Onofri [Onofri, A. 2018. ‘The Publicity of Thought.’ Philosophical Quarterly 68 (272): 521–541.] proposes an individuation criterion for thoughts that purports to satisfy both shareability (the notion that different thinkers, or a single thinker at different times, can and generally do think type-identical thoughts) and Frege's constraint (according to which two thoughts are different if it is possible for a rational subject to endorse one while rejecting the other). I argue that his proposal fails to satisfy Frege's constraint. (...) Then I propose a modification to Onofri's proposal to fix the problem. (shrink)

Number words seemingly function both as adjectives attributing cardinality properties to collections, as in Frege’s ‘Jupiter has four moons’, and as names referring to numbers, as in Frege’s ‘The number of Jupiter’s moons is four’. This leads to what Thomas Hofweber calls Frege’s Other Puzzle: How can number words function as modifiers and as singular terms if neither adjectives nor names can serve multiple semantic functions? Whereas most philosophers deny that one of these uses is genuine, we instead argue that (...) number words, like many related expressions, are polymorphic, having multiple uses whose meanings are systematically related via type shifting. (shrink)

So-called 'Frege cases' pose a challenge for anyone who would hope to treat the contents of beliefs (and similar mental states) as Russellian propositions: It is then impossible to explain people's behavior in Frege cases without invoking non-intentional features of their mental states, and doing that seems to undermine the intentionality of psychological explanation. In the present paper, I develop this sort of objection in what seems to me to be its strongest form, but then offer a response to it. (...) I grant that psychological explanation must invoke non-intentional features of mental states, but it is of crucial importance which such features must be referenced. -/- It emerges from a careful reading of Frege's own view that we need only invoke what I call 'formal' relations between mental states. I then claim that referencing such 'formal' relations within psychological explanation does not undermine its intentionality in the way that invoking, say, neurological features would. The central worry about this view is that either (a) 'formal' relations bring narrow content in through back door or (b) 'formal' relations end up doing all the explanatory work. Various forms of each worry are discussed. The crucial point, ultimately, is that the present strategy for responding to Frege cases is not available either to the 'psycho-Fregean', who would identify the content of a belief with its truth-value, nor even to someone who would identify the content of a belief with a set of possible worlds. It requires the sort of rich semantic structure that is distinctive of Russellian propositions. There is therefore no reason to suppose that the invocation of 'formal' relations threatens to deprive content of any work to do. (shrink)

A presentation and discussion of Gottlob Frege's understanding of language, both natural and artificial, with close attention to his texts.

Frege's puzzle is a fundamental challenge for accounts of mental and linguistic representation. This piece surveys a family of recent approaches to the puzzle that posit representational relations. I identify the central commitments of relational approaches and present several arguments for them. I also distinguish two kinds of relationism—semantic relationism and formal relationism—corresponding to two conceptions of representational relations. I briefly discuss the consequences of relational approaches for foundational questions about propositional attitudes, intentional explanation, and compositionality.

It is often claimed that the theory of function levels proposed by Frege in Grundgesetze der Arithmetik anticipates the hierarchy of types that underlies Church’s simple theory of types. This claim roughly states that Frege presupposes a type of functions in the sense of simple type theory in the expository language of Grundgesetze. However, this view makes it hard to accommodate function names of two arguments and view functions as incomplete entities. I propose and defend an alternative interpretation of first-level (...) function names in Grundgesetze into simple type-theoretic open terms rather than into closed terms of a function type. This interpretation offers a still unhistorical but more faithful type-theoretic approximation of Frege’s theory of levels and can be naturally extended to accommodate second-level functions. It is made possible by two key observations that Frege’s Roman markers behave essentially like open terms and that Frege lacks a clear criterion for distinguishing between Roman markers and function names. (shrink)

