Synthese

  The paper seeks a perfectly general argument regarding the non-contingent limits to any (human or non-human) knowledge. After
 expressing disappointment with the history of philosophy on this score, an argument is grounded in Fitch's proof, which demonstrates
 the unknowability of some truths. The necessity of this unknowability is then defended by arguing for the necessity of Fitch's
 premise'viz., there this is in fact some ignorance.
 
	

  We give a unified account of some results in the development of Polyadic Inductive Logic in the last decade with particular
 reference to the Principle of Spectrum Exchangeability, its consequences for Instantial Relevance, Language Invariance and
 Johnson's Sufficientness Principle, and the corresponding de Finetti style representation theorems.
 
	

  The philosophical technical term supervenience' is frequently used in the philosophy of mind as a concise way of characterizing
 the core idea of physicalism in a manner that is neutral with respect to debates between reductive physicalists and nonreductive
 physicalists. I argue against this alleged neutrality and side with reductive physicalists. I am especially interested here
 in debates between psychoneural reductionists and nonreductive functionalist physicalists. Central to my arguments will be
 considerations concerning how best to articulate the spirit of the idea of supervenience. I argue for a version of supervenience,
 fine-grained supervenience,' which is the claim that if, at a given time, a single entity instantiates two distinct mental
 properties, it must do so in virtue of instantiating two distinct physical properties. I argue further that despite initial
 appearances to the contrary, such a construal of supervenience can be embraced only by reductive physicalists.
 
	

Advances in belief dynamics: Introduction
	

  The notion of cognitive act is of importance for an epistemology that is apt for constructive type theory, and for epistemology
 in general. Instead of taking knowledge attributions as the primary use of the verb ˜to know' that needs to be given an account
 of, and understanding a first-person knowledge claim as a special case of knowledge attribution, the account of knowledge
 that is given here understands first-person knowledge claims as the primary use of the verb ˜to know'. This means that a cognitive
 act is an act that counts as cognitive from a first-person point of view. The method of linguistic phenomenology is used to
 explain or elucidate our epistemic notions. One of the advantages of the theory is that an answer can be given to some of
 the problems in modern epistemology, such as the Gettier problem.
 
	

  I argue against the tendency in the philosophy of science literature to link abduction to the inference to the best explanation
 (IBE), and in particular, to claim that Peircean abduction is a conceptual predecessor to IBE. This is not to discount either
 abduction or IBE. Rather the purpose of this paper is to clarify the relation between Peircean abduction and IBE in accounting
 for ampliative inference in science. This paper aims at a proper classification'not justification'of types of scientific reasoning.
 In particular, I claim that Peircean abduction is an in-depth account of the process of generating explanatory hypotheses,
 while IBE, at least in Peter Lipton's thorough treatment, is a more encompassing account of the processes both of generating
 and of evaluating scientific hypotheses. There is then a two-fold problem with the claim that abduction is IBE. On the one
 hand, it conflates abduction and induction, which are two distinct forms of logical inference, with two distinct aims, as
 shown by Charles S. Peirce; on the other hand it lacks a clear sense of the full scope of IBE as an account of scientific
 inference.
 
	

  Both traditional and naturalistic epistemologists have long assumed that the examination of human psychology has no relevance
 to the prescriptive goal of traditional epistemology, that of providing first-person guidance in determining the truth. Contrary
 to both, I apply insights about the psychology of human perception and concept-formation to a very traditional epistemological
 project: the foundationalist approach to the epistemic regress problem. I argue that direct realism about perception can help
 solve the regress problem and support a foundationalist account of justification, but only if it is supplemented by an abstractionist
 theory of concept-formation, the view that it is possible to abstract concepts directly from the empirically given. Critics
 of direct realism like Laurence BonJour are correct that an account of direct perception by itself does not provide an adequate
 account of justification. However a direct realist account of perception can inform the needed theory of concept-formation,
 and leading critics of abstractionism like McDowell and Sellars, direct realists about perception themselves, fail to appreciate
 the ways in which their own views about perception help fill gaps in earlier accounts of abstractionism. Recognizing this
 undercuts both their objections to abstractionism and (therefore) their objections to foundationalism.
 
