This paper briefly recounts the importance of the notion of natural axiomatizations for explicating hypothetico‐deductivism, empirical significance, theoretical reduction, and organic fertility. Problems for the account of natural axiomatizations developed by John Watkins in Science and Scepticism and the revised account developed by Elie Zahar are demonstrated. It is then shown that Watkins's account can be salvaged from various counter‐examples in a principled way by adding the demand that every axiom of a natural axiomatization should be part of the content (...) of the theory being axiomatized. The crucial point here is that content cannot simply be identified with the set of logical consequences of a theory, but must be restricted to a proper subset of the consequence set. It is concluded that the revised Watkins account has certain advantages over the account of natural axiomatizations offered in Gemes. (shrink)

A novel conceptual framework is introduced for the Complexity Levels Theory in a Categorical Ontology of Space and Time. This conceptual and formal construction is intended for ontological studies of Emergent Biosystems, Super-complex Dynamics, Evolution and Human Consciousness. A claim is defended concerning the universal representation of an item’s essence in categorical terms. As an essential example, relational structures of living organisms are well represented by applying the important categorical concept of natural transformations to biomolecular reactions and relational structures that (...) emerge from the latter in living systems. Thus, several relational theories of living systems can be represented by natural transformations of organismic, relational structures. The ascent of man and other living organisms through adaptation, is viewed in novel categorical terms, such as variable biogroupoid representations of evolving species. Such precise but flexible evolutionary concepts will allow the further development of the unifying theme of local-to-global approaches to highly complex systems in order to represent novel patterns of relations that emerge in super- and ultra-complex systems in terms of compositions of local procedures. Solutions to such local-to-global problems in highly complex systems with ‘broken symmetry’ might be possible to be reached with the help of higher homotopy theorems in algebraic topology such as the generalized van Kampen theorems (HHvKT). Categories of many-valued, Łukasiewicz-Moisil (LM) logic algebras provide useful concepts for representing the intrinsic dynamic ‘asymmetry’ of genetic networks in organismic development and evolution, as well as to derive novel results for (non-commutative) Quantum Logics. Furthermore, as recently pointed out by Baianu and Poli (Theory and applications of ontology, vol 1. Springer, Berlin, in press), LM-logic algebras may also provide the appropriate framework for future developments of the ontological theory of levels with its complex/entangled/intertwined ramifications in psychology, sociology and ecology. As shown in the preceding two papers in this issue, a paradigm shift towards non-commutative, or non-Abelian, theories of highly complex dynamics—which is presently unfolding in physics, mathematics, life and cognitive sciences—may be implemented through realizations of higher dimensional algebras in neurosciences and psychology, as well as in human genomics, bioinformatics and interactomics. (shrink)

An overview of the following three related papers in this issue presents the Emergence of Highly Complex Systems such as living organisms, man, society and the human mind from the viewpoint of the current Ontological Theory of Levels. The ontology of spacetime structures in the Universe is discussed beginning with the quantum level; then, the striking emergence of the higher levels of reality is examined from a categorical—relational and logical viewpoint. The ontological problems and methodology aspects discussed in the first (...) two papers are followed by a rigorous paper based on Category Theory, Algebraic Topology and Logic that provides a conceptual and mathematical basis for a Categorical Ontology Theory of Levels. The essential links and relationships between the following three papers of this issue are pointed out, and further possible developments are being considered. (shrink)

An overview of the following three related papers in this issue presents the Emergence of Highly Complex Systems such as living organisms, man, society and the human mind from the viewpoint of the current Ontological Theory of Levels. The ontology of spacetime structures in the Universe is discussed beginning with the quantum level; then, the striking emergence of the higher levels of reality is examined from a categorical—relational and logical viewpoint. The ontological problems and methodology aspects discussed in the first (...) two papers are followed by a rigorous paper based on Category Theory, Algebraic Topology and Logic that provides a conceptual and mathematical basis for a Categorical Ontology Theory of Levels. The essential links and relationships between the following three papers of this issue are pointed out, and further possible developments are being considered. (shrink)

