The subject of this article is Modal-Epistemic Arithmetic (MEA), a theory introduced by Horsten to interpret Epistemic Arithmetic (EA), which in turn was introduced by Shapiro to interpret Heyting Arithmetic. I will show how to interpret MEA in EA such that one can prove that the interpretation of EA is MEA is faithful. Moreover, I will show that one can get rid of a particular Platonist assumption. Then I will discuss models for MEA in light (...) of the problems of logical omniscience and logical competence. Awareness models, impossible worlds models and syntactical models have been introduced to deal with the first problem. Certain conditions on the accessibility relations are needed to deal with the second problem. I go on to argue that those models are subject to the problem of quantifying in, for which I will provide a solution. (shrink)

The subject of the first section is Carnapian modal logic. One of the things I will do there is to prove that certain description principles, viz. the ''self-predication principles'', i.e. the principles according to which a descriptive term satisfies its own descriptive condition, are theorems and that others are not. The second section will be devoted to Carnapian modal arithmetic. I will prove that, if the arithmetical theory contains the standard weak principle of induction, modal truth collapses to truth. (...) Then I will propose a different formulation of Carnapian modal arithmetic and establish that it is free of collapse. Noteworthy is that one can retain the standard strong principle of induction. I will occupy myself in the third section with Carnapian epistemic logic and arithmetic. Here too it is claimed that the standard weak principle of induction is invalid and that the alternative principle is valid. In the fourth and last section I will get back to the self-predication principles and I will point to some of the consequences if one adds them to Carnapian Epistemic arithmetic. The interaction of self-predication principles and the strong principle of induction results in a collapse of de re knowability. (shrink)

Philosophers of science since Nagel have been interested in the links between intertheoretic reduction and explanation, understanding and other forms of epistemic progress. Although intertheoretic reduction is widely agreed to occur in pure mathematics as well as empirical science, the relationship between reduction and explanation in the mathematical setting has rarely been investigated in a similarly serious way. This paper examines an important particular case: the reduction of arithmetic to set theory. I claim that the reduction is unexplanatory. (...) In defense of this claim, I offer evidence from mathematical practice, and I respond to contrary suggestions due to Steinhart, Maddy, Kitcher and Quine. I then show how, even if set-theoretic reductions are generally not explanatory, set theory can nevertheless serve as a legitimate foundation for mathematics. Finally, some implications of my thesis for philosophy of mathematics and philosophy of science are discussed. In particular, I suggest that some reductions in mathematics are probably explanatory, and I propose that differing standards of theory acceptance might account for the apparent lack of unexplanatory reductions in the empirical sciences. (shrink)

The central topic of this article is (the possibility of) de re knowledge about natural numbers and its relation with names for numbers. It is held by several prominent philosophers that (Peano) numerals are eligible for existential quantification in epistemic contexts (‘canonical’), whereas other names for natural numbers are not. In other words, (Peano) numerals are intimately linked with de re knowledge about natural numbers, whereas the other names for natural numbers are not. In this article I am looking (...) for an explanation of this phenomenon. It is argued that the standard induction scheme plays a key role. (shrink)

A crucial part of the contemporary interest in logicism in the philosophy of mathematics resides in its idea that arithmetical knowledge may be based on logical knowledge. Here an implementation of this idea is considered that holds that knowledge of arithmetical principles may be based on two things: (i) knowledge of logical principles and (ii) knowledge that the arithmetical principles are representable in the logical principles. The notions of representation considered here are related to theory-based and structure-based notions of representation (...) from contemporary mathematical logic. It is argued that the theory-based versions of such logicism are either too liberal (the plethora problem) or are committed to intuitively incorrect closure conditions (the consistency problem). Structure-based versions must on the other hand respond to a charge of begging the question (the circularity problem) or explain how one may have a knowledge of structure in advance of a knowledge of axioms (the signature problem). This discussion is significant because it gives us a better idea of what a notion of representation must look like if it is to aid in realizing some of the traditional epistemic aims of logicism in the philosophy of mathematics. (shrink)

This book is written so as to be ‘accessible to philosophers without a mathematical background’. The reviewer can assure the reader that this aim is achieved, even if only by focusing throughout on just one example of an arithmetical truth, namely ‘7+5=12’. This example’s familiarity will be reassuring; but its loneliness in this regard will not. Quantified propositions — even propositions of Goldbach type — are below the author’s radar.The author offers ‘a new kind of arithmetical epistemology’, one which ‘respects (...) certain important intuitions’ 1 : apriorism, realism, and empiricism. The book contains some clarification of these ‘isms’, and some thoughtful critiques of major positions regarding them, as espoused by such representative figures as Boghossian, Bealer, Peacocke, Field, Bostock, Maddy, Locke, Kant, C.I. Lewis, Ayer, Quine, Fodor, and McDowell. The philosophical reader will find some interest and value in these wider-ranging discussions. Our concern in this review, however, is to examine closely the original positive proposal on offer.Arithmetical truths, the author maintains, are conceptual truths. Knowing truths like 7+5=12 involves no ‘epistemic reliance on any empirical evidence’; but that, she says, is not to claim ‘epistemic independence of the senses altogether’. She wants to show that "experience grounds our concepts … and then mere conceptual examination enables us to learn arithmetical truths ." Concepts that are ‘appropriately sensitive’ to ‘the nature of [an independent] reality’ she calls grounded. Because of the role of grounded concepts, ‘arithmetical truths explain our arithmetical beliefs in the right sort of way for those beliefs to count as knowledge’ .In the context of her concentration on the special nature of arithmetical knowledge, the author offers what could strike some bystanders as an unnecessarily over-ambitious account of knowledge tout court. Knowledge, for the author, is "true belief which … ". (shrink)

