In the spirit of James and Dewey, I ask what one might want from a theory of knowledge. Much Anglophone epistemology is centered on questions that were once highly pertinent, but are no longer central to broader human and scientific concerns. The first sense in which epistemology without history is blind lies in the tendency of philosophers to ignore the history of philosophical problems. A second sense consists in the perennial attraction of approaches to knowledge that divorce knowing subjects from (...) their societies and from the tradition of socially assembling a body of transmitted knowledge. When epistemology fails to use the history of inquiry as a laboratory in which methodological claims can be tested, there is a third way in which it becomes blind. Finally, lack of attention to the growth of knowledge in various domains leaves us with puzzles about the character of the knowledge we have. I illustrate this last theme by showing how reflections on the history of mathematics can expand our options for understanding mathematical knowledge. (shrink)

The phenomenological movement begins in the Prolegomena to Husserl’s Logical Investigations as a philosophy of logic. Despite this, remarkably little attention has been paid to Husserl’s arguments in the Prolegomena in the contemporary philosophy of logic. In particular, the literature spawned by Gilbert Harman’s work on the normative status of logic is almost silent on Husserl’s contribution to this topic. I begin by raising a worry for Husserl’s conception of ‘pure logic’ similar to Harman’s challenge to explain the connection between (...) logic and reasoning. If logic is the study of the forms of all possible theories, it will include the study of many logical consequence relations; by what criteria, then, should we select one consequence relation as correct? I consider how Husserl might respond to this worry by looking to his late account of the ‘genealogy of logic’ in connection with Gurwitsch’s claim that ‘[i]t is to prepredicative perceptual experience … that one must return for a radical clarification and for the definitive justification of logic’. Drawing also on Sartre and Heidegger, I consider how prepredicative experience might constrain or guide our selection of a logical consequence relation and our understanding of connectives like implication and negation. (shrink)

Hartry Field's formulation of an epistemological argument against platonism is only valid if knowledge is constrained by a causal clause. Contrary to recent claims (e.g. in Liggins (2006), Liggins (2010)), Field's argument therefore fails the very same criterion usually taken to discredit Benacerraf's earlier version.

Philosophy of mathematics is in an alienated state. While regarded by the profession as a serious and legitimate subdiscipline, a passing knowledge of its subject matter is considered something of a luxury—or at least not required of a conscientious philosopher the way a passing knowledge of logic is. Philosophy of mathematics is thus regarded with a benign neglect: best left to the experts, whose opinions should be deferred to, but mostly irrelevant to the central concerns of the working philosopher. Its (...) practitioners, however, often display a strikingly different attitude. Much of the enthusiasm for the subject matter derives from the recognition that undertaking and evaluating a position in the philosophy of mathematics involves undertaking and evaluating substantive commitments of general philosophical interest. Indeed many practitioners, though by no means blind to the intrinsic interest of their discipline, regard philosophy of mathematics also as a means of addressing more general issues in philosophy. Unfortunately the significance of philosophy of mathematics to the work of the nonspecialist has for the most part been under appreciated. (shrink)

objects are standardly taken to be causally inert, but this claim is rarely explicitly argued for. In the context of his platonism about musical works, in order for musical works to be audible, Julian Dodd argues that abstracta are causally efficacious in virtue of their concrete tokens participating in events. I attempt to provide a principled argument for the causal inertness of abstracta by first rejecting Dodd’s arguments from events, and then extending and generalizing the causal exclusion argument to the (...) abstract/concrete distinction. For reasons of parsimony, if concrete tokens or instantiations of abstract objects account for all causal work, then there is no reason to attribute causal efficacy to abstracta, and thus reason to maintain their causal inertness. I then consider how one of the main arguments against causal exclusion, namely Stephen Yablo’s notion of “proportionality”, could be modified to support the causal efficacy of abstracta. I argue that from a few simple premises Yablo’s account in fact supports their causal inertness. Having a principled reason for the causal inertness of abstracta appears to entail that the musical platonist must admit that we never literally hear the musical work, but only its performances. I sketch a solution to this problem available to Dodd, so that the musical platonist can maintain that musical works are abstract objects and are causally inert while retaining their audibility. (shrink)

