The aim of this paper is to discuss the “Austro-American” logical empiricism proposed by physicist and philosopher Philipp Frank, particularly his interpretation of Carnap’s Aufbau, which he considered the charter of logical empiricism as a scientific world conception. According to Frank, the Aufbau was to be read as an integration of the ideas of Mach and Poincaré, leading eventually to a pragmatism quite similar to that of the American pragmatist William James. Relying on this peculiar interpretation, Frank intended to bring (...) about a rapprochement between the logical empiricism of the Vienna Circle in exile and American pragmatism. In the course of this project, in the last years of his career, Frank outlined a comprehensive, socially engaged philosophy of science that could serve as a “link between science and philosophy”. (shrink)

A short summary of Carnap’s Logical Syntax of Language.

I argue for two theses about semantically anomalous utterances (more commonly called "category mistakes") like "sequestered slaps reel evergreen rights". First, semantic anomaly generates a unique form of semantically enforced quantifier domain restriction. Second, the best explanation for why anomaly interacts with quantifiers in this way is that anomalous utterances are truth-valueless. After arguing for these points, I trace out two consequences these theses have in semantics and logic. First, I argue they motivate a trivalent semantics on which truth-valueless material (...) has an unsual positive role to play in the compositional semantics of truth-evaluable utterances. Second, I argue that the interaction of anomaly with quantifiers generates a unique form of classical inference failure, and also provides special motivations for reconceptualizing our logical consequence relations. (shrink)

Traditional geometry concerns itself with planimetric and stereometric considerations, which are at the root of the division between plane and solid geometry. To raise the issue of the relation between these two areas brings with it a host of different problems that pertain to mathematical practice, epistemology, semantics, ontology, methodology, and logic. In addition, issues of psychology and pedagogy are also important here. To our knowledge there is no single contribution that studies in detail even one of the aforementioned areas.

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.

Logical pluralism has been in vogue since JC Beall and Greg Restall 2006 articulated and defended a new pluralist thesis. Recent criticisms such as Priest 2006a and Field 2009 have suggested that there is a relationship between their type of logical pluralism and the meaning-variance thesis for logic. This is the claim, often associated with Quine 1970, that a change of logic entails a change of meaning. Here we explore the connection between logical pluralism and meaning-variance, both in general and (...) for Beall and Restall's theory specifically. We argue that contrary to what Beall and Restall claim, their type of pluralism is wedded to meaning-variance. We then develop an alternative form of logical pluralism that circumvents at least some forms of meaning-variance. (shrink)

It has been argued that ethically correct robots should be able to reason about right and wrong. In order to do so, they must have a set of do’s and don’ts at their disposal. However, such a list may be inconsistent, incomplete or otherwise unsatisfactory, depending on the reasoning principles that one employs. For this reason, it might be desirable if robots were to some extent able to reason about their own reasoning—in other words, if they had some meta-ethical capacities. (...) In this paper, we sketch how one might go about designing robots that have such capacities. We show that the field of computational meta-ethics can profit from the same tools as have been used in computational metaphysics. (shrink)

This paper examines the role of ?situations? in John Dewey's philosophy of logic. To do this properly it is necessary to contrast Dewey's conception of experience and mentality with views characteristic of modern epistemology. The primary difference is that, rather than treat experience as peripheral and or external to mental functions (reason, etc.), we should treat experience as a field in and as a part of which thinking takes place. Experience in this broad sense subsumes theory and fact, hypothesis and (...) evidence, reason and observation, thought and perception. Logic in this view is a formal study of the generic features of all possible kinds of experience in this broad (thick, deep, wide, multifaceted) sense. The goal of this paper is to explain what Dewey thinks a situation is in the context of this view of experience, and to argue for the fundamental importance of that idea for logic and philosophy in general. (shrink)

Whereas an inference (deductive as well as inductive) is usually viewed as being valid in virtue of its argument form, the present paper argues that scientific reasoning is material inference, i.e., justified in virtue of its content. A material inference is licensed by the empirical content embodied in the concepts contained in the premises and conclusion. Understanding scientific reasoning as material inference has the advantage of combining different aspects of scientific reasoning, such as confirmation, discovery, and explanation. This approach explains (...) why these different aspects (including discovery) can be rational without conforming to formal schemes, and why scientific reasoning is local, i.e., justified only in certain domains and contingent on particular empirical facts. The notion of material inference also fruitfully interacts with accounts of conceptual change and psychological theories of concepts. (shrink)

