This is the most comprehensive book ever published on philosophical methodology. A team of thirty-eight of the world's leading philosophers present original essays on various aspects of how philosophy should be and is done. The first part is devoted to broad traditions and approaches to philosophical methodology. The entries in the second part address topics in philosophical methodology, such as intuitions, conceptual analysis, and transcendental arguments. The third part of the book is devoted to essays about the interconnections between philosophy (...) and neighbouring fields, including those of mathematics, psychology, literature and film, and neuroscience. (shrink)

Intuition is sometimes derided as an abstruse or esoteric phenomenon akin to crystal-ball gazing. Such derision appears to be fuelled primarily by the suggestion, evidently endorsed by traditional rationalists such as Plato and Descartes, that intuition is a kind of direct, immediate apprehension akin to perception. This paper suggests that although the perceptual analogy has often been dismissed as encouraging a theoretically useless metaphor, a quasi-perceptualist view of intuition may enable rationalists to begin to meet the challenge of supplying a (...) theoretically satisfying treatment of their favoured epistemic source. It is argued, first, that intuitions and perceptual experiences are at a certain level of abstraction the same type of mental state, presentations, which are distinct from beliefs, hunches, inclinations, attractions, and seemings. The notion of a presentation is given a positive explication, which identifies its characteristic features, accounts for several of its substantive psychological roles, and systematically locates it in a threefold division among types of contentful states. Subsequently, it is argued that presentations, intuitive no less than sensory, are by their nature poised to play a distinctive epistemic role. Specifically, in the case of intuition, we encounter an intellectual state that is so structured as to provide justification without requiring justification in turn—something which may, thus, be thought of as ‘given’. (shrink)

La rinascita negli ultimi decenni di un nutrito dibattito intorno alla nozione di analiticità dopo le critiche a suo tempo mosse da Quine alla batteria di nozioni utilizzate da Rudolf Carnap (ad esempio, postulati di significato, regole semantiche, definizioni implicite, convenzioni e stipulazioni esplicite) prende le mosse da una riflessione critica sulle argomentazioni di Quine e tenta, da un lato, di approfondire meglio il legame fra analiticità e conoscenza a priori, e, dall’altro, di capire meglio il ruolo che la definizione (...) può svolgere nella costituzione del significato e nella formulazione di verità concettuali. Questa nuova concezione è detta “epistemica” ed ha fra i suoi più autorevoli fautori Crispin Wright, Bob Hale e Paul Boghossian. Boghossian, al pari di molti filosofi critici della nuova concezione epistemica, come Timothy Williamson, conviene però con Quine nel sostenere che gli enunciati analitici hanno portata fattuale e vertono anch’essi sul mondo, oltre che sul linguaggio. Anche per questa ragione essi possono rendere possibile una genuina estensione delle nostre conoscenze. Tuttavia una seconda linea di obiezioni facenti capo dapprima a Paul Horwich, e in seguito agli stessi Wright e Hale, mette in evidenza rispettivamente due difficoltà corrispondenti alle questioni dell’arroganza e dell’accettazione. In questa discussione una parte importante è svolta dalla ripresa e della discussione del condizionale di Carnap, impiegato per rendere conto del ruolo che i termini teorici svolgono nel quadro dell’intera teoria cui appartengono, senza con ciò sposare le conseguenze dell’olismo quineano. La tesi centrale che questo lavoro cerca di rendere plausibile è che una lettura attenta degli ultimi scritti di Carnap mostri come il carattere aperto che egli attribuisce ai termini teorici in ragione, sia dello loro intrinseca indeterminatezza, sia delle revisioni imposte dalle scoperte scientifiche, è perfettamente compatibile con la fattorizzazione del contenuto di una teoria scientifica data in una parte linguistica, il condizionale di Carnap, riguardante la costituzione del significato di un certo termine teorico, e nella sua controparte empirica, che consente di registrare l’impatto dell’esperienza sulla teoria in questione. Se praticabile, questa concezione può a buon diritto entrare nel novero delle teorie epistemiche dell’analiticità, senza accampare alcuna pretesa di far rivivere i fasti della conoscenza a priori classica. (shrink)

