A semantic theory is committed to semantic monism just in case every particular semantic property posited by the theory is a member of the same kind. The commitment to semantic monism appears to draw some support from the need to provide a compositional semantics, since taking a single kind of semantic property as key to a semantic theory affords a uniform pattern on the basis of which the meaning of any given sentence can be compositionally determined. This line of support (...) highlights a tension between the principle of compositionality and taking a more pluralistic approach to semantic theorizing. In this essay, that tension is relieved, leaving open the prospect of a pluralistic semantic theory that observes the principle of compositionality. (shrink)

The present article is the first of a trilogy of papers, devoted to analysing the influence of semantic Platonism on contemporary philosophy of language. In the present article, I lay out the discussion by contrasting semantic Platonism with two other views of linguistic meaning: the socio-environmental conception of meaning and semantic anti-representationalism. Then, I identify six points in which the impregnation of semantic theory with Platonism can be particularly felt, resulting in shortcomings and inaccuracies of various kinds. These points are (...) the following: the limitations of regarding logico-philosophical analysis as the only working methodology; the tendency to avoid investigating a number of aspects of linguistic meaning; the recurring confusion between sentences, statements, and propositions; the weakness of transcendent assumptions about meaning; the weakness of meaning assumptions adopted on the basis of pure intuition; and inconsistencies caused by some over-eager attempts to escape semantic Platonism. (shrink)

The principle of compositionality requires that the meaning of a complex expression remains the same after substitution of synonymous expressions. Alleged counterexamples to compositionality seem to force a theoretical choice: either apparent synonyms are not synonyms or synonyms do not syntactically occur where they appear to occur. Some theorists have instead looked to Frege’s doctrine of “reference shift” according to which the meaning of an expression is sensitive to its linguistic context. This doctrine is alleged to retain the relevant claims (...) about synonymy and substitution while respecting the compositionality principle. Thus, Salmon (Philos Rev 115(4):415, 2006) and Glanzberg and King (Philosophers’ Imprint 20(2):1–29, 2020) offer occurrence-based accounts of variable binding, and Pagin and Westerståhl (Linguist Philos 33(5):381–415, 2010c) argue that an occurrence-based semantics delivers a compositional account of quotation. Our thesis is this: the occurrence-based strategies resolve the apparent failures of substitutivity in the same general way as the standard expression-based semantics do. So it is a myth that a Frege-inspired occurrence-based semantics affords a genuine alternative strategy. (shrink)

The idea underlying the Begriffsschrift account of identities was that the content of a sentence is a function of the things it is about. If so, then if an identity a=b is about the content of its contained terms and is true, then a=a and a=b have the same content. But they do not have the same content; so, Frege concluded, identities are not about the contents of their contained terms. The way Frege regarded the matter is that in an (...) identity the terms flanking the symbol for identity do not have their ordinary contents, but instead have themselves as their contents. In ?Uber Sinn und Bedeutung? Frege became convinced that if an identity a=bis about the signs aand b, then it expresses no proper knowledge. So, since it is evident that many such identities do express proper knowledge, Frege concluded that identities are not about their contained signs. So he became convinced that his Begriffsschrift account was incorrect. What was the error in the argument that led Frege to that account? It was thinking that the content of a sentence is a function of the contents of its constituent signs, that is, the things it is about. (shrink)

Assertion plays a crucial dual role in Frege's conception of logic, a formal and a transcendental one. A recurrent complaint is that Frege's inclusion of the judgement-stroke in the Begriffsschrift is either in tension with his anti-psychologism or wholly superfluous. Assertion, the objection goes, is at best of merely psychological significance. In this paper, I defend Frege against the objection by giving reasons for recognising the central logical significance of assertion in both its formal and its transcendental role.

Some philosophers have argued that the open-endedness of the set concept has revisionary consequences for the semantics and logic of set theory. I consider (several variants of) an argument for this claim, premissed on the view that quantification in mathematics cannot outrun our conceptual abilities. The argument urges a non-standard semantics for set theory that allegedly sanctions a non-classical logic. I show that the views about quantification the argument relies on turn out to sanction a classical semantics and logic after (...) all. More generally, this article constitutes a case study in whether the need to account for conceptual progress can ever motivate a revision of semantics or logic. I end by expressing skepticism about the prospects of a so-called non-proof-based justification for this kind of revisionism about set theory. (shrink)