Abstract objects are standardly taken to be causally inert, however principled arguments for this claim are rarely given. As a result, a number of recent authors have claimed that abstract objects are causally efficacious. These authors take abstracta to be temporally located in order to enter into causal relations but lack a spatial location. In this paper, I argue that such a position is untenable by showing first that causation requires its relata to have a temporal location, but second, that (...) if an entity is temporally located then it is spatiotemporally located since this follows from the theory of Relativity. Since abstract objects lack a spatiotemporal location, then if something is causally efficacious, it is not abstract. (shrink)

Scanlon’s Being Realistic about Reasons (BRR) is a beautiful book – sleek, sophisticated, and programmatic. One of its key aims is to demystify knowledge of normative and mathematical truths. In this article, I develop an epistemological problem that Scanlon fails to explicitly address. I argue that his “metaphysical pluralism” can be understood as a response to that problem. However, it resolves the problem only if it undercuts the objectivity of normative and mathematical inquiry.

In this paper, I argue that religious belief is epistemically equivalent to mathematical belief. Abstract beliefs don't fall under ‘naive’, evidence-based analyses of rationality. Rather, their epistemic permissibility depends, I suggest, on four criteria: predictability, applicability, consistency, and immediate acceptability of the fundamental axioms. The paper examines to what extent mathematics meets these criteria, juxtaposing the results with the case of religion. My argument is directed against a widespread view according to which belief in mathematics is clearly rationally acceptable whereas (...) belief in religion is not. The paper also aims to make some of the implications of contemporary mathematics available to philosophers working in different fields. (shrink)

Pluralist mathematical realism, the view that there exists more than one mathematical universe, has become an influential position in the philosophy of mathematics. I argue that, if mathematical pluralism is true (and we have good reason to believe that it is), then mathematical realism cannot (easily) be justified by arguments from the indispensability of mathematics to science. This is because any justificatory chain of inferences from mathematical applications in science to the total body of mathematical theorems can cover at most (...) one mathematical universe. Indispensability arguments may thus lose their central role in the debate about mathematical ontology. (shrink)

The existence of fundamental moral disagreements is a central problem for moral realism and has often been contrasted with an alleged absence of disagreement in mathematics. However, mathematicians do in fact disagree on fundamental questions, for example on which set-theoretic axioms are true, and some philosophers have argued that this increases the plausibility of moral vis-à-vis mathematical realism. I argue that the analogy between mathematical and moral disagreement is not as straightforward as those arguments present it. In particular, I argue (...) that pluralist accounts of mathematics render fundamental mathematical disagreements compatible with mathematical realism in a way in which moral disagreements and moral realism are not. 11. (shrink)

I argue that recent attempts to deflect Access Problems for realism about a priori domains such as mathematics, logic, morality, and modality using arguments from evolution result in two kinds of explanatory overkill: the Access Problem is eliminated for contentious domains, and realist belief becomes viciously immune to arguments from dispensability, and to non-rebutting counter-arguments more generally.

This paper offers a defense of Charles Parsons’ appeal to mathematical intuition as a fundamental factor in solving Benacerraf’s problem for a non-eliminative structuralist version of Platonism. The literature is replete with challenges to his well-known argument that mathematical intuition justifies our knowledge of the infinitude of the natural numbers, in particular his demonstration that any member of a Hilbertian stroke string ω-sequence has a successor. On Parsons’ Kantian approach, this amounts to demonstrating that for an “arbitrary” or “vaguely represented” (...) string of strokes, we can always “add” one more stroke. Critics have contested the cogency of a notion of an arbitrary object, our capacity to vaguely represent a definite object, and the role of spatial and temporal representation in the demonstration that we can “add” one more. The bulk of this paper is devoted to demonstrating how to meet all extant criticisms of his key argument. Critics have also suggested that Parsons’ whole approach is misbegotten because the appeal to mathematical intuition inevitably falls short of providing a complete solution to Benacerraf’s problem. Since the natural numbers are essentially and exclusively characterized by their structural properties, they cannot be identified with any particular model of arithmetic, and thus a notion of intuition will fail to capture the universality of arithmetic, its applicability to all entities. This paper also explains why we should not reject appeal to mathematical intuition even though it is not itself sufficient to fully “close the gap” on Benacerraf’s challenge. (shrink)

Scientific realists often appeal to some version of the conjunction objection to argue that scientific instrumentalism fails to do justice to the full empirical import of scientific theories. Whereas the conjunction objection provides a powerful critique of scientific instrumentalism, I will show that mathematical instnrunentalism escapes the conjunction objection unscathed.