Logic begins but does not end with the study of truth and falsity. Within truth there are the modes of truth, ways of being true: necessary truth and contingent truth. When a proposition is true, we may ask whether it could have been false. If so, then it is contingently true. If not, then it is necessarily true; it must be true; it could not have been false. Falsity has modes as well: a false proposition that could not have been (...) true is impossible or necessarily false; one that could have been true is merely contingently false. The proposition that some humans are over seven feet tall is contingently true; the proposition that all humans over seven feet tall are over six feet tall is necessarily true; the proposition that some humans are over seven feet tall and under six feet tall is impossible, and the proposition that some humans are over nine feet tall is contingently false. Of these four modes of truth, let us focus on necessity, plus a fifth: possibility. A proposition is possible if it is or could have been true; hence propositions that are either necessarily true, contingently true, or contingently false are possible. Notions that are similar to the modes of truth in being concerned with what might have been are called modal. Dispositions are modal notions, for example the disposition of fragility. Relatedly, there are counterfactual conditionals, for example “if this glass were dropped, it would break.” And the notion of supervenience is modal.1 But let us focus here on necessity and possibility. Modal words are notoriously ambiguous (or at least context-sensitive2). I may reply to an invitation to give a talk in England by saying “I can’t come; I have to give a talk in California the day before”. This use of “can’t” is perfectly appropriate. But it would be equally appropriate for me to say that I could cancel my talk in California (although that would be rude) and give the talk in England instead. What I cannot do is give both talks.. (shrink)

It is just over fifty years since the publication of Quine’s ‘Two Dogmas of Empiricism’. That paper expresses a broad vision of the system of relations between meaning, experience, and the rational formation of belief. The deepest challenges the paper poses come not from the detailed argument of its first four sections – formidable though that is – but from the visionary material in its last two sections.1 It is this visionary material that is likely to force the reader to (...) revise, to deepen, or to rethink her position on fundamental issues about the relations between meaning, experience, rationality, and, above all, the a priori. Does what is right in Quine’s argument exclude any rationalist view of these relations? How should a rationalist view be formulated? Those are the questions I will be addressing. I start with the critical part of this task, a consideration of the strengths and weaknesses of Quine’s vision. Drawing on the constraints emerging from that critical discussion, I will then turn to the positive task of articulating and defending a rival conception. The rival conception can be described as a Generalized Rationalism. (shrink)

Recent Carnap scholarship suggests that the received view of the Carnap-Quine analyticity debate is importantly mistaken. It has been suggested that Carnap’s analyticity distinction is immune from Quine’s criticisms. This is either because Quine did not understand Carnap’s use of analytic-ity, or because Quine did not appreciate that, rather than dispelling dog-mas, he was merely offering an alternate framework for philosophy. It has also been suggested that ultimately nothing of substance turns on this dis-pute. I am sympathetic to these reassessments (...) and their rejection of the re-ceived view, but argue that they fail to pay proper attention to Carnap’s metaphysical deflationism. For it is there that Quine’s arguments ultimately make contact with Carnap, undermining his metaphysical deflationism. Moreover, the viability of deflationism is directly related to the viability of Carnap’s view of philosophy as methodologically distinct from science. Hence, Quine’s criticisms make contact with the deepest aspects of Carnap’s views. (shrink)

Tarski's 1936 paper, “On the concept of logical consequence”, is a rather philosophical, non-technical paper that leaves room for conflicting interpretations. My purpose is to review some important issues that explicitly or implicitly constitute its themes. My discussion contains four sections: terminological and conceptual preliminaries, Tarski's definition of the concept of logical consequence, Tarski's discussion of omega-incomplete theories, and concluding remarks concerning the kind of conception that Tarski's definition was intended to explicate. The third section involves subsidiary issues, such as (...) Tarski's discussion concerning the distinction between material and formal consequence and the important question ofthe criterion for distinguishing between logical and non-logical terms.§1. Preliminaries. In this paper an argument is a two-part system composed of a set of propositions P and a single proposition c. The expression ‘c is a [logical] consequence of P’ is used with the same meaning as the expression ‘c is [logically] implied by P’. The expressions ‘is a logical consequence of’ and the converse ‘implies’ are relational. Often, I shall be talking in the same sense of validity of an argument. Validity is a property of arguments; an argument with premise-set P and conclusion c is valid if and only if P implies c; i.e., c is a logical consequence of P. Notice that this notion of argument is strictly ontic; it does not involve any agent that thinks, determines or establishes that a given proposition is or is not a consequence of a given set of propositions. (shrink)