This paper analyzes the rapid and unexpected rise of deep learning within Artificial Intelligence and its applications. It tackles the possible reasons for this remarkable success, providing candidate paths towards a satisfactory explanation of why it works so well, at least in some domains. A historical account is given for the ups and downs, which have characterized neural networks research and its evolution from “shallow” to “deep” learning architectures. A precise account of “success” is given, in order to sieve out (...) aspects pertaining to marketing or sociology of research, and the remaining aspects seem to certify a genuine value of deep learning, calling for explanation. The alleged two main propelling factors for deep learning, namely computing hardware performance and neuroscience findings, are scrutinized, and evaluated as relevant but insufficient for a comprehensive explanation. We review various attempts that have been made to provide mathematical foundations able to justify the efficiency of deep learning, and we deem this is the most promising road to follow, even if the current achievements are too scattered and relevant for very limited classes of deep neural models. The authors’ take is that most of what can explain the very nature of why deep learning works at all and even very well across so many domains of application is still to be understood and further research, which addresses the theoretical foundation of artificial learning, is still very much needed. (shrink)

Investigation and analysis of the history of the concepts employed in contemporary philosophy of mind could significantly change the contemporary debate about the explainability of consciousness. Philosophical investigation of the history of the concept of qualia and the concept of scientific explanation most often presupposed in contemporary discussions of consciousness reveals the origin of both concepts in some of the most interesting philosophical debates of the twentieth century. In particular, a historical investigation of the inheritance of concepts of the elements (...) of experience and the nature of scientific explanation from C. I. Lewis and Rudolf Carnap to contemporary theorists like David Chalmers shows the profound continuity of these concepts throughout the analytic tradition, despite important changes in the dimensions of philosophical relevance and significance that have characterized the emerging debate. I argue that, despite the significant methodological shift from the foundationalist epistemology of the 1920s to today's functionalist explanations of the mind, the problem of explaining consciousness has remained the problem of analysing or describing the logical and relational structure of immediate, given experience. Appreciation of this historical continuity of form recommends a more explicit discussion of the philosophical reasons for the underlying distinction between structure and content, reasons that trace to Lewis and Carnap's influential but seldom-discussed understanding of the relationship between subjectivity, conceived as the realm of private, ineffable contents, and objectivity, understood as public, linguistic expressibility. With this historical background in mind, the contemporary debate about the explanation of consciousness can be re-interpreted as a debate about the relationship between ineffable experience and structurally conceived meaning. (shrink)

True beliefs and truth-preserving inferences are, in some sense, good beliefs and good inferences. When an inference is valid though, it is not merely truth-preserving, but truth-preserving in all cases. This motivates my question: I consider a Modus Ponens inference, and I ask what its validity in particular contributes to the explanation of why the inference is, in any sense, a good inference. I consider the question under three different definitions of ‘case’, and hence of ‘validity’: the orthodox definition given (...) in terms of interpretations or models, a metaphysical definition given in terms of possible worlds, and a substitutional definition defended by Quine. I argue that the orthodox notion is poorly suited to explain what's good about a Modus Ponens inference. I argue that there is something good that is explained by a certain kind of truth across possible worlds, but the explanation is not provided by metaphysical validity in particular; nothing of value is explained by truth across all possible worlds. Finally, I argue that the substitutional notion of validity allows us to correctly explain what is good about a valid inference. (shrink)

Name der Zeitschrift: Semiotica Jahrgang: 2015 Heft: 205 Seiten: 37-86.