Peter Geach proposed a substitutional construal of quantification over thirty years ago. It is not standardly substitutional since it is not tied to those substitution instances currently available to us; rather, it is pegged to possible substitution instances. We argue that (i) quantification over the real numbers can be construed substitutionally following Geach's idea; (ii) a price to be paid, if it is that, is intuitionism; (iii) quantification, thus conceived, does not in itself relieve us of ontological commitment to real (...) numbers. (shrink)

The present paper discusses a proposal which says,roughly and with several qualifications, that thecollection of mathematical truths is identical withthe set of theorems of ZFC. It is argued that thisproposal is not as easily dismissed as outright falseor philosophically incoherent as one might think. Some morals of this are drawn for the concept ofmathematical knowledge.

In recent work, E. J. Lowe presents an essence-based account of our knowledge of metaphysical modality that he claims to be superior to its main competitors. I argue that knowledge of essences alone, without knowledge of a suitable bridge principle, is insufficient for knowing that something is metaphysically necessary or metaphysically possible. Yet given Lowe's other theoretical commitments, he cannot account for our knowledge of the needed bridge principle, and so his essence-based modal epistemology remains incomplete. In addition to that, (...) Lowe's account implies a psychologically unrealistic reconstruction of how we ordinarily acquire knowledge of metaphysical modalities. The discussion of Lowe's suggestive essence-based account is also intended as a case study that illustrates a more general problem in the epistemology of modality: the great difficulty of explaining our modal knowledge in terms of a single overtly nonmodal kind of knowledge. The failure of Lowe's account suggests that such a sweeping reductive explanation of our modal knowledge might simply not be available. This should be good news for those philosophers who champion less reductive or more pluralistic accounts of our modal knowledge. (shrink)

. What are thought experiments, and how do they generate knowledge? More specifically, what sorts of intentional acts must one perform in order to carry out a thought experiment, what sorts of objects are such acts directed toward, and how are those objects made present in such acts? I argue on phenomenological grounds that the proper objects of thought experiments are, in certain cases, uninstantiated universals and relations among them. I will also argue that, in the best of cases, we (...) intuit or “see” these universals and their relations to one another, and respond to some objections to this view. (shrink)

According to Field’s influential incompleteness objection, Tarski’s semantic theory of truth is unsatisfactory since the definition that forms its basis is incomplete in two distinct senses: (1) it is physicalistically inadequate, and for this reason, (2) it is conceptually deficient. In this paper, I defend the semantic theory of truth against the incompleteness objection by conceding (1) but rejecting (2). After arguing that Davidson and McDowell’s reply to the incompleteness objection fails to pass muster, I argue that, within the constraints (...) of a non-reductive physicalism and a holism concerning the concepts of truth, reference and meaning, conceding Field’s physicalistic inadequacy conclusion while rejecting his conceptual deficiency conclusion is a promising reply to the incompleteness objection. (shrink)

In this paper, I argue that for the purposes of ordinary reasoning, sentences about properties of concrete objects can be replaced with sentences concerning how things in our universe would be related to inscriptions were there a pluriverse. Speaking loosely, pluriverses are composites of universes that collectively realize every way a universe could possibly be. As such, pluriverses exhaust all possible meanings that inscriptions could take. Moreover, because universes necessarily do not influence one another, our universe would not be any (...) different intrinsically if there were a pluriverse. These two facts enable anti-realists about abstract objects to replace, e.g. talk of anatomical features with talk of the inscriptions concerning anatomical structure that would exist were there a pluriverse. The availability of such replacements enables anti-realists to carry out essential ordinary reasoning without referring to properties, thereby making room for a consistent anti-realist worldview. The inscriptions of the would-be pluriverse are so numerous and varied that sentences about them can play the roles in ordinary reasoning served by simple sentences about properties of concrete objects. (shrink)

In this paper, I argue that all expressions for abstract objects are meaningless. My argument closely follows David Lewis’ argument against the intelligibility of certain theories of possible worlds, but modifies it in order to yield a general conclusion about language pertaining to abstract objects. If my Lewisian argument is sound, not only can we not know that abstract objects exist, we cannot even refer to or think about them. However, while the Lewisian argument strongly motivates nominalism, it also undermines (...) certain nominalist theories. (shrink)