Recent attempts to answer ontological questions through conceptual analysis have been controversial. Still, it seems reasonable to assume that if the existence of certain things analytically follows from sentences we already accept, then there is no further ontological commitment involved in affirming the existence of those things. More generally, it is plausible that whenever a sentence analytically entails another, the conjunction of those sentences requires nothing more of the world for its truth than the former sentence alone. In his ‘Analyticity (...) and Ontology’, Louis deRosset tries to produce counterexamples to these principles by means of linguistic stipulations. I aim to show where his arguments go wrong. (shrink)

Neo-Fregeans need their stipulation of Hume's Principle — $NxFx=NxGx \leftrightarrow \exists R (Fx \,1\hbox {-}1_R\, Gx)$ — to do two things. First, it must implicitly define the term-forming operator ‘Nx…x…’, and second it must guarantee that Hume's Principle as a whole is true. I distinguish two senses in which the neo-Fregeans might ‘stipulate’ Hume's Principle, and argue that while one sort of stipulation fixes a meaning for ‘Nx…x…’ and the other guarantees the truth of Hume's Principle, neither does both.

Platonism about mathematics (or mathematical platonism) isthe metaphysical view that there are abstract mathematical objectswhose existence is independent of us and our language, thought, andpractices. Just as electrons and planets exist independently of us, sodo numbers and sets. And just as statements about electrons and planetsare made true or false by the objects with which they are concerned andthese objects' perfectly objective properties, so are statements aboutnumbers and sets. Mathematical truths are therefore discovered, notinvented., Existence. There are mathematical objects.

What is mathematics about? And if it is about some sort of mathematical reality, how can we have access to it? This is the problem raised by Plato, which still today is the subject of lively philosophical disputes. This book traces the history of the problem, from its origins to its contemporary treatment. It discusses the answers given by Aristotle, Proclus and Kant, through Frege's and Russell's versions of logicism, Hilbert's formalism, Gödel's platonism, up to the the current debate on (...) Benacerraf's dilemma and the indispensability argument. Through the considerations of themes in the philosophy of language, ontology, and the philosophy of science, the book aims at offering an historically-informed introduction to the philosophy of mathematics, approached through the lenses of its most fundamental problem. (shrink)

In Boghossian's 1997 paper, 'Analyticity' he presented an account of a prioriknowledge of basic logical principles as available by inference from knowledge of their role in determining the meaning of the logical constants by implicit definitiontogether with knowledge of the meanings so-determined that we possess through ourprivileged access to meaning. Some commentators (e.g. BonJour (1998), Glüer (2003),Jenkins (2008)) have objected that if the thesis of implicit definition on which he relieswere true, knowledge of the meaning of the constants would presuppose (...) knowledge of the very logical principles knowledge of which the account purports to explain. Aconsequence would seem to be that implicit definition is incompatible with privilegedaccess. I argue that whilst it is possible for Boghossian to defend against theseobjections the form of argument he proposes does exhibit a subtle form of questionbegging such that it exhibits a transmission of warrant-failure. (shrink)

According to the most popular non-skeptical views about intuition, intuitions justify beliefs because they are based on understanding. More precisely: if intuiting that p justifies you in believing that p it does so because your intuition is based on your understanding of the proposition that p. The aim of this paper is to raise some challenges for accounts of intuitive justification along these lines. I pursue this project from a non-skeptical perspective. I argue that there are cases in which intuiting (...) that p justifies you in believing that p, but such that there is no compelling reason to think this is because your intuition is based on your understanding of the proposition that p. (shrink)