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)

Recently O'Grady argued that Quine's "Two Dogmas" misses its mark when Carnap's use of the analyticity distinction is understood in the light of his deflationism. While in substantial agreement with the stress on Carnap's deflationism, I argue that O'Grady is not sufficiently sensitive to the difference between using the analyticity distinction to support deflationism, and taking a deflationary attitude towards the distinction itself; the latter being much more controversial. Being sensitive to this difference, and viewing Quine as having reason to (...) insist on a nonarbitrary analyticity distinction, we see that "Two Dogmas" makes direct contact with Carnap's deflationism. We must look beyond "Two Dogmas" to Quine's other critiques of analyticity to understand why the arbitrariness of the distinction threatens to undermine or overextend Carnap's deflationism. (edited). (shrink)

Traditionally, the proponents of empiricism sought for the starting point of knowledge in sensations that happen to us when we open our sense organs to the world. They analyzed the functioning of human faculties of sensation and cognition and the way these faculties are activated so as to discover the origin of ideas. Thus, they insisted on the priority of particulars to universals in the body of synthetic knowledge, and granted empirical facts the authority of truth. For that reason, they (...) are opposed to the rationalists, who maintained that the most important part of synthetic knowledge is derived solely from first principles or ideas, and that these principles or ideas are “innate”—that reason can ascertain their truth intuitively without the use of the senses.Logical positivism belongs to the empiricist tradition. However, it distinguishes itself from its empiricist predecessors in a very important way, so that its proponents thought they could overcome the difficulties raised against the older empiricists. (shrink)

Michael Friedman’s Dynamics of Reason is a welcome contribution to the ongoing articulation of philosophical perspectives for understanding the sciences in the context of post-positivist philosophy of science. Two perspectives that have gained advocacy since the demise of the “received view” are Quinean naturalism and Kuhnian relativism. In his 1999 Stanford lectures, Friedman articulates and defends a neo-Kantian perspective for philosophy of science that opposes both of these perspectives. His proffered neo-Kantian perspective is presented within the context of the problem (...) of theory change or “scientific revolutions,” and its main feature is a conception of scientific knowledge that requires “relativized constitutive a priori principles.” The lectures make up the first part of the book; the second part of the book, “Fruits of Discussion,” is a further elaboration and defence of the ideas advanced in the lectures. The resulting book serves as a useful sequel to Friedman’s impressive historical studies in Foundations of Space-Time Theories, Kant and the Exact Sciences, and Reconsidering Logical Positivism. In the preface, Friedman tells us that this book represents the philosophical viewpoint that he has arrived at as a result of completing these works. As such, it is not surprising that the prominent themes of the book are ones that have occupied Friedman’s attention in the past, viz., the importance of a priori principles in the exact sciences, the conventionalism of the logical positivists, and, more generally, an articulation of what remains defensible in neo-Kantian philosophy of science. (shrink)

In concluding section 2, chapter VI of part II of [6], Duhem claimed:... the physicist can never subject an isolated hypothesis to experimental test, but only a whole group of hypotheses...... when the experiment is in disagreement with his predictions, what he learns is that at least one of the hypotheses constituting this group is unacceptable and ought to be modified; but the experiment does not designate which one should be changed'.

Some philosophers are metaphilosophical deflationists for metasemantic reasons. These theorists take standard philosophical assertions to be defective in some manner. There are various versions of metasemantic metaphilosophical deflationism, but a trap awaits any global version of it: metasemantics itself is a part of philosophy, so in deflating philosophy these theorists have thereby deflated the foundation of their deflationism. The present article discusses this issue and the prospects for an adequate response to the trap. Contrary to most historical responses, the article (...) argues that the best response to the trap is to adopt a local but still pervasive metasemantic deflationism. Such a response might seem ad hoc, but the article argues that the human activity of philosophy isn't a natural kind, and that a heterogeneous metaphilosophy of the appropriate kind is well motivated. (shrink)

