A Benacerraf–Field challenge is an argument intended to show that common realist theories of a given domain are untenable: such theories make it impossible to explain how we’ve arrived at the truth in that domain, and insofar as a theory makes our reliability in a domain inexplicable, we must either reject that theory or give up the relevant beliefs. But there’s no consensus about what would count here as a satisfactory explanation of our reliability. It’s sometimes suggested that giving such (...) an explanation would involve showing that our beliefs meet some modal condition, but realists have claimed that this sort of modal interpretation of the challenge deprives it of any force: since the facts in question are metaphysically necessary and so obtain in all possible worlds, it’s trivially easy, even given realism, to show that our beliefs have the relevant modal features. Here I show that this claim is mistaken—what motivates a modal interpretation of the challenge in the first place also motivates an understanding of the relevant features in terms of epistemic possibilities rather than metaphysical possibilities, and there are indeed epistemically possible worlds where the facts in question don’t obtain. (shrink)

Sensitivity has sometimes been thought to be a highly epistemologically significant property, serving as a proxy for a kind of responsiveness to the facts that ensure that the truth of our beliefs isn’t just a lucky coincidence. But it's an imperfect proxy: there are various well-known cases in which sensitivity-based anti-luck conditions return the wrong verdicts. And as a result of these failures, contemporary theorists often dismiss such conditions out of hand. I show here, though, that a sensitivity-based understanding of (...) epistemic luck can be developed that respects what was attractive about sensitivity-based approaches in the first place but that's immune to these failures. (shrink)

The original publication of the article contains two formatting errors, the second of which significantly inhibits readability.

Gödel has argued that we can cultivate the intuition or perception of abstractconcepts in mathematics and logic. Gödel's ideas about the intuition of conceptsare not incidental to his later philosophical thinking but are related to many otherthemes in his work, and especially to his reflections on the incompleteness theorems.I describe how some of Gödel's claims about the intuition of abstract concepts are related to other themes in his philosophy of mathematics. In most of this paper, however,I focus on a central (...) question that has been raised in the literature on Gödel: what kind of account could be given of the intuition of abstract concepts? I sketch an answer to this question that uses some ideas of a philosopher to whom Gödel also turned in this connection: Edmund Husserl. The answer depends on how we understand the conscious directedness toward objects and the meaning of the term abstract in the context of a theory of the intentionality of cognition. (shrink)

Gödel has argued that we can cultivate the intuition or ‘perception’ of abstractconcepts in mathematics and logic. Gödel's ideas about the intuition of conceptsare not incidental to his later philosophical thinking but are related to many otherthemes in his work, and especially to his reflections on the incompleteness theorems.I describe how some of Gödel's claims about the intuition of abstract concepts are related to other themes in his philosophy of mathematics. In most of this paper, however,I focus on a central (...) question that has been raised in the literature on Gödel: what kind of account could be given of the intuition of abstract concepts? I sketch an answer to this question that uses some ideas of a philosopher to whom Gödel also turned in this connection: Edmund Husserl. The answer depends on how we understand the conscious directedness toward ‘objects’ and the meaning of the term ‘abstract’ in the context of a theory of the intentionality of cognition. (shrink)

Paul Benacerraf’s argument that mathematical realism is apparently incompatible with mathematical knowledge has been widely thought to also show that a priori knowledge in general is problematic. Although many philosophers have rejected Benacerraf’s argument because it assumes a causal theory of knowledge, some maintain that Benacerraf nevertheless put his finger on a genuine problem, even though he didn’t state the problem in its most challenging form. After diagnosing what went wrong with Benacerraf’s argument, I argue that a new, more challenging, (...) version of Benacerraf’s problem can be constructed. The new version—what I call the Defeater Version—of Benacerraf’s problem makes use of a no-defeater condition on knowledge and justification. I conclude by arguing that the best way to avoid the problem is to construct a theory of how a priori judgments reliably track the facts. I also suggest four different kinds of theories worth pursuing. (shrink)

The psychological orientation treats semantics as a matter of idealized computation over symbolic structures, and semantic relations like denotation as relations between linguistic expressions and these structures. I argue that results similar to Gödel's incompleteness theorems and Tarski's theorem on truth create foundational difficulties for this view of semantics.