This paper argues for and explores the implications of the following epistemological principle for knowability a priori (with 'Ka' abbreviating 'it is knowable a priori that'). -/- (AK) For all ϕ, ψ such that ϕ semantically presupposes ψ: if Ka(ϕ), Ka(ψ). -/- Well-known arguments for the contingent a priori and a priori knowledge of logical truth founder when the semantic presuppositions of the putative items of knowledge are made explicit. Likewise, certain kinds of analytic truth turn out to carry semantic (...) presuppositions that make them ineligible as items of a priori knowledge. -/- On a happier note, I argue that (AK) offers an appealing, theory-neutral explanation of the a posteriori character of certain necessary identities, as well as an interesting rationalization for a commonplace linguistic maneuver in philosophical work on the a priori. (shrink)

Many philosophers claim that understanding a logical constant (e.g. ‘if, then’) fundamentally consists in having dispositions to infer according to the logical rules (e.g. Modus Ponens) that fix its meaning. This paper argues that such dispositionalist accounts give us the wrong picture of what understanding a logical constant consists in. The objection here is that they give an account of understanding a logical constant which is inconsistent with what seem to be adequate manifestations of such understanding. I then outline an (...) alternative account according to which understanding a logical constant is not to be understood dispositionally, but propositionally. I argue that this account is not inconsistent with intuitively correct manifestations of understanding the logical constants. (shrink)

The paper argues that the theory of Implicit Definition cannot give an account of knowledge of logical principles. According to this theory, the meanings of certain expressions are determined such that they make certain principles containing them true; this is supposed to explain our knowledge of the principles as derived from our knowledge of what the expressions mean. The paper argues that this explanation succeeds only if Implicit Definition can account for our understanding of the logical constants, and that fully (...) understanding a logical constant in turn requires the ability to apply it correctly in particular cases. It is shown, however, that Implicit Definition cannot account for this ability, even if it draws on introduction rules for the logical constants. In particular, Implicit Definition cannot account for our ability to apply negation in particular cases. Owing to constraints relating to the unique characterisation of logical constants, invoking the notion of rejection does not remedy the situation. Given its failure to explain knowledge of logic, the prospects of Implicit Definition to explain other kinds of a priori knowledge are even worse. (shrink)

Alberto Coffa used the phrase "the Copernican turn in semantics" to denote a revolutionary transformation of philosophical views about the connection between the meanings of words and the acceptability of sentences and arguments containing those words. According to the new conception resulting from the Copernican turn, here called "the Copernican view", rules of use are constitutive of the meanings of words. This view has been linked with two doctrines: (A) the instances of meaning-constitutive rules are analytically and a priori true (...) or valid; (B) to grasp a meaning is to accept its rules. The pros and cons of different versions of the Copernican view, ascribable to Wittgenstein, Carnap, Gentzen, Dummett, Prawitz, Boghossian and other authors, will be weighed. A new version will be proposed, which implies neither (A) nor (B). (shrink)

A shift from a metaphysical framework of substance to one of process enables an integrated account of the emergence of normative phenomena. I show how substance assumptions block genuine ontological emergence, especially the emergence of normativity, and how a process framework permits a thermodynamic-based account of normative emergence. The focus is on two foundational forms of normativity, that of normative function and of representation as emergent in a particular kind of function. This process model of representation, called interactivism, compels changes (...) in many related domains. The discussion ends with brief attention to three domains in which changes are induced by the representational model: perception, learning, and language. (shrink)

It has been known for a few years that no more than Pi-1-1 comprehension is needed for the proof of "Frege's Theorem". One can at least imagine a view that would regard Pi-1-1 comprehension axioms as logical truths but deny that status to any that are more complex—a view that would, in particular, deny that full second-order logic deserves the name. Such a view would serve the purposes of neo-logicists. It is, in fact, no part of my view that, say, (...) Delta-3-1 comprehension axioms are not logical truths. What I am going to suggest, however, is that there is a special case to be made on behalf of Pi-1-1 comprehension. Making the case involves investigating extensions of first-order logic that do not rely upon the presence of second-order quantifiers. A formal system for so-called "ancestral logic" is developed, and it is then extended to yield what I call "Arché logic". (shrink)

