This paper argues that Carnap both did not view and should not have viewed Frege's project in the foundations of mathematics as misguided metaphysics. The reason for this is that Frege's project was to give an explication of number in a very Carnapian sense — something that was not lost on Carnap. Furthermore, Frege gives pragmatic justification for the basic features of his system, especially where there are ontological considerations. It will be argued that even on the question of the (...) independent existence of abstract objects, Frege and Carnap held remarkably similar views. I close with a discussion of why, despite all this, Frege would not accept the principle of tolerance. (shrink)

Propositionalism is the view that intentional attitudes, such as belief, are relations to propositions. Propositionalists argue that propositionalism follows from the intuitive validity of certain kinds of inferences involving attitude reports. Jubien (2001) argues powerfully against propositions and sketches some interesting positive proposals, based on Russell’s multiple relation theory of judgment, about how to accommodate “propositional phenomena” without appeal to propositions. This paper argues that none of Jubien’s proposals succeeds in accommodating an important range of propositional phenomena, such as the (...) aforementioned validity of attitude-report inferences. It then shows that the notion of a predication act-type, which remains importantly Russellian in spirit, is sufficient to explain the range of propositional phenomena in question, in particular the validity of attitude-report inferences. The paper concludes with a discussion of whether predication act-types are really just propositions by another name. (shrink)

This paper argues that Frege is not the metaphysical platonist about mathematics that he is standardly taken to be. It is shown that Frege’s project has two distinct stages: the identification of what is true of our ordinary notions, and then the provision of a systematic account that shares the identified features. Neither of these stages involves much metaphysics. The paper criticizes in detail Dummett’s interpretation of §§55-61 of Grundlagen. These sections fall under the heading ‘Every number is a self-subsistent (...) object’ and are described by Dummett as containing the worst arguments put forward by Frege. It is argued that essentially all of Dummett’s interpretive points are mistaken. Finally, I show that Frege’s claims about the independence of mathematics from humans and their activities does not commit him to any particularly metaphysical position either. (shrink)

This paper is divided in five sections. Section 11.1 sketches the history of the distinction between speech act with negative content and negated speech act, and gives a general dynamic interpretation for negated speech act. “Downdate semantics” for AGM contraction is introduced in Section 11.2. Relying on semantically interpreted contraction, Section 11.3 develops the dynamic semantics for constative and directive speech acts, and their external negations. The expressive completeness for the formal variants of natural language utterances, none of which is (...) a retraction, has been proved in Section 11.4. The last section gives a laconic answer to the question posed in the title of the paper. (shrink)

This paper concerns Carnap’s early contributions to formal semantics in his work on general axiomatics between 1928 and 1936. Its main focus is on whether he held a variable domain conception of models. I argue that interpreting Carnap’s account in terms of a fixed domain approach fails to describe his premodern understanding of formal models. By drawing attention to the second part of Carnap’s unpublished manuscript Untersuchungen zur allgemeinen Axiomatik, an alternative interpretation of the notions ‘model’, ‘model extension’ and ‘submodel’ (...) in his theory of axiomatics is presented. Specifically, it is shown that Carnap’s early model theory is based on a convention to simulate domain variation that is not identical but logically comparable to the modern account. (shrink)

O presente manual tem como intenção constituir um guia para uma disciplina introdutória de filosofia da linguagem. Foi elaborado a partir da leccionação da disciplina de Filosofia da Linguagem I na Faculdade de Letras da Universidade do Porto desde 2001. A disciplina de Filosofia da Linguagem I ocupa um semestre lectivo e proporciona aos estudantes o primeiro contacto sistemático com a área da filosofia da linguagem. Pretende-se que este manual ofereça aos estudantes os instrumentos necessários não apenas para acompanhar uma (...) iniciação ao campo da filosofia da linguagem mas também para o estudo e a investigação autónomos posteriores. Para isso é percorrido um trajecto que conduz das intuições pré-teóricas acerca de linguagem, de que todos dispomos, até um conhecimento disciplinar específico, histórico e temático, da filosofia da linguagem. Em termos práticos, são considerados como precedentes da disciplina de Filosofia da Linguagem I – mesmo se, pelo existem actualmente precedências em sentido estrito – as disciplinas de Lógica I e II e de Filosofia do Conhecimento I e II. Os programas dessas disciplinas nos últimos anos estiveram presentes por trás da elaboração do manual. (shrink)