	

  Stewart Shapiro recently argued that there is no higher-order vagueness. More specifically, his thesis is: (ST) ˜So-called
 second-order vagueness in ˜F' is nothing but first-order vagueness in the phrase ˜competent speaker of English' or ˜competent
 user of F''. Shapiro bases (ST) on a description of the phenomenon of higher-order vagueness and two accounts of ˜borderline
 case' and provides several arguments in its support. We present the phenomenon (as Shapiro describes it) and the accounts;
 then discuss Shapiro's arguments, arguing that none is compelling. Lastly, we introduce the account of vagueness Shapiro would
 have obtained had he retained compositionality and show that it entails true higher-order.
 
	

  There exists a considerable body of work on epistemic logics for resource-bounded reasoners. In this paper, we concentrate
 on a less studied aspect of resource-bounded reasoning, namely, on the ascription of beliefs and inference rules by the agents
 to each other. We present a formal model of a system of bounded reasoners which reason about each other's beliefs, and investigate
 the problem of belief ascription in a resource-bounded setting. We show that for agents whose computational resources and
 memory are bounded, correct ascription of beliefs cannot be guaranteed, even in the limit. We propose a solution to the problem
 of correct belief ascription for feasible agents which involves ascribing reasoning strategies, or preferences on formulas, to other agents, and show that if a resource-bounded agent knows the reasoning strategy of another
 agent, then its ascription of beliefs to the other agent is correct in the limit.
 
	

  It is argued that the conjunction effect has a disjunctive analog of strong interest for the realism“antirealism debate. It
 is possible that a proper theory is more confirmed than its (more probable) observational sub-theory and hence than the latter's
 disjunctive equivalent, i.e., the disjunction of all proper theories that are empirically equivalent to the given one. This
 is illustrated by a toy model.
 
	

  This paper considers the nature and role of axioms from the point of view of the current debates about the status of category
 theory and, in particular, in relation to the algebraic' approach to mathematical structuralism. My aim is to show that category
 theory has as much to say about an algebraic consideration of meta-mathematical analyses of logical structure as it does about
 mathematical analyses of mathematical structure, without either requiring an assertory mathematical or meta-mathematical background theory as a foundation', or turning meta-mathematical
 analyses of logical concepts into philosophical' ones. Thus, we can use category theory to frame an interpretation of mathematics according to which we can be structuralists all the way down.
 
	

  Crupi et al. (Think Reason 14:182“199, 2008) have recently advocated and partially worked out an account of the conjunction
 fallacy phenomenon based on the Bayesian notion of confirmation. In response, Schupbach (2009) presented a critical discussion
 as following from some novel experimental results. After providing a brief restatement and clarification of the meaning and
 scope of our original proposal, we will outline Schupbach's results and discuss his interpretation thereof arguing that they
 do not actually undermine our point of view if properly construed. Finally, we will foster such a claim by means of some novel
 data.
 
	

  According to a once influential view of selection, it consists of repeated cycles of replication and interaction. It has been
 argued that this view is wrong: replication is not necessary for evolution by natural selection. I analyze the nine most influential
 arguments for this claim and defend the replication“interaction conception of selection against these objections. In order
 to do so, however, the replication“interaction conception of selection needs to be modified significantly. My proposal is
 that replication is not the copying of an entity, the replicator, but the copying of a property. Thus, we can have a replication
 process without there being a replicator that is being copied.
 
	

  In a famous experiment by Tversky and Kahneman (Psychol Rev 90:293“315, 1983), featuring Linda the bank teller, the participants
 assign a higher probability to a conjunction of propositions than to one of the conjuncts, thereby seemingly committing a
 probabilistic fallacy. In this paper, we discuss a slightly different example featuring someone named Walter, who also happens
 to work at a bank, and argue that, in this example, it is rational to assign a higher probability to the conjunction of suitably
 chosen propositions than to one of the conjuncts. By pointing out the similarities between Tversky and Kahneman's experiment
 and our example, we argue that the participants in the experiment may assign probabilities to the propositions in question
 in such a way that it is also rational for them to give the conjunction a higher probability than one of the conjuncts.
 
	

  A recent argument by Hawthorne and Lasonen-Aarnio purports to show that we can uphold the principle that competently forming
 conjunctions is a knowledge-preserving operation only at the cost of a rampant skepticism about the future. A key premise
 of their argument is that, in light of quantum-mechanical considerations, future contingents never quite have chance 1 of
 being true. We argue, by drawing attention to the order of magnitude of the relevant quantum probabilities, that the skeptical
 threat of Hawthorne and Lasonen-Aarnio's argument is illusory.
 