Those who aim to give an account of modal knowledge face two challenges: the integration challenge of reconciling an account of what is involved in knowing modal truths with a plausible story about how we can come to know them, and the reliability challenge of giving a plausible account of how we could have evolved a reliable capacity to acquire modal knowledge. I argue that recent counterfactual and dispositional accounts of modal knowledge cannot solve these problems regarding specifically metaphysical modal (...) truths—leaving us with the threat of skepticism about large portions of metaphysics, and certain other areas of philosophy. I argue, however, that both of these problems look insuperable only if we assume that metaphysical modal discourse serves a describing or tracking function. If we adopt instead a normativist approach to metaphysical modal discourse, which sees the basic function of modal discourse as giving us perspicuous ways of conveying, reasoning with, and renegotiating semantic rules, the problems show up very differently. The modal normativist can give a plausible response to both of the classic problems of how we can come to know metaphysical modal truths. (shrink)

A common anti-realist strategy is to argue that moral realism (or at least the non-naturalist form of it) should be abandoned because it cannot adequately make room for moral knowledge and justified moral belief, for example in view of an evolutionary account of the origins of moral beliefs or of the existence of radical moral disagreement. Why is that (alleged) fact supposed to undermine realism? I examine and discuss three possible answers to this question. According to the answer that I (...) think holds most promise, it undermines realism because it renders realism “epistemically incoherent” (in a sense explicated in the paper), and a central aim of the paper is to elaborate and defend that suggestion against certain objections. I end by briefly commenting on the more general significance of the discussion, by considering some other areas (epistemology and vagueness) where similar questions might be raised. (shrink)

“What kind of psychological theory could relate our use of words to sets of possible worlds?” So queries a recent author, but the question is rhetorical, the insinuation being that any analysis or explanation of semantical notions in terms of possible worlds will involve an account that won't square with a naturalistic view of language acquisition or use. Such feelings are widespread; my purpose here is to argue that they are unjustified.

That laws of nature play a vital role in explanation, prediction, and inductive inference is far clearer than the nature of the laws themselves. My hope here is to shed some light on the nature of natural laws by developing and defending the view that they involve genuine relations between properties. Such a position is suggested by Plato, and more recent versions have been sketched by several writers.~ But I am not happy with any of these accounts, not so much (...) because they lack detail or engender minor difficulties, though they do, but because they share a quite fundamental defect. My goal here is to make this defect clear and, more importantly, to present a rather different version of this general conception of laws that avoids it. I begin by considering several features of natural laws and argue that these are best explained by the view that laws involve properties, that this involvement takes the form of a genuine relation between properties, and, finally, that the relation is a metaphysically necessary one. In the second section I start at the other end, and by reflecting on the nature of properties arrive at a similar account of natural laws. In the final section I develop this account in more detail, with emphasis on the nature of the relation between properties it invokes. Along the way several natural objections to the account are answered. (shrink)

Text se věnuje možnosti uspokojivé epistemologie matematického platonismu: otázce, jak je možné získat znalost o entitách, které jsou abstraktní a na mysli nezávislé. První část textu se zaměřuje na vymezení platonismu a formulaci epistemologických námitek, představuje námitky Paula Benacerrafa a Hartryho Fielda. Ve druhé části je představena a analyzována matematická intuice postulovaná Kurtem Gödelem. Gödelova epistemologická strategie je upřesněna pomocí otázek: (1) O jaký typ intuice se jedná? (2) Jedná se o spolehlivý zdroj znalosti? (3) Podává Gödel nějaké vysvětlení mechanismu (...) intuice? (shrink)