Are Fregean thoughts compositionally complex and composed of senses? We argue that, in Begriffsschrift, Frege took 'conceptual contents' to be unstructured, but that he quickly moved away from this position, holding just two years later that conceptual contents divide of themselves into 'function' and 'argument'. This second position is shown to be unstable, however, by Frege's famous substitution puzzle. For Frege, the crucial question the puzzle raises is why "The Morning Star is a planet" and "The Evening Star is a (...) planet" have different contents, but his second position predicts that they should have the same content. Frege's response to this antinomy is of course to distinguish sense from reference, but what has not previously been noticed is that this response also requires thoughts to be compositionally complex, composed of senses. That, however, raises the question just how thoughts are composed from senses. We reconstruct a Fregean answer, one that turns on an insistence that this question must be understood as semantic rather than metaphysical. It is not a question about the intrinsic nature of residents of the third realm but a question about how thoughts are expressed by sentences. (shrink)

Commonsense epistemology regards perceptual experience as a distinctive source of knowledge of the world around us, unavailable in ‘blindsight’. This is often interpreted in terms of the idea that perceptual experience, through its representational content, provides us with justifying reasons for beliefs about the world around us. I argue that this analysis distorts the explanatory link between perceptual experience and knowledge, as we ordinarily conceive it. I propose an alternative analysis, on which representational content plays no explanatory role: we make (...) perceptual knowledge intelligible by appeal to experienced objects and features. I also present an account of how the commonsense scheme, thus interpreted, is to be defended: not by tracing the role of experience to its contribution in meeting some general condition on propositional knowledge (such as justification), but by subverting the assumption that it has to be possible to make the role of experience intelligible in terms of some such contribution. (shrink)

In this article I contrast in two ways those conceptions of semantic theory deriving from Richard Montague's Intensional Logic (IL) and later developments with conceptions that stick pretty closely to a far weaker semantic apparatus for human first languages. IL is a higher-order language incorporating the simple theory of types. As such, it endows predicates with a reference. Its intensional features yield a conception of propositional identity (namely necessary equivalence) that has seemed to many to be too coarse to be (...) acceptable. In the most usual expositions, it takes the object of linguistic explication to be the sentence in a context, as in Kaplan, 1977. This last has led to recent speculations about 'shifted' contexts. IL may be contrasted with a more linguistically (representationally) bound conception of propositions and interpretation of their predicational and functional parts, and with the explication, not of sentences in contexts, but of potential utterances, relative to the antecedent referential intentions of their speakers. We may then advance, as an empirical hypothesis about all human languages, that contexts never shift, and propose that apparent counterexamples stem from the misconstrual of linguistically coded anaphoric relations, relations that are wanted independently anyway. Donald Davidson's posthumous volume Truth and Predication mounts a sustained criticism of the notion of predicate reference. This criticism is not decisive. However, it may put the ball in the other court, insofar as it asks for a justification of what IL takes as given. Elaborations of IL using structured propositions, recently defended in King, 2007, recognize the problem of predicate reference, and the correlative issue of the 'unity of the proposition'; but I do not see that they can do better than bite the bullet already bitten in IL. I agree with Frege's insight that full justification of predicate reference pushes the boundaries of natural language, and to that extent may not be found within the semantic (as opposed to general scientific) enterprise. (shrink)

Frege's theory of indirect contexts and the shift of sense and reference in these contexts has puzzled many. What can the hierarchy of indirect senses, doubly indirect senses, and so on, be? Donald Davidson gave a well-known 'unlearnability' argument against Frege's theory. The present paper argues that the key to Frege's theory lies in the fact that whenever a reference is specified (even though many senses determine a single reference), it is specified in a particular way, so that giving a (...) reference implies giving a sense; and that one must be 'acquainted' with the sense. It is argued that an indirect sense must be 'immediately revelatory' of its reference. General principles for Frege's doctrine of sense and reference are sated, for both direct and indirect quotation, to be understood iteratively. I also discuss Frege's doctrine of tensed and first person statements in the light of my analysis. The views of various other authors are examined. The conclusion is to ascribe to Frege an implicit doctrine of acquaintance similar to that of Russell. (shrink)