We show how removing faith-based beliefs in current philosophies of classical and constructive mathematics admits formal, evidence-based, definitions of constructive mathematics; of a constructively well-defined logic of a formal mathematical language; and of a constructively well-defined model of such a language. -/- We argue that, from an evidence-based perspective, classical approaches which follow Hilbert's formal definitions of quantification can be labelled `theistic'; whilst constructive approaches based on Brouwer's philosophy of Intuitionism can be labelled `atheistic'. -/- We then adopt what may (...) be labelled a finitary, evidence-based, `agnostic' perspective and argue that Brouwerian atheism is merely a restricted perspective within the finitary agnostic perspective, whilst Hilbertian theism contradicts the finitary agnostic perspective. -/- We then consider the argument that Tarski's classic definitions permit an intelligence---whether human or mechanistic---to admit finitary, evidence-based, definitions of the satisfaction and truth of the atomic formulas of the first-order Peano Arithmetic PA over the domain N of the natural numbers in two, hitherto unsuspected and essentially different, ways. -/- We show that the two definitions correspond to two distinctly different---not necessarily evidence-based but complementary---assignments of satisfaction and truth to the compound formulas of PA over N. -/- We further show that the PA axioms are true over N, and that the PA rules of inference preserve truth over N, under both the complementary interpretations; and conclude some unsuspected constructive consequences of such complementarity for the foundations of mathematics, logic, philosophy, and the physical sciences. -/- . (shrink)

One central aim of science is to provide explanations of natural phenomena. What role(s) does mathematics play in achieving this aim? How does mathematics contribute to the explanatory power of science? Rules to Infinity defends the thesis, common though perhaps inchoate among many members of the Vienna Circle, that mathematics contributes to the explanatory power of science by expressing conceptual rules, rules which allow the transformation of empirical descriptions. Mathematics should not be thought of as describing, in any substantive sense, (...) an abstract realm of eternal mathematical objects, as traditional platonists have thought. In Rules to Infinity, this view, which I call mathematical normativism, is updated with contemporary philosophical tools, and it is argued that normativism is compatible with mainstream semantic theory. This allows the normativist to accept that there are mathematical truths, while resisting the platonistic idea that there exist abstract mathematical objects that explain such truths. Furthermore, Rules to Infinity defends a particular account of the distinction between scientific explanations that are in some sense distinctively mathematical – those that explain natural phenomena in some uniquely mathematical way – and those that are only standardly mathematical, and it lays out desiderata for any account of this distinction. Normativism is compared with other prominent views in the philosophy of mathematics such as neo-Fregeanism, fictionalism, conventionalism, and structuralism. Rules to Infinity serves as an entry point into debates at the forefront of philosophy of science and mathematics, and it defends novel positions in these debates. (shrink)

Anti-exceptionalism about logic is the Quinean view that logical theories have no special epistemological status, in particular, they are not self-evident or justified a priori. Instead, logical theories are continuous with scientific theories, and knowledge about logic is as hard-earned as knowledge of physics, economics, and chemistry. Once we reject apriorism about logic, however, we need an alternative account of how logical theories are justified and revised. A number of authors have recently argued that logical theories are justified by abductive (...) argument (e.g. Gillian Russell, Graham Priest, Timothy Williamson). This paper explores one crucial question about the abductive strategy: what counts as evidence for a logical theory? I develop three accounts of evidential confirmation that an anti-exceptionalist can accept: (1) intuitions about validity, (2) the Quine-Williamson account, and (3) indispensability arguments. I argue, against the received view, that none of the evidential sources support classical logic. (shrink)

In this paper I will investigate the possibility of completing a Positivist style account of demarcation. One reason for pursuing this project is that standard criticisms of Positivism do not have the bite against the demarcation project that they are often assumed to have. To argue this will be the burden of the first part of this paper. The other reason is that new research in logic has provided machinery not available to the Positivists; machinery that shows promise for solving (...) some of the technical problems faced by Positivists' account of demarcation. To argue this will be the burden of the second part of this paper. (shrink)

Commentary on Peter Olen's book "Wilfrid Sellars and the Foundations of Normativity", originally prepared for an 'Author Meets Critics' session organized by Carl Sachs for the Eastern Division Meeting of the APA in Savannah, Georgia, on 5th January, 2018.