Our relationship to the infinite is controversial. But it is widely agreed that our powers of reasoning are finite. I disagree with this consensus; I think that we can, and perhaps do, engage in infinite reasoning. Many think it is just obvious that we can't reason infinitely. This is mistaken. Infinite reasoning does not require constructing infinitely long proofs, nor would it gift us with non-recursive mental powers. To reason infinitely we only need an ability to perform infinite inferences. I (...) argue that we have this ability. My argument looks to our best current theories of inference and considers examples of apparent infinite reasoning. My position is controversial, but if I'm right, our theories of truth, mathematics, and beyond could be transformed. And even if I'm wrong, a more careful consideration of infinite reasoning can only deepen our understanding of thinking and reasoning. -/- (Note for readers: the paper's brief discussion of uniform reflection and omega inconsistency is misleading. The imagined interlocutor's argument makes an assumption about the PA-provability of provability generalizations that, while true for the Godel sentence's instances, is unjustified, in general. This means my position is stronger against this objection than the paper suggests, since omega inconsistent theories are not automatically inconsistent with their uniform reflection principles, you also need to assume the arithmetically true Pi-2 sentences.). (shrink)

Some philosophers have argued that putative logical disagreements aren't really disagreements at all since when you change your logic you thereby change the meanings of your logical constants. According to this picture classical logicians and intuitionists don't really disagree, they just mean different things by terms like “not” and “or”. Quine gave an infamous “translation argument” for this view. Here I clarify the change of logic, change of meaning (CLCM) thesis, examine and find fault with Quine's translation argument for the (...) thesis, offer a modified translation argument in its stead, defend my modified argument from a crucial objection, discuss where the CLCM thesis leaves logical disputes, and discuss if and how the thesis coheres with Quine's influential view of logic. (shrink)

Theories of meaning developed within the analytic tradition, starting with Gottlob Frege, and within continental philosophy, starting with Husserl, can be distinguished by their disagreement about the phenomenon of collapse or failure of meaning. Our text focuses on Frege’s legacy, taken up by Rudolph Carnap, which culminated in a view of the collapse of meaning defined first by a purely syntactic conception of categorial error and second, when Tarski entered the scene, by the paradoxes created by the conflict between the (...) use of the predicate truth and the concept of proof. As positivism’s conventionalism and late model-theoretic semantics became the paradigms derived from this position, the result, in our view, was a conception of meaning success and meaning failure dominated by dependence on a technological conception. We will argue that this dependence leads to the inability to evaluate the breaks in rational parameters and crises of meaning addressed by the phenomenological and transcendental perspectives. Husserl’s critique of logic as technology is the basis for the reflexive standpoint on the phenomena of meaning failure that leads to a theoretical and eidetic ideal approach to that phenomenon. It is then suggested that this phenomenological reflective standpoint on the problem of meaning failure is the origin of the doors that lead to the divergent paths between the analytic and continental traditions. Thus, this is an article with three argumentative phases connected into a larger unity. The first phase presents Husserl’s critique of a purely extensional, syntactic, and recursive conception of logical consequence and the concept of truth; the second presents Hussel’s larger conception of meaning-failure; the third—presented in an appendix— presents a lesson on the division between continental and analytic philosophy. (shrink)

in april 1933, two bright young Ph.D.s were elected to the Harvard Society of Fellows: the psychologist B. F. Skinner and the philosopher/logician W. V. Quine. Both men would become among the most influential scholars of their time; Skinner leads the "Top 100 Most Eminent Psychologists of the 20th Century," whereas philosophers have selected Quine as the most important Anglophone philosopher after the Second World War.1 At the height of their fame, Skinner and Quine became "Edgar Pierce twins"; the latter (...) obtaining the endowed chair at Harvard's department of philosophy, the former taking up the position at Harvard's psychology department.2Besides these biographical parallels, there also... (shrink)

The question of the political potential possessed by the philosophies of the Vienna Circle is complex for more than one reason. It is so partly due to the politically heterogeneous membership of the Circle, partly due to the difficult if not extreme political circumstances under which they had to operate, and partly due to the variable meanings of the parameter "political," some of which are and some of which are not compatible with, in turn, variable versions of the doctrine of (...) the value-neutrality of science. For instance, philosophies of science may steadfastly be standing guard against pseudo-scientific nonsense being paraded as worthy of credence in public discourse, this concern for intellectual hygene... (shrink)