I develop a new reading of Frege’s argument for the indefinability of truth. I concentrate on what Frege literally says in the passage that contains the argument. This literal reading of the passage establishes that the indefinability argument is an arguably sound argument to the following conclusion: provided that the Fregean conception of judgment—which has recently been countered by Hanks—is correct and that truth is a property of truth-bearers, a vicious infinite regress is produced. Given this vicious regress, Frege chooses (...) to reject that truth is a property of truth-bearers. Frege’s choice leads to a unique version of the Fregean conception of judgment. His unique conception of judgment can cope with Hanks’s recent criticisms against the Fregean conception. (shrink)

According to an influential variety of the representational view of perceptual experience—the singular content view—the contents of perceptual experiences include singular propositions partly composed of the particular physical object a given experience is about or of. The singular content view faces well-known difficulties accommodating hallucinations; I maintain that there is also an analogue of Frege's puzzle that poses a significant problem for this view. In fact, I believe that this puzzle presents difficulties for the theory that are unique to (...) perception in that strategies that have been developed to respond to Frege's puzzle in the case of belief cannot be employed successfully in the case of perception. Ultimately, I maintain that this perceptual analogue of Frege's puzzle provides a compelling reason to reject the singular content view of perceptual experience. (shrink)

Many philosophers have argued or taken for granted that Frege's puzzle has little or nothing to do with identity statements. I show that this is wrong, arguing that the puzzle can only be motivated relative to a thinker's beliefs about the identity or distinctness of the relevant object. The result is important, as it suggests that the puzzle can be solved, not by a semantic theory of names or referring expressions as such, but simply by a theory of identity (...) statements. To show this, I sketch a framework for developing solutions of this sort. I also consider how this result could be implemented by two influential solutions to Frege's puzzle, Perry's referential-reflexivism and Fine's semantic relationism. (shrink)

I trace changes to Frege's understanding of numbers, arguing in particular that the view of arithmetic based in geometry developed at the end of his life (1924–1925) was not as radical a deviation from his views during the logicist period as some have suggested. Indeed, by looking at his earlier views regarding the connection between numbers and second-level concepts, his understanding of extensions of concepts, and the changes to his views, firstly, in between Grundlagen and Grundgesetze, and, later, after (...) learning of Russell's paradox, this position is a natural position for him to have retreated to, when properly understood. (shrink)

There are two common reactions to Frege’s claim that some senses and thoughts are private. Privatists accept both private senses and thoughts, while intersubjectivists don’t accept either. Both sides agree on a pair of tacit assumptions: first, that private senses automatically give rise to private thoughts; and second, that private senses and thoughts are the most problematic entities to which Frege’s remarks on privacy give rise. The aim of this paper is to show that both assumptions are mistaken. This will (...) motivate a so far neglected, reconciliatory position between privatism and intersubjectivism according to which all thoughts are public while some senses are private. (shrink)

In a series of recent works, Kit Fine, 605–631, 2003, 2007) has sketched a novel solution to Frege’s puzzle. Radically departing from previous solutions, Fine argues that Frege’s puzzle forces us to reject compositionality. In this paper we first provide an explicit formalization of the relational semantics for first-order logic suggested, but only briefly sketched, by Fine. We then show why the relational semantics alone is technically inadequate, forcing Fine to enrich the syntax with a coordination schema. Given this enrichment, (...) we argue, that that the semantics is compositional. We then examine the deep consequences of this result for Fine’s proposed solution to Frege’s puzzle. We argue that Fine has mis-diagnosed his own solution–his attempted solution does not deny compositionality. The correct characterization of Fine’s solution fits him more comfortably among familiar solutions to the puzzle. (shrink)

The following essay reconsiders the ontological and logical issues around Frege’s Basic Law (V). If focuses less on Russell’s Paradox, as most treatments of Frege’s Grundgesetze der Arithmetik (GGA)1 do, but rather on the relation between Frege’s Basic Law (V) and Cantor’s Theorem (CT). So for the most part the inconsistency of Naïve Comprehension (in the context of standard Second Order Logic) will not concern us, but rather the ontological issues central to the conflict between (BLV) and (CT). These ontological (...) issues are interesting in their own right. And if and only if in case ontological considerations make a strong case for something like (BLV) we have to trouble us with inconsistency and paraconsistency. These ontological issues also lead to a renewed methodological reflection what to assume or recognize as an axiom. (shrink)