The logical empiricists often appear as a foil for feminist theories. Their emphasis on the individualistic nature of knowledge and on the value-neutrality of science seems directly opposed to most feminist concerns. However, several recent works have highlighted aspects of Carnap's views that make him seem like much less of a straightforwardly positivist thinker. Certain of these aspects lend themselves to feminist concerns much more than the stereotypical picture would imply.

In this paper I argue that pluralism at the level of logical systems requires a certain monism at the meta-logical level, and so, in a sense, there cannot be pluralism all the way down. The adequate alternative logical systems bottom out in a shared basic meta-logic, and as such, logical pluralism is limited. I argue that the content of this basic meta-logic must include the analogue of logical rules Modus Ponens and Universal Instantiation. I show this through a detailed analysis (...) of the ‘adoption problem’, which manifests something special about MP and UI. It appears that MP and UI underwrite the very nature of a logical rule of inference, due to all rules of inference being conditional and universal in their structure. As such, all logical rules presuppose MP and UI, making MP and UI self-governing, basic, unadoptable, and required in the meta-logic for the adequacy of any logical system. (shrink)

Anti-exceptionalism about logic takes logic to be, as the name suggests, unexceptional. Rather, in naturalist fashion, the anti-exceptionalist takes logic to be continuous with science, and considers logical theories to be adoptable and revisable accordingly. On the other hand, the Adoption Problem aims to show that there is something special about logic that sets it apart from scientific theories, such that it cannot be adopted in the way the anti-exceptionalist proposes. In this paper I assess the damage the Adoption Problem (...) causes for anti-exceptionalism, and show that it is also problematic for exceptionalist positions too. My diagnosis of why the Adoption Problem affects both positions is that the self-governance of basic logical rules of inference prevents them from being adoptable, regardless of whether logic is exceptional or not. (shrink)

Logical monists and pluralists disagree about how many correct logics there are; the monists say there is just one, the pluralists that there are more. Could it turn out that both are wrong, and that there is no logic at all?

Do numbers exist? Carnap (1956 [1950]) famously argues that this question can be understood in an “internal” and in an “external” sense, and calls “external” questions “non-cognitive”. Carnap also says that external questions are raised “only by philosophers” (p. 207), which means that, in his view, philosophers raise ”non-cognitive” questions. However, it is not clear how the internal/external distinction and Carnap’s related views about philosophy should be understood. This paper provides a new interpretation. I draw attention to Carnap’s distinction between (...) purely external statements, which are independent from all frameworks, and pragmatic external statements, which concern which framework one should adopt, and argue that the latter express noncognitive mental states. Specifically, I argue that “frameworks” are systems of rules for the assessment of statements, which are utterances of ordinary language sentences. Pragmatic external statements express noncognitive dispositions to follow only certain rules of assessment. For instance, “numbers exist” understood as a pragmatic external statement expresses a noncognitive disposition to use only rules of assessment according to which numbers do exist. Carnap can thereby be understood as proposing a distinctive form of noncognitivism about ontology that is in some respects analogous to norm-expressivism in metaethics. (shrink)

Since 2016, there has been an explosion of academic work and journalism that fixes its subject matter using the terms ‘fake news’ and ‘post-truth’. In this paper, I argue that this terminology is not up to scratch, and that academics and journalists ought to completely stop using the terms ‘fake news’ and ‘post-truth’. I set out three arguments for abandonment. First, that ‘fake news’ and ‘post-truth’ do not have stable public meanings, entailing that they are either nonsense, context-sensitive, or contested. (...) Secondly, that these terms are unnecessary, because we already have a rich vocabulary for thinking about epistemic dysfunction. Thirdly, I observe that ‘fake news’ and ‘post-truth’ have propagandistic uses, meaning that using them legitimates anti-democratic propaganda, and runs the risk of smuggling bad ideology into conversations. (shrink)