This paper concerns the recent debate on the nature and motivations of the epistemological project advanced in Rudolf Carnap's (1891-1970) Aufbau. Much of this debate has been initiated by Michael Friedman and Alan Richardson who argue (against the received view of the Aufbau as a foundationalist defense of empiricism) that Carnap's epistemological project is located in the tradition of neo-Kantian epistemology. On this revisionist reading of the Aufbau, Carnap's project is not motivated to address traditional empiricist problems regarding the justification (...) of knowledge, but rather to show how objective knowledge is possible. A central aspect of the Aufbau that is neglected in the revisionists' analysis is the role of epistemic justification in Carnap's project. The aim of the present study is to argue that although the general epistemology in the Aufbau can be cast as neo-Kantian, Carnap's method of construction theory (or rational reconstruction) is formulated precisely as an empiricist method for the justification of conceptual knowledge. Construction theory radically redefines `empirical justification' into a formal-conventional notion, and is part of Carnap's more general agenda of redefining epistemology as a purely formal discipline. (shrink)

Michael Friedman’s Dynamics of Reason is a welcome contribution to the ongoing articulation of philosophical perspectives for understanding the sciences in the context of post-positivist philosophy of science. Two perspectives that have gained advocacy since the demise of the “received view” are Quinean naturalism and Kuhnian relativism. In his 1999 Stanford lectures, Friedman articulates and defends a neo-Kantian perspective for philosophy of science that opposes both of these perspectives. His proffered neo-Kantian perspective is presented within the context of the problem (...) of theory change or “scientific revolutions,” and its main feature is a conception of scientific knowledge that requires “relativized constitutive a priori principles.” The lectures make up the first part of the book; the second part of the book, “Fruits of Discussion,” is a further elaboration and defence of the ideas advanced in the lectures. The resulting book serves as a useful sequel to Friedman’s impressive historical studies in Foundations of Space-Time Theories, Kant and the Exact Sciences, and Reconsidering Logical Positivism. In the preface, Friedman tells us that this book represents the philosophical viewpoint that he has arrived at as a result of completing these works. As such, it is not surprising that the prominent themes of the book are ones that have occupied Friedman’s attention in the past, viz., the importance of a priori principles in the exact sciences, the conventionalism of the logical positivists, and, more generally, an articulation of what remains defensible in neo-Kantian philosophy of science. (shrink)

I modify and generalize Carnap’s notion of frameworks as a way of unpacking Goodman’s metaphor of “making worlds with symbols”. My frameworks provide, metaphorically, a way of making worlds out of symbols in as much as all our framework-bound access to the world is through frameworks that always stand to be improved in accuracy, precision, and usually both. Such improvement is characterized in pragmatist terms.

We provide for the first time an exact translation into English of the Polish version of Alfred Tarski's classic 1936 paper, whose title we translate as ‘On the Concept of Following Logically’. We also provide in footnotes an exact translation of all respects in which the German version, used as the basis of the previously published and rather inexact English translation, differs from the Polish. Although the two versions are basically identical, to an extent that is even uncanny, we note (...) more than 400 differences. Several dozen of these are substantive differences due to revisions by Tarski to the Polish version which he did not incorporate in the German version. With respect to these revisions the Polish version should be regarded as more authoritative than the German. Hence scholars limited to an English translation should use ours. (shrink)

In the 1930s, Carnap set out to incorporate psychology into the unity of science, by showing that all cognitively meaningful sentences of psychology can be translated into the language of physics. I will argue that Carnap, relying on his notion of protocol languages, defends a physicalistic philosophy of psychology that shows due appreciation to 'introspection' as a strictly subjective, but reliable way to verify sentences about one’s own mind. Second, I will point out that Carnap’s philosophy of psychology not only (...) takes into account overt behaviour, but must comprise neurophysiological processes as well. Last, I will show that Carnap aims to develop a philosophy of psychology that does justice to the ongoing changeability of scientific knowledge. (shrink)