Positivism, in its standard outlook, is normative contextualism: If legal reasons are content-independent, then their content may vary with the context or point of view. Despite several advantages vis-à-vis strong metaphysical conceptions of reasons, contextualism implies relativism, which may lead further to the fragmentation of the point of view of agency. In his Oxford Hart Lecture, Coleman put forward a fresh account of the moral semantics of legal content, one that lays claim to preserving the unity of agency while retaining (...) the social facts thesis, which has been a key intuition of positivism. The present essay identifies potential weaknesses with this account and proposes a reconstruction along rationalist lines: First, it advances a descriptive account of reflective agency that is delivered in terms of a modest conceptual analysis; secondly, this is combined with a context-sensitive or "buck-passing" account of value, which illustrates that substantive reasons for action must be anchored, ontologically speaking, to particular social practices (Social Dependency Thesis). In the end the unity of agency comes at an affordable price, for it is no longer necessary to resort to metaphysical necessity and the most demanding conditions this imposes, in order to defend it. (shrink)

Is linguistic understanding a form of knowledge? I clarify the question and then consider two natural forms a positive answer might take. I argue that, although some recent arguments fail to decide the issue, neither positive answer should be accepted. The aim is not yet to foreclose on the view that linguistic understanding is a form of knowledge, but to develop desiderata on a satisfactory successor to the two natural views rejected here.

This dissertation is about the structure of thought. Following Gottlob Frege, I define a thought as the sort of content relevant to determining whether an assertion is true or false. The historical component of the dissertation involves interpreting Frege’s actual views on the structure of thought. I argue that Frege did not think that a thought has a unique decomposition into its component senses, but rather the same thought can be decomposed into senses in a variety of distinct ways. I (...) extend Frege’s position and use it to develop an account of the hierarchy of senses, the senses expressed by indexicals and demonstratives, and the distinction between logical and non-logical structure. I also discuss various connections with the nature of meta-representation, our capacity for reflective judgment, some aspects of the structure of conscious experience, the way we perceive regions of space and durations of time, and our conscious awareness of our own perceptions and events of thinking. (shrink)

What is the relationship between the world and logic, between intuition and language, between objects and their quantitative determinations? Rationalists, on the one hand, hold that the world is structured in a rational way. Representationalists, on the other hand, assume that language, logic, and mathematics are only the means to order and describe the intuitively given world. In World and Logic, Jens Lemanski takes up three surprising arguments from Arthur Schopenhauer’s hitherto undiscovered Berlin Lectures, which concern the philosophy of language, (...) logic, and mathematics. Based on these arguments, Lemanski develops a new position entitled ‘rational representationalism’: the world is always structured by human beings according to linguistic, logical, and mathematical principles, but the basic vocabulary of these structural descriptions already contains metaphors taken from the world around us. (shrink)

Alonzo Church (1903–1995) was a renowned mathematical logician, philosophical logician, philosopher, teacher and editor. He was one of the founders of the discipline of mathematical logic as it developed after Cantor, Frege and Russell. He was also one of the principal founders of the Association for Symbolic Logic and the Journal of Symbolic Logic. The list of his students, mathematical and philosophical, is striking as it contains the names of renowned logicians and philosophers. In this article, we focus primarily on (...) Church’s philosophical contributions. (For an account of his life and academic history see the Introduction to The Collected Works of Alonzo Church (2019).) However, we also discuss his mathematical results when it is desirable to do so in order to pursue a philosophical issue. (shrink)

In this paper, I argue that an adequate meta-semantic framework capable of accommodating the range of projects currently identified as projects in conceptual engineering must be sensitive to the fact that concepts (and hence projects relating to them) fall into distinct kinds. Concepts can vary, I will argue, with respect to their direction of determination, their modal range, and their temporal range. Acknowledging such variations yields a preliminary taxonomy of concepts and generates a meta-semantic framework that allows us both to (...) accommodate the full range of cases and to identify a proper subset of concepts for special ameliorative consideration. Ignoring such variations, in contrast, leads to a restricted meta-semantic framework that accommodates only a subset of the particular projects while generating implausible accounts of others. (shrink)