One of the philosophical uses of Dedekind’s categoricity theorem for Peano Arithmetic is to provide support for semantic realism. To this end, the logical framework in which the proof of the theorem is conducted becomes highly significant. I examine different proposals regarding these logical frameworks and focus on the philosophical benefits of adopting open-ended schemas in contrast to second order logic as the logical medium of the proof. I investigate Pederson and Rossberg’s critique of the ontological advantages of open-ended (...) arithmetic when it comes to establishing the categoricity of Peano Arithmetic and show that the critique is highly problematic. I argue that Pederson and Rossberg’s ontological criterion deliver the bizarre result that certain first order subsystems of Peano Arithmetic have a second order ontology. As a consequence, the application of the ontological criterion proposed by Pederson and Rossberg assigns a certain type of ontology to a theory, and a different, richer, ontology to one of its subtheories. (shrink)

We propose that, for the purpose of studying theoretical properties of the knowledge of an agent with Artificial General Intelligence (that is, the knowledge of an AGI), a pragmatic way to define such an agent’s knowledge (restricted to the language of Epistemic Arithmetic, or EA) is as follows. We declare an AGI to know an EA-statement φ if and only if that AGI would include φ in the resulting enumeration if that AGI were commanded: “Enumerate all the EA-sentences (...) which you know.” This definition is non-circular because an AGI, being capable of practical English communication, is capable of understanding the everyday English word “know” independently of how any philosopher formally defines knowledge; we elaborate further on the non-circularity of this circular-looking definition. This elegantly solves the problem that different AGIs may have different internal knowledge definitions and yet we want to study knowledge of AGIs in general, without having to study different AGIs separately just because they have separate internal knowledge definitions. Finally, we suggest how this definition of AGI knowledge can be used as a bridge which could allow the AGI research community to import certain abstract results about mechanical knowing agents from mathematical logic. (shrink)

The mind-body problem is one of the important topics in philosophy of mind and cognitive science. Following the analytical tradition of linguistic and logical analysis, we focus on two aspects of the mind- body problem: one is around Gödel's incompleteness theorem, and the other is on cognitive logic, especially on the question of whether Epistemological Arithmetic and machines are private. In the former case, in response to the popular view that the Gödel Incompleteness Theorem supports dualism in the mind-body (...) problem, H. Putnam constructs a counter-argument that defends the computationalist agenda: the equivalence of mind and Turing machine. In this regard, the paper discusses Putnam's line of analysis and then argues that it is unsound. In the latter case, the paper examines in detail the cognitive form of the expression of privateness and concludes, together with recent results in EA, that the existence of privateness in Turing machines is logically untenable and, therefore, we argue that the mind is not equivalent to a machine in terms of cognitive ability and privateness, i.e., the computationalist agenda is not valid. (shrink)

Daniel Isaacson has advanced an epistemic notion of arithmetical truth according to which the latter is the set of truths that we grasp on the basis of our understanding of the structure of natural numbers alone. Isaacson’s thesis is then the claim that Peano Arithmetic (PA) is the theory of finite mathematics, in the sense that it proves all and only arithmetical truths thus understood. In this paper, we raise a challenge for the thesis and show how it (...) can be overcome. We introduce the concept of purity for theories of arithmetic: a theory of arithmetic is pure when it only proves arithmetical truths. Then, we argue that, under Isaacson’s thesis, some PA-provable truths—including transfinite induction claims for infinite ordinals and some consistency statements—are seemingly not arithmetical in Isaacson’s sense, and hence that Isaacson’s thesis might entail the impurity of PA. Nonetheless, we conjecture that the advocate of Isaacson’s thesis can avoid this undesirable consequence: the arithmetical nature, as understood by Isaacson, of all contentious PA-provable statements can be justified. As a case study, we explore how this is done for transfinite induction claims with infinite ordinals below ε0. To this end, we show that the PA-proof of such claims employs exclusively resources from finite mathematics, and that ordinals below ε0 are finitary objects despite being infinite. (shrink)

This paper considers whether incompatibilism, the view that negation is to be explained in terms of a primitive notion of incompatibility, and Fregeanism, the view that arithmetical truths are analytic according to Frege’s definition of that term in §3 of Foundations of Arithmetic, can both be upheld simultaneously. Both views are attractive on their own right, in particular for a certain empiricist mind-set. They promise to account for two philosophical puzzling phenomena: the problem of negative truth and the problem (...) of epistemic access to numbers. For an incompatibilist, proofs of numerical non-identities must appeal to primitive incompatibilities. I argue that no analytic primitive incompatibilities are forthcoming. Hence incompatibilists cannot be Fregeans. (shrink)