According to methodological anti-exceptionalism, logic follows a scientific methodology. There has been some discussion about which methodology logic has. Authors such as Priest, Hjortland and Williamson have argued that logic can be characterized by an abductive methodology. We choose the logical theory that behaves better under a set of epistemic criteria. In this paper, I analyze some important discussions in the philosophy of logic, and I show that they presuppose different methodologies, involving different notions of evidence and different epistemic values. (...) I argue that, rather than having a specific methodology such as abductivism, logic can be characterized by methodological pluralism. This position can also be seen as the application of scientific pluralism to the realm of logic. (shrink)

On a widespread reading, the Carnap-Quine debate about ontology concerns the objectivity and non-triviality of ontological claims. I argue that this view mischaracterizes Carnap’s aims in “Empiricism, Semantics, and Ontology” : Carnap’s fundamental goal is to free up decisions about scientific language from constraints deriving from ontological doctrine. The contention, based on his internal/external distinction, that ontological claims are either meaningless or trivial was Carnap’s means to achieving this more fundamental goal. Setting the record straight on this point brings out (...) three important and often overlooked features of Carnap’s views on ontology. First, the target of Carnap’s critique in ESO is not Quine’s mature views on ontology, as laid out in “On What There Is”. Rather, Carnap is responding to arguments for nominalism that were given by Tarski, Goodman, and Quine in the 1940s. Second, a more general rejection of conservatism in theory choice is essential to Carnap’s aims and is implicit in his fundamental views on language. Third, even if it turns out to be tenable, the i/e distinction is not adequate for Carnap’s aim in ESO. Drawing on his basic conception of scientific language, I will suggest an alternative approach on his behalf. (shrink)

European Journal of Philosophy, Volume 29, Issue 4, Page 864-886, December 2021.

In this paper, the connection between logicism and the principle of tolerance in Carnap’s philosophy of logic and mathematics is to be presented in terms of the history of its development. Such development is conditioned by two lines of criticism to Carnap’s attempt to combine Logicism and Conventionalism, the first of which comes from Gödel, the second from Alfred Tarski. The presentation will take place in three steps. First, the Logicism of Carnap before the publication of The Logical Syntax of (...) Language will be analyzed in its main features. Second, the relationship between Logicism and the Principle of Tolerance at the time of the publication of Logical Syntax, and thirdly, in the so-called semantical phase of Carnap’s thought will be examined. On the basis of the two preceding points, we will then critically analyze two interpretations of the possibility to maintain a philosophical position like that of Carnap nowadays. (shrink)

The main topic of this essay is symbolic mathematics or the method of symbolic construction, which I trace to the end of the sixteenth century when Franciscus Vieta invented the algebraic symbolism and started to use the word ‘symbolic’ in the relevant, non-ontological sense. This approach has played an important role for many of the great inventions in modern mathematics such as the introduction of the decimal place-value system of numeration, Descartes’ analytic geometry, and Leibniz’s infinitesimal calculus. It was also (...) central for the rigorization movement in mathematics in the late nineteenth century, as well as for the mathematics of modern physics in the 20th century.However, the nature of symbolic mathematics has been concealed and confused due to the strong influence of the heritage from the Euclidean and Aristotelian traditions. This essay sheds some light on what has been concealed by approaching some of the crucial issues from a historical perspective. Furthermore, I argue that the conception of modern mathematics as symbolic mathematics was essential to Wittgenstein’s approach to the foundations and nature of mathematics. This connection between Wittgenstein’s thought and symbolic mathematics provides the resources for countering the still prevalent view that he defended an uttrely idiosyncratic conception, disconnected from the progress of serious science. Instead, his project can be seen as clarifying ideas that have been crucial to the development of mathematics since early modernity. (shrink)

In this paper I examine a neglected question concerning the centerpiece of Carnap's philosophy: the principle of tolerance. The principle of tolerance states that we are free to devise and adopt any well-defined form of language or linguistic framework we please. A linguistic framework defines framework-internal standards of correct reasoning that guide us in our first-order scientific pursuits. The choice of a linguistic framework, on the other hand, is an ‘external’ question to be settled on pragmatic grounds and so not (...) itself constrained by these standards. However, even if choosing a framework is a practical matter, we would nevertheless expect the process of framework selection to be subject to rational norms. But which norms might those be? And where do they come from? I begin by showing that these questions are crucial to the success of Carnap's entire philosophical project. I then offer a response on behalf of the Carnapian which guarantees the rationality of the process of framework selection, while remaining true to Carnap's firm commitment to tolerance. (shrink)