Frege's conception of the logical categories has vexed commentators for decades. In this dissertation, I argue that it revolves around two forms of internality. The first is the internality of its use in the expression of judgment to the sign. A proper understanding of that internality reveals how Frege's philosophical logic cannot be fit into the framework given by the contemporary syntax/semantics distinction. The second is the internality that obtains between the way in which Begriffsschrift signs stratify into different categories, (...) on the one hand, and the way in which the realm of Bedeutungen stratifies into logical categories, on the other hand. A proper understanding of this internality reveals how Frege's conception of the relation between language and the world is neither a form of realism nor a form of linguistic idealism. To come to understand Frege's conception of the logical categories, is to come to understand both these forms of internality by coming to understand how they hang together. (shrink)

On a now orthodox view, humans and many other animals possess a “number sense,” or approximate number system, that represents number. Recently, this orthodox view has been subject to numerous critiques that question whether the ANS genuinely represents number. We distinguish three lines of critique – the arguments from congruency, confounds, and imprecision – and show that none succeed. We then provide positive reasons to think that the ANS genuinely represents numbers, and not just non-numerical confounds or exotic substitutes for (...) number, such as “numerosities” or “quanticals,” as critics propose. In so doing, we raise a neglected question: numbers of what kind? Proponents of the orthodox view have been remarkably coy on this issue. But this is unsatisfactory since the predictions of the orthodox view, including the situations in which the ANS is expected to succeed or fail, turn on the kind of number being represented. In response, we propose that the ANS represents not only natural numbers, but also non-natural rational numbers. It does not represent irrational numbers, however, and thereby fails to represent the real numbers more generally. This distances our proposal from existing conjectures, refines our understanding of the ANS, and paves the way for future research. (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)

Conceptual engineering is to be explained by appeal to the externalist distinction between concepts and conceptions. If concepts are determined by non-conceptual relations to objective properties rather than by associated conceptions (whether individual or communal), then topic preservation through semantic change will be possible. The requisite level of objectivity is guaranteed by the possibility of collective error and does not depend on a stronger level of objectivity, such as mind-independence or independence from linguistic or social practice more generally. This means (...) that the requisite level of objectivity is exhibited not only by natural kinds, but also by a wide range of philosophical kinds, social kinds and artefactual kinds. The alternative externalist accounts of conceptual engineering offered by Herman Cappelen and Derek Ball fall back into a kind of descriptivism which is antithetical to externalism and fails to recognise this basic level of objectivity. (shrink)

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)

Intellectualists about knowledge how argue that knowing how to do something is knowing the content of a proposition (i.e, a fact). An important component of this view is the idea that propositional knowledge is translated into behavior when it is presented to the mind in a peculiarly practical way. Until recently, however, intellectualists have not said much about what it means for propositional knowledge to be entertained under thought's practical guise. Carlotta Pavese fills this gap in the intellectualist view by (...) modeling practical modes of thought after Fregean senses. In this paper, I take up her model and the presuppositions it is built upon, arguing that her view of practical thought is not positioned to account for much of what human agents are able to do. (shrink)

This paper aims to provide hyperintensional foundations for mathematical platonism. I examine Hale and Wright's (2009) objections to the merits and need, in the defense of mathematical platonism and its epistemology, of the thesis of Necessitism. In response to Hale and Wright's objections to the role of epistemic and metaphysical modalities in providing justification for both the truth of abstraction principles and the success of mathematical predicate reference, I examine the Necessitist commitments of the abundant conception of properties endorsed by (...) Hale and Wright and examined in Hale (2013), and demonstrate how a two-dimensional approach to the epistemology of mathematics is consistent with Hale and Wright's notion of there being non-evidential epistemic entitlement rationally to trust that abstraction principles are true. A choice point that I flag is that between availing of intensional or hyperintensional semantics. The hyperintensional semantic approach that I advance is a topic-sensitive epistemic two-dimensional truthmaker semantics. I countenance a hyperintensional semantics for novel epistemic abstractionist modalities. I suggest that observational type theory can be applied to first-order abstraction principles in order to make abstraction principles recursively enumerable. Epistemic and metaphysical states and possibilities may thus be shown to play a constitutive role in vindicating the reality of mathematical objects and truth, and in providing a conceivability-based route to the truth of abstraction principles as well as other axioms and propositions in mathematics. (shrink)

