Many normative nonnaturalists find normative naturalism to be completely implausible. Naturalists and nonnaturalists agree, provided they are realists, that there are normative properties, such as moral ones. Naturalists hold that these properties are similar in all metaphysically important respects to properties that all would agree to be natural ones, such as such as meteorological or economic ones. It is this view that the nonnaturalists I have in mind find to be hopeless. They hold that normative properties are just too different (...) from natural properties for it to be possible they are natural properties. I aim to defuse this intuition. “Non-analytic naturalism” has made progress in defusing the intution. According to non-analytic naturalists, normative properties can be represented in thought in two ways, by an ordinary normative concept and by a naturalistic concept, where, the non-analytic naturalist concedes, normative concepts are not, and are not analyzable in terms of, naturalistic concepts. Non-analytic naturalism seems to avoid many of the standard objections to naturalism, but the Just Too Different intuition is resilient in the face of non-analytic naturalism, for even if one thinks that normative concepts are not analyzable at all, one might think that clarity about the concepts can show that naturalism is hopeless. I therefore think it is important for naturalists to address the intuition directly. In this paper, I argue that the intuition plausibly rests on certain characteristic pre-theoretical ways of thinking of the normative properties that we acquire in the ordinary course of moral learning, together with a drive to vindicate these ways of thinking, something of which people may be unaware. This drive to vindicate our ways of thinking is pervasive, and it is characteristic of rational agents. It explains our tendency to think well of those we love, for example, and to think ill of those with whom we are angry. It also explains a strong inclination to form beliefs that, if true, would seemingly vindicate our ways of thinking of normative properties. A result of this, I contend, is the intuition that normative naturalism cannot be true. Yet, as I further argue, the vindication process does not track the truth and the drive to vindicate our states of mind cannot be relied on as a guide to the metaphysics of normativity. (shrink)

Many normative nonnaturalists find normative naturalism to be completely implausible. Naturalists and nonnaturalists agree, provided they are realists, that there are normative properties, such as moral ones. Naturalists hold that these properties are similar in all metaphysically important respects to properties that all would agree to be natural ones, such as such as meteorological or economic ones. It is this view that the nonnaturalists I have in mind find to be hopeless. They hold that normative properties are just too different (...) from natural properties for it to be possible they are natural properties. I aim to defuse this intuition. “Non-analytic naturalism” has made progress in defusing the intution. According to non-analytic naturalists, normative properties can be represented in thought in two ways, by an ordinary normative concept and by a naturalistic concept, where, the non-analytic naturalist concedes, normative concepts are not, and are not analyzable in terms of, naturalistic concepts. Non-analytic naturalism seems to avoid many of the standard objections to naturalism, but the Just Too Different intuition is resilient in the face of non-analytic naturalism, for even if one thinks that normative concepts are not analyzable at all, one might think that clarity about the concepts can show that naturalism is hopeless. I therefore think it is important for naturalists to address the intuition directly. In this paper, I argue that the intuition plausibly rests on certain characteristic pre-theoretical ways of thinking of the normative properties that we acquire in the ordinary course of moral learning, together with a drive to vindicate these ways of thinking, something of which people may be unaware. This drive to vindicate our ways of thinking is pervasive, and it is characteristic of rational agents. It explains our tendency to think well of those we love, for example, and to think ill of those with whom we are angry. It also explains a strong inclination to form beliefs that, if true, would seemingly vindicate our ways of thinking of normative properties. A result of this, I contend, is the intuition that normative naturalism cannot be true. Yet, as I further argue, the vindication process does not track the truth and the drive to vindicate our states of mind cannot be relied on as a guide to the metaphysics of normativity. (shrink)

According to a view going back to Plato, the aim of philosophy is to acquire knowledge and there is a method to acquire knowledge, namely a method of discovery. In the last century, however, this view has been completely abandoned, the attempt to give a rational account of discovery has been given up, and logic has been disconnected from discovery. This paper outlines a way of reconnecting logic with discovery.

In the past century the received view of definition in mathematics has been the stipulative conception, according to which a definition merely stipulates the meaning of a term in other terms which are supposed to be already well known. The stipulative conception has been so absolutely dominant and accepted as unproblematic that the nature of definition has not been much discussed, yet it is inadequate. This paper examines its shortcomings and proposes an alternative, the heuristic conception.