The workshop took place in Leuven, Belgium, and was hosted by the KU Leuven's Centre for Logic and Analytic Philosophy. The workshop’s theme was the syntactical treatment of (alethic, epistemic, etc.) modalities. The standard view on modalities nowadays is that they are operators. Syntactic theories, however, treat modalities as predicates, and thus have to assume a background theory which is sufficiently strong to encode its own formulas (usually, one works with some system of arithmetic and Gödel coding). As (...) a consequence, such theories suffer from paradoxes of self-referentiality. For example, just as the liar sentence states of itself that it is false, the knower sentence states of itself that it is unknown. Kaplan and Montague (1960: 'A paradox regained', Notre Dame J. Formal Logic, vol. 1, pp. 79–90) famously showed that any sufficiently strong theory that contains the knower is inconsistent. (shrink)

There is a long-standing gap in the literature as to whether Gödelian incompleteness constitutes a challenge for Neo-Logicism, and if so how serious it is. In this paper, I articulate and address the challenge in detail. The Neo-Logicist project is to demonstrate the analyticity of arithmetic by deriving all its truths from logical principles and suitable definitions. The specific concern raised by Gödel’s first incompleteness theorem is that no single sound system of logic syntactically implies all arithmetical truths. I (...) set out some responses that initially seem appealing and explain why they are not compelling. The upshot is that Neo-Logicism either offers an epistemic route only to some truths of arithmetic; or that it has to move from a syntactic to a semantic notion of logical consequence, which risks undermining its epistemic goals. I conclude by considering Crispin Wright’s recent attempt to address Gödelian incompleteness, which I argue is not satisfactory. (shrink)

In this paper, I start by describing and examining the main results about the option of formalizing the Yablo Paradox in arithmetic. As it is known, although it is natural to assume that there is a right representation of that paradox in first order arithmetic, there are some technical results that give rise to doubts about this possibility. Then, I present some arguments that have challenged that Yablo’s construction is non-circular. Just like that, Priest (1997) has argued that (...) such formalization shows that Yablo’s Paradox involves implicit circularity. In the same direction, Beall (2001) has introduced epistemic factors in this discussion. Even more, Priest has also argued that the introduction of infinitary reasoning would be of little help. Finally, one could reject definitions of circularity in term of fixed-point adopting non-well-founded set theory. Then, one could hold that the Yablo paradox and the Liar paradox share the same non-well-founded structure. So, if the latter is circular, the first is too. In all such cases, I survey Cook’s approach (2006, forthcoming) on those arguments for the charge of circularity. In the end, I present my position and summarize the discussion involved in this volume. En este artículo, describo y examino los principales resultados vinculados a la formalización de la paradoja de Yablo en la aritmética. Aunque es natural suponer que hay una representación correcta de la paradoja en la aritmética de primer orden, hay algunos resultados técnicos que hacen surgir dudas acerca de esta posibilidad. Más aún, presento algunos argumentos que han cuestionado que la construcción de Yablo no sea circular. Así, Priest (1997) ha argumentado que la formalización de la paradoja de Yablo en la aritmética de primer orden muestra que la misma involucra implícitamente circularidad. En la misma dirección, Beall (2001) ha introducido factores epistémicos en esta discusión. Más aún, Priest ha también argumentado que la introducción de razonamiento infinitario como complemento de la formalización en la aritmética sería de poca ayuda. Finalmente, se podría rechazar todo intento de dar definiciones de circularidad en términos de puntos fijos adoptando teoría de conjuntos infundados. Entonces, se podría sostener que la paradoja de Yablo y la del mentiroso comparten la misma estructura infundada. Por eso, si la última es circular, también lo es la primera. En todos los casos, presento el enfoque de Roy Cook (2006, en prensa) sobre estos argumentos que atribuyen circularidad a la construcción de Yablo. En el final, presento mi posición y un breve resumen de la discusión involucrada en este volumen. (shrink)

According to Quine, Charles Parsons, Mark Steiner, and others, Russell’s logicist project is important because, if successful, it would show that mathematical theorems possess desirable epistemic properties often attributed to logical theorems, such as aprioricity, necessity, and certainty. Unfortunately, Russell never attributed such importance to logicism, and such a thesis contradicts Russell’s explicitly stated views on the relationship between logic and mathematics. This raises the question: what did Russell understand to be the philosophical importance of logicism? Building on recent (...) work by Andrew Irvine and Martin Godwyn, I argue that Russell thought a systematic reduction of mathematics increases the certainty of known mathematical theorems (even basic arithmetical facts) by showing mathematical knowledge to be coherently organized. The paper outlines Russell’s theory of coherence, and discusses its relevance to logicism and the certainty attributed to mathematics. (shrink)