By drawing attention to these facts and to the relationship between Cantor’s and Husserl's ideas, I have tried to contribute to putting Frege's attack on Husserl "in the proper light" by providing some insight into some of the issues underling criticisms which Frege himself suggested were not purely aimed at Husserl's book. I have tried to undermine the popular idea that Frege's review of the Philosophy of Arithmetic is a straightforward, objective assessment of Husserl’s book, and to give (...) some specific reasons for thinking that the uncritical reading of Frege's review has unfairly distorted philosophers' perception of a work they do not know very well. (shrink)

_ Source: _Volume 95, Issue 3, pp 368 - 413 Frege famously maintained that concepts are not objects. A key argument of Frege’s for this view is, in outline, as follows: if we are to account for the unity of thought, concepts must be deemed _unsaturated_; since objects are, by contrast, saturated entities, concepts cannot be objects. The author investigates what can be made of this argument and, in particular, of the unsaturated/saturated distinction it invokes. Systematically exploring a range of (...) reconstructions suggested by Frege’s writings, and drawing on contemporary work, the author illustrates that no plausible reconstruction is forthcoming. In essence, it is altogether unclear how to simultaneously substantiate, on the one hand, the claim that unsaturated entities must be recognized in order to account for unity and, on the other, the claim that unsaturatedness is incompatible with objecthood. (shrink)

Gottlob Frege and Ludwig Wittgenstein (the later Wittgenstein) are often seen as polar opposites with respect to their fundamental philosophical outlooks: Frege as a paradigmatic "realist", Wittgenstein as a paradigmatic "anti-realist". This opposition is supposed to find its clearest expression with respect to mathematics: Frege is seen as the "arch-platonist", Wittgenstein as some sort of "radical anti-platonist". Furthermore, seeing them as such fits nicely with a widely shared view about their relation: the later Wittgenstein is supposed to have developed his (...) ideas in direct opposition to Frege. The purpose of this paper is to challenge these standard assumptions. I will argue that Frege's and Wittgenstein's basic outlooks have something crucial in common; and I will argue that this is the result of the positive influence Frege had on Wittgenstein. (shrink)

An investigation of Frege's various contributions to the study of language, focusing on three of his most famous doctrines: that concepts are unsaturated, that sentences refer to truth-values, and that sense must be distinguished from reference.

Why should one think Frege's definition of the ancestral correct? It can be proven to be extensionally correct, but the argument uses arithmetical induction, and that seems to undermine Frege's claim to have justified induction in purely logical terms. I discuss such circularity objections and then offer a new definition of the ancestral intended to be intensionally correct; its extensional correctness then follows without proof. This new definition can be proven equivalent to Frege's without any use of (...) arithmetical induction. This proves, without any use of arithmetical induction, that Frege's definition is extensionally correct and so answers the circularity objections. (shrink)

Why did Frege offer only proper names as examples of presupposition triggers? Some scholars claim that Frege simply did not care about the full range of presuppositional phenomena. This paper argues, in contrast, that he had good reasons for employing an extremely narrow notion of ‘Voraussetzung’. On Frege’s view, many devices that are now construed as presupposition triggers either express several thoughts at once or merely ‘illuminate’ a thought in a particular way. Fregean presuppositions, in contrast, are essentially tied to (...) names. (shrink)