According to the species of neo-logicism advanced by Hale and Wright, mathematical knowledge is essentially logical knowledge. Their view is found to be best understood as a set of related though independent theses: (1) neo-fregeanism-a general conception of the relation between language and reality; (2) the method of abstraction-a particular method for introducing concepts into language; (3) the scope of logic-second-order logic is logic. The criticisms of Boolos, Dummett, Field and Quine (amongst others) of these theses are explicated and assessed. (...) The issues discussed include reductionism, rejectionism, the Julius Caesar problem, the Bad Company objections, and the charge that second-order logic is set theory in disguise. (shrink)

In virtue of what are we justified in employing the rule of inference Modus Ponens? One tempting approach to answering this question is to claim that we are justified in employing Modus Ponens purely in virtue of facts concerning meaning or concept-possession. In this paper, we argue that such meaning-based accounts cannot be accepted as the fundamental account of our justification.

I argue that Neo-Fregean accounts of arithmetical language and arithmetical knowledge tacitly rely on a thesis I call [Success by Default]—the thesis that, in the absence of reasons to the contrary, we are justified in thinking that certain stipulations are successful. Since Neo-Fregeans have yet to supply an adequate defense of [Success by Default], I conclude that there is an important gap in Neo-Fregean accounts of arithmetical language and knowledge. I end the paper by offering a naturalistic remedy.

Once Hilbert asserted that the axioms of a theory `define` theprimitive concepts of its language `implicitly''. Thus whensomeone inquires about the meaning of the set-concept, thestandard response reads that axiomatic set-theory defines itimplicitly and that is the end of it. But can we explainthis assertion in a manner that meets minimum standards ofphilosophical scrutiny? Is Jané (2001) wrong when hesays that implicit definability is ``an obscure notion''''? Doesan explanation of it presuppose any particular view on meaning?Is it not a scandal (...) of the philosophy of mathematics that no answersto these questions are around? We submit affirmative answers to allquestions. We argue that a Wittgensteinian conception of meaninglooms large beneath Hilbert''s conception of implicit definability.Within the specific framework of Horwich''s recent Wittgensteiniantheory of meaning called semantic deflationism, we explain anexplicit conception of implicit definability, and then go on toargue that, indeed, set-theory, defines the set-conceptimplicitly according to this conception. We also defend Horwich''sconception against a recent objection from the Neo-Fregeans Hale and Wright (2001). Further, we employ the philosophicalresources gathered to dissolve all traditional worries about thecoherence of the set-concept, raisedby Frege, Russell and Max Black, and whichrecently have been defended vigorously by Hallett (1984) in hismagisterial monograph Cantorian set-theory and limitationof size. Until this day, scandalously, these worries havebeen ignored too by philosophers of mathematics. (shrink)

Neo-Fregeanism in the philosophy of mathematics consists of two main parts: the logicist thesis, that mathematics (or at least branches thereof, like arithmetic) all but reduce to logic, and the platonist thesis, that there are abstract, mathematical objects. I will here focus on the ontological thesis, platonism. Neo-Fregeanism has been widely discussed in recent years. Mostly the discussion has focused on issues specific to mathematics. I will here single out for special attention the view on ontology which underlies the neo-Fregeans’ (...) claims about mathematical objects, and discuss this view in a broader setting. (shrink)

Clark and Chalmers propose that the mind extends further than skin and skull. If they are right, then we should expect this to have some effect on our way of knowing our own mental states. If the content of my notebook can be part of my belief system, then looking at the notebook seems to be a way to get to know my own beliefs. However, it is at least not obvious whether self-ascribing a belief by looking at my notebook (...) is a case of introspection the same way that knowing my non-extended beliefs is. Traditionally this sort of introspection is thought to be privileged and special in ways that the extended introspection case seems not to be. There is nothing privileged about looking at my notebook. Anyone could do it. The aim of the paper is to find out how to understand extended introspection and whether there is something privileged and special about knowing one’s own extended beliefs. Moreover, the notebook case has close analogs using twenty-first century technology. It seems possible to know our beliefs that are extended to smartphones, wearable technology or a cloud-based data store. First, I present the case of extended introspection. I then discuss whether it should be understood as ordinary introspection or as mind-reading. Both seem to be bad fits, which finally prompts an original account for extended introspection based on epistemic rules. (shrink)