It is commonly assumed that classical logic is the embodiment of a realist ontology. In “Sets and Semantics”, however, Jonathan Lear challenged this assumption in the particular case of set theory, arguing that even if one is a set-theoretic Platonist, due attention to a special feature of set theory leads to the conclusion that the correct logic for it is intuitionistic. The feature of set theory Lear appeals to is the open-endedness of the concept of set. This article advances reasons (...) internal to Lear’s account to show that his argument for intuitionistic set theory is unsuccessful. (shrink)

We reconstruct essential features of Lagrange’s theory of analytical functions by exhibiting its structure and basic assumptions, as well as its main shortcomings. We explain Lagrange’s notions of function and algebraic quantity, and we concentrate on power-series expansions, on the algorithm for derivative functions, and the remainder theorem—especially on the role this theorem has in solving geometric and mechanical problems. We thus aim to provide a better understanding of Enlightenment mathematics and to show that the foundations of mathematics did not, (...) for Lagrange, concern the solidity of its ultimate bases, but rather purity of method—the generality and internal organization of the discipline. (shrink)

Suppose we have an idea of what counts as communication, more precisely as a communicative event. Then we have the further task of dividing communicative events into successful and unsuccessful. Part of this task is to find a basis for this evaluation, i.e. appropriate properties of speaker and hearer. It is argued that success should be evaluated in terms of a relation between thought contents of speaker and hearer. This view is labelled ‘classical’, since it is justifiably attributable to both (...) Locke and Frege (section 2). Most of the paper is devoted to discussing competing contemporary views, such as behaviorist/pragmatist views (section 4), requirements of knowledge (section 5), of reliability (section 6) and that success should be defined in terms of public language semantics rather than in terms of thought content (section 7). (shrink)

Alex Oliver; XI*—A Few More Remarks on Logical Form, Proceedings of the Aristotelian Society, Volume 99, Issue 1, 1 June 1999, Pages 247–272, https://doi.org/10.

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.

This paper discusses George Boole’s two distinct approaches to the explanatory relationship between logical and psychological theory. It is argued that, whereas in his first book he attributes a substantive role to psychology in the foundation of logical theory, in his second work he abandons that position in favour of a linguistically conceived foundation. The early Boole espoused a type of psychologism and later came to adopt a type of anti-psychologism. To appreciate this invites a far-reaching reassessment of his philosophy (...) of logic. (shrink)

This paper argues for an ontological distinction between two kinds of universals, 'kinds of tropes' such as 'wisdom' and properties such as 'the property of being wise'. It argues that the distinction is parallel to that between two kinds of collections, pluralities such as 'the students' and collective objects such as 'the class'. The paper argues for the priortity of distributive readings with pluralities on the basis of predicates of extent or shape, such 'large' or 'long'.

Based on the notion of a trope, this paper gives a novel analysis of identificational sentences such as 'this is Mary','this is a beautiful woman', 'this looks like Mary', or 'this is the same lump of clay, but not the same statue as that'.

This paper is concerned with the relationship between the metaphysical doctrine of realism about the external world and semantic realism, as characterised by Michael Dummett. I argue that Dummett's conception of the relationship is flawed, and that Crispin Wright's account of the relationship, although designed to avoid the problems which beset Dummett's, nevertheless fails for similar reasons. I then aim to show that despite the fact that Dummett and Wright both fail to give a plausible account of the relationship between (...) semantic realism and the metaphysical doctrine of realism, the semantic issue and the metaphysical issue are importantly related. I outline the precise sense in which the evaluation of semantic realism is relevant to the evaluation of realism about the external world, a sense overlooked by opponents of Dummett, such as Simon Blackburn and Michael Devitt. I finish with some brief remarks on metaphysics, semantics, and the nature of philosophy, and suggest that Dummett's arguments against semantic realism can retain their relevance to metaphysical debate even if we reject Dummett's idea that the theory of meaning is thefoundation of all philosophy. (shrink)

The transition from the traditional to the representational theory of measurement around the turn of the century was accompanied by little sustained criticism of the former. The most forceful critique was Bertrand Russell''s 1897 Mind paper, On the relations of number and quantity. The traditional theory has it that real numbers unfold from the concept of continuous quantity. Russell''s critique identified two serious problems for this theory: (1) can magnitudes of a continuous quantity be defined without infinite regress; and (2) (...) can additive relations between such magnitudes exist if magnitudes are not divisible? The present paper shows how the traditional theory answers these questions and compares the traditional and representational theories as contributions to our understanding of the logic of application. (shrink)