According to Frege, we need a criterion for recognising when different sentences express the same thought to make progress in logic. He himself hedged his own equipollence criterion with a number of provisos. In the literature on Frege, little attention has been paid to the problems these provisos raise. In this paper, I will argue that Fregeans have ignored these provisos at their peril. For without these provisos, Frege’s criterion yields wrong results; but with the provisos in place, it is (...) of no use for Frege’s purposes. This is connected to what Frege took to be the ‘greatest difficulty for philosophy’: natural language sentences don’t just express thoughts; they convey evaluations and communicative hints. Because of this, Frege’s recognition criterion for thoughts cannot be applied to them and we cannot make logical progress by ‘recognising a thought in different linguistic guises’. (shrink)

This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. David Elohim examines the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, undecidable (...) propositions, and abstraction principles in the philosophy of mathematics; to the modal and hyperintensional profiles of the logic of rational intuition; and to the types of intention, when the latter is interpreted as a hyperintensional mental state. Chapter \textbf{2} argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal and hyperintensional cognitivism and modal and hyperintensional expressivism. Elohim develops a novel, topic-sensitive truthmaker semantics for dynamic epistemic logic, and develops a novel, dynamic two-dimensional semantics grounded in two-dimensional hyperintensional Turing machines. Chapter \textbf{3} provides an abstraction principle for epistemic (hyper-)intensions. Chapter \textbf{4} advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter \textbf{5} applies the fixed points of the modal $\mu$-calculus in order to account for the iteration of epistemic states in a single agent, by contrast to availing of modal axiom 4 (i.e. the KK principle). The fixed point operators in the modal $\mu$-calculus are rendered hyperintensional, which yields the first hyperintensional construal of the modal $\mu$-calculus in the literature and the first application of the calculus to the iteration of epistemic states in a single agent instead of the common knowledge of a group of agents. Chapter \textbf{6} advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter \textbf{7} provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapters \textbf{2} and \textbf{4} is availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. -/- Chapters \textbf{8-12} provide cases demonstrating how the two-dimensional hyperintensions of hyperintensional, i.e. topic-sensitive epistemic two-dimensional truthmaker, semantics, solve the access problem in the epistemology of mathematics. Chapter \textbf{8} examines the interaction between Elohim's hyperintensional semantics and the axioms of epistemic set theory, large cardinal axioms, the Epistemic Church-Turing Thesis, the modal axioms governing the modal profile of $\Omega$-logic, Orey sentences such as the Generalized Continuum Hypothesis, and absolute decidability. These results yield inter alia the first hyperintensional Epistemic Church-Turing Thesis and hyperintensional epistemic set theories in the literature. Chapter \textbf{9} examines the modal and hyperintensional commitments of abstractionism, in particular necessitism, and epistemic hyperintensionality, epistemic utility theory, and the epistemology of abstraction. Elohim countenances a hyperintensional semantics for novel epistemic abstractionist modalities. Elohim suggests, too, that higher observational type theory can be applied to first-order abstraction principles in order to make first-order abstraction principles recursively enumerable, i.e. Turing machine computable, and that the truth of the first-order abstraction principle for two-dimensional hyperintensions is grounded in its being possibly recursively enumerable and the machine being physically implementable. Chapter \textbf{10} examines the philosophical significance of hyperintensional $\Omega$-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter \textbf{11} provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter \textbf{12} avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of hyperintensional epistemic two-dimensional semantics in order to account for the interaction between interpretational and objective modalities and the truthmakers thereof. This yields the first hyperintensional category theory in the literature. Elohim invents a new mathematical trick in which first-order structures are treated as categories, and Vopenka's principle can be satisfied because of the elementary embeddings between the categories and generate Vopenka cardinals in the category of Set in category theory. Chapter \textbf{13} examines modal responses to the alethic paradoxes. Elohim provides a counter-example to epistemic closure for logical deduction. Chapter \textbf{14} examines, finally, the modal and hyperintensional semantics for the different types of intention and the relation of the latter to evidential decision theory. (shrink)