Wright claims that “the epistemology of good abstraction principles should be assimilated to that of basic principles of logical inference”. In this paper I follow Wright’s recommendation, but I consider a different epistemology of logic, namely anti-exceptionalism. Anti-exceptionalism’s main contention is that logic is not a priori, and that the choice between rival logics should be based on abductive criteria such as simplicity, adequacy to the data, strength, fruitfulness, and consistency. This paper’s goal is to lay down the foundations for (...) an application of the anti-exceptionalist methodology to abstraction principles. In Sect. 1 I outline my strategy. I show that anti-exceptionalism has a bearing on the so-called Bad Company problem (Sect. 2), and explore some versions of anti-exceptionalism about abstraction (Sect. 3). I then consider new criteria for choosing between rival abstraction principles, and, in particular, between consistent revisions of Frege’s Basic Law V (Sect. 4). I finally consider how the abstractionist can compare between competing criteria (Sect. 5), and argue that anti-exceptionalists should be pluralists about abstraction (Sect. 6). (shrink)

This is a thesis in support of the conceptual yoking of analytic truth to a priori knowledge. My approach is a semantic one; the primary subject matter throughout the thesis is linguistic objects, such as propositions or sentences. I evaluate arguments, and also forward my own, about how such linguistic objects’ truth is determined, how their meaning is fixed and how we, respectively, know the conditions under which their truth and meaning are obtained. The strategy is to make explicit what (...) is distinctive about analytic truths. The objective is to show that truths, known a priori, are trivial in a highly circumscribed way. My arguments are premised on a language-relative account of analytic truth. The language relative account which underwrites much of what I do has two central tenets: 1. Conventionalism about truth and, 2. Non-factualism about meaning. I argue that one decisive way of establishing conventionalism and non-factualism is to prioritise epistemological questions. Once it is established that some truths are not known empirically an account of truth must follow which precludes factual truths being known non-empirically. The function of Part 1 is, chiefly, to render Carnap’s language-relative account of analytic truth. I do not offer arguments in support of Carnap at this stage, but throughout Parts 2 and 3, by looking at more current literature on a priori knowledge and analytic truth, it becomes quickly evident that I take Carnap to be correct, and why. In order to illustrate the extent to which Carnap’s account is conventionalist and non-factualist I pose his arguments against those of his predecessors, Kant and Frege. Part 1 is a lightly retrospective background to the concepts of ‘analytic’ and ‘a priori’. The strategy therein is more mercenary than exegetical: I select the parts from Kant and Frege most relevant to Carnap’s eventual reaction to them. Hereby I give the reasons why Carnap foregoes a factual and objective basis for logical truth. The upshot of this is an account of analytic truth (i.e. logical truth, to him) which ensures its trivial nature. In opposition to accounts of a priori knowledge, which describe it as knowledge gained from rational apprehension, I argue that it is either knowledge from logical deduction or knowledge of stipulations. I therefore reject, in Part 2, three epistemologies for knowing linguistic conventions (e.g. implicit definitions): 1. intuition, 2. inferential a priori knowledge and, 3. a posteriori knowledge. At base, all three epistemologies are rejected because they are incompatible with conventionalism and non-factualism. I argue this point by signalling that such accounts of knowledge yield unsubstantiated second-order claims and/or they render the relevant linguistic conventions epistemically arrogant. For a convention to be arrogant it must be stipulated to be true. The stipulation is then considered arrogant when its meaning cannot be fixed, and its truth cannot be determined without empirical ‘work’. Once a working explication of ‘a priori’ has been given, partially in Part 1 (as inferential) and then in Part 2 (as non-inferential) I look, in Part 3, at an apriorist account of analytic truth, which, I argue, renders analytic