This thesis is about how deduction is analytic and, at the same time, informative. In the first two chapters I am after the question of the justification of deduction. This justification is circular in the sense that to explain how deduction works we use some basic deductive rules. However, this circularity is not trivial as not every rule can be justified circularly. Moreover, deductive rules may not need suasive justification because they are not ampliative. Deduction preserves meaning, that is, the (...) meaning of non-logical vocabulary of any theory which is developed by deductive reasoning remains unchanged. It means that deduction adds no information to what we already had in our premises. This is why deduction is analytic. -/- However, there are many ways deduction can be informative. In the next three chapters, I will pick a specific kind of deductive reasoning, namely arithmetical reasoning, and will attempt to understand the nature of information we obtain by this kind of reasoning. There is a difference between simple deductive moves such as inferring `Socrates is mortal' from `All human are mortal' and `Socrates is human', and inferring that a relation is reflexive given that it is directed, symmetric and transitive. The latter is more complicated and not as easy to prove as the former. Therefore it is informative and the proof we construct to prove it puts us in an epistemic position that we were not in before having the proof. To be more specific, I show that concepts we need to confirm the conclusion are made in the process of proving the conclusion. (shrink)

Metaepistemology may be partly characterized as the study of the nature, aims, methods and legitimacy of epistemology. Given such a characterization, most epistemological views and theories have an important metaepistemological aspect or, at least, a number of more or less explicit metaepistemological commitments. Metaepistemology is an important area of philosophy because it exemplifies that philosophy must serve as its own meta-discipline by continuously reflecting critically on its own methods and aims. Even though philosophical methodology may be regarded as a branch (...) of epistemology, epistemology itself is as much in need of metaphilosophical examination as other core disciplines of philosophy. Moreover, metaepistemology is important because it bears significantly on first-order epistemological questions. Indeed, many of the most prominent contemporary debates in philosophy have a distinctly metaepistemological aspect. For example, the debates between rationalists and empiricists do not only concern the nature of cognition of specific areas – perception, arithmetic, logic and so forth – but also general metaepistemological questions about whether it is realistic and desirable that epistemology be naturalized. Likewise, the debates between epistemic internalists and externalists include metaepistemological debates about whether the proper focus for epistemology should be the cognizer’s rational perspective or some more objective property of the cognizer’s epistemic position. Similarly, the debates concerning the relationship between folk epistemology and epistemological theorizing include metaepistemological debates about how empirical data concerning folk epistemology should impact epistemology itself. Each of these debates provides an example of how first-order epistemological issues are deeply connected, and sometimes inseparable from, metaepistemological considerations. (shrink)

Information-theoretic approaches to formal logic analyze the "common intuitive" concepts of implication, consequence, and validity in terms of information content of propositions and sets of propositions: one given proposition implies a second if the former contains all of the information contained by the latter; one given proposition is a consequence of a second if the latter contains all of the information contained by the former; an argument is valid if the conclusion contains no information beyond that of the premise-set. This (...) paper locates information-theoretic approaches historically, philosophically, and pragmatically. Advantages and disadvantages are identified by examining such approaches in themselves and by contrasting them with standard transformation-theoretic approaches. Transformation-theoretic approaches analyze validity (and thus implication) in terms of transformations that map one argument onto another: a given argument is valid if no transformation carries it onto an argument with all true premises and false conclusion. Model-theoretic, set-theoretic, and substitution-theoretic approaches, which dominate current literature, can be construed as transformation-theoretic, as can the so-called possible-worlds approaches. Ontic and epistemic presuppositions of both types of approaches are considered. Attention is given to the question of whether our historically cumulative experience applying logic is better explained from a purely information-theoretic perspective or from a purely transformation-theoretic perspective or whether apparent conflicts between the two types of approaches need to be reconciled in order to forge a new type of approach that recognizes their basic complementarity. (shrink)

Responding rationally to the information that others disagree with one’s beliefs requires assessing the epistemic credentials of the opposing beliefs. Conciliatory accounts of disagreement flow in part from holding that these assessments must be independent from one’s own initial reasoning on the disputed matter. I argue that this claim, properly understood, does not have the untoward consequences some have worried about. Moreover, some of the difficulties it does engender must be faced by many less conciliatory accounts of disagreement.

It is clear that lack of awareness of the consequences of an action can undermine moral responsibility and blame for these consequences. But when and how it does so is controversial. Sometimes an agent believing that the outcome might occur is excused because it seemed unlikely to her, and sometimes an agent having no idea that it would occur is nevertheless to blame. A low or zero degree of belief might seem to excuse unless the agent “should have known better”, (...) but it is unclear how to spell out this normative condition. -/- This chapter combines (a) an independently motivated account of responsibility, blame, and credit as grounded in a normal explanatory relation between agential qualities and objects of responsibility with (b) the familiar Strawsonian idea that moral blame and credit depend on the agent’s quality of will. The resulting explanatory quality of will condition on moral responsibility is then further motivated by being shown to account for the effects on moral blame and credit of justifications, as well as of excuses and undermined control in cases not involving ignorance. -/- The explanatory quality of will condition is finally applied to cases involving various degrees of lack of awareness. Though this condition itself involves no awareness requirement, it is shown how it accounts for the degrees to which lack of awareness can excuse. It is also explained how lack of awareness fails as an excuse exactly when the agent should have known better and can be blamed for not doing so. (shrink)

Expressivists about epistemic modals deny that ‘Jane might be late’ canonically serves to express the speaker’s acceptance of a certain propositional content. Instead, they hold that it expresses a lack of acceptance. Prominent expressivists embrace pragmatic expressivism: the doxastic property expressed by a declarative is not helpfully identified with that sentence’s compositional semantic value. Against this, we defend semantic expressivism about epistemic modals: the semantic value of a declarative from this domain is the property of doxastic attitudes it (...) canonically serves to express. In support, we synthesize data from the critical literature on expressivism—largely reflecting interactions between modals and disjunctions—and present a semantic expressivism that readily predicts the data. This contrasts with salient competitors, including: pragmatic expressivism based on domain semantics or dynamic semantics; semantic expressivism à la Moss [2015]; and the bounded relational semantics of Mandelkern [2019]. (shrink)