Truth by convention, once thought to be the foundation of a uniquely promising approach to explaining our access to the truth in nonempirical domains, is nowadays widely considered an absurdity. Its fall from grace has been due largely to the influence of an argument that can be sketched as follows: our linguistic conventions have the power to make it the case that a sentence expresses a particular proposition, but they can’t by themselves generate truth; whether a given proposition is true—and (...) so whether the sentence that expresses it is true—is a matter of what the world is like, which means it isn’t a matter of convention alone. The consensus is that this argument is decisive against truth by convention. Strikingly, though, it has rarely been formulated with much precision. Here I provide a new rendering of the argument, one that reveals its structure and makes transparent just what assumptions it requires, and then I assess conventionalists’ prospects for resisting each of those assumptions. I conclude that the consensus is mistaken: contrary to what is almost universally thought, there remains a promising way forward for the conventionalist project. Along the way, I clarify conventionalists’ commitments by thinking about what truth by convention would need to be like in order for conventionalism to do the epistemological work it’s intended to do. (shrink)

I offer an analysis of the sentence "the concept horse is a concept". It will be argued that the grammatical subject of this sentence, "the concept horse", indeed refers to a concept, and not to an object, as Frege once held. The argument is based on a criterion of proper-namehood according to which an expression is a proper name if it is so rendered in Frege's ideography. The predicate "is a concept", on the other hand, should not be thought of (...) as referring to a function. It will be argued that the analysis of sentences of the form "C is a concept" requires the introduction of a new form of statement. Such statements are not to be thought of as having function--argument form, but rather the structure subject--copula--predicate. (shrink)

This paper has three interdependent aims. The first is to make Reichenbach’s views on induction and probabilities clearer, especially as they pertain to his pragmatic justification of induction. The second aim is to show how his view of pragmatic justification arises out of his commitment to extensional empiricism and moots the possibility of a non-pragmatic justification of induction. Finally, and most importantly, a formal decision-theoretic account of Reichenbach’s pragmatic justification is offered in terms both of the minimax principle and the (...) dominance principle. (shrink)

This paper aims to vindicate the thesis that cognitive computational properties are abstract objects implemented in physical systems. I avail of the equivalence relations countenanced in Homotopy Type Theory, in order to specify an abstraction principle for epistemic intensions. The homotopic abstraction principle for epistemic intensions provides an epistemic conduit into our knowledge of intensions as abstract objects. I examine, then, how intensional functions in Epistemic Modal Algebra are deployed as core models in the philosophy of mind, Bayesian perceptual psychology, (...) and the program of natural language semantics in linguistics, and I argue that this provides abductive support for the truth of homotopic abstraction. Epistemic modality can thus be shown to be both a compelling and a materially adequate candidate for the fundamental structure of mental representational states, comprising a fragment of the Language of Thought. (shrink)

I argue that Quinean naturalists’ holism-based arguments against analyticity and apriority are more difficult to resist than is generally supposed, for two reasons. First, although opponents of naturalism sometimes dismiss these arguments on the grounds that the holistic premises on which they depend are unacceptably radical, it turns out that the sort of holism required by these arguments is actually quite minimal. And second, although it’s true, as Grice and Strawson pointed out long ago, that these arguments can succeed only (...) if there isn’t any principled criterion for meaning change, such a criterion turns out to be hard to come by. David Chalmers has recently argued that such a criterion must exist, since the norms governing belief revision are subject to obvious exceptions that can be explained only by appeal to meaning change. But this, I argue, is incorrect: if choices about how to use language are themselves rationally assessable, then there are no such exceptions to be explained. To show that this is so, I formulate a new kind of coherence norm that may be useful for reasoning formally about the relationship between meaning and evidence. (shrink)

We discuss in this paper the question of the scope of the principle of tolerance about languages promoted in Carnap's The Logical Syntax of Language and the nature of the analogy between it and the rudimentary conventionalism purportedly exhibited in the work of Poincaré and Hilbert. We take it more or less for granted that Poincaré and Hilbert do argue for conventionalism. We begin by sketching Coffa's historical account, which suggests that tolerance be interpreted as a conventionalism that allows us (...) complete freedom to select whatever language we wish—an interpretation that generalizes the conventionalism promoted by Poincaré and Hilbert which allows us complete freedom to select whatever axiom system we wish for geometry. We argue that such an interpretation saddles Carnap with a theory of meaning that has unhappy consequences, a theory we believe he did not hold. We suggest that the principle of linguistic tolerance in fact has a more limited scope; but within that scope the analogy between tolerance and geometric conventionalism is quite tight. (shrink)