Why does God allow evil? One hypothesis is that God desires the existence and activity of free creatures but He was unable to create a world with such creatures and such activity without also allowing evil. If Molinism is true, what probability should be assigned to this hypothesis? Some philosophers claim that a low probability should be assigned because there are an infinite number of possible people and because we have no reason to suppose that such creatures will choose one (...) way rather than another. Arguments like this depend on the principle of indifference. But that principle is rejected by most philosophers of probability. Some philosophers claim that a low probability should be assigned because doing otherwise violates intuitions about freewill. But such arguments can be addressed through strategies commonly employed to defend theories with counterintuitive results across ethics and metaphysics. (shrink)

There is no interesting entailment either way between theism and various forms of realism. Taking its cue from Dummett’s characterisation of realism and his discussion of it with respect to theistic belief, this paper argues both that theism does not follow from realism, and that God cannot be appealed to in order to secure bivalence for an otherwise indeterminate subject matter. In both cases, significant appeal is made to the position that God is not a language user, which in turn (...) is motivated by an account of understanding as aptitude possession. The resulting picture sits comfortably with the apophatism common within living religious traditions and with the view that the philosophy of religion ought to reorientate itself away from metaphysics towards more practical questions. (shrink)

We can introduce singular terms for ordered pairs by means of an abstraction principle. Doing so proves useful for a number of projects in the philosophy of mathematics. However there is a question whether we can appeal to the abstraction principle in good faith, since a version of the Caesar Problem can be generated, posing the worry that abstraction fails to introduce expressions which refer determinately to the requisite sort of object. In this note I will pose the difficulty, and (...) then propose a solution. Since my solution appeals to a plausible constraint on the introduction of new expressions to a language, it is of interest independently of the particular case of terms for pairs. Since these provide the occasion for discussion we should nonetheless review the use of abstraction for pairs before the argumentative business of the paper commences. (shrink)

In this paper, I challenge those interpretations of Frege that reinforce the view that his talk of grasping thoughts about abstract objects is consistent with Russell's notion of acquaintance with universals and with Gödel's contention that we possess a faculty of mathematical perception capable of perceiving the objects of set theory. Here I argue the case that Frege is not an epistemological Platonist in the sense in which Gödel is one. The contention advanced is that Gödel bases his Platonism on (...) a literal comparison between mathematical intuition and physical perception. He concludes that since we accept sense perception as a source of empirical knowledge, then we similarly should posit a faculty of mathematical intuition to serve as the source of mathematical knowledge. Unlike Gödel, Frege does not posit a faculty of mathematical intuition. Frege talks instead about grasping thoughts about abstract objects. However, despite his hostility to metaphor, he uses the notion of ‘grasping’ as a strategic metaphor to model his notion of thinking, i.e., to underscore that it is only by logically manipulating the cognitive content of mathematical propositions that we can obtain mathematical knowledge. Thus, he construes ‘grasping’ more as theoretical activity than as a kind of inner mental ‘seeing’. (shrink)

Non-naturalist realists are committed to the belief, famously voiced by Parfit, that if there are no non-natural facts then nothing matters. But it is morally objectionable to conditionalise all our moral commitments on the question of whether there are non-natural facts. Non-natural facts are causally inefficacious, and so make no difference to the world of our experience. And to be a realist about such facts is to hold that they are mind-independent. It is compatible with our experiences that there are (...) no non-natural facts, or that they are very different from what we think. As Nagel says, realism makes scepticism intelligible. So the non-naturalist must hold that you might be wrong that your partner matters, even if you are correct about every natural, causal fact about your history and relationship. But to hold that conditional attitude to your partner would be a moral betrayal. So believing non-naturalist realism involves doing something immoral. (shrink)

The question of how we can know anything about ideal entities to which we do not have access through our senses has been a major concern in the philosophical tradition since Plato's Phaedo. This article focuses on the paradigmatic case of mathematical knowledge. Following a suggestion by Gödel, we employ concepts and ideas from Husserlian phenomenology to argue that mathematical objects – and ideal entities in general – are recognized in a process very closely related to ordinary perception. Our analysis (...) combines Husserl's insights into the nature of perception and the phenomena of evidence and justification with case studies of the role of intuition in axiomatic set theory. (shrink)

I examine various claims to the effect that Cantor's Continuum Hypothesis and other problems of higher set theory are ill-posed questions. The analysis takes into account the viability of the underlying philosophical views and recent mathematical developments.