Neologicists have sought to ground mathematical knowledge in abstraction. One especially obstinate problem for this account is the bad company problem. The leading neologicist strategy for resolving this problem is to attempt to sift the good abstraction principles from the bad. This response faces a dilemma: the system of ‘good’ abstraction principles either falls foul of the Scylla of inconsistency or the Charybdis of being unable to recover a modest portion of Zermelo–Fraenkel set theory with its intended generality. This article (...) argues that the bad company problem is due to the ‘static’ character of abstraction on the neologicist's account and develops a ‘dynamic’ account of abstraction that avoids both horns of the dilemma. 1 Introduction2ion Reconstructed3 From Bad to Worse4 Abstraction Reconceived5 Bad Company Made GoodA AppendixA.1SemanticsA.2LogicA.3ConsistencyA.4Strength. (shrink)

What is the point of developing an epistemology for a topic—for example, morality? When is it appropriate to develop the epistemology of a topic? For many topics—for example, the topic of socks—we see no need to develop a special epistemology. Under what conditions, then, does a topic deserve its own epistemology? I seek to answer these questions in this article. I provide a criterion for deciding when we are warranted in developing an epistemological theory for a topic. I briefly apply (...) this criterion to moral epistemology and argue that some approaches to moral epistemology should be abandoned. I also argue that we can develop an epistemology for a topic without committing ourselves to a specific substantive theory of justification, such as reliabilism or coherentism, if we work within a suitably neutral framework. (shrink)

How should one conceive of the method of mathematics, if one takes a naturalist stance? Mathematical knowledge is regarded as the paradigm of certain knowledge, since mathematics is based on the axiomatic method. Natural science is deeply mathematized, and science is crucial for any naturalist perspective. But mathematics seems to provide a counterexample both to methodological and ontological naturalism. To face this problem, some naturalists try to naturalize mathematics relying on Darwinism. But several difficulties arise when one tries to naturalize (...) in this way the traditional view of mathematics, according to which mathematical knowledge is certain and the method of mathematics is the axiomatic method. This paper suggests that, in order to naturalize mathematics through Darwinism, it is better to take the method of mathematics not to be the axiomatic method. (shrink)

This article presents a challenge that those philosophers who deny the causal interpretation of explanations provided by population genetics might have to address. Indeed, some philosophers, known as statisticalists, claim that the concept of natural selection is statistical in character and cannot be construed in causal terms. On the contrary, other philosophers, known as causalists, argue against the statistical view and support the causal interpretation of natural selection. The problem I am concerned with here arises for the statisticalists because the (...) debate on the nature of natural selection intersects the debate on whether mathematical explanations of empirical facts are genuine scientific explanations. I argue that if the explanations provided by population genetics are regarded by the statisticalists as non-causal explanations of that kind, then statisticalism risks being incompatible with a naturalist stance. The statisticalist faces a dilemma: either she maintains statisticalism but has to renounce naturalism; or she maintains naturalism but has to content herself with an account of the explanations provided by population genetics that she deems unsatisfactory. This challenge is relevant to the statisticalists because many of them see themselves as naturalists. (shrink)

The propensity interpretation of fitness draws on the propensity interpretation of probability, but advocates of the former have not attended sufficiently to problems with the latter. The causal power of C to bring about E is not well-represented by the conditional probability Pr. Since the viability fitness of trait T is the conditional probability Pr, the viability fitness of the trait does not represent the degree to which having the trait causally promotes surviving. The same point holds for fertility fitness. (...) This failure of trait fitness to capture causal role can also be seen in the fact that coextensive traits must have the same fitness values even if one of them promotes survival and the other is neutral or deleterious. Although the fitness of a trait does not represent the trait’s causal power to promote survival and reproduction, variation in fitness in a population causally promotes change in trait frequencies; in this sense, fitness variation is a population-level propensity. (shrink)