	

  In this paper, I shall discuss a problem that arises when you try to combine an attractive account of what constitutes evidence
 with an independently plausible account of the kind of access we have to our evidence. According to E = K, our evidence consists
 of what we know. According to the principle of armchair access, we can know from the armchair what our evidence is. Combined,
 these claims entail that we can have armchair knowledge of the external world. Because it seems that the principle of armchair
 access is supported by widely shared intuitions about epistemic rationality, it seems we ought to embrace an internalist conception
 of evidence. I shall argue that this response is mistaken. Because externalism about evidence can accommodate the relevant
 intuitions about epistemic rationality, the principle of armchair access is unmotivated. We also have independent reasons
 for preferring externalism about evidence to the principle of armchair access.
 
	

  This paper introduces a little-known episode in the history of physics, in which a mathematical proof by Pierre Fermat vindicated
 Galileo's characterization of freefall. The first part of the paper reviews the historical context leading up to Fermat's
 proof. The second part illustrates how a physical and a mathematical insight enabled Fermat's result, and that a simple modification
 would satisfy any of Fermat's critics. The result is an illustration of how a purely theoretical argument can settle an apparently
 empirical debate.
 
	

Introduction to the Special Issue: Probability, Confirmation and Fallacies
	

  In this paper we compare different models of vagueness viewed as a specific form of subjective uncertainty in situations of
 imperfect discrimination. Our focus is on the logic of the operator clearly' and on the problem of higher-order vagueness.
 We first examine the consequences of the notion of intransitivity of indiscriminability for higher-order vagueness, and compare
 several accounts of vagueness as inexact or imprecise knowledge, namely Williamson's margin for error semantics, Halpern's
 two-dimensional semantics, and the system we call Centered semantics. We then propose a semantics of degrees of clarity, inspired
 from the signal detection theory model, and outline a view of higher-order vagueness in which the notions of subjective clarity
 and unclarity are handled asymmetrically at higher orders, namely such that the clarity of clarity is compatible with the
 unclarity of unclarity.
 
	

  This paper describes a formal measure of epistemic justification motivated by the dual goal of cognition, which is to increase
 true beliefs and reduce false beliefs. From this perspective the degree of epistemic justification should not be the conditional
 probability of the proposition given the evidence, as it is commonly thought. It should be determined instead by the combination
 of the conditional probability and the prior probability. This is also true of the degree of incremental confirmation, and
 I argue that any measure of epistemic justification is also a measure of incremental confirmation. However, the degree of
 epistemic justification must meet an additional condition, and all known measures of incremental confirmation fail to meet
 it. I describe this additional condition as well as a measure that meets it. The paper then applies the measure to the conjunction
 fallacy and proposes an explanation of the fallacy.
 
	

  Confirmation of a hypothesis by evidence can be measured by one of the so far known incremental measures of confirmation.
 As we show, incremental measures can be formally defined as the measures of confirmation satisfying a certain small set of
 basic conditions. Moreover, several kinds of incremental measure may be characterized on the basis of appropriate structural
 properties. In particular, we focus on the so-called Matthew properties: we introduce a family of six Matthew properties including
 the reverse Matthew effect; we further prove that incremental measures endowed with reverse Matthew effect are possible; finally,
 we shortly consider the problem of the plausibility of Matthew properties.
 
	

  Tom Stoneham put forward an argument purporting to show that coherentists are, under certain conditions, committed to the
 conjunction fallacy. Stoneham considers this argument a reductio ad absurdum of any coherence theory of justification. I argue that Stoneham neglects the distinction between degrees of confirmation
 and degrees of probability. Once the distinction is in place, it becomes clear that no conjunction fallacy has been committed.
 