This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. David Elohim examines the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, undecidable (...) propositions, and abstraction principles in the philosophy of mathematics; to the modal and hyperintensional profiles of the logic of rational intuition; and to the types of intention, when the latter is interpreted as a hyperintensional mental state. Chapter \textbf{2} argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal and hyperintensional cognitivism and modal and hyperintensional expressivism. Elohim develops a novel, topic-sensitive truthmaker semantics for dynamic epistemic logic, and develops a novel, dynamic two-dimensional semantics grounded in two-dimensional hyperintensional Turing machines. Chapter \textbf{3} provides an abstraction principle for epistemic (hyper-)intensions. Chapter \textbf{4} advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter \textbf{5} applies the fixed points of the modal $\mu$-calculus in order to account for the iteration of epistemic states in a single agent, by contrast to availing of modal axiom 4 (i.e. the KK principle). The fixed point operators in the modal $\mu$-calculus are rendered hyperintensional, which yields the first hyperintensional construal of the modal $\mu$-calculus in the literature and the first application of the calculus to the iteration of epistemic states in a single agent instead of the common knowledge of a group of agents. Chapter \textbf{6} advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter \textbf{7} provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapters \textbf{2} and \textbf{4} is availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. -/- Chapters \textbf{8-12} provide cases demonstrating how the two-dimensional hyperintensions of hyperintensional, i.e. topic-sensitive epistemic two-dimensional truthmaker, semantics, solve the access problem in the epistemology of mathematics. Chapter \textbf{8} examines the interaction between Elohim's hyperintensional semantics and the axioms of epistemic set theory, large cardinal axioms, the Epistemic Church-Turing Thesis, the modal axioms governing the modal profile of $\Omega$-logic, Orey sentences such as the Generalized Continuum Hypothesis, and absolute decidability. These results yield inter alia the first hyperintensional Epistemic Church-Turing Thesis and hyperintensional epistemic set theories in the literature. Chapter \textbf{9} examines the modal and hyperintensional commitments of abstractionism, in particular necessitism, and epistemic hyperintensionality, epistemic utility theory, and the epistemology of abstraction. Elohim countenances a hyperintensional semantics for novel epistemic abstractionist modalities. Elohim suggests, too, that higher observational type theory can be applied to first-order abstraction principles in order to make first-order abstraction principles recursively enumerable, i.e. Turing machine computable, and that the truth of the first-order abstraction principle for two-dimensional hyperintensions is grounded in its being possibly recursively enumerable and the machine being physically implementable. Chapter \textbf{10} examines the philosophical significance of hyperintensional $\Omega$-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter \textbf{11} provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter \textbf{12} avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of hyperintensional epistemic two-dimensional semantics in order to account for the interaction between interpretational and objective modalities and the truthmakers thereof. This yields the first hyperintensional category theory in the literature. Elohim invents a new mathematical trick in which first-order structures are treated as categories, and Vopenka's principle can be satisfied because of the elementary embeddings between the categories and generate Vopenka cardinals in the category of Set in category theory. Chapter \textbf{13} examines modal responses to the alethic paradoxes. Elohim provides a counter-example to epistemic closure for logical deduction. Chapter \textbf{14} examines, finally, the modal and hyperintensional semantics for the different types of intention and the relation of the latter to evidential decision theory. (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.

What is the cognitive value of the concept of truth? What epistemic difference does the concept of truth make to those who grasp it? This paper employs a new perspective for thinking about the concept of truth and recent debates concerning it, organized around the question of the cognitive value of the concept of truth. The paper aims to defend a substantively correct and dialectically optimal account of the cognitive value of the concept of truth. This perspective is employed in (...) understanding the critical discussion around what Hartry Field has called “the incorporation model” for extending a deflationary view of truth to foreign sentences. Field's original intentions in discussing the incorporation model were to defend the deflationary view from some counterintuitive consequences concerning the understanding of truth attributions to foreign sentences. However, more recently, philosophers unencumbered by deflationary commitments have taken over the incorporation model for their own inflationary purposes. In particular, and in my terms, these philosophers can be understood as making what I argue is the ultimately too radical suggestion that the cognitive value of the concept of truth is to allow the incorporation not only of the linguistically foreign, but also of the conceptually alien. I clarify this dialectic en route to explaining and arguing for the cognitive inflationary view, according to which the cognitive value of the concept of truth is is to make possible the proprietary kind and quality of knowledge allowed by reflective clarity over the concepts and thoughts that one already has. (shrink)