This paper identifies a tension in Frege’s philosophy and offers a diagnosis of its origins. Frege’s Context Principle can be used to dissolve the problem of propositional unity. However, Frege’s official response to the problem does not invoke the Context Principle, but the distinction between ‘saturated’ and ‘unsaturated’ propositional constituents. I argue that such a response involves assumptions that clash with the Context Principle. I suggest, however, that this tension is not generated by deep-seated philosophical commitments, but by Frege’s occasional (...) attempt to take a dubious shortcut in the justification of his conception of propositional structure. (shrink)

What makes certain definitions fruitful? And how can definitions play an explanatory role? The purpose of this paper is to examine these questions via an investigation of Frege’s treatment of definitions. Specifically, I pursue this issue via an examination of Frege’s views about the scientific unification of logic and arithmetic. In my view, what interpreters have failed to appreciate is that logicism is a project of unification, not reduction. For Frege, unification involves two separate steps: (1) an account of the (...) content expressed by arithmetical claims and (2) the justification of that content. The distinction between these steps allows us to see that there are two notions of definition at play in Frege’s logicist work, viz., one concerned with conceptual analysis, the other concerned with the construction of gap-free proof. I then use this discussion to explain how Frege employs his definitions to defend an epistemological thesis about arithmetic, and to clarify Grundlagen’s fruitfulness condition of definitions, and thereby address two interpretive puzzles from the recent literature. (shrink)

This essay examines Frege's reaction to Russell's Paradox and his views about the grounding of existence claims in mathematics. It is argued that Frege's strict requirements on existential proofs would rule out the attempt to ground arithmetic in. It is hoped that this discussion will help to clarify the ways in which Frege's position is both coherent and significantly different from the neo-logicist position on the issues of: what's required for proofs of existence; the connection between models, consistency, and existence; (...) and the prospects for a logical grounding of arithmetic in the wake of the paradox. (shrink)

Peter Geach famously holds that there is no such thing as absolute identity. There are rather, as Geach sees it, a variety of relative identity relations, each essentially connected with a particular monadic predicate. Though we can strictly and meaningfully say that an individual a is the same man as the individual b, or that a is the same statue as b, we cannot, on this view, strictly and meaningfully say that the individual a simply is b. It is difficult (...) to find anything like a persuasive argument for this doctrine in Geach's work. But one claim made by Geach is that his account of identity is the account most naturally aligned with Frege's widely admired treatment of cardinality. And though this claim of an affinity between Frege's and Geach's doctrines has been challenged, the challenge has been resisted. William Alston and Jonathan Bennett, indeed, go further than Geach to argue that Frege's doctrine implies Geach's. If Alston and Bennett are right, then those who favor a broadly Fregean treatment of cardinality have no choice but to adopt Geach's doctrine of relative identity. And because contemporary set-theoretic accounts of cardinality are essentially Fregean in all respects relevant to this issue (see §11 below), it follows from Alston and Bennett's claim that virtually every standard modern treatment of cardinality requires a 'relativized' treatment of identity. The purpose of this paper is to argue against the implication claimed by Alston and Bennett. Despite some superficial similarities between Frege's treatment of cardinality and Geach's treatment of identity, the two doctrines are fundamentally opposed. Frege's account of cardinality, and its set-theoretic descendants, are all inconsistent with the claim that identity is 'relative' in Geach's sense. (shrink)

After the publication of Begriffsschrift, a conflict erupted between Frege and Schröder regarding their respective logical systems which emerged around the Leibnizian notions of lingua characterica and calculus ratiocinator. Both of them claimed their own logic to be a better realisation of Leibniz’s ideal language and considered the rival system a mere calculus ratiocinator. Inspired by this polemic, van Heijenoort (1967b) distinguished two conceptions of logic—logic as language and logic as calculus—and presented them as opposing views, but did not explain (...) Frege’s and Schröder’s conceptions of the fulfilment of Leibniz’s scientific ideal. -/- In this paper I explain the reasons for Frege’s and Schröder’s mutual accusations of having created a mere calculus ratiocinator. On the one hand, Schröder’s construction of the algebra of relatives fits with a project for the reduction of any mathematical concept to the notion of relative. From this stance I argue that he deemed the formal system of Begriffsschrift incapable of such a reduction. On the other hand, first I argue that Frege took Boolean logic to be an abstract logical theory inadequate for the rendering of specific content; then I claim that the language of Begriffsschrift did not constitute a complete lingua characterica by itself, more being seen by Frege as a tool that could be applied to scientific disciplines. Accordingly, I argue that Frege’s project of constructing a lingua characterica was not tied to his later logicist programme. (shrink)