	

  An alleged counterexample to causal decision theory, put forward by Andy Egan, is studied in some detail. It is argued that
 Egan rejects the evaluation of causal decision theory on the basis of a description of the decision situation that is different
 from'indeed inconsistent with'the description on which causal decision theory makes its evaluation. So the example is not
 a counterexample to causal decision theory. Nevertheless, the example shows that causal decision theory can recommend unratifiable acts (acts that once decided upon appear sub-optimal) which presents a problem in the dynamics of intentions (as a decision
 is the forming of an intention to act). It is argued that we can defuse this problem if we hold that decision theory is a
 theory of rational decision making rather than a theory of rational acts. It is shown how decisions can have epistemic side-effects
 that are not mediated by the act and that there are cases where one can only bring oneself to perform the best act by updating
 by imaging rather than by conditioning. This provides a pragmatic argument for updating by imaging rather than by conditioning in these cases.
 
	

  So far no known measure of confirmation of a hypothesis by evidence has satisfied a minimal requirement concerning thresholds
 of acceptance. In contrast, Shogenji's new measure of justification (Shogenji, Synthese, this number 2009) does the trick.
 As we show, it is ordinally equivalent to the most general measure which satisfies this requirement. We further demonstrate
 that this general measure resolves the problem of the irrelevant conjunction. Finally, we spell out some implications of the
 general measure for the Conjunction Effect; in particular we give an example in which the effect occurs in a larger domain,
 according to Shogenji justification, than Carnap's measure of confirmation would have led one to expect.
 
	

  Crupi et al. (2008) offer a confirmation-theoretic, Bayesian account of the conjunction fallacy'an error in reasoning that
 occurs when subjects judge that Pr(h
 1 & h
 2|e) > Pr(h
 1|e). They introduce three formal conditions that are satisfied by classical conjunction fallacy cases, and they show that these
 same conditions imply that h
 1 & h
 2 is confirmed by e to a greater extent than is h
 1 alone. Consequently, they suggest that people are tracking this confirmation relation when they commit conjunction fallacies.
 I offer three experiments testing the merits of Crupi et al.'s account specifically and confirmation-theoretic accounts of
 the conjunction fallacy more generally. The results of Experiment 1 show that, although Crupi et al.'s conditions do seem
 to be causally linked to the conjunction fallacy, they are not necessary for it; there exist cases that do not meet their
 three conditions in which subjects still tend to commit the fallacy. The results of Experiments 2 and 3 show that Crupi et al.'s
 conditions, and those offered by other confirmation-theoretic accounts of the fallacy, are not sufficient for the fallacy
 either; there exist cases that meet all three of CFT's conditions in which subjects do not tend to commit the fallacy. Additionally,
 these latter experiments show that such confirmation-theoretic conditions are at best only weakly causally relevant to the
 presence of the conjunction fallacy. Given these findings, CFT's account specifically, and any general confirmation-theoretic
 account more broadly, falls short of offering a satisfying explanation of the presence of the conjunction fallacy.
 
	

  Multiple contraction (simultaneous contraction by several sentences) and iterated contraction are investigated in the framework
 of specified meet contraction (s.m.c.) that is extended for this purpose. Multiple contraction is axiomatized, and so is finitely
 multiple contraction (contraction by a finite set of sentences). Two ways to reduce finitely multiple contraction to contraction
 by single sentences are introduced. The reduced operations are axiomatically characterized and their properties are investigated.
 Furthermore, it is shown how iterated contraction can be reduced to single-step, single-sentence contraction. However, in
 this framework the outcome of iterated contraction depends unavoidably on the order in which the inputs are received. This
 order-dependence makes it impossible to treat two inputs on an equal footing. Therefore it is often preferable to perform
 changes involving several pieces of information as multiple rather than iterated change.
 
	

  The paper attempts to give a solution to the Fitch's paradox though the strategy of the reformulation of the paradox in temporal
 logic, and a notion of knowledge which is a kind of ceteris paribus modality. An analogous solution has been offered in a different context to solve the problem of metaphysical determinism.
 
	

  We inquire into the question whether the Aristotelian or classical ideal of science has been realised by the Model Revolution, initiated at Stanford University during the 1950s and spread all around
 the world of philosophy of science'salute Suppes. The guiding principle of the Model Revolution is: a scientific theory is a set of structures in the domain of discourse of axiomatic set-theory, characterised by a set-theoretical predicate. We expound some critical reflections on the Model Revolution; the conclusions
 will be that the philosophical problem of what a scientific theory is has not been solved yet'pace Suppes. While reflecting critically on the Model Revolution, we also explore a proposal of how to complete the Revolution
 and briefly address the intertwined subject of scientific representation, which has come to occupy center stage in philosophy of science over the past decade.
 
