Synthese

  
 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.