Theories of epistemic justification are commonly assessed by exploring their predictions about particular hypothetical cases – predictions as to whether justification is present or absent in this or that case. With a few exceptions, it is much less common for theories of epistemic justification to be assessed by exploring their predictions about logical principles. The exceptions are a handful of ‘closure’ principles, which have received a lot of attention, and which certain theories of justification are well known to (...) invalidate. But these closure principles are only a small sample of the logical principles that we might consider. In this paper, I will outline four further logical principles that plausibly hold for justification and two which plausibly do not. While my primary aim is just to put these principles forward, I will use them to evaluate some different approaches to justification and (tentatively) conclude that a ‘normic’ theory of justification best captures its logic. (shrink)

Questions about the transparency of evidence are central to debates between factive and non-factive versions of mentalism about evidence. If all evidence is transparent, then factive mentalism is false, since no factive mental states are transparent. However, Timothy Williamson has argued that transparency is a myth and that no conditions are transparent except trivial ones. This paper responds by drawing a distinction between doxastic and epistemic notions of transparency. Williamson's argument may show that no conditions are doxastically transparent, but (...) it fails to show that no conditions are epistemically transparent. Moreover, this reinstates the argument from the transparency of evidence against factive mentalism. (shrink)

This paper argues that group attitudes can be assessed in terms of standards of rationality and that group-level rationality need not be due to individual-level rationality. But it also argues that groups cannot be collective epistemic agents and are not collectively responsible for collective irrationality. I show that we do not need the concept of collective epistemic agency to explain how group-level irrationality can arise. Group-level irrationality arises because even rational individuals can fail to reason about how their (...) attitudes will combine with those of others. In some cases they are morally responsible for this failure, in others they are not. Moreover, the argument for collective epistemic agency is incoherent because reasons-for-groups are ipso facto reasons-for-individual. Instead of talking about reasons-for-groups, we should therefore distinguish between self-regarding reasons and group-regarding reasons. Both kinds of reasons are reasons-for-individuals. These conceptual considerations in favour of moderate individualism are strengthened by an analysis of our moral practice of responding to collective shortfalls of rationality and by the unpalatable moral implications of collectivism about epistemic agency. There is no need to change the subject. Groups can be rational or irrational, but they do not reason. (shrink)

Scientists imagine for epistemic reasons, and these imaginings can be better or worse. But what does it mean for an imagining to be epistemically better or worse? There are at least three metaepistemological frameworks that present different answers to this question: epistemological consequentialism, deontic epistemology, and virtue epistemology. This paper presents empirical evidence that scientists adopt each of these different epistemic frameworks with respect to imagination, but argues that the way they do this is best explained if scientists (...) are fundamentally epistemic consequentialists about imagination. (shrink)

Epistemic constitutivism (EC) holds that the nature of believing is such that it gives rise to a standard of correctness and that other epistemic normative notions (e.g., reasons for belief) can be explained in terms of this standard. If defensible, this view promises an attractive and unifying account of epistemic normativity. However, EC faces a forceful objection: that constitutive standards of correctness are never enough for generating normative reasons. This paper aims to defend EC in the face (...) of this objection. I do so in two steps. First, I dispute a crucial assumption underlying the case against EC: that constitutive standards of correctness in general are ‘reason-giving’ only if and because there is also a prior reason to comply with them. Second, I outline a strategy of how EC can meet the challenge of explaining what’s special about the activity of believing such that, unlike other standard-governed activities, it is capable of generating normative reasons. (shrink)

This chapter discusses epistemic objections to non-naturalist moral realism. The goal of the chapter is to determine which objections are pressing and which objections can safely be dismissed. The chapter examines five families of objections: (i) one involving necessary conditions on knowledge, (ii) one involving the idea that the causal history of our moral beliefs reflects the significant impact of irrelevant influences, (iii) one relying on the idea that moral truths do not play a role in explaining our moral (...) beliefs, (iv) one involving the claim that if moral realism is true then our moral beliefs are unlikely to be reliable, and (v) one involving the claim that moral realism is incompatible with there being a plausible explanation of our reliability about morality. The overall conclusion of the chapter is that the final objection is by far the most pressing. (shrink)

Recent experimental evidence from developmental psychology and cognitive neuroscience indicates that humans are equipped with unlearned elementary mathematical skills. However, formal mathematics has properties that cannot be reduced to these elementary cognitive capacities. The question then arises how human beings cognitively deal with more advanced mathematical ideas. This paper draws on the extended mind thesis to suggest that mathematical symbols enable us to delegate some mathematical operations to the external environment. In this view, mathematical symbols are not only used to (...) express mathematical concepts—they are constitutive of the mathematical concepts themselves. Mathematical symbols are epistemic actions, because they enable us to represent concepts that are literally unthinkable with our bare brains. Using case-studies from the history of mathematics and from educational psychology, we argue for an intimate relationship between mathematical symbols and mathematical cognition. (shrink)

Journal of Political Philosophy, EarlyView.