	

Erratum to: Synthese special issue: representing philosophy
	

  
 Noesis is an Internet search engine dedicated to mapping the profession of philosophy online. In this paper, I recount the history
 of the project's development since 1998 and discuss the role it may play in representing philosophy optimally, adequately,
 fairly, and accessibly. Unlike many other representations of philosophy, Noesis is dynamic in the sense that it constantly changes and inclusive in the sense that it lets the profession speak for itself
 about what philosophy is, how it is practiced, and why it is important. In this paper, I explain how Noesis is dynamic and inclusive. I close by suggesting why such a communitarian representation of the profession is both timely
 and necessary.
 
	

  The mass/count distinction attracts a lot of attention among cognitive scientists, possibly because it involves in fundamental
 ways the relation between language (i.e. grammar), thought (i.e. extralinguistic conceptual systems) and reality (i.e. the
 physical world). In the present paper, I explore the view that the mass/count distinction is a matter of vagueness. While
 every noun/concept may in a sense be vague, mass nouns/concepts are vague in a way that systematically impairs their use in
 counting. This idea has never been systematically pursued, to the best of my knowledge. I make it precise relying on supervaluations
 (more specifically, ˜data semantics') to model it. I identify a number of universals pertaining to how the mass/count contrast
 is encoded in the languages of the world, along with some of the major dimensions along which languages may vary on this score.
 I argue that the vagueness based model developed here provides a useful perspective on both. The outcome (besides shedding
 light on semantic variation) seems to suggest that vagueness is not just an interface phenomenon that arises in the interaction
 of Universal Grammar (UG) with the Conceptual/Intentional System (to adopt Chomsky's terminology), but it is actually part
 of the architecture of UG.
 
	

  Color adjectives have played a central role in work on language typology and variation, but there has been relatively little
 investigation of their meanings by researchers in formal semantics. This is surprising given the fact that color terms have
 been at the center of debates in the philosophy of language over foundational questions, in particular whether the idea of
 a compositional, truth-conditional theory of natural language semantics is even coherent. The challenge presented by color
 terms is articulated in detail in the work of Charles Travis. Travis argues that structurally isomorphic sentences containing
 color adjectives can shift truth value from context to context depending on how they are used and in the absence of effects
 of vagueness or ambiguity/polysemy, and concludes that a deterministic mapping from structures to truth conditions is impossible.
 The goal of this paper is to provide a linguistic perspective on this issue, which we believe defuses Travis' challenge. We
 provide empirical arguments that color adjectives are in fact ambiguous between gradable and nongradable interpretations,
 and that this simple ambiguity, together with independently motivated options concerning scalar dimension within the gradable
 reading accounts for the Travis facts in a simpler, more constrained, and thus ultimately more successful fashion than recent
 contextualist analyses such as those in Szabó (Perspectives on semantics, pragmatics and discourse: A festschrift for Ferenc
 Kiefer, 2001) or Rothschild and Segal (Mind Lang, 2009).
 
	

Introduction
	

  This paper presents a novel semantic analysis of unit names (like pound and meter) and gradable adjectives (like tall, short and happy), inspired by measurement theory (Krantz et al. In Foundations of measurement: Additive and Polynomial Representations, 1971).
 Based on measurement theory's four-way typology of measures, I claim that different adjectives are associated with different
 types of measures whose special characteristics, together with features of the relations denoted by unit names, explain the
 puzzling limited distribution of measure phrases, as well as unit-based comparisons between predicates (as in the table is longer than it is wide). All considered, my analyses support the view that the grammar of natural languages is sensitive to features of measurement
 theory.
 
	

  In a number of recent papers Duncan Pritchard argues that virtue epistemology's central ability condition'one knows that p
 if and only if one has attained cognitive success (true belief) because of the exercise of intellectual ability'is neither
 necessary nor sufficient for knowledge. This paper discusses and dismisses a number of responses to Pritchard's objections
 and develops a new way of defending virtue epistemology against them.
 
