic quantification theory without any syntactic accommodation of scopal differences among denoting phrases such as 'all φ', 'every φ', (...) and 'any φ' on the one hand, and 'some φ' and 'a φ' on the other. The case provides an especially vivid illustration of the general point that structural (or ideological) austerity can be paid for in the coin of ontological extravagance. (shrink)

The role of memory in one’s cognition of sentential meaning is a pivotal topic in Indian philosophical debates on the nature of language. The Bhāṭṭa Mīmāṃsakas claim in their doctrine of abhihitānvaya that words denote word-meanings which in turn lead one to sentential meaning, with memory playing only a limited role in this process. The Prābhākara Mīmāṃsakas however assign memory a central role and assert that each word in a sentence denotes the connected sentential meaning. This paper is a philosophical (...) and philological study of the arguments presented by the influential Prābhākara thinker Śālikanātha in his Vākyārthamātṛkā-I in order to substantiate the role of memory as part of the doctrine of anvitābhidhāna. The VM-I commences these discussions with an objection of the Bhāṭṭa pūrvapakṣin against this Prābhākara doctrine, and thereafter proceeds to refute this objection by demonstrating the role of memory, specifically in regard to word-meaning. Śālikanātha lays out his refutation by means of several layers of intricate argumentation, and this paper attempts to follow the text closely and present cogently his philosophical reasoning. The aim of this paper is thus to not only demonstrate the early pre-empting of this Bhāṭṭa objection by Śālikanātha himself but also his own responses to this, thereby enabling one to understand with greater clarity a cornerstone of the elaborate doctrine of anvitābhidhāna. (shrink)

Nelson Goodman argued convincingly that in order to understand the representation relation one should dissociate it from the relation of resemblance because of the logical differences between the two concepts. Resemblance is reflexive and symmetric whereas representation is not. Furthermore, Goodman suggested that what lies at the core of representation is denotation. According to Goodman, if X represents Y then X must denote Y, but he recognized that by opting for an analysis of representation only based on this idea (...) of denotation we run into problems. There are two reasons for this. The first reason is that X could be considered to be a representation of Y by mere stipulation. The second reason is that in many cases X represents Y but Y does not exist and thus there is nothing that X denotes. Both of these problems are important when addressing questions about scientific representation. First, we do not think that we do justice to scientific practices by thinking that scientific models represent by mere stipulation. Second, some of our scientific models represent what we often label ideal systems or ideal states of affairs, and if such systems do not exist in the actual world then it would also not make much sense to claim that our models denote such systems. I argue in this paper that there is a way to overcome these two problems and explicate “representation” by means of “denotation”. (shrink)

A modified version of Normann's hierarchy of domains with totality [9] is presented and is shown to be suitable for interpretation of Martin-Löf's intuitionistic type theory. This gives an interpretation within classical set theory, which is natural in the sense that $\Sigma$ -types are interpreted as sets of pairs and $\Pi$ -types as sets of choice functions. The hierarchy admits a natural definition of the total objects in the domains, and following an idea of Berger [3] this makes possible an (...) interpretation where a type is defined to be true if its interpretation contains a total object. In particular, the empty type contains no total objects and will therefore be false (in any non-empty context). In addition, there is a natural equivalence relation on the total objects, so we derive a hierarchy of topological spaces (quotient spaces wrt. the Scott topology), and give a second interpretation using this hierarchy. (shrink)

The author states: "in a recent article searle has shown the odd irrelevance of russell's criticisms of frege in the famous paper 'on denoting'. I here offer an explanation of the oddity: russell had excusably, But wrongly, Conflated frege's distinction between sinn and bedeutung with his own distinction between what an expression 'means' and what it 'denotes'.".

The present paper argues that ‘mature mathematical formalisms’ play a central role in achieving representation via scientific models. A close discussion of two contemporary accounts of how mathematical models apply—the DDI account (according to which representation depends on the successful interplay of denotation, demonstration and interpretation) and the ‘matching model’ account—reveals shortcomings of each, which, it is argued, suggests that scientific representation may be ineliminably heterogeneous in character. In order to achieve a degree of unification that is compatible with (...) successful representation, scientists often rely on the existence of a ‘mature mathematical formalism’, where the latter refers to a—mathematically formulated and physically interpreted—notational system of locally applicable rules that derive from (but need not be reducible to) fundamental theory. As mathematical formalisms undergo a process of elaboration, enrichment, and entrenchment, they come to embody theoretical, ontological, and methodological commitments and assumptions. Since these are enshrined in the formalism itself, they are no longer readily obvious to either the novice or the proficient user. At the same time as formalisms constrain what may be represented, they also function as inferential and interpretative resources. (shrink)