The value of optimality modeling has long been a source of contention amongst population biologists. Here I present a view of the optimality approach as at once playing a crucial explanatory role and yet also depending on external sources of confirmation. Optimality models are not alone in facing this tension between their explanatory value and their dependence on other approaches; I suspect that the scenario is quite common in science. This investigation of the optimality approach thus serves as a case (...) study, on the basis of which I suggest that there is a widely felt tension in science between explanatory independence and broad epistemic interdependence, and that this tension influences scientific methodology. (shrink)

Collective deliberation is fuelled by disagreements and its epistemic value depends, inter alia, on how the participants respond to each other in disagreements. I use this accountability thesis to argue that deliberation may be valued not just instrumentally but also for its procedural features. The instrumental epistemic value of deliberation depends on whether it leads to more or less accurate beliefs among the participants. The procedural epistemic value of deliberation hinges on the relationships of mutual accountability that (...) characterize appropriately conducted deliberation. I will argue that it only comes into view from the second-person standpoint. I shall explain what the second-person standpoint in the epistemic context entails and how it compares to Stephen Darwall’s interpretation of the second-person standpoint in ethics. (shrink)

“Proof of concept” is a phrase frequently used in descriptions of research sought in program announcements, in experimental studies, and in the marketing of new technologies. It is often coupled with either a short definition or none at all, its meaning assumed to be fully understood. This is problematic. As a phrase with potential implications for research and technology, its assumed meaning requires some analysis to avoid it becoming a descriptive category that refers to all things scientifically exciting. I provide (...) a short analysis of proof of concept research and offer an example of it within synthetic biology. I suggest that not only are there activities that circumscribe new epistemological categories but there are also associated normative ethical categories or principles linked to the research. I examine these and provide an outline for an alternative ethical account to describe these activities that I refer to as “extended agency ethics”. This view is used to explain how the type of research described as proof of concept also provides an attendant proof of principle that is the result of decision-making that extends across practitioners, their tools, techniques, and the problem solving activities of other research groups. (shrink)

This article examines epistemic impacts of social media, merging Gibson’s affordance theory with the notion of selective permeability, which holds people encounter objective differences in a setting because of their distinct capacities, only here applying the idea to online spaces. I start by circumscribing my deployment of “affordances,” taking care not to totally divorce the term from Gibson’s intent, as often happens in information technologies research. I next detail ways that selective permeability characterizes online epistemic landscapes, focusing on (...) how factors (like culture) moderate normative standards for sharing information. This leads to a discussion about selective receptivity and blindness to information in the context of social media—a situation that amplifies political divides and renders antagonists mutually incomprehensible. This segues into my final topic: an exposition of how social media can make the offline world more selectively hostile to some. An additional proposition is that practical habits cultivated on networking apps can modulate what affordances are present in offline arenas, as opposed to just affecting which ones get noticed. Throughout, I suggest that selective permeability answers an increasingly recognized challenge: the difficulty of generalizing conclusions about one app to others and across cultures, ages, etc. Ultimately, my aim is not only to explicate how social media fragments common social knowledge but to defend selective permeability as an epistemic template for comprehending social media. (shrink)

We motivate the idea that presupposition is a transparent attitude. We then explain why epistemic opacity is not a serious problem for Robert Stalnaker's theory of content and conversation. We conclude with critical remarks about John Hawthorne and Ofra Magidor's alternative theory.

According to one sort of epistemic relativist, normative epistemic claims (e.g., evidence E justifies hypothesis H) are never true or false simpliciter, but only relative to one or another epistemic system. In chapter 6 of Fear of Knowledge, Paul Boghossian objects to this view on the ground that its central notions cannot be explained, and that it cannot account for the normativity of epistemic discourse. This paper explores how the dogged relativist might respond.

In a possible world framework, an agent can be said to know a proposition just in case the proposition is true at all worlds that are epistemically possible for the agent. Roughly, a world is epistemically possible for an agent just in case the world is not ruled out by anything the agent knows. If a proposition is true at some epistemically possible world for an agent, the proposition is epistemically possible for the agent. If a proposition is true at (...) all epistemically possible worlds for an agent, the proposition is epistemically necessary for the agent, and as such, the agent knows the proposition. -/- This framework presupposes an underlying space of worlds that we can call epistemic space. Traditionally, worlds in epistemic space are identified with possible worlds, where possible worlds are the kinds of entities that at least verify all logical truths. If so, given that epistemic space consists solely of possible worlds, it follows that any world that may remain epistemically possible for an agent verifies all logical truths. As a result, all logical truths are epistemically necessary for any agent, and the corresponding framework only allows us to model logically omniscient agents. This is a well-known consequence of the standard possible world framework, and it is generally taken to imply that the framework cannot be used to model non-ideal agents that fall short of logical omniscience. -/- A familiar attempt to model non-ideal agents within a broadly world involving framework centers around the use of impossible worlds where the truths of logic can be false. As we shall see, if we admit impossible worlds where “anything goes” in epistemic space, it is easy to avoid logical omniscience. If any logical falsehood is true at some impossible world, then any logical falsehood may remain epistemically possible for some agent. As a result, we can use an impossible world involving framework to model extremely non-ideal agents that do not know any logical truths. -/- A much harder, and considerably less investigated challenge is to ensure that the resulting epistemic space can also be used to model moderately ideal agents that are not logically omniscient but nevertheless logically competent. Intuitively, while such agents may fail to rule out impossible worlds that verify complex logical falsehoods, they are nevertheless able to rule out impossible worlds that verify obvious logical falsehoods. To model such agents, we need a construction of a non-trivial epistemic space that partly consists of impossible worlds where not "anything goes". This involves imposing substantive constraints on impossible worlds to eliminate from epistemic space, say, trivially impossible worlds that verify obvious logical falsehoods. -/- The central aim of this dissertation is to investigate the nature of such non-trivially impossible worlds and the corresponding epistemic spaces. To flag my conclusions, I argue that successful constructions of epistemic spaces that can safely navigate between the Charybdis of logical omniscience and the Scylla of of “anything goes” are hard, if not impossible to find. (shrink)