truth non-trivial. The particular subject matter here is the implicit definitions of logical terms. The opposition’s argument holds that logical truths are known a priori (this is part of their identification criteria) and that their meaning is factually based. From here it follows that analytic truth, being determined by factually based meaning, is also factual. I oppose these arguments by exposing the internal inconsistencies; that implicit definition is premised on the arbitrary stipulation of truth which is inconsistent with saying that there are facts which determine the same truth. In doing so, I endorse the standard irrealist position about implicit definition and analytic truth (along with the “early friends of implicit definition” such as Wittgenstein and Carnap). What is it that I am trying to get at by doing all of the abovementioned? Here is a very abstracted explanation. The unmitigated realism of the rationalists of old, e.g. Plato, Descartes, Kant, have stoically borne the brunt of the allegation of yielding ‘synthetic a priori’ claims. The anti-rationalist phase of this accusation I am most interested in is that forwarded by the semantically driven empiricism of the early 20th century. It is here that the charge of the ‘synthetic a priori’ really takes hold. Since then new methods and accusatory terms are employed by, chiefly, non-realist positions. I plan to give these proper attention in due course. However, it seems to me that the reframing of the debate in these new terms has also created the illusion that current philosophical realism, whether naturalistic realism, realism in science, realism in logic and mathematics, is somehow not guilty of the same epistemological and semantic charges levelled against Plato, Descartes and Kant. It is of interest to me that in, particularly, current analytic philosophy (given its rationale) realism in many areas seems to escape the accusation of yielding synthetic priori claims. Yet yielding synthetic a priori claims is something which realism so easily falls prey to. Perhaps this is a function of the fact that the phrase, ‘synthetic a priori’, used as an allegation, is now outmoded. This thesis is nothing other than an indictment of metaphysics, or speculative philosophy (this being the crime), brought against a specific selection of realist arguments. I, therefore, ask of my reader to see my explicit, and perhaps outmoded, charge of the ‘synthetic a priori’ levelled against respective theorists as an attempt to draw a direct comparison with the speculative metaphysics so many analytic philosophers now love to hate. I think the phrase ‘synthetic a priori’ still does a lot of work in this regard, precisely because so many current theorists wrongly think they are immune to this charge. Consequently, I shall say much about what is not permitted. Such is, I suppose, the nature of arguing ‘against’ something. I’ll argue that it is not permitted to be a factualist about logical principles and say that they are known a priori. I’ll argue that it is not permitted to say linguistic conventions are a posteriori, when there is a complete failure in locating such a posteriori conventions. Both such philosophical claims are candidates for the synthetic a priori, for unmitigated rationalism. But on the positive side, we now have these two assets: Firstly, I do not ask us to abandon any of the linguistic practises discussed; merely to adopt the correct attitude towards them. For instance, where we use the laws of logic, let us remember that there are no known/knowable facts about logic. These laws are therefore, to the best of our knowledge, conventions not dissimilar to the rules of a game. And, secondly, once we pass sentence on knowing, a priori, anything but trivial truths we shall have at our disposal the sharpest of philosophical tools. A tool which can only proffer a better brand of empiricism. (shrink)

Though the divide between reason-based and causal-explanatory approaches in psychiatry and psychopathology is old and deeply rooted, current trends involving multi-factorial explanatory models and evidence-based approaches to interpersonal psychotherapy, show that it has already been implicitly bridged. These trends require a philosophical reconsideration of how reasons can be causes. This paper contributes to that trajectory by arguing that Donald Davidson’s classic paradigm of 1963 is still a valid option.