We propose a reconstruction of the constellation of problems and philosophical positions on the nature and number of the primitives of logic in four authors of the nineteenth century logical scene: Peano, Padoa, Frege and Peirce. We argue that the proposed reconstruction forces us to recognize that it is in at least four different senses that a notation can be said to be simpler than another, and we trace the origins of these four senses in the writings of these authors. (...) We conclude that Frege, and even more so Peirce, developed new notations not to make drawing logical conclusions easier but in order to answer the needs of logical analysis. (shrink)

In (1959), Carnap famously attacked Heidegger for having constructed an insane metaphysics based on a misconception of both the logical form and the semantics of ordinary language. In what follows, it will be argued that, once one appropriately (i.e., in a Russellian fashion) reads Heidegger’s famous sentence that should paradigmatically exemplify such a misconception, i.e., “the nothing nothings”, there is nothing either logically or semantically wrong with it. The real controversy as to how that sentence has to be evaluated—not as (...) to its meaning but as to its truth—lies at the metaphysico- ontological level. For in order for the sentence to be true one has to endorse an ontology of impossibilia and Leibniz’s principle of the identity of indiscernibles. (shrink)

There has been considerable recent debate about whether Kant's account of intuitions implies that their content is conceptual. This debate, however, has failed to make significant progress because of the absence of discussion, let alone consensus, as to the meaning of ‘content’ in this context. Here I try to move things forward by focusing on the kind of content associated with Frege's notion of ‘sense ’, understood as a mode of presentation of some object or property. I argue, first, that (...) Kant takes intuitions to have a content in this sense, and, secondly, that Kant clearly takes the content of intuitions, so understood, to be distinct in kind from that possessed by concepts. I then show how my account can respond to the most serious objections to previous non-conceptualist interpretations.Send article to KindleTo send this article to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle. Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply. Find out more about the Kindle Personal Document Service.The Non-Conceptuality of the Content of Intuitions: A New ApproachVolume 18, Issue 1Clinton Tolley DOI: https://doi.org/10.1017/S1369415412000313Your Kindle email address Please provide your Kindle [email protected]@kindle.com Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Dropbox To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Dropbox. The Non-Conceptuality of the Content of Intuitions: A New ApproachVolume 18, Issue 1Clinton Tolley DOI: https://doi.org/10.1017/S1369415412000313Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Google Drive To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Google Drive. The Non-Conceptuality of the Content of Intuitions: A New ApproachVolume 18, Issue 1Clinton Tolley DOI: https://doi.org/10.1017/S1369415412000313Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Export citation. (shrink)

This thesis comprises three main chapters—each comprising one relatively standalone paper. The unifying theme is fragmentalism about truth, which is the view that the predicate “true” either expresses distinct concepts or expresses distinct properties. -/- In Chapter 1, I provide a formal development of alethic pluralism. Pluralism is the view that there are distinct truth properties associated with distinct domains of subject matter, where a truth property satisfies certain truth-characterizing principles. On behalf of pluralists, I propose an account of logic (...) and semantics that shows how they can answer central conceptual and logical challenges for their view. -/- In Chapter 2, I motivate and develop a modal account of propositions on the basis of an iterative conception of propositions, where the modality is logico-mathematical. The modal account of propositions takes the conception to motivate an inherently potential hierarchy of propositions. I show that the account helps provide satisfying solutions to the intensional paradoxes of Russell-Myhill, Kaplan, and Prior. -/- In Chapter 3, I propose that “true” is polysemous. I suggest that “true” is initially polysemous between correspondence truth and disquotational truth, and further polysemous between the meanings corresponding to the subconcepts of the concept truth generated by the indefinite extensibility of that concept. I show that the proposal provides satisfying solutions to the semantic paradoxes. (shrink)

Frege's docent's dissertation Rechnungsmethoden, die sich auf eine Erweiterung des Grössenbegriffes gründen(1874) contains indications of a bold attempt to extend arithmetic. According to it, arithmetic means the science of magnitude, and magnitude must be understood structurally without intuitive support. The main thing is insight into the formal structure of the operation of ?addition?. It turns out that a general ?magnitude domain? coincides with a (commutative) group. This is an interesting connection with simultaneous developments in abstract algebra. As his main application, (...) Frege studies iterations of functions. He does not yet pose the question of existence proofs. Measurement of magnitudes is also connected to numbers, but the discussion is here ambiguous in a way which calls for the systematic account of numbers in Grundgesetze. (shrink)