To consider metaphysical claims a priori and devoid of empirical content, is a rather commonplace received opinion. This paper attempts an exploration of a contemporary philosophical heresy: it is possible to test metaphysical claims if they play an indispensable role in producing empirical success, i.e. novel predictions. To do so one, firstly, needs to express the metaphysical claims employed in the logico-mathematical language of a scientific theory, i.e. to explicate them. Secondly, one should have an understanding of what it is (...) to test and to verify or to falsify a metaphysical claim. Finally, one also need to consider the philosophical practice of testing a metaphysical claim. These three aspects are introduced in this paper and they are illustrated by means of the metaphysical concept of common cause and the principle of the common cause. (shrink)

In this paper, I defend the metalinguistic solution to the problem of mathematical omniscience for the possible-worlds account of propositions by combining it with a computational model of knowledge and belief. The metalinguistic solution states that the objects of belief and ignorance in mathematics are relations between mathematical sentences and what they express. The most pressing problem for the metalinguistic strategy is that it still ascribes too much mathematical knowledge under the standard possible-worlds model of knowledge and belief on which (...) these are closed under entailment. I first argue that Stalnaker's fragmentation strategy is insufficient to solve this problem. I then develop an alternative, computational strategy: I propose a model of mathematical knowledge and belief adapted from the algorithmic model of Halpern et al. which, when combined with the metalinguistic strategy, entails that mathematical knowledge and belief require computational abilities to access metalinguistic information, and thus aren't closed under entailment. As I explain, the computational model generalizes beyond mathematics to a version of the functionalist theory of knowledge and belief that motivates the possible-worlds account in the first place. I conclude that the metalinguistic and computational strategies yield an attractive functionalist, possible-worlds account of mathematical content, knowledge, and inquiry. (shrink)

In this paper, I argue from a metasemantic principle to the existence of analytic sentences. According to the metasemantic principle, an external feature is relevant to determining which concept one expresses with an expression only if one is disposed to treat this feature as relevant. This entails that if one isn’t disposed to treat external features as relevant to determining which concept one expresses, and one still expresses a given concept, then something other than external features must determine that one (...) does. I argue that, in such cases, what determines that one expresses the concept also puts one in a position to know that certain sentences are true—these sentences are thus analytic relative to this determination basis. Finally, I argue that there are such cases: some sentences are analytic relative to what determines that we express certain key concepts, and these sentences include ones that have always been thought to be the best candidates for being analytic, namely, stipulative truths, and first principles of mathematics. (shrink)

I argue against the view that metalinguistic usage is a form of conversational implicature. That view, suggested by Thomasson (Anal Philos 57(4):1-28, 2016) and Belleri (Philos Stud 174(9):2211–2226, 2017), has been most recently fleshed out by Mankowitz (Synthese 199:5603–5622, 2021). I provide two types of criticism to the implicature view. From an empirical point of view, metalinguistic usage differs in key respects from standard cases of conversational implicature. From a conceptual standpoint, I argue that the calculation algorithm provided by the (...) implicature view makes undesirable predictions. Although my main objective is negative, I end the paper by sketching an alternative neo-Stalnakerian view of metalinguistic usage, that can be gathered from work by Barker (Linguist Philos 25(1):1–36, 2002; Inquiry 56(2–3):240–257, 2013) and others. (shrink)

According to a growing consensus in the secondary literature on Quine, the judgment Quine makes in favor of the nominalism outlined in “Steps Toward a Constructive Nominalism” is in tension with the naturalism he later adopts. In this paper, I show the consensus view is mistaken by showing that Quine’s judgment is rooted in a naturalistic standard of clarity. Moreover, I argue that Quine late in his career is committed to accepting one plausible reading of his judgment in 1947. In (...) making these arguments, I draw attention to a version of naturalism that misreadings of Quine have prevented philosophers from appreciating, and thereby articulate and clarify a version of naturalism I recommend philosophers investigate today. (shrink)