Convinced that the classically undecidable problems of mathematics possess determinate truth values, Gödel issued a programmatic call to search for new axioms for their solution. The platonism underlying his belief in the determinateness of those questions in combination with his conception of intuition as a kind of perception have struck many of his readers as highly problematic. Following Gödel's own suggestion, this article explores ideas from phenomenology to specify a meaning for his mathematical realism that allows for a defensible epistemology.

It is argued that mathematical statements are "a posteriori synthetic" statements of a very special sort, To be called "structure-Analytic" statements. They follow logically from the axioms defining the mathematical structure they are describing--Provided that these axioms are "consistent". Yet, Consistency of these axioms is an empirical claim: it may be "empirically verifiable" by existence of a finite model, Or may have the nature of an "empirically falsifiable hypothesis" that no contradiction can be derived from the axioms.

This paper offers a detailed criticism of different versions of modal scepticism proposed by Van Inwagen and Hawke, and, against these views, attempts to vindicate our reliance on thought experiments in philosophy. More than one different meaning of “ modal scepticism” will be distinguished. Focusing mainly on Hawke’s more detailed view I argue that none of these versions of modal scepticism is compelling, since sceptical conclusions depend on an untenable and, perhaps, incoherent modal epistemology. With a detailed account of modal (...) defeaters at hand I argue that Van Inwagen and Hawke’s scepticism is either groundless, or it leads to boundless and unacceptable modal scepticism. Additionally, I show that Hawke’s conception of analogical modal reasoning is problematic. Either his principle of similarity is arbitrary or it begs the question about modal scepticism. In contrast to Hawke’s restricted view of analogical modal reasoning, I present two examples of analogy-based modal justification of philosophically relevant possibility claims. My criticism of modal scepticism also shows that there is no good reason to insist on a sharp distinction between an unproblematic and a presumably dubious kind of modality. The upshot is that in absence of proper defeaters both Yablo-style conceivability and properly applied analogical reasoning are reliable guides to possibility, and also that modal justification comes in degrees. The proposed framework of defeaters of modal justification as well as the analysed examples of analogical modal reasoning trace out interesting new areas for further discussions. (shrink)

Non-actualist theories promise straightforward accounts of meaning, truth and reference of fictional discourse but are ostensibly saddled with a Selection Problem, that multiple possible candidates satisfy the role-descriptions associated with names used in fictions and no principled way to distinguish between them; yet if names are referential, there can only be one referent. The problem is often taken to be a serious—even decisive—obstacle for non-actualism, and the aim of this article is to show that the challenge can be met. I (...) suggest that storytellers and authors fix the referents of referential terms they use by arbitrary selecting referents through simple acts of stipulation, and then determine which of the worlds containing the relevant individuals serve as truth-makers for the story by adding properties to the characters. The resulting view of reference is consistent with reasonable, foundational requirements on reference, such as a causal-historical theory, and can moreover be used to support plausible theories of truth in fiction and facilitate elegant models of fiction as a type of discourse. (shrink)

Knowing is something that we do not have much of a theory about., p. 365.)Interest has recently been shown in causal theories of perception, memory, inference, reference, truth, justification and belief, as well as in a more general “causal theory of knowledge” which would embrace and connect all of these concepts within a broad epistemological framework. The burden of this paper is that prospects are poor for an interesting and general enough causal theory of knowledge. A threat to generality arises (...) from the causal theory's difficulties with knowledge of general truths. A threat to interest arises when attempts to accommodate general truths lead to a weakening of the notion of “causal connection” appealed to, making dubious the explanatory force of such an appeal. (shrink)

It is traditionally held that our knowledge of necessity is a priori; but the familiar theories of a priori knowledge – platonism and conventionalism – have now been discredited, and replaced by either modal skepticism or a posteriori essentialism. The main thesis of this paper is that Kant's theory of a priori knowledge, when detached from his transcendental idealism, offers a genuine alternative to these unpalatable options. According to Kant's doctrine, all epistemic necessity is grounded directly or indirectly on our (...) capacity for clear and distinct rational intuition. Insight, in turn, depends upon functions of the imagination for creating “mental models” of necessary truths. This doctrine is well exemplified by Kant's account of our knowledge of simple analytic truths. (shrink)

The article argues that modal concepts should be explained in terms of the essences or nature of things: necessarily p if, and because, there is something the nature of which ensures that p; possibly p if, and because, there is nothing whose nature rules out its being true that p. The theory is defended against various objections and difficulties, including ones arising from attributing essences to contingent individuals.