This paper argues against the claim that Frege is committed to an infinite hierarchy of senses. Carnap and Kripke, along with many others, argue the contrary; I expose where all such arguments go astray. Invariably these arguments assume (without citation) that Frege holds that sense and reference are always distinct. This is the fulcrum upon which the hierarchy is hoisted. The counter to this assumption is based on two important but neglected passages. The locution ‘indirect sense’ has no ontological significance (...) for Frege. It was just a ‘short expression’ (his term) to indicate that the customary relation between sign, sense, and reference is suspended in what he called the exception case of indirect context. Once the hierarchy is abandoned, the alleged problem of just what indirect sense is, as well as questions as to why Frege said so little about it and why he did not examine iterative indirect contexts are resolved. Of course, with no hierarchy, Davidson’s “unlearnability argument” turns out to be a non-starter. Some objections to my interpretation are considered and answered. Additionally, comparisons to Dummett’s one-level view of sense, which is similar to mine are made, as well as to some two-level views (Parsons and Skiba). (shrink)

Frege's attempt to provide a foundation for the possibility of language and communication, like Kant's attempt to provide a foundation for the possibility of knowledge, fails to provide us with something absolute and foundational in a fixed sense. However, both these philosophers succeed in showing something about necessity that can be preserved independently of their absolutisms. Part III of this paper will provide reasons for accepting this thesis, while Parts I and II will provide an expository background on (...) class='Hi'>Frege's view in preparation for supporting the thesis. (shrink)

It is widely taken that the first-order part of Frege's Begriffsschrift is complete. However, there does not seem to have been a formal verification of this received claim. The general concern is that Frege's system is one axiom short in the first-order predicate calculus comparing to, by now, the standard first-order theory. Yet Frege has one extra inference rule in his system. Then the question is whether Frege's first-order calculus is still deductively sufficient as far as the (...) first-order completeness is concerned. In this short note we confirm that the missing axiom is derivable from his stated axioms and inference rules, and hence the logic system in the Begriffsschrift is indeed first-order complete. (shrink)

Gottlob Frege maintained that two name-containing identity sentences, represented schematically as a=a and a=b,can both be true in virtue of the same object’s self-identity but nonetheless, puzzlingly, differ in their epistemic profiles. Frege eventually resolved his puzzlement by locating the source of the purported epistemic difference between the identity sentences in a difference in the Sinne, or senses, expressed by the names that the sentences contain. -/- Thus, Frege portrayed himself as describing a puzzle that can be posed prior to (...) and independently of any particular theoretical position regarding names, and then resolving that puzzle with his theory of Sinn and Bedeutung. In this paper, I suggest that Frege’s presentation is problematic. If attempt is made to characterize the epistemic status of true identity sentences without appeal to Frege’s theoretical commitments, then what initially seemed puzzling largely dissolves. It turns out that, in order to generate puzzlement, Frege must invoke the theoretical account that he uses the puzzle to establish the purported necessity of. (shrink)

This paper explores the relationship between Hume's Prinicple and Basic Law V, investigating the question whether we really do need to suppose that, already in Die Grundlagen, Frege intended that HP should be justified by its derivation from Law V.

Frege claims that sentences of the form ‘A’ are equivalent to sentences of the form ‘it is true that A’ (The Equivalence Thesis). Frege also says that there are fictional names that fail to refer, and that sentences featuring fictional names fail to refer as a result. The thoughts such sentences express, Frege says, are also fictional, and neither true nor false. Michael Dummett argues that these claims are inconsistent. But his argument requires clarification, since there are two ways The (...) Equivalence Thesis has been formulated, according as the thesis equates the senses or the referents of the relevant sentences. -/- I have two aims in this paper. The first is to demonstrate that a sameness of sense thesis is inconsistent with Frege’s other theses. The second is to argue that a sameness of reference thesis is consistent with them. Thus, all else being equal, Frege ought to endorse a sameness of reference, rather than a sameness of sense thesis. (shrink)