For several decades, there has been a debate in the philosophical literature concerning whether those of us who live in developed countries are morally required to give some of our money to aid agencies. Many contributors to this debate have apparently taken it that one may simply assume that the effects of the work such agencies do are overwhelmingly positive. If one turns to the literature on such agencies that has emerged in recent decades, however, one finds a number of (...) concerns about such agencies and the work they do that put that assumption in serious doubt. This situation raises a number of pressing questions, many of which have received little or no attention from philosophers. After articulating a number of those questions, I focus mainly on what I call the ‘Epistemic Question (for potential contributors to aid agencies)’: How can those of us who are not experts in international aid arrive at an estimate concerning the effects of the work aid agencies do that we have at least some good reason to believe accurate? (shrink)

The paper discusses approaches to Epistemic Contextualism that model the satisfaction of the predicate ‘know’ in a given context C in terms of the notion of belief/fact-matching throughout a contextually specified similarity sphere of worlds that is centred on actuality. The paper offers three counterexamples to approaches of this type and argues that they lead to insurmountable difficulties. I conclude that what contextualists (and Subject-Sensitive Invariantists) have traditionally called the ‘epistemic standards’ of a given context C cannot be (...) explicated in terms of a contextually specified similarity sphere that is centred on actuality. The mentioned accounts of epistemic relevance and thus the corresponding accounts of the context-sensitivity (or subject-sensitivity) of ‘knows’ are to be rejected. (shrink)

This paper presents a diagrammatic notation for visualizing epistemic entities and relations. The notation was created during the Visualizing Worldviews project funded by the University of Toronto’s Jackman Humanities Institute and has been further developed by the scholars participating in the university’s Research Opportunity Program. Since any systematic diagrammatic notation should be based on a solid ontology of the respective domain, we first outline the current state of the scientonomic ontology. We then proceed to providing diagrammatic tools for visualizing (...) the epistemic entities and relations of this ontology. These basic diagramming techniques allow us to construct diagrams of various types for both synchronic and diachronic visualizations. The paper concludes by highlighting some future research directions. As the notation presented here is de facto accepted and used in scientonomy, the paper suggests no modifications. (shrink)

Statements containing epistemic modals (e.g., “by spring 2023 most European countries may have the Covid-19 pandemic under control”) are common expressions of epistemic uncertainty. In this paper, previous published findings (Knobe & Yalcin, 2014; Khoo & Phillips, 2018) on the opposition between Contextualism and Relativism for epistemic modals are re-examined. It is found that these findings contain a substantial degree of individual variation. To investigate whether participants differ in their interpretation of epistemic modals, an experiment with (...) multiple phases and sessions is used to classify participants according to the three semantic theories of Relativism, Contextualism, and Objectivism. Through this study, some of the first empirical evidence for the kind of truth-value shifts postulated by semantic Relativism is presented. It is furthermore found that participants’ disagreement judgments match their truth evaluations and that participants are capable of distinguishing between truth and justification. In a second experimental session, it is investigated whether participants thus classified follow the norm of retraction which Relativism uses to account for argumentation with epistemic modals. Here the results are less favorable for Relativism. In a second experiment, these results are replicated and the normative beliefs of participants concerning the norm of retraction are investigated following work on measuring norms by Bicchieri (2017). Again, it is found that on average participants show no strong preferences concerning the norm of retraction for epistemic modals. Yet, it was found that participants who had committed to Objectivism and had training in logics applied the norm of retraction to might-statements. These results present a substantial challenge to the account of argumentation with epistemic modals presented in MacFarlane (2014), as discussed. Keywords: Epistemic Modals, Relativism, Norm Conflicts, Retraction, Semantics, Truth Conditions, Argumentation. (shrink)

In the first section of this paper I present epistemic evidentialism and, in the following two sections, I discuss that view with counterexamples. I shall defend that adequately supporting evidence is a necessary, but not a sufficient, condition for epistemic justification. Although we need epistemic elements other than evidence in order to have epistemic justification, there can be no epistemically justified belief without evidence. However, there are other kinds of justification beyond the epistemic justification, such (...) as prudential or moral justification; therefore, there is room for justified beliefs (in a prudential or moral sense) without evidence. (shrink)