In theTractatus, Wittgenstein advocates two major notational innovations in logic. First, identity is to be expressed by identity of the sign only, not by a sign for identity. Secondly, only one logical operator, called “N” by Wittgenstein, should be employed in the construction of compound formulas. We show that, despite claims to the contrary in the literature, both of these proposals can be realized, severally and jointly, in expressively complete systems of first-order logic. Building on early work of Hintikka’s, we (...) identify three ways in which the first notational convention can be implemented, show that two of these are compatible with the text of theTractatus, and argue on systematic and historical grounds, adducing posthumous work of Ramsey’s, for one of these as Wittgenstein’s envisaged method. With respect to the second Tractarian proposal, we discuss how Wittgenstein distinguished between general and non-general propositions and argue that, claims to the contrary notwithstanding, an expressively adequate N-operator notation is implicit in theTractatuswhen taken in its intellectual environment. We finally introduce a variety of sound and complete tableau calculi for first-order logics formulated in a Wittgensteinian notation. The first of these is based on the contemporary notion of logical truth as truth in all structures. The others take into account the Tractarian notion of logical truth as truth in all structures over one fixed universe of objects. Here the appropriate tableau rules depend on whether this universe is infinite or finite in size, and in the latter case on its exact finite cardinality.As it is obviously easy to express how propositions can be constructed by means of this operation and how propositions are not to be constructed by means of it, this must be capable of exact expression.5.503. (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 two-dimensional (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 two-dimensional (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)

In the middle of last century metaphysics was widely criticized, ridiculed, and committed to the flames. During this period a handful of philosophers, against several anti-metaphysical trends, defended metaphysics and articulated novel metaphysical doctrines. Donald C. Williams was one of these philosophers. But while his contributions to metaphysics are well known his defence of metaphysics is not and yet it played a key part in the development and revival of metaphysics. In this paper I present his defence of metaphysics in (...) its historical context. I also show how his defence is relevant in response to recent attacks on metaphysics. (shrink)

The last two decades have seen a surge of support for normative quietism: most notably, from Dworkin, Nagel, Parfit and Scanlon. Detractors like Enoch and McPherson object that quietism is incompatible with realism about normativity. The resulting debate has stagnated somewhat. In this paper I explore and defend a more promising way of developing that objection: I’ll argue that if normative quietism is true, we can create reasons out of thin air, so normative realists must reject normative quietism.

I aim to show that a semantic minimalist need not also be a semantic internalist. §I introduces minimalism and internalism and argues that there is a prima facie case for a minimalist being an internalist. §II sketches some positive arguments for internalism which, if successful, show that a minimalist must be an internalist. §III goes on to reject these arguments and contends that the prima facie case for uniting minimalism and internalism is also not compelling. §IV returns to an objection (...) from §I and argues for a way to meet it which does not depend on giving up semantic externalism. (shrink)

Probabilistic realism and syntactical positivism were two among outdated theories that Feigl criticised on account of their semantical poverty. In this paper, I argue that a refined version of probabilistic realism, which relies on what Feigl specified as the pragmatic description of the symbolic behaviour of scientists’ estimations and foresight, is defendable. This version of statistical realism does not need to make the plausibility of realist thesis dependent on the conventional acceptance of a constructed semantic metalanguage. I shall rely on (...) the Prediction Error Minimisation theory to support my probabilistic version of realism with a scientifically-informed and naturalistically plausible statistical account of the theories-world relationship which has a pragmatic ring to it. (shrink)

Consequence is at the heart of logic; an account of consequence, of what follows from what, offers a vital tool in the evaluation of arguments. Since philosophy itself proceeds by way of argument and inference, a clear view of what logical consequence amounts to is of central importance to the whole discipline. In this book JC Beall and Greg Restall present and defend what thay call logical pluralism, the view that there is more than one genuine deductive consequence relation, a (...) position which has profound implications for many linguists as well as for philosophers. We should not search for one true logic, since there are many. (shrink)

The logical empiricists often appear as a foil for feminist theories. Their emphasis on the individualistic nature of knowledge and on the value-neutrality of science seems directly opposed to most feminist concerns. However, several recent works have highlighted aspects of Carnap's views that make him seem like much less of a straightforwardly positivist thinker. Certain of these aspects lend themselves to feminist concerns much more than the stereotypical picture would imply.