Frege believes that the content of declarative sentences divides into a thought and its ‘colouring’, perhaps combined with assertoric force. He further thinks it is important to separate the thought from its colouring. To do this, a criterion which determines sameness of sense between sentences must be deployed. But Frege provides three criteria for this task, each of which adjudicate on different grounds. In this article, rather than expand on criticisms levelled at two of the criteria offered, the author focuses (...) on the most promising candidate. As it stands, this criterion has problems, but not insuperable ones. He suggests an adjusted criterion that relies on the epistemic notion of triviality. He recommends this criterion as both harmonious with Frege’s broader thought and preferable to alternatives offered. The moral is that Frege individuates thoughts by deploying an epistemic concept, and this is the only suitable way for him to do so. (shrink)

There is no doubt that social interaction plays an important role in language-learning, as well as in concept acquisition. In surprising contrast, social interaction makes only passing appearance in our most promising naturalistic theories of content. This is particularly true in the case of mental content (e.g., Cummins, 1996; Dretske, 1981, 1988; Fodor, 1987, 1990a; Millikan, 1984); and insofar as linguistic content derives from mental content (Grice, 1957), social interaction seems missing from our best naturalistic theories of both.1 In this (...) paper, I explore the ways in which even the most individualistic of theories of mental content can, and should, accommodate social effects. I focus especially on the way in which inferential relations, including those that are socially taught, influence language-learning and concept acquisition. I argue that these factors affect the way subjects conceive of mental and linguistic content. Such effects have a dark side: the social and inferential processes in question give rise to misleading intuitions about content itself. They create the illusion that content and inferential relations are more deeply intertwined than they actually are. This illusion confounds an otherwise attractive solution to what is known as ‘Frege’s puzzle’ (Salmon, 1986). I.. (shrink)

Frege discussed Mill’s empiricist ideas and Kant’s rationalist ideas about the nature of mathematics, and employed Set Theory and logico-philosophical notions to develop a new concept for the natural numbers. All this is objectively exposed by this paper.

I argue that Frege's so-called "concept 'horse' problem" is not one problem but many. When these different sub-problems are distinguished, some emerge as more tractable than others. I argue that, contrary to a widespread scholarly assumption originating with Peter Geach, there is scant evidence that Frege engaged with the general problem of the inexpressibility of logical category distinctions in writings available to Wittgenstein. In consequence, Geach is mistaken in his claim that in the Tractatus Wittgenstein simply accepts from Frege (...) certain lessons about the inexpressibility of logical category distinctions and the say-show distinction. In truth, Wittgenstein drew his own morals about these matters, quite possibly as the result of reflecting on how the general problem of the inexpressibility of logical category distinctions arises in Frege's writings , but also, quite possibly, by discerning certain glimmerings of these doctrines in the writings of Russell. (shrink)

I take issue with Glezakos’s explanation of why Frege’s puzzle is un-puzzling. On her view, Frege’s statement – how can sentences of the form a=a and a=b, if true, differ in cognitive value if they express the same semantic content/are made true by the same object’s self-identity? – should not be considered any puzzling either because it is on the whole circular, or because, neutrally stated, it cannot even be set up. I argue against this that if, as she takes (...) it, Frege’s statement is “problematic” it is not for the reasons she gives, but because it rests upon a couple of questionable assumptions: i) there is no ambiguity as to which aspect of the sign (in its relation to the referent) is relevant to a neutral statement of the puzzle ii) it is of the (sentence) forms themselves one may sensibly say they differ in cognitive value. (shrink)

The purpose of this paper is to reconstruct Frege’s argument against the relativity of truth contained in his posthumous writing Logic from 1897. Two points are made. The first is that the argument is a performative version of the common objection that truth relativism is incoherent: it is designed to show that the assertion of the relativity of truth involves a performative incoherence, because the absoluteness of truth is a success condition for making assertions. From a modern point of view, (...) the central premise of the argument, that the successful making of assertions depends on the absoluteness of truth, is highly doubtful. The second point is that this premise can be made plausible within the framework of Frege’s conception of truth and assertion: it can be derived from his thesis that, in order to put something forward as true, we do not need the word ‘true’, but only the assertoric force. (shrink)