	

  Fitch's argument purports to show that for any unknown truth, p, there is an unknowable truth, namely, that p is true and unknown; for a contradiction follows from the assumption that it is possible to know that p is true and unknown. In earlier work I argued that there is a sense in which it is possible to know that p is true and unknown, from a counterfactual perspective; that is, there can be possible, non-actual knowledge, of the actual
 situation, that in that situation, p is true and unknown. Here I further elaborate that claim and respond to objections by Williamson, who argued that there cannot
 be non-trivial knowledge of this kind. I give conditions which suffice for such non-trivial counterfactual knowledge.
 
	

  The article investigates Cassirer's developing interest in the cultural sciences to display how his Philosophy of Symbolic Forms constitutes a philosophy of culture. The core concept in such a philosophy of culture is the symbolic formation that both
 possesses a structured-structuring dimension and appears as an historical process in which culture shows itself as a temporal
 creation. The philosophy of culture displays ˜life in meaning', that is reality as it exhibits human reality manifested in
 and through the medium of linguistic, artistic, religious, scientific and so on' action and behaviour. This reality, therefore,
 is mediation between culture and nature through human spirit. Cassirer's philosophy of culture connects back to Kant's transcendental
 idealism by emphasizing that any concept of reality establishes itself through a modalization of reality, e.g. that reality
 constitutes itself in the mode of interpretation. This makes the basis for Cassirer's characteristic understanding of hermeneutics
 where cultural development is regarded as drama.
 
	

  This paper presents a generalized form of Fitch's paradox of knowability, with the aim of showing that the questions it raises
 are not peculiar to the topics of knowledge, belief, or other epistemic notions. Drawing lessons from the generalization,
 the paper offers a solution to Fitch's paradox that exploits an understanding of modal talk about what could be known in terms
 of capacities to know. It is argued that, in rare cases, one might have the capacity to know that p even if it is metaphysically impossible for anyone to know that p, and that recognizing this fact provides the resources to solve Fitch's paradox.
 
	

  This is a reply to Timothy Williamson's paper ˜Tennant's Troubles'. It defends against Williamson's objections the anti-realist's
 knowability principle based on the author's ˜local' restriction strategy involving Cartesian propositions, set out in The Taming of the True. Williamson's purported Fitchian reductio, involving the unknown number of books on his table, is analyzed in detail and shown to be fallacious. Williamson's attempt
 to cause problems for the anti-realist by means of a supposed rigid designator generates a contradiction with arithmetic right
 away, upon instantiating the obviously relevant theorem that every natural number is provably odd or provably even. The paper
 also explains and formulates a globally restricted knowability principle, which likewise blocks the attempted reductio.
 
	

  Three different ways in which systems of axioms can contribute to the discovery of new notions are presented and they are
 illustrated by the various ways in which lattices have been introduced in mathematics by Schröder et al. These historical episodes reveal that the axiomatic method is not
 only a way of systematizing our knowledge, but that it can also be used as a fruitful tool for discovering and introducing
 new mathematical notions. Looked at it from this perspective, the creative aspect of axiomatics for mathematical practice is brought to the fore.
 
	

  It is almost universally acknowledged that first-order logic (FOL), with its clean, well-understood syntax and semantics,
 allows for the clear expression of philosophical arguments and ideas. Indeed, an argument or philosophical theory rendered
 in FOL is perhaps the cleanest example there is of representing philosophy'. A number of prominent syntactic and semantic
 properties of FOL reflect metaphysical presuppositions that stem from its Fregean origins, particularly the idea of an inviolable
 divide between concept and object. These presuppositions, taken at face value, reflect a significant metaphysical viewpoint,
 one that can in fact hinder or prejudice the representation of philosophical ideas and arguments. Philosophers have of course
 noticed this and have, accordingly, sought to alter or extend traditional FOL in novel ways to reflect a more flexible and
 egalitarian metaphysical standpoint. The purpose of this paper, however, is to document and discuss how similar adaptations'
 to FOL'culminating in a standardized framework known as Common Logic'have evolved out of the more practical and applied encounter of FOL with the problem of representing, sharing, and reasoning
 upon information on World Wide Web.
 
	

Introduction to knowability and beyond
	

  Truth's universal knowability entails its discovery. This threatens antirealism, which is thought to require it. Fortunately,
 antirealism is not committed to it. Avoiding it requires adoption (and extension) of Dag Prawitz's position in his long-term
 disagreement with Michael Dummett on the notion of provability involved in intuitionism's identification of it with truth.
 Antirealism (intuitionism generalized) must accommodate a notion of lost-opportunity truth (a kind of recognition-transcendent
 truth), and even truth consisting in the presence of unperformable verifications. Dummett's position cannot abide this, while
 Prawitz's can. Antirealism's epistemic notion of truth derives from general features of its meaning theory, not from a universal
 knowability principle.
 