In this paper, I maintain—contrary to those commentators who regard him as a principled republican—that at the core of Spinoza’s political theory is an instrumental, rather than an intrinsic, defense of democratic procedures. Specifically, Spinoza embraces democratic decision procedures primarily because they tend to result in better decisions, defined relative to a procedure-independent standard of correctness or goodness. In contemporary terms, Spinoza embraces an epistemic defense of democracy. I examine Spinoza’s defense of collective governance, showing not only how it (...) differs from other accounts of his time but also how it might contribute to current debates about the epistemic standing of popular governing bodies. In the opening section I defend the thesis that has been contested in recent years that Spinoza was, in fact, a consistent democrat. The second section focuses on procedural (i.e., intrinsic) defenses of democracy, paying particular attention to the republican version of proceduralism that was prominent in Spinoza’s time. And in the final section I present my case for reading Spinoza as an epistemic democrat, comparing his epistemic defense with contemporary versions. What we find are not only striking anticipations of contemporary arguments, but also largely neglected lines of argumentation that reveal both the potential epistemic advantages and disadvantages of democracy. (shrink)

Contrastivism about knowledge is the view that one does not just know some proposition. It is more adequate to say that one knows something rather than something else: I know that I am looking at a tree rather than a bush but I do not know that I am looking at a tree rather than a cleverly done tree imitation. Knowledge is a three-place relation between a subject, a proposition and a contrast set of propositions. There are several advantages of (...) a contrastivist view but also certain problems with it. (shrink)

Some epistemologists think that the Bayesian ideals matter because we can approximate them. That is, our attitudes can be more or less close to the ones of our ideal Bayesian counterpart. In this paper, I raise a worry for this justification of epistemic ideals. The worry is this: In order to correctly compare agents to their ideal counterparts, we need to imagine idealized agents who have the same relevant information, knowledge, or evidence. However, there are cases in which one’s (...) ideal counterpart cannot have one’s information, knowledge, or evidence. In these situations, agents cannot compare themselves to their ideal counterpart. (shrink)

In “Epistemology Naturalized” Quine famously suggests that epistemology, properly understood, “simply falls into place as a chapter of psychology and hence of natural science” (1969, 82). Since the appearance of Quine’s seminal article, virtually every epistemologist, including the later Quine (1986, 664), has repudiated the idea that a normative discipline like epistemology could be reduced to a purely descriptive discipline like psychology. Working epistemologists no longer take Quine’s vision in “Epistemology Naturalized” seriously. In this paper, I will explain why I (...) think this is a mistake. (shrink)

In “The Possibility of Epistemic Nudging” (2021), I address a phenomenon that is widely neglected in the current literature on nudges: intentional doxastic nudging, i.e. people’s intentional influence over other people’s beliefs, rather than over their choices. I argue that, at least in brute cases, nudging is not giving reasons, but rather bypasses reasoning altogether. More specifically, nudging utilizes psychological heuristics and the nudged person’s biases in smart ways. The goal of my paper is to defend the claim that (...) nudging, even when it bypasses reasoning, can result in justified beliefs and knowledge. As I argue, it takes two things to accomplish this goal: suitable meta-epistemological views and appropriate circumstances. If a broadly reliabilist account of justified beliefs and knowledge is correct, and if the relevant belief-forming methods are externally individuated in the right way, then nudging to knowledge is possible. If, in addition, the nudger is knowledgeable, epistemically benevolent and systematically effective, then nudging to knowledge will become reality. In their replies Neil Levy (2021) and Jonathan Matheson and Valerie Joly Chock (2021), put pressure on my argument from different angles. Levy thinks that a better case can be made for his view that nudging is giving testimonial reasons, and finds my objections to this view unconvincing. Matheson and Joly Chock, on the other hand, point out that acquiring knowledge through nudging (i.e. epistemic nudging) is compatible with evidentialism, even if nudging is not giving reasons. On their view, evidentialism provides an explanation of epistemic nudging that is superior to my own account, which, according to them, also suffers from a number of counterintuitive consequences. I am grateful to my critics for raising these concerns, because considering them deepens our perspective on the target phenomenon, and has made me think harder about the relevant epistemological issues. Nevertheless, I am convinced that my core claims can be defended against these criticisms. (shrink)

The paper considers a generalization of Peano arithmetic, Hilbert arithmetic as the basis of the world in a Pythagorean manner. Hilbert arithmetic unifies the foundations of mathematics (Peano arithmetic and set theory), foundations of physics (quantum mechanics and information), and philosophical transcendentalism (Husserl’s phenomenology) into a formal theory and mathematical structure literally following Husserl’s tracе of “philosophy as a rigorous science”. In the pathway to that objective, Hilbert arithmetic identifies by itself information related to finite (...) sets and series and quantum information referring to infinite one as both appearing in three “hypostases”: correspondingly, mathematical, physical and ontological, each of which is able to generate a relevant science and area of cognition. Scientific transcendentalism is a falsifiable counterpart of philosophical transcendentalism. The underlying concept of the totality can be interpreted accordingly also mathematically, as consistent completeness, and physically, as the universe defined not empirically or experimentally, but as that ultimate wholeness containing its externality into itself. (shrink)