I present several arguments which provide what I consider to be a definitive argument against certain forms of masculine language in their so-called sexually neutral usage. In the first part, I concentrate on the use of the word and I defend the idea that it embodies a perverse contingent a priori. In the second part, I examine how this pernicious a prioriinfects the pronominal system of French. I conclude with an undoubtedly surprising linguistic and feminist criticism of a recent decision (...) by the Office de la langue franbec to feminize job titles, arguing instead that the problem lies elsewhere and hence so does an efficient solution. (shrink)

As part of his attack on Frege’s ‘myth’ that senses reside in the third realm, Dummett alleges that Frege’s view that all objects are selbständig is an underlying mistake, since some objects depend upon others. Whatever the merits of Dummett’s other arguments against Frege’s conception of sense, this objection fails. First, Frege’s view that senses are third-realm entities is not traceable to his view that all objects are selbständig. Second, while Frege recognizes that there are objects that are dependent upon (...) other objects, he does not take this to compromise the Selbständigkeit of any objects. Thus, Frege’s doctrine that objects are selbständig does not make the claim of absolute independence that Dummett appears to have taken it to make. Nevertheless, in order to make a good case against Frege based on the dependency of senses, Dummett need only establish his claim that senses depend upon expressions: appeal to an absolute conception of independence is unnece... (shrink)

The paper addresses a popular argument that accounts of assertion in terms of constitutive norms are incompatible with conventionalism about assertion. The argument appeals to an alleged modal asymmetry: constitutive rules are essential to the acts they characterize, and therefore the obligations they impose necessarily apply to every instance; conventions are arbitrary, and thus can only contingently regulate the practices they establish. The paper argues that this line of reasoning fails to establish any modal asymmetry, by invoking the distinction between (...) the non-discriminating existence across possible worlds of types of practices and institutions defined by constitutive rules, and the discriminating existence of those among them that are actually in force, and hence truly normative. The necessity of practices defined by constitutive rules that the argument relies on concerns the former, while conventionalist claims are only about the latter. The paper should thus contribute to get a better understanding of what social constructs conceived as defined by constitutive norms are. It concludes by suggesting considerations that are relevant to deciding whether assertion is in fact conventional. (shrink)

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

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

According to the species of neo-logicism advanced by Hale and Wright, mathematical knowledge is essentially logical knowledge. Their view is found to be best understood as a set of related though independent theses: (1) neo-fregeanism-a general conception of the relation between language and reality; (2) the method of abstraction-a particular method for introducing concepts into language; (3) the scope of logic-second-order logic is logic. The criticisms of Boolos, Dummett, Field and Quine (amongst others) of these theses are explicated and assessed. (...) The issues discussed include reductionism, rejectionism, the Julius Caesar problem, the Bad Company objections, and the charge that second-order logic is set theory in disguise. (shrink)

This paper takes issue with Derek Sankey's: ‘Minds, Brains, and Differences in Personal Understanding’, Educational Philosophy and Theory, 39 (2007), pp. 543–558 on the questions of the post-pedagogical classroom and the forms of knowledge. I then try to show that a theory of meaning framed in terms of normative pragmatics is better able than the brain science Sankey relies on to account for the concept of a person or self; the central educational concept of personal understanding; the relation between being (...) a person and membership of the species Homo sapiens; the role of mental images in meaningfulness; the functioning of figurative language; and the Gadamerian notion of understanding as constitutive of the self. It is necessary on the way to answer Sankey's criticisms of correctness, a concept on which any normative theory must rely. (shrink)

The goal of this paper is to make sense of relativism about truth. There are two key ideas. (1) To be a relativist about truth is to allow that a sentence or proposition might be assessment-sensitive: that is, its truth value might vary with the context of assessment as well as the context of use. (2) Making sense of relativism is a matter of understanding what it would be to commit oneself to the truth of an assessment-sensitive sentence or proposition.