This paper pursues two goals. Its first goal is to clear up the “identity problem” faced by the structuralist interpretation of mathematics. Its second goal, through the consideration of examples coming in particular from the theory of permutations, is to examine cases of misunderstandings in mathematics fit to cast some light on mathematical understanding in general. The common thread shared by these two goals is the notion of setting. The study of a mathematical object almost always goes together with the (...) choice of a particular setting, and the understanding of the workings of mathematical settings is an essential component of mathematical knowledge. It is claimed that the recognition of mathematical settings, as features distinct from both mathematical structures and the systems which instantiate those structures, allows one to classify most of understandable misunderstandings in mathematics, and also to solve the identity problem. (shrink)

According to Alberto Coffa in The Semantic Tradition from Kant to Carnap, Kant’s account of mathematical judgment is built on a ‘semantic swamp’. Kant’s primitive semantics led him to appeal to pure intuition in an attempt to explain mathematical necessity. The appeal to pure intuition was, on Coffa’s line, a blunder from which philosophy was forced to spend the next 150 years trying to recover. This dismal assessment of Kant’s contributions to the evolution of accounts of mathematical necessity is fundamentally (...) backward-looking. Coffa’s account of how semantic theories of the a priori evolved out of Kant’s doctrine of pure intuition rightly emphasizes those developments, both scientific and philosophical, that collectively served to undermine the plausibility of Kant’s account. What is missing from Coffa’s story, apart from any recognition of Kant’s semantic innovations, is an attempt to appreciate Kant’s philosophical context and the distinctive perspective from which Kant viewed issues in the philosophy of mathematics. When Kant’s perspective and context are brought out, he can not only be seen to have made a genuinely progressive contribution to the development of accounts of mathematical necessity, but also to be relevant to contemporary issues in the philosophy of mathematics in underappreciated ways. (shrink)

According to Alberto Coffa in The Semantic Tradition from Kant to Carnap, Kant’s account of mathematical judgment is built on a ‘semantic swamp’. Kant’s primitive semantics led him to appeal to pure intuition in an attempt to explain mathematical necessity. The appeal to pure intuition was, on Coffa’s line, a blunder from which philosophy was forced to spend the next 150 years trying to recover. This dismal assessment of Kant’s contributions to the evolution of accounts of mathematical necessity is fundamentally (...) backward-looking. Coffa’s account of how semantic theories of the a priori evolved out of Kant’s doctrine of pure intuition rightly emphasizes those developments, both scientific and philosophical, that collectively served to undermine the plausibility of Kant’s account. What is missing from Coffa’s story, apart from any recognition of Kant’s semantic innovations, is an attempt to appreciate Kant’s philosophical context and the distinctive perspective from which Kant viewed issues in the philosophy of mathematics. When Kant’s perspective and context are brought out, he can not only be seen to have made a genuinely progressive contribution to the development of accounts of mathematical necessity, but also to be relevant to contemporary issues in the philosophy of mathematics in underappreciated ways. (shrink)

Epistemology has recently witnessed a number of efforts to rehabilitate rationalism, to defend the existence and importance of a priori knowledge or warrant construed as the product of rational insight or apprehension (Bealer 1987; Bigelow 1992; BonJour 1992, 1998; Burge 1998; Butchvarov 1970; Katz 1998; Plantinga 1993). This effort has sometimes been coupled with an attack on naturalistic epistemology, especially in BonJour 1994 and Katz 1998. Such coupling is not surprising, because naturalistic epistemology is often associated with thoroughgoing empiricism and (...) the rejection of the a priori. In this paper, however, I shall present a conception of naturalistic epistemology that is entirely compatible with a priori justification or knowledge. The resulting conception, I claim, gives us a better appreciation of the respective merits of the rational and the empirical, as well as a better understanding of how moderate epistemological naturalism comports, at least in principle, with moderate rationalism. This paper defends moderate rationalism; but it does not defend everything rationalists have often wanted, only what it is reasonable to grant them. (shrink)