In this paper I present a new theory of propositions, according to which propositions are abstract mathematical objects: well-formed formulas together with models. I distinguish the theory from a number of existing views and explain some of its advantages  chief amongst which are the following. On this view, propositions are unified and intrinsically truth-bearing. They are mind- and language-independent and they are governed by logic. The theory of propositions is ontologically innocent. It makes room for an appropriate interface with (...) formal semantics and it does not enforce an overly fine or overly coarse level of granularity. (shrink)

In recent discussions concerning the definition of argument, it has been maintained that the word ‘argument’ exhibits the process-product ambiguity, or an act/object ambigu-ity. Drawing on literature on lexical ambiguity we argue that ‘argument’ is not ambiguous. The term ‘argu-ment’ refers to an object, not to a speech act. We also examine some of the important implications of our argument by considering the question: what sort of abstract objects are arguments?

Field’s challenge to platonists is the challenge to explain the reliable match between mathematical truth and belief. The challenge grounds an objection claiming that platonists cannot provide such an explanation. This objection is often taken to be both neutral with respect to controversial epistemological assumptions, and a comparatively forceful objection against platonists. I argue that these two characteristics are in tension: no construal of the objection in the current literature realises both, and there are strong reasons to think that no (...) version of Field’s epistemological objection which has both Neutrality and Force can be construed. (shrink)

The idea that justified modal belief can be accounted for in terms of empirically justified, non-modal belief is enjoying increasing popularity in the epistemology of modality. One alleged reason to prefer modal empiricism over more traditional, rationalist modal epistemologies is that empiricism avoids the problem with the integration challenge that arise for rationalism, assuming that we want to be realists about modal metaphysics. In this paper, I argue that given two very reasonable constraints on what it means to meet the (...) integration challenge for modality, empiricism is currently at best on a par with, but potentially worse off than, rationalist alternatives, with respect to the integration challenge. (shrink)

Mathematical abstraction is the process of considering and ma­nipulating operations, rules, methods and concepts divested from their refe­rence to real world phenomena and circumstances, and also deprived from the content connected to particular applications. There is no one single way of per­forming mathematical abstraction. The term “abstraction” does not name a unique procedure but a general process, which goes many ways that are mostly simultaneous and intertwined; in particular, the process does not amount only to logical subsumption. I will consider (...) comparatively how philosophers consi­der abstraction and how mathematicians perform it, with the aim to bring to light the fundamental thinking processes at play, and to illustrate by signifi­cant examples how much intricate and multi-leveled may be the combination of typical mathematical techniques which include axiomatic method, invariance principles, equivalence relations and functional correspondences. (shrink)

Sometimes we give truth-conditions for sentences of a discourse in other terms. According to Agustín Rayo, when doing so it is sometimes legitimate to use the terms of that very discourse, so long as the terms do not occur in the truth-conditions themselves. I argue that giving truth-conditions in this "outscoping" way prevents one from answering "discourse threat" (for example, the threat of indeterminacy).

Psychologists debate whether mental attributes can be quantified or whether they admit only qualitative comparisons of more and less. Their disagreement is not merely terminological, for it bears upon the permissibility of various statistical techniques. This article contributes to the discussion in two stages. First it explains how temperature, which was originally a qualitative concept, came to occupy its position as an unquestionably quantitative concept (§§1–4). Specifically, it lays out the circumstances in which thermometers, which register quantitative (or cardinal) differences, (...) became distinguishable from thermoscopes, which register merely qualitative (or ordinal) differences. I argue that this distinction became possible thanks to the work of Joseph Black, ca. 1760. Second, the article contends that the model implicit in temperature’s quantitative status offers a better way for thinking about the quantitative status of mental attributes than models from measurement theory (§§5–6). (shrink)

The paper seeks to answer two new questions about truth and scientific change: What lessons does the phenomenon of scientific change teach us about the nature of truth? What light do recent developments in the theory of truth, incorporating these lessons, throw on problems arising from the prevalence of scientific change, specifically, the problem of pessimistic meta-induction?

In this paper a parallel is drawn between the problem of epistemic access to abstract objects in mathematics and the problem of epistemic access to idealized systems in the physical sciences. On this basis it is argued that some recent and more traditional approaches to solving these problems are problematic.