	

  We describe an ontology of philosophy that is designed to aid navigation through philosophical literature, including literature
 in the form of encyclopedia articles and textbooks and in both printed and digital forms. The ontology is designed also to
 serve integration and structuring of data pertaining to the philosophical literature, and in the long term also to support
 reasoning about the provenance and contents of such literature, by providing a representation of the philosophical domain
 that is oriented around what philosophical literature is about.
 
	

  The modern notion of the axiomatic method developed as a part of the conceptualization of mathematics starting in the nineteenth
 century. The basic idea of the method is the capture of a class of structures as the models of an axiomatic system. The mathematical
 study of such classes of structures is not exhausted by the derivation of theorems from the axioms but includes normally the
 metatheory of the axiom system. This conception of axiomatization satisfies the crucial requirement that the derivation of
 theorems from axioms does not produce new information in the usual sense of the term called depth information. It can produce
 new information in a different sense of information called surface information. It is argued in this paper that the derivation
 should be based on a model-theoretical relation of logical consequence rather than derivability by means of mechanical (recursive)
 rules. Likewise completeness must be understood by reference to a model-theoretical consequence relation. A correctly understood
 notion of axiomatization does not apply to purely logical theories. In the latter the only relevant kind of axiomatization
 amounts to recursive enumeration of logical truths. First-order axiomatic' set theories are not genuine axiomatizations.
 The main reason is that their models are structures of particulars, not of sets. Axiomatization cannot usually be motivated
 epistemologically, but it is related to the idea of explanation.
 
	

  The best defense of the doctrine of the Incarnation implies that traditional Christianity has a special stake in the knowability
 paradox, a stake not shared by other theistic perspectives or by non-traditional accounts of the Incarnation. Perhaps, this
 stake is not even shared by antirealism, the view most obviously threatened by the paradox. I argue for these points, concluding
 that these results put traditional Christianity at a disadvantage compared to other viewpoints, and I close with some comments
 about the extent of the burden incurred.
 
	

Synthese special issue: representing philosophy
	

The axiomatic method, the order of concepts and the hierarchy of sciences: an introduction
	

  In this paper I consider two accounts of scientific discovery, Robert Hudson's and Peter Achinstein's. I assess their relative
 success and I show that while both approaches are similar in promising ways, and address experimental discoveries well, they
 could address the concerns of the discovery sceptic more explicitly than they do. I also explore the implications of their
 inability to address purely theoretical discoveries, such as those often made in mathematical physics. I do so by showing
 that extending Hudson's or Achinstein's account to such cases can sometimes provide a misleading analysis about who ought
 to be credited as a discoverer. In the final sections of the paper I work out some revisions to the Hudson/Achinstein account
 by drawing from a so-called structural realist view of theory change. Finally, I show how such a modified account of discovery
 can answer sceptical critics such as Musgrave or Woolgar without producing misleading analyses about who ought to receive
 credit as a discoverer in cases from the mathematical sciences. I illustrate the usefulness of this approach by providing
 an analysis of the case of the discovery of the Casimir effect.
 
	

  The paper discusses Bernard Bolzano's epistemological approach to believing and knowing with regard to the epistemic requirements
 of an axiomatic model of science. It relates Bolzano's notions of believing, knowing and evaluation to notions of infallibility,
 immediacy and foundational truth. If axiomatic systems require their foundational truths to be infallibly known, this knowledge
 involves both evaluation of the infallibility of the asserted truth and evaluation of its being foundational. The twofold
 attempt to examine one's assertions and to do so by searching for the objective grounds of the truths asserted lies at the
 heart of Bolzano's notion of knowledge. However, the explanatory task of searching for grounds requires methods that cannot
 warrant infallibility. Hence, its constitutive role in a conception of knowledge seems to imply the fallibility of such knowledge.
 I argue that the explanatory task contained in Bolzanian knowing involves a high degree of epistemic virtues, and that it
 is only through some salient virtue that the credit of infallibility can distinguish Bolzanian knowing from a high degree
 of Bolzanian believing.