§0. Alonzo Church's contributions to philosophy and to that most philosophical part of logic, intensional logic, are impressive indeed. He wrote relatively few papers actually devoted to specifically philosophical issues, as distinguished from related technical work in logic. Many of his contributions appear in reviews for The Journal of Symbolic Logic, and it can hardly be maintained that one finds there a “philosophical system”. But there occur a clearly articulated and powerful methodology, terse arguments, often of “crushing cogency”, and philosophical (...) observations of the first importance.Many of the less formal philosophical contributions center around questions concerning meaning, but there are important clarifications and insights into matters of the epistemology and ontology of the sciences, especially the formal sciences.1.1. The logistic method. Church's writings on philosophical matters exhibit an unwavering commitment to what he called the “logistic method”. The term did not catch on and now one would just speak of “formalization”. The use of these ideas is now so common and familiar among logicians and logically-oriented philosophers that they are simply taken for granted. But they deserve to be celebrated and re-emphasized, for there are philosophers who seriously underestimate and even consciously reject these techniques. (shrink)

In “Empiricism, Semantics, and Ontology” Camap drew his famous distinction between ‘internal’ and ‘external’ questions of existence, pronouncing the former meaningful and the latter meaningless. In The Significance of Philosophical Scepticism, Barry Stroud understands Carnap to be applying the verification criterion of meaningfulness in order to refute Cartesian skepticism. I suggest that Stroud misrepresents both Carnap's aim and method. Camap was responding to critics who suggested that his willingness to quantify over abstract entities in his work in semantics violated his (...) commitment to empiricism. He rejected that criticism as presupposing a super‐scientific standpoint from which constraints on the admissible domain of entities of science could be delivered. Carnap wanted to insulate science from the imposition of first‐philosophical metaphysical prejudice, not to defuse scepticism by appeal to verificationism. (shrink)

A critical notice of David J. Chalmers, Constructing the World (Oxford University Press,2012).

George Frederick Stout fut, dans la philosophie du XXe siècle, le principal promoteur de la thèse à tendance nominaliste du particularisme des qualités, selon laquelle chaque propriété d'une entité individuelle quelconque est elle-même une entité individuelle. On examine ici de façon critique les arguments avancés par Stout en faveur de cette doctrine ontologique ainsi que les objections qui lui ont été adressées. N'ayant trouvé au bout du compte aucun argument décisif ni d'un côté ni de l'autre, on suggère, dans une (...) veine inspirée de Carnap, de réinterpréter la thèse originale comme une recommandation relative à l'adoption d'un certain langage.George Frederick Stout was, in twentieth century philosophy, the leading defender of the nominalistically oriented thesis of the particularisation of qualities, according to which each property of an individual is itself an individual. This paper is a critical discussion of the arguments put forward by Stout for this ontological view and of the objections raised by his opponents. Since no decisive argument is found on either side, it is suggested, in a Carnapian mood, to reconstruct the original thesis as a proposal for the adoption of a certain language. (shrink)

Using a base of philosophical athropology, this article suggests that an ethical analysis of persuasion must include not just the logic human response, but culture and experience as well. The authors propose potential maxims for ethical behavior in advertising and public relations and applies them to two case studies, political advertising and the Bridgestone/Firestone controversy.

The purpose of this paper is to discuss conditions of rationality for scientific research (SR) where "conditions" are understood as "necessary conditions". This will be done in the following way: First, I shall deal with the aim of SR since conditions of rationality (for SR) are to be understood as necessary means for reaching the aim (goal) of SR. Subsequently, the following necessary conditions will be discussed: Rational Communication, Methodological Rules, Ideals of Rationality and its Realistic Aspects, Methodological and Ontological (...) Conditions (Universality, Rules for Experiments, Causality), and Metaphysical Presuppositions and Extrapolations. (shrink)

Inductive probability is the logical concept of probability in ordinary language. It is vague but it can be explicated by defining a clear and precise concept that can serve some of the same purposes. This paper presents a general method for doing such an explication and then a particular explication due to Carnap. Common criticisms of Carnap's inductive logic are examined; it is shown that most of them are spurious and the others are not fundamental.

This paper investigates the determinacy of mathematics. We begin by clarifying how we are understanding the notion of determinacy before turning to the questions of whether and how famous independence results bear on issues of determinacy in mathematics. From there, we pose a metasemantic challenge for those who believe that mathematical language is determinate, motivate two important constraints on attempts to meet our challenge, and then use these constraints to develop an argument against determinacy and discuss a particularly popular approach (...) to resolving indeterminacy, before offering some brief closing reflections. We believe our discussion poses a serious challenge for most philosophical theories of mathematics, since it puts considerable pressure on all views that accept a non-trivial amount of determinacy for even basic arithmetic. (shrink)