Saul Kripke once noted that there is a tight connection between computation and de re knowledge of whatever the computation acts upon. For example, the Euclidean algorithm can produce knowledge of _which number_ is the greatest common divisor of two numbers. Arguably, algorithms operate directly on syntactic items, such as strings, and on numbers and the like only via how the numbers are represented. So we broach matters of _notation_. The purpose of this article is to explore the relationship between (...) the notations acceptable for computation, the usual idealizations involved in theories of computability, flowing from Alan Turing’s monumental work, and de re propositional attitudes toward numbers and other mathematical objects. (shrink)

The Generalized Integration Challenge is the task of providing, for a given domain of discourse, a simultaneously acceptable metaphysics, epistemology and metasemantics and showing them to be so. In this paper, we focus on a metaethical position for which seems particularly acute: the brand of normative realism which takes normative properties to be mind-independent and causally inert. The problem is that these metaphysical commitments seem to make normative knowledge impossible. We suggest that bringing metasemantics into play can help to resolve (...) this puzzle. We propose an independently plausible metasemantic constraint on reference determination and show how it can provide a plausible response to for this brand of normative realism. (shrink)

Argues that there are two distinct senses in which knowledge is incompatible with accidental truth - each of which can be traced to a distinct role played by everyday knowledge attributions.

There are many domains about which we think we are reliable. When there is prima facie reason to believe that there is no satisfying explanation of our reliability about a domain given our background views about the world, this generates a challenge to our reliability about the domain or to our background views. This is what is often called the reliability challenge for the domain. In previous work, I discussed the reliability challenges for logic and for deductive inference. I argued (...) for four main claims: First, there are reliability challenges for logic and for deduction. Second, these reliability challenges cannot be answered merely by providing an explanation of how it is that we have the logical beliefs and employ the deductive rules that we do. Third, we can explain our reliability about logic by appealing to our reliability about deduction. Fourth, there is a good prospect for providing an evolutionary explanation of the reliability of our deductive reasoning. In recent years, a number of arguments have appeared in the literature that can be applied against one or more of these four theses. In this paper, I respond to some of these arguments. In particular, I discuss arguments by Paul Horwich, Jack Woods, Dan Baras, Justin Clarke-Doane, and Hartry Field. (shrink)

The paper argues that no second order theory is ontologically commited to anything beyond what its individual variables range over.

Accounts of modality in terms of fictional possible worlds face an objection based on the idea that when modal claims are analysed in terms of fictions, the connection between analysans and analysandum seems artificial. Strong modal fictionalism, the theory according to which modal claims are analysed in terms of a fiction, has been defended by, among others, Seahwa Kim, who has recently claimed that the philosophical objection that the connection between modality and fictions is artificial can be met. I propose (...) a new way of spelling out the intuition of artificiality and show that strong modal fictionalism should be rejected. (shrink)

We present a memorial summary of the professional life and contributions to logic of John Corcoran. We also provide a full list of his many publications.Courtesy of Lynn Corcoran.

In this paper, I address some puzzles about Frege’s conception of how we “grasp” thoughts. I focus on an enigmatic passage that appears near the end of Frege’s great essay “The Thought.” In this passage Frege refers to a “non-sensible something” without which “everyone would remain shut up in his inner world.” I consider and criticize Wolfgang Malzkorn’s interpretation of the passage. According to Malzkorn, Frege’s view is that ideas [Vorstellungen] are the means by which we grasp thoughts. My counter-proposal (...) is that language enables us to grasp thoughts (ideas are merely their baggage or “trappings,” as Frege puts it). One significant consequence of my interpretation is that it helps challenge the standard reading of Frege according to which he is a metaphysical platonist about thoughts. My interpretation thus provides support for the deflationary, anti-ontological reading spelled out by readers like Thomas Ricketts and Wolfgang Carl. As Ricketts puts it, Frege’s distinction between the objective and the subjective, rather than being an ontological doctrine, “lodges in the contrast between asserting something and giving vent to a feeling.”. (shrink)