The paper surveys different notions of implicit definition. In particular, we offer an examination of a kind of definition commonly used in formal axiomatics, which in general terms is understood as providing a definition of the primitive terminology of an axiomatic theory. We argue that such “structural definitions” can be semantically understood in two different ways, namely as specifications of the meaning of the primitive terms of a theory and as definitions of higher-order mathematical concepts or structures. We analyze these (...) two conceptions of structural definition both in the history of modern axiomatics and in contemporary philosophical debates. Based on that, we give a systematic assessment of the underlying semantics of these two ways of understanding the definiens of such definitions, by considering alternative model-theoretic and inferential accounts of meaning. (shrink)

According to the most popular account of the a priori, which we might call Analytic Account of the A Priori, we can explain the a priori in terms of the notion of analyticity. According to the least popular account of the a priori, the explanation of the a priori proceeds by appealing to the faculties used in the acquisition of a priori knowledge, such as the faculty of rational intuition – call this Rationalist Account of the A Priori. The main (...) aim of this paper is to challenge the analytic account of the a priori to motivate a return to rationalism. To achieve this aim, I discuss and challenge two very different analytic accounts of the a priori: a concept-based account that relies on meaning-justification links, and an understanding-based account that does not rely on such links. I argue that the former is both extensionally inadequate and explanatorily deficient, and the latter can be made to work but only by employing such a rich notion of understanding that renders it a form of rationalism in disguise. I conclude by motivating a rationalist faculty-based account of the a priori. (shrink)

Truth by convention, once thought to be the foundation of a uniquely promising approach to explaining our access to the truth in nonempirical domains, is nowadays widely considered an absurdity. Its fall from grace has been due largely to the influence of an argument that can be sketched as follows: our linguistic conventions have the power to make it the case that a sentence expresses a particular proposition, but they can’t by themselves generate truth; whether a given proposition is true—and (...) so whether the sentence that expresses it is true—is a matter of what the world is like, which means it isn’t a matter of convention alone. The consensus is that this argument is decisive against truth by convention. Strikingly, though, it has rarely been formulated with much precision. Here I provide a new rendering of the argument, one that reveals its structure and makes transparent just what assumptions it requires, and then I assess conventionalists’ prospects for resisting each of those assumptions. I conclude that the consensus is mistaken: contrary to what is almost universally thought, there remains a promising way forward for the conventionalist project. Along the way, I clarify conventionalists’ commitments by thinking about what truth by convention would need to be like in order for conventionalism to do the epistemological work it’s intended to do. (shrink)

We may define words or concepts, and we may also, as Aristotle and others have thought, define the things for which words stand and of which concepts are concepts. Definitions of words or concepts may be explicit or implicit, and may seek to report preexisting synonymies, as Quine put it, but they may instead be wholly or partly stipulative. Definition by abstraction, of which Hume’s principle is a much discussed example, seek to define a term-forming operator, such as the number (...) operator, by fixing the truth-conditions of identity-statements featuring terms formed by means of that operator. Such definitions are a species of implicit definition. They are typically at least partly stipulative. Definitions of things, or real definitions, are, by contrast, typically conceived as true or false statements about the nature or essence of their definienda, and so not stipulative. There thus appears to be an obvious and head-on clash between taking Hume’s principle as an implicit and at least partly stipultative definition of the number operator and taking it as a real definition, stating the nature or essence of cardinal numbers. This paper argues that this apparent tension can be resolved, and that resolving it sheds light on part of the epistemology or essence and necessity, showing how some of our knowledge of essence and necessity can be a priori. (shrink)

According to Brandom’s conceptual role semantics, to grasp a concept involves a commitment to drawing certain inferences. This is a consequence of the inferentialist thesis that the meaning of a term is given by its justification through assertibility conditions. Inferential commitments come out from a material notion of inference which underwrites human rational discourse and activity. In this paper I discuss a problem of Brandom’s semantics allegedly exposed in an argument by Paul Boghossian against Dummett’s and Brandom’s substantive conception of (...) meaning. I contend that Boghossian’s analysis is dubious because it overlooks an important difference between Dummett’s and Brandom’s positions related respectively to a monotonic and a non-monotonic view of the norm underwriting meaning. (shrink)