The main objective of this paper is to examine how theories of truth and reference that are in a broad sense Fregean in character are threatened by antinomies; in particular by the Epimenides paradox and versions of the so-called Russell-Myhill antinomy, an intensional analogue of Russell’s more well-known paradox for extensions. Frege’s ontology of propositions and senses has recently received renewed interest in connection with minimalist theories that take propositions (thoughts) and senses (concepts) as the primary bearers of truth and (...) reference. In this paper, I will present a rigorous version of Frege’s theory of sense and denotation and show that it leads to antinomies. I am also going to discuss ways of modifying Frege’s semantical and ontological framework in order to avoid the paradoxes. In this connection, I explore the possibility of giving up the Fregean assumption of a universal domain of absolutely all objects, containing in addition to extensional objects also abstract intensional ones like propositions and singular concepts. I outline a cumulative hierarchy of Fregean propositions and senses, in analogy with Gödel’s hierarchy of constructible sets. In this hierarchy, there is no domain of all objects. Instead, every domain of objects is extendible with new objects that, on pain of contradiction, cannot belong to the given domain. According to this approach, there is no domain containing absolutely all propositions or absolutely all senses. (shrink)

Many scholars claim that Frege's theory of colouring is committed to a radical form of subjectivism or emotivism. Some other scholars claim that Frege's concept of colouring is a precursor to Grice's notion of conventional implicature. I argue that both of these claims are mistaken. Finally, I propose a taxonomy of Fregean colourings: for Frege, there are purely aesthetic colourings, communicative colourings or hints, non-communicative colourings.

This paper provides a new approach to a family of outstanding logical and semantical puzzles, the most famous being Frege's puzzle. The three main reductionist theories of propositions (the possible-worlds theory, the propositional-function theory, the propositional-complex theory) are shown to be vulnerable to Benacerraf-style problems, difficulties involving modality, and other problems. The nonreductionist algebraic theory avoids these problems and allows us to identify the elusive nondescriptive, non-metalinguistic, necessary propositions responsible for the indicated family of puzzles. The algebraic approach is (...) also used to defend antiexistentialism against existentialist prejudices. The paper closes with a suggestion about how this theory of content might enable us to give purely semantic (as opposed to pragmatic) solutions to the puzzles based on a novel formulation of the principle of compositionality. (shrink)

This paper discusses Frege's account of definition by induction in Grundgesetze and the two key theorems Frege proves using it.

Gottlob Frege (1848-1925) has been called ‘the undisputed father of analytic philosophy’ and ‘the most important logician since Aristotle.’ Even if his impact on philosophy were to extend no further than his decisive influence on leading early twentieth-century thinkers of the stature of Bertrand Russell, Ludwig Wittgenstein and Rudolf Carnap, that alone would assure him a notable place in the history of modern philosophy. Nevertheless, there are other areas of Frege’s intellectual activity that have largely escaped the attention of his (...) commentators. One of these is his seldom-noticed attempt late in life to write about political theology. In this reconstruction of Frege’s view, based on a context-sensitive close reading of his fragmentary writing on theology, I document Frege’s commitment to a highly politicized conception of theology’s public role. This conception is infused with the ideology of Germany’s Far-Right völkisch (pan-German ethnic-nationalist) movement and steeped in the political strife of early Weimar-era Germany. Frege’s interest in theology was evidently rooted not so much in conventionally spiritual concerns as in the decidedly innerweltlich desire to help turn the tide in German politics in favor of the ultranationalist Far Right. His theology was, accordingly, a political theology of völkisch, antisemitic, and anti-socialist nationalism. (shrink)

Frege's essay "Der Gedanke.Eine logische Untersuchung" was first published in the Beitrage zur Philosophie des Deutschen Idealismus for 1918-1919 and is one of three related logical studies published as a complete work by Gunther Patzig entitled Logische Untersuchungen in Gottingen, 1966 .