The paper challenges a widely held interpretation of Frege's conception of logic on which the constituent clauses of basic law V have the same sense. I argue against this interpretation by first carefully looking at the development of Frege's thoughts in Grundlagen with respect to the status of abstraction principles. In doing so, I put forth a new interpretation of Grundlagen §64 and Frege's idea of ‘recarving of content’. I then argue that there is strong evidence in Grundgesetze that Frege (...) did not hold the relevant sense-identity claim regarding basic law V. (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)

According to Frege, expressions shift their reference when they occur in indirect contexts: in “Anna believes that Plato is wise” the expression “Plato” no longer refers to Plato but to what is ordinarily its sense. Many philosophers, including Carnap, Davidson, Burge, Parsons, Kripke and Künne, believe that on Frege's view the iteration of indirect context creating operators gives rise to an infinite hierarchy of senses. While the former two take this to be problematic, the latter four welcome the hierarchy with (...) open arms. In this paper I argue that the hierarchy should be avoided and that it can be avoided. (shrink)

That there are analytic truths may challenge a principle of the homogeneity of truth. Unlike standard conceptions, in which analyticity is couched in terms of "truth in virtue of meanings", Frege's notions of analytic and a priori concern justification, respecting a principle of the homogeneity of truth. Where there is no justification these notions do not apply, Frege insists. Basic truths and axioms may be analytic (or a priori), though unprovable, which means there is a form of justification which is (...) not (deductive) proof. This is also required for regarding singular factual propositions as a posteriori. A Fregean direction for explicating this wider notion of justification is suggested in terms of his notion of sense (Sinn)—modes in which what the axioms are about are given—and its general epistemological significance is sketched. (shrink)

The Linda paradox is a key topic in current debates on the rationality of human reasoning and its limitations. We present a novel analysis of this paradox, based on the notion of verisimilitude as studied in the philosophy of science. The comparison with an alternative analysis based on probabilistic confirmation suggests how to overcome some problems of our account by introducing an adequately defined notion of verisimilitudinarian confirmation.

Mates’s Puzzle has flown below many philosophers’ radar, despite its relations to both Frege’s Puzzle and the Paradox of Analysis. We explain the relations amongst these puzzles on the way to arguing that Mates’s Puzzle suggests a generalization of Frege’s Puzzle, and of the sense-reference distinction itself, in the form of hierarchy of senses. We explain how Mates’s Puzzle and the hierarchy, to different degrees, illuminate each other, and how their connection is missed in the literature. However, we argue that (...) the potential of Mates’s Puzzle to illuminate the hierarchy is yet to be fully actualised. We suggest that in order to do better, we need to formulate Mates’s Puzzle as a puzzle in the philosophy of thought and not as puzzle in the philosophy of language. What is needed, to which the present paper is a precursor, is an account of the cognitive significance of higher-order senses. (shrink)

In 1893 and 1903, two volumes of the most important of Frege’s works Grundegezte der Arithmetik were published. This period can be called the peak of Frege’s logicism. Although the subject of truth in Frege’s logical and philosophical works has been repeatedly investigated, there is a lack of studies on his view in this period, especially in Polish literature. In this article, therefore, I carry out the following research task: to collect and order Frege’s statements about truth during the period (...) of publishing the two volumes of Grundegezte der Arithmetik. I refer to the texts published during Frege’s life, published posthumously and his correspondence. Particularly noteworthy are: Grundegezte der Arithmetik and the unpublished Logik. That is why there are two separate sections dedicated to these two texts, whereas the discussions of truth from other texts are grouped thematically: the problem of antinomy, geometry, expression of generality, and others. The subject of truth appears there in relation to logic, philosophy of language, philosophy of logic, philosophy of mathematics and ontology. (shrink)