I present an argument for an interpretation ofKant's views on the nature of the ‘content [Inhalt]’ of ‘cognition [Erkenntnis]’. In contrast to one of the longest standing interpretations ofKant's views on cognitive content, which ascribes toKant a straightforwardly psychologistic understanding of content, and in contrast as well to the more recently influential reading ofKant put forward byMcDowell and others, according to whichKant embraces a version ofRussellianism, I argue thatKant's views on this topic are of a much moreFregean bent than has (...) traditionally been admitted or appreciated. I conclude by providing a sketch of how a better grasp ofKant's views on cognitive content in general can help bring into sharper relief what is, and what is not, at stake in the recent debates over whether Kant accepts a particular kind of cognitive content—namely, non‐conceptual content. (shrink)

The Reference Principle states that co-referring expressions are everywhere intersubstitutable salva congruitate. On first glance, looks like a truism, but a truism with some bite: transforms difficult philosophical questions about co-reference into easy grammatical questions about substitutability. This has led a number of philosophers to think that we can use to make short work of certain longstanding metaphysical debates. For example, it has been suggested that all we need to do to show that the predicate ‘ is a horse’ does (...) not refer to a property is point out that ‘ is a horse’ and ‘the property of being a horse’ are not everywhere intersubstitutable salva congruitate. However, when we understand ‘substitution’ in the simplest and most straightforward way, is no truism; in fact, natural languages are full of counterexamples to the principle. In this paper, I introduce a new notion of substitution, and then develop and argue for a version of that is immune to these counterexamples. Along the way I touch on the following topics: the relation between argument forms and their natural language instances; the reification of sense; the difference between terms and predicates; and the relation between reference and disquotation. I end by arguing that my new version of cannot be used to settle metaphysical debates quite as easily as some philosophers would like. (shrink)

Beliefs have what I will call ‘propositional content’. A belief is always a belief that so-and-so: a belief that grass is green, or a belief that snow is white, or whatever. Other things have propositional content too, such as sentences, judgments and assertions. The Standard View amongst philosophers is that what it is to have a propositional content is to stand in an appropriate relation to a proposition. Moreover, on this view, propositions are objects, i.e. the kind of thing you (...) can refer to with singular terms. For example, on the Standard View, we should parse the sentence ‘Simon believes that Sharon is funny’ as: [Simon] believes [that Sharon is funny]; ‘Simon’ is a term referring to a thinking subject, ‘that Sharon is funny’ is a term referring to a proposition, and ‘x believes y’ is a dyadic predicate expressing the believing relation. In this paper, I argue against the Standard View. This is how I think we should parse ‘Simon believes that Sharon is funny’: [Simon] believes that [Sharon is funny]; here we have a singular term, ‘Simon’, a sentence ‘Sharon is funny’, and a ‘prenective’ joining them together, ‘x believes that p’. On this Prenective View, we do not get at the propositional content of someone’s belief by referring to a reified proposition with a singular term; we simply use the sentence ‘Sharon is funny’ to express that content for ourselves. I argue for the Prenective View in large part by showing that an initially attractive version of the Standard View is actually vulnerable to the same objection that Wittgenstein used against Russell’s multiple-relation theory of judgment. (shrink)

The issues surrounding the Caesar problem are assumed to be inert as far as ongoing mathematics is concerned. This paper aims to correct this impression by spelling out the ways that, in their historical context, Frege's remarks would have had considerable resonance with work that other mathematicians such as Riemann and Dedekind were doing. The search for presentation‐independent characterizations of objects and global definitions was seen as bound up with fundamental methodological questions in complex analysis and number theory.

Hans Herzberger as a philosopher and logician has shown deep interest both in the philosophy of Gottlob Frege, and in the topic of the inexpressible and the ineffable. In the fall of 1982, he taught at the University of Toronto, together with André Gombay, a course on Frege's metaphysics, philosophy of language, and foundations of arithmetic. Again, in the fall of 1986, he taught a seminar on the philosophy of language that dealt with 'the limits of discursive symbolism in several (...) domains of human experience.' The course description continues by saying: 'Special attention will be given to the paradoxes underlying various doctrines of the inexpressible and the tensions inherent in those paradoxes. Some doctrines of .. (shrink)