The ex ante Pareto principle has an intuitive pull, and it has been a principle of central importance since Harsanyi’s defence of utilitarianism. The principle has been used to criticize and refine a range of positions in welfare economics, including egalitarianism and prioritarianism. But this principle faces a serious problem. I have argued elsewhere :303-323 2017) that the concept of ex ante Pareto superiority is not well defined, because its application in a choice situation concerning a fixed population can depend (...) on how the members of that population are designated. I show in this paper that in almost all cases of policy choice, there will be numerous sets of rival designators for the same fixed population. I explore two ways that we might complete the definition of ex ante Pareto superiority. I call these the ‘supervaluationist’ reading and the ‘subvaluationist’ reading. I reject the subvaluationist reading as uncharitable, and argue that the supervaluationist reading is the most promising interpretation of the ex ante Pareto principle. I end by exploring some of the implications of this principle for prioritarianism and egalitarianism. (shrink)

It has been known for a few years that no more than Pi-1-1 comprehension is needed for the proof of "Frege's Theorem". One can at least imagine a view that would regard Pi-1-1 comprehension axioms as logical truths but deny that status to any that are more complex—a view that would, in particular, deny that full second-order logic deserves the name. Such a view would serve the purposes of neo-logicists. It is, in fact, no part of my view that, (...) say, Delta-3-1 comprehension axioms are not logical truths. What I am going to suggest, however, is that there is a special case to be made on behalf of Pi-1-1 comprehension. Making the case involves investigating extensions of first-order logic that do not rely upon the presence of second-order quantifiers. A formal system for so-called "ancestral logic" is developed, and it is then extended to yield what I call "Arché logic". (shrink)

It would be an understatement to say that Russell was interested in Cantorian diagonal paradoxes. His discovery of the various versions of Russell’s paradox—the classes version, the predicates version, the propositional functions version—had a lasting effect on his views in philosophical logic. Similar Cantorian paradoxes regarding propositions—such as that discussed in §500 of The Principles of Mathematics—were surely among the reasons Russell eventually abandoned his ontology of propositions.1 However, Russell’s reasons for abandoning what he called “denoting concepts”, and his rejection (...) of similar “semantic dualisms” such as Frege’s theory of sense and reference—at least in “On Denoting”—made no explicit mention of any Cantorian paradox. My aim in this paper is to argue that such paradoxes do pose a problem for certain theories such as Frege’s, and early Russell’s, about how definite descriptions are meaningful. My first aim is simply to lay out the problem I have in mind. Next, I shall turn to arguing that the theories of descriptions endorsed by Frege and by Russell prior to “On Denoting” are susceptible to the problem. Finally, I explore what responses a.. (shrink)

This paper describes both an exegetical puzzle that lies at the heart of Frege’s writings—how to reconcile his logicism with his definitions and claims about his definitions—and two interpretations that try to resolve that puzzle, what I call the “explicative interpretation” and the “analysis interpretation.” This paper defends the explicative interpretation primarily by criticizing the most careful and sophisticated defenses of the analysis interpretation, those given my Michael Dummett and Patricia Blanchette. Specifically, I argue that Frege’s text either are inconsistent (...) with the analysis interpretation or do not support it. I also defend the explicative interpretation from the recent charge that it cannot make sense of Frege’s logicism. While I do not provide the explicative interpretation’s full solution to the puzzle, I show that its main competitor is seriously problematic. (shrink)

In this paper we compare the propositional logic of Frege’s Grundgesetze der Arithmetik to modern propositional systems, and show that Frege does not have a separable propositional logic, definable in terms of primitives of Grundgesetze, that corresponds to modern formulations of the logic of “not”, “and”, “or”, and “if…then…”. Along the way we prove a number of novel results about the system of propositional logic found in Grundgesetze, and the broader system obtained by including identity. In particular, we show that (...) the propositional connectives that are definable in terms of Frege’s horizontal, negation, and conditional are exactly the connectives that fuse with the horizontal, and we show that the logical operators that are definable in terms of the horizontal, negation, the conditional, and identity are exactly the operators that are invariant with respect to permutations on the domain that leave the truth-values fixed. We conclude with some general observations regarding how Frege understood his logic, and how this understanding differs from modern views. (shrink)