W latach 1893 i 1903 ukazały się dwa tomy najważniejszego dzieła Fregego Grundegezte der Arithmetik. Ten okres można nazwać „szczytem logicyzmu” Fregego. Chociaż temat prawdy w logiczno-filozoficznej twórczości Fregego był podejmowany wielokrotnie, to brakuje pozycji skupiającej się na badaniu poglądów w tym okresie. Dotyczy to w szczególności literatury polskiej. Moim zadaniem jest zebranie i uporządkowanie wszystkich wypowiedzi Fregego na temat prawdy w okresie wydawania wspomnianych tomów. Realizując to zadanie, badam użycie tego pojęcia w pierwszym tomie Grundegezte der Arithmetik oraz w (...) niepublikowanym tekście Logik. Podejmuję zagadnienie funkcjonowania tego terminu w szczególnych kontekstach: antynomii, geometrii i wyrażania ogólności. Na koniec zasygnalizuję kwestię sposobu rozumienia późniejszych wypowiedzi Fregego na temat prawdy. (shrink)

After presenting Kripke’s criticism to Frege’s ideas on context dependence of thoughts, I present two recent attempts of considering cognitive aspects of context dependent expressions inside a truth conditional pragmatics or semantics: Recanati’s non-descriptive modes of presentation (MOPs) and Kaplan’s ways of having in mind (WHIMs). After analysing the two attempts and verifying which answers they should give to the problem discussed by Kripke, I suggest a possible interpretation of these attempts: to insert a procedural or algorithmic level in semantic (...) representations of indexicals. That a function may be computed by different procedures might suggest new possibilities of integrating contextual cognitive aspects in model theoretic semantic. (shrink)

At the beginning of Die Grundlagen der Arithmetik [1884], Frege observes that “it is in the nature of mathematics to prefer proof, where proof is possible”. This, of course, is true, but thinkers differ on why it is that mathematicians prefer proof. And what of propositions for which no proof is possible? What of axioms? This talk explores various notions of self-evidence, and the role they play in various foundational systems, notably those of Frege and Zermelo. I argue that both (...) programs are undermined at a crucial point, namely when self-evidence is supported by holistic and even pragmatic considerations. (shrink)

This paper has a two-fold objective: to provide a balanced, multi-faceted account of the origins of logicism; to rehabilitate Richard Dedekind as a main logicist. Logicism should be seen as more deeply rooted in the development of modern mathematics than typically assumed, and this becomes evident by reconsidering Dedekind's writings in relation to Frege's. Especially in its Dedekindian and Fregean versions, logicism constitutes the culmination of the rise of ?pure mathematics? in the nineteenth century; and this rise brought with it (...) an inter-weaving of methodological and epistemological considerations. The latter aspect illustrates how philosophical concerns can grow out of mathematical practice, as opposed to being imposed on it from outside. It also sheds new light on the legacy and the lasting significance of logicism today. (shrink)

In a famous passage (A68/B93), Kant writes that “the understanding can make no other use of […] concepts than that of judging by means of them.” Kant's thought is often called the thesis of the priority of judgments over concepts. We find a similar sounding priority thesis in Frege: “it is one of the most important differences between my mode of interpretation and the Boolean mode […] that I do not proceed from concepts, but from judgments.” Many interpreters have thought (...) that Frege's priority principle is close to (or at least derivable from) Kant's. I argue that it is not. Nevertheless, there was a gradual historical development that began with Kant's priority thesis and culminated in Frege's new logic. (shrink)

A strong, strictly virtue- based , and at the same time truth-centered framework for virtue epistemology (VE) is proposed that bases VE upon a clearly motivating epistemic virtue, inquisitiveness or curiosity in a very wide sense, characterizes the purely executive capacities-virtues as a means for the truth-goal set by the former, and, finally, situates the remaining, partly motivating and partly executive virtues in relation to this central stock of virtues. Character-trait epistemic virtues are presented as hybrids, partly moral, partly purely (...) epistemic. In order to make the approach virtue- based , it is argued that the central virtue (inquisitiveness or curiosity) is responsible for the value of truth: truth is valuable to cognizers because they are inquisitive, and most other virtues are a means for satisfying inquisitiveness. On can usefully combine this virtue-based account of the motivation for acquiring knowledge with a Sosa-style analysis of the concept “knowledge”, which brings to the forefront virtues-capacities, in order to obtain a full-blooded, “strong” VE. (shrink)

Translated from: W.V.O.Quine, W. H. O. (1986): Philosophy of Logic. Second Edition. Harvard University Press. Cambridge, Massachusetts and London, England, 47-61.