Some of the concerns which motivate attempts to provide a philosophical reduction of nomological necessity are briefly introduced in I. In II, Hempel's treatment of the paradoxes is contrasted with a position which holds that nomological necessity is a pragmatic dimension of laws of nature, and that this pragmatic dimension is of such a type that it prevents laws of nature from contraposing. Such a position is, however, untenable unless (i) the sense of 'pragmatics' at issue is specified, and the (...) possibility of pragmatic differences resulting in differences in confirmation is defended, and (ii) a relevant pragmatic difference between contrapositives is indicated. III attempts to satisfy condition (i) by developing a new sense of pure pragmatics and argues that some remarks by Goodman and Scheffler together with work on the logic of explanation by Dr. Rescher and myself suggest that nomological contrapositives are not pragmatically equivalent (i.e. substitutable salva veritate in the pure pragmatics of an ideal scientific language). If such is the case, condition (ii) is also satisfied. (shrink)

In this paper I investigate how differences in approach to truth and logic (in particular, a deflationist vs. a substantivist approach to these fields) affect philosophers’ views concerning pluralism and normativity in these fields. My perspective on truth and logic is largely epistemic, focusing on the role of truth in knowledge (rather than on the use of the words “true” and “truth” in natural language), and my reference group includes Carnap (1934), Harman (1986), Horwich (1990), Wright (1992), Beall and Restall (...) (2006), Field (2009), Lynch (2009), and Sher (2016a).1 Whenever possible, I focus on positive rather than negative views on the issues involved, although in some cases this is not possible. (shrink)

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)

How many logics do logical pluralists adopt, or are allowed to adopt, or ought to adopt, in arguing for their view? These metatheoretical questions lurk behind much of the discussion on logical pluralism, and have a direct bearing on normative issues concerning the choice of a correct logic and the characterization of valid reasoning. Still, they commonly receive just swift answers – if any. Our aim is to tackle these questions head on, by clarifying the range of possibilities that logical (...) pluralists have at their disposal when it comes to the metatheory of their position, and by spelling out which routes are advisable. We explore ramifications of all relevant responses to our question: no logic, a single logic, more than one logic. In the end, we express skepticism that any proposed answer is viable. This threatens the coherence of current and future versions of logical pluralism. (shrink)

In Sect. 1 it is argued that systems of logic are exceptional, but not a priori necessary. Logics are exceptional because they can neither be demonstrated as valid nor be confirmed by observation without entering a circle, and their motivation based on intuition is unreliable. On the other hand, logics do not express a priori necessities of thinking because alternative non-classical logics have been developed. Section 2 reflects the controversies about four major kinds of non-classical logics—multi-valued, intuitionistic, paraconsistent and quantum (...) logics. Its purpose is to show that there is no particular domain or reason that demands the use of a non-classical logic; the particular reasons given for the non-classical logic can also be handled within classical logic. The result of Sect. 2 is substantiated in Sect. 3, where it is shown (referring to other work) that all four kinds of non-classical logics can be translated into classical logic in a meaning-preserving way. Based on this fact a justification of classical logic is developed in Sect. 4 that is based on its representational optimality. It is pointed out that not many but a few non-classical logics can be likewise representationally optimal. However, the situation is not symmetric: classical logic has ceteris paribus advantages as a unifying metalogic, while non-classical logics can have local simplicity advantages. (shrink)

It is well known that Ernest Gellner made substantial use of his knowledge of the social sciences in philosophy. Here I discuss how he used it on the basis of a few examples taken from Gellner’s philosophical output. It is argued that he made a number of highly original “translations”, or re-interpretations, of philosophical theories and problems using his knowledge of the social sciences. While this method is endorsed, it is also argued that some of Gellner’s translations crossed the line (...) between the original and the idiosyncratic. (shrink)