On the background of explaining their different notions of analyticity, their different views on definitions, and some aspects of Frege’s notion of sense, three important Kantian strands that interweave into Frege’s view are exposed. First, Frege’s remarkable view that arithmetic, though analytic, contains truths that “extend our knowledge”, and by Kant’s use of the term, should be regarded synthetic. Secondly, that our arithmetical (and logical) knowledge depends on a sort of a capacity to recognize and identify objects, which are given (...) us in particular ways, constituting their senses (Sinne). Third, that there is a sense in which Frege’s view of definitions and explications gives new substance to Kant’s leading idea of analyticity, namely, the containment of a truth or a concept in another. In all these, Frege’s view does not endorse the Kantian strands as they are, but gives them special and sometimes quite sophisticated twists. (shrink)

Chalmers, responding to Braun, continues arguments from Chalmers for the conclusion that Bayesian considerations favor the Fregean in the debate over the objects of belief in Frege’s puzzle. This short paper gets to the heart of the disagreement over whether Bayesian considerations can tell us anything about Frege’s puzzle and answers, no, they cannot.

Saul Kripke's puzzle about belief demonstrates the lack of soundness of the traditional argument for the Fregean fundamental principle that the sentences 'S believes that a is F' and 'S believes that b is F' can differ in truth value even if a = b. This principle is a crucial premise in the traditional Fregean argument for the existence of semantically relevant senses, individuative elements of beliefs that are sensitive to our varying conceptions of what the beliefs are about. Joseph (...) Owens has offered a new argument for this fundamental principle, one that is not subject to Kripke's criticisms. I argue that even though Owens' argument avoids Kripke's criticisms, it has other flaws. (shrink)

A standard strategy for defending a claim of non-identity is one which invokes Leibniz’s Law. (1) Fa (2) ~Fb (3) (∀x)(∀y)(x=y ⊃ (∀P)(Px ⊃ Py)) (4) a=b ⊃ (Fa ⊃ Fb) (5) a≠b In Kalderon’s view, this basic strategy underlies both Moore’s Open Question Argument (OQA) as well as (a variant formulation of) Frege’s puzzle (FP). In the former case, the argument runs from the fact that some natural property—call it “F-ness”—has, but goodness lacks, the (2nd order) property of its (...) being an open question whether everything that instantiates it is good to the conclusion that goodness and F-ness are distinct. And in the latter case, the argument runs from the fact that that Hesperus has, but Phosphorus lacks, the property of being believed by the ancient astronomers to be visible in the evening sky to the conclusion that Hesperus and Phosphorus are distinct. Kalderon argues that both the OQA and FP fail because in neither case is there good reason to believe that both (1) and (2) are true. The reason we are tempted to believe that they are true is because we mistake de dicto claims for de re claims. In order for FP to go through, the truth of the following de re claims needs to be established: FP1) Hesperus was believed by the ancient astronomers to be visible in the evening sky. (shrink)

Commentators regularly attribute to Frege realist, idealist, and quietist responses to metaphysical questions concerning the abstract objects he calls ‘thoughts’. But despite decades of effort, the evidence offered on behalf of these attributions remains unconvincing. I argue that Frege deliberately avoids commitment to any of these positions, as part of a metaphysical separatist policy motivated by the fact that logic is epistemologically autonomous from metaphysics. Frege’s views and arguments prove relevant to current attempts to argue for epistemological autonomy, particularly that (...) of ethics. (shrink)

I critically discuss Dale Jacquette’s Frege: A Philosophical Biography. First, I provide a short overview of Jacquette’s book. Second, I evaluate Jacquette’s interpretation of Frege’s three major works, Begriffsschrift, Grundlagen der Arithmetik and Grundgesetze der Arithmetik; and conclude that the author does not faithfully represent their content. Finally, I offer some technical and general remarks.