| |
What is the relation between parts taken together and the whole that they compose? The recent literature appears to be dominated by two different answers to this question, which are normally thought of as being incompatible. According to the first, parts taken together are identical to the whole that they compose. According to the second, the whole is grounded in its parts. The aim of this paper is to make some theoretical room for the view according to which parts ground (...) the whole they compose while being, at the same time, identical to it. (shrink) | |
Frege claims that the laws of logic are characterized by their “generality,” but it is hard to see how this could identify a special feature of those laws. I argue that we must understand this talk of generality in normative terms, but that what Frege says provides a normative demarcation of the logical laws only once we connect it with his thinking about truth and science. He means to be identifying the laws of logic as those that appear in every (...) one of the scientific systems whose construction is the ultimate aim of science, and in which all truths have a place. Though an account of logic in terms of scientific systems might seem hopelessly antiquated, I argue that it is not: a basically Fregean account of the nature of logic still looks quite promising. (shrink) | |
[This Invited Paper will be published in December 2016.]. | |
ABSTRACT‘expressionist’ accounts of applied mathematics seek to avoid the apparent Platonistic commitments of our scientific theories by holding that we ought only to believe their mathematics-free nominalistic content. The notion of ‘nominalistic content’ is, however, notoriously slippery. Yablo's account of non-catastrophic presupposition failure offers a way of pinning down this notion. However, I argue, its reliance on possible worlds machinery begs key questions against Platonism. I propose instead that abstract expressionists follow Geoffrey Hellman's lead in taking the assertoric content of (...) empirical science to be irreducibly modal, using the ‘non-interference’ of mathematical objects as justification for detaching nominalistic consequences. (shrink) No categories | |
Propositions are about things, i.e., for each proposition, there are some things that it is about. Propositions also represent, i.e., each proposition represents some thing or things to be some way. There is a debate about whether propositions are structured and have the things that they are about as their constituents, or simple. I argue that they are structured. I do this by arguing that some propositions are about things that they do not represent. This follows from two constraints on (...) acceptable theories of propositions, which I state and defend. A familiar example of a structured theory can explain the fact that some propositions are about things that they do not represent. I argue that the theory can explain the fact because it says that propositions are structured. My example of a structured theory is a neo‐Russellian theory. The most prominent example of a simple theory cannot explain that fact, because it says that propositions are not structured. My example of a simple theory is Merricks' primitivist theory. (shrink) | |
This paper sheds light on an epistemological dimension of Frege’s “On Sense and Reference.” Under my suggested reading of it, one of its aims is to suggest a picture about propositional knowledge and its production. According to this picture, judgment, which produces propositional knowledge, is identification of the truth-value True with the reference of a given sentence. The propositional knowledge that p, produced by the judgment that p, consists in the knowledge of the identity between the True and the reference (...) of “p.” Judgment as such is a primitive kind of identification. It produces non-propositional knowledge of the identity of the True to which propositional knowledge is reduced. (shrink) | |
Despite its importance for early analytic philosophy, Gottlob Frege's account of existence statements, according to which they classify concepts, has been thought to succumb to a number of well-worn criticisms. This article does two things. First, it argues that, by remaining faithful to the letter of Frege's claim that concepts are functions, the Fregean account can be saved from many of the standard criticisms. Second, it examines the problem that Frege's account fails to generalize to cases which involve definite descriptions (...) and proper names. To deal with this the proffered analysis deviates from the letter of Frege's views, while remaining within its spirit. It proposes, in opposition to Frege, that expressions which grammatically look like singular terms should not always be read as referring to objects, but are sometimes best analysed as indicating functions. (shrink) | |
It is argued that we should distinguish ontic truth––the True––that Frege claimed is sui generis and indefinable, from the semantic concept, for which Tarski provided a definition. Frege’s argument that truth is not definable is clarified and Wittgenstein’s introduction of the distinction between saying and showing is interpreted as an attempted response to Frege’s rejection of the correspondence theory. It is argued that conflicts between realism and Dummettian anti-realism result from their proponents not thoroughly distinguishing between the two closely connected (...) ways of thinking about truth. Last, the distinction is used to clarify and endorse the Fregean claim that all true sentences indicate the True, identified as ontic truth. (shrink) | |