In this paper I address the question 'How is knowledge of logical truths possible'. The sought-after explanation should be independent of what the true story about logical truth is. In particular, I try to account for the epistemic warrant that is conferred upon logical beliefs when they are neither inferred from other beliefs nor grounded on empirical evidence or testimony. The need for such an account is motivated by the apparent failure of the notions ofanalyticity on the one hand and (...) intuition on the other in addressing the relevant question. I end up defending an account according to which warranted logical beliefs can be grounded on pure reasoning: they can be inferentially formed on the basis of pieces of suppositional reasoning. (shrink)

No presente artigo, trato da questão 'Como o conhecimento de verdades lógicas é possível?'. A explicação que procuro deveria ser independente de qual é a verdadeira teoria sobre verdades lógicas. Mais especificamente, tento explicar a natureza do status epistêmico conferido sob crenças em proposições lógicas quando tais crenças não são inferidas de outras crenças, ou sequer baseadas em evidência empírica ou testemunho. A necessidade de tal teoria é motivada pela aparente falha das noções de analiticidade e intuição em responder à (...) questão mencionada. Termino defendendo uma teoria de acordo com a qual crenças lógicas com status epistêmico positivo podem ser embasadas em puro raciocínio: elas podem ser formadas inferencialmente com base em raciocínio envolvendo suposições. (shrink)

Human beings can have “strongly certain” beliefs—indubitable, veridical beliefs with a unique phenomenology—about necessarily true propositions like 2+2=4. On the plausible assumption that mathematical entities are platonic abstracta, naturalist theories fail to provide an adequate causal explanation for such beliefs because they cannot show how the propositional content of the causally inert abstracta can figure in a chain of physical causes. Theories which explain such beliefs as “corresponding” to the abstracta, but without any causal relationship, entail impossibilities. God, or a (...) very god-like being, provides the best causal explanation for such beliefs. (shrink)

Some accounts of mental content represent the objects of belief as structured, using entities that formally resemble the sentences used to express and report attitudes in natural language; others adopt a relatively unstructured approach, typically using sets or functions. Currently popular variants of the latter include classical and neo-classical propositionalism, which represent belief contents as sets of possible worlds and sets of centered possible worlds, respectively; and property self-ascriptionism, which employs sets of possible individuals. I argue against their contemporary proponents (...) that all three views are ineluctably plagued by generation gaps: they either overgenerate beliefs, undergenerate them, or both. (shrink)

Modal structuralism promises an interpretation of set theory that avoids commitment to abstracta. This article investigates its underlying assumptions. In the first part, I start by highlighting some shortcomings of the standard axiomatisation of modal structuralism, and propose a new axiomatisation I call MSST (for Modal Structural Set Theory). The main theorem is that MSST interprets exactly Zermelo set theory plus the claim that every set is in some inaccessible rank of the cumulative hierarchy. In the second part of the (...) article, I look at the prospects for supplementing MSST with a modal structural reflection principle, as suggested in Hellman (2015). I show that Hellman’s principle is inconsistent (Theorem 5.32), and argue that modal structural reflection principles in general are either incompatible with modal structuralism or extremely weak. (shrink)

In this paper I argue for a view of groups, things like teams, committees, clubs and courts. I begin by examining features all groups seem to share. I formulate a list of six features of groups that serve as criteria any adequate theory of groups must capture. Next, I examine four of the most prominent views of groups currently on offer—that groups are non-singular pluralities, fusions, aggregates and sets. I argue that each fails to capture one or more of the (...) criteria. Last, I develop a view of groups as realizations of structures. The view has two components. First, groups are entities with structure. Second, since groups are concreta, they exist only when a group structure is realized. A structure is realized when each of its functionally defined nodes or places are occupied. I show how such a view captures the six criteria for groups, which no other view of groups adequately does, while offering a substantive answer to the question, “What are groups?”. (shrink)