Husserl and Frege reject logical psychologism, the view that logical laws are psychological 'laws of thought'. This paper offers an account of these famous objections and argues that their crucial premise, the necessity of logical laws, is justified with reference to a problematic metaphysics. However, this premise can be established in a more plausible way, namely via a transcendental argument which starts from the practice of rational criticism. This argument is developed through a discussion of Quine's holism, which at first (...) appears to make the idea of the necessity of logical laws even less plausible, but eventually turns out to speak in favor of this view. (shrink)

I propose a fourfold categorisation of entities according to whether or not they possess determinate identity-conditions and whether or not they are determinately countable. Some entities – which I call ‘individual objects’ – have both determinate identity and determinate countability: for example, persons and animals. In the case of entities of a kind K belonging to this category, we are in principle always entitled to expect there to be determinate answers to such questions as ‘Is x the same K as (...) y?’ and ’How many Ks are there satisfying condition C?’, even if we may sometimes be unable in practice to discover what these answers are. But other entities apparently lack either determinate identity, or determinate countability, or both. In these terms I try to explain certain important ontological differences between familiar macroscopic objects and various rather more esoteric entities, such as the ‘particles’ of quantum physics, quantities of material stuff, and tropes or property instances. (shrink)

On the most prominent account, understanding what was said is always propositional knowledge of what was said. I develop a more minimal alternative, according to which understanding is sometimes a distinctive attitude towards what was said—to a first approximation, entertaining what was said. The propositional knowledge account has been supported on the basis of its capacity to explain testimonial knowledge transmission. I argue that it is not so supported.

I discuss the conjecture that understanding what is said in an utterance is to be modelled as knowing what is said in that utterance. My main aim is to present a number of alter- native models, as a prophylactic against premature acceptance of the conjecture as the only game in town. I also offer preliminary assessments of each of the models, including the propositional knowledge model, in part by considering their respective capacities to sub-serve the transmission of knowledge through testimony. (...) In each case, the preliminary assessment is unfavourable. I end by very briefly sketching an additional model as an object for future consideration. (shrink)

This paper is about first‐person thoughts—thoughts about oneself that are expressible through uses of first‐person pronouns. It is widely held that first‐person thoughts cannot be shared. My aim is to postpone rejection of the more natural view that such thoughts about oneself can be shared. I sketch an account on which such thoughts can be shared and indicate some ways in which deciding the fate of the account will depend upon further work.

Determined by Reasons: A Competence Account of Acting for a Normative Reason, by MantelSusanne. New York and London: Routledge, 2018. Pp. xiii + 190.

Science depends on judgments of the bearing of evidence on theory. Scientists must judge whether an observation or the result of an experiment supports, disconfirms, or is simply irrelevant to a given hypothesis. Similarly, scientists may judge that, given all the available evidence, a hypothesis ought to be accepted as correct or nearly so, rejected as false, or neither. Occasionally, these evidential judgments can be made on deductive grounds. If an experimental result strictly contradicts a hypothesis, then the truth of (...) the data deductively entails the falsity of the hypothesis. In the great majority of cases, however, the connection between evidence and hypothesis is non-demonstrative, or inductive. In particular, this is so whenever a general hypothesis is inferred to be correct on the basis of the available data, since the truth of the data will not deductively entail the truth of the hypothesis. It always remains possible that the hypothesis is false even though the data are correct. (shrink)

In this paper, we investigate (1) what can be salvaged from the original project of "logicism" and (2) what is the best that can be done if we lower our sights a bit. Logicism is the view that "mathematics is reducible to logic alone", and there are a variety of reasons why it was a non-starter. We consider the various ways of weakening this claim so as to produce a "neologicism". Three ways are discussed: (1) expand the conception of logic (...) used in the reduction, (2) allow the addition of analytic-sounding principles to logic so that the reduction is not to "logic alone" but to logic and truths knowable a priori, and (3) revise the conception of "reducible". We show how the current versions of neologicism fit into this classification scheme, and then focus on a kind of neologicism which we take to have the most potential for achieving the epistemological goals of the original logicist project. We argue that that the "weaker" the form of neologicism, the more likely it is to be a new form of logicism, and show how our preferred system, though mathematically weak, is metaphysically and epistemogically strong, and can "reduce" arbitrary mathematical theories to logic and analytic truths, if given a legitimate new sense of "reduction". (shrink)

In §57 of the Foundations of Arithmetic, Frege famously turns to natural language to support his claim that numbers are ‘self-subsistent objects’:I have already drawn attention above to the fact th...

Quineans have taken the basic expression of ontological commitment to be an assertion of the form '' x '', assimilated to theEnglish ''there is something that is a ''. Here I take the existential quantifier to be introduced, not as an abbreviation for an expression of English, but via Tarskian semantics. I argue, contrary to the standard view, that Tarskian semantics in fact suggests a quite different picture: one in which quantification is of a substitutional type apparently first proposed by (...) Geach. The ontological burden is borne by constant symbols, and truth is defined separately from reference. (shrink)