Hermann's Weyl Das Kontinuum has inspired several studies in logic and foundations of mathematics over the last century. The book provides a remarkable reconstruction of a large portion of classical mathematics on a predicative basis. However, diverging interpretations of the predicative system formulated by Weyl have been proposed in the literature. In the present work, I analyze an early formalization of Weyl's ideas proposed by [Casari, E. 1964. Questioni di Filosofia Della Matematica, Milano: Feltrinelli] and compare it with other, more (...) well-known, accounts, such as those proposed respectively by Feferman and Avron. In this way, I fill a gap in the literature on Weyl's predicative mathematics by shedding light on an interpretation that has never been studied. Moreover, Casari's work is plausibly the first systematic reconstruction of Weyl's system. In particular, I highlight the different insights about predicativity that can be found in Weyl's work. Casari's reconstruction focuses on the logical and mathematical processes described by Weyl in the first part of his book. Through the analysis of this unexplored perspective, I shed light on fundamental aspects of Weyl's work and elucidate the alleged ambiguities it presents. In particular, in line with Avron's most recent reconstruction of Weyl's ideas, this analysis supports a stronger conception of predicativity than what is commonly attributed to Weyl in the literature. As a result, this work not only provides an analysis of a neglected interpretation of Das Kontinuum, but also contributes to elucidating Weyl's classical conception of predicativity. (shrink) | |
Michael Dummett has argued that a formal semantics for our language is inadequate unless it can be shown to illuminate to our actual practice of speaking and understanding. This paper argues that Frege’s account of the semantics of predicate expressions according to which the reference of a predicate is a concept (a function from objects to truth values) has exactly the required characteristics. The first part of the paper develops a model for understanding the distinction between objects and concepts as (...) an ontological distinction. It argues that, ontologically, we can take a Fregean function to be generated by a property detection device that can register for any object the presence or absence of that property. This provides a direct connection between the semantics of sentences and the structure of perceptual judgment. The second part of the paper deals with arguments that have been mounted against the coherence of Frege’s semantics. It argues that some of these are question begging, while others are correct in so far as Frege’s claim is untenable if we assume that the syntactic categories singular term and predicate are primary, and the ontological categories are simply projections of these syntactic categories. However, the objections dissipate once we recognize that an independent ontological characterization of the distinction is available. (shrink) | |
Frege is an anti-psychologist about logic who takes logic to be sharply distinguished from psychology. However, Frege also takes judgment, which seems to be a subject of psychology, to be essential to logic. Van der Schaar attempts to explain away this tension by arguing that judgments relevant to logic in Frege are not mental actions psychology deals with. Against this reading, I show that for Frege, judgments are mental actions consistently. The tension in question should be explained away by clarifying (...) the sense in which judgment is essential to logic for Frege. He takes judgment to be essential to logic because he thinks that logic requires judgments to be performed. Logic requires logicians to be committed to truth, and it is by judgments that we are committed to truth. If Frege takes judgment to be essential to logic only in this sense, he is not thereby committed to logical psychologism. (shrink) | |
Dummettian anti-realism–the refusal to endorse bivalence–is generally thought to be associated with idealism This paper argues that this is only true of the position developed by early Dummett. In a later manifestation Dummettian anti-realism is better thought of as providing the logic for anti-realisms of an error theoretic kind. Early on Dummett distinguished deep from shallow arguments for giving up bivalence: deep arguments followed a strong ‘sufficiency’ reading of Frege’s context principle, and made the sentence the primary vehicle of meaning. (...) Enriched by an account of truth in terms of verifiability, deep arguments implied a form of linguistic idealism. From within a perspective that had already made ontology relative to theory, it was natural for the difference between realism and idealism to hinge on the notion of truth for sentences. Having given up the distinction between deep and shallow arguments against bivalence, Dummett, post 1990, asserts that every rejection of bivalence leads to a form of anti-realism. In the intervening years, he has also come to cast doubt on the sufficiency reading of the context principle, particularly as developed by Crispin Wright. These doubts open the space for some more simple-minded criticisms of this strong version of the context principle, developed in the paper. Once the sufficiency reading of the context principle is given up, arguments for failing to assert bivalence come to hinge on beliefs about ‘genuine’ existence. These forms of anti-realism cannot be taken to imply idealism. Rather, in many cases they will be the expression of views of an error-theoretic kind, that are quite compatible with a thorough-going rejection of idealism. (shrink) | |