One of the important discussions in the philosophy of mathematics, is that centered on Benacerraf’s Dilemma. Benacerraf’s dilemma challenges theorists to provide an epistemology and semantics for mathematics, based on their favourite ontology. This challenge is the point on which all philosophies of mathematics are judged, and clarifying how we might acquire mathematical knowledge is one of the main occupations of philosophers of mathematics. In this thesis I argue that this discussion has overlooked an important part of mathematics, namely mathematics (...) as it is exercised by ordinary people. I do so by looking at the different theories that have been put forward in the recent debate, and showing for each of these that they are unable to account for the mathematical practices of ordinary people. In order to show that these practices do need to be accounted for, I also argue that ordinary people are doing mathematics, i.e. that they engage in properly mathematical practices. Because these practices are properly mathematical, they should be accounted for by any philosophy of mathematics. The conclusion of my thesis, then, is that current theories fail to do something that they should do, while remaining neutral on how well they perform when it comes to accounting for the practices of professional mathematicians. (shrink)

The neo-Fregeans have argued that definition by abstraction allows us to introduce abstract concepts such as direction and number in terms of equivalence relations such as parallelism between lines and one-one correspondence between concepts. This paper argues that definition by abstraction suffers from the fact that an equivalence relation may not be sufficient to determine a unique concept. Frege’s original verdict against definition by abstraction is thus reinstated.

Review of *New Essays on the A Priori*, an excellent collection edited by Paul Boghossian and Christopher Peacocke. Contributors include: Tyler Burge; Quassim Cassam; Philip Kitcher; Penelope Maddy; Hartry Field; Paul Horwich; Peter Railton; Stephen Yablo; Bob Hale; Crispin Wright; Frank Jackson; Stewart Shapiro; Michael Friedman; Martin Davies; Bill Brewer; and Thomas Nagel.

A number of formal constraints on acceptable abstraction principles have been proposed, including conservativeness and irenicity. Hume’s Principle, of course, satisfies these constraints. Here, variants of Hume’s Principle that allow us to count concepts instead of objects are examined. It is argued that, prima facie, these principles ought to be no more problematic than HP itself. But, as is shown here, these principles only enjoy the formal properties that have been suggested as indicative of acceptability if certain constraints on the (...) size of the continuum hold. As a result, whether or not these higher-order versions of Hume’s Principle are acceptable seems to be independent of standard (ZFC) set theory. This places the abstractionist in an uncomfortable dilemma: Either there is some inherent difference between counting objects and counting concepts, or new criteria for acceptability will need to be found. It is argued that neither horn looks promising. (shrink)

A noção de analiticidade teve um papel central em vários debates filosóficos, em particular durante a primeira metade do século XX. Na sequência do influente artigo de W. V. Quine “Dois Dogmas do empirismo” (1951), a noção passou a ser vista com grande cepticismo. Mais recentemente, Paul Boghossian, no artigo “Analiticidade Reconsiderada” (1996), propôs uma forma de compreender a noção que é, putativamente, imune às críticas de Quine. O interesse na noção de analiticidade ficou desta forma renovado, assim como a (...) sua centralidade no debate acerca da possibilidade do conhecimento a priori. O principal objectivo deste artigo consiste em introduzir a noção de analiticidade e os principais problemas que esta enfrenta. (shrink)

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

Wright claims that his and Hale’s abstractionist neologicist project is primarily epistemological in aim. Its epistemological aims include establishing the possibility of a priori mathematical knowledge, and establishing the possibility of reference to abstract mathematical objects. But, as Wright acknowledges, there is a question of how neologicist epistemology applies to actual, ordinary mathematical beliefs. I take up this question, focusing on arithmetic. Following a suggestion of Hale and Wright, I consider the possibility that the neologicist account provides an idealised reconstruction (...) of how people acquire cognition of numbers or arithmetical knowledge. I conclude that it is unlikely that this account can be used to reconstruct even idealised answers to pressing questions about our actual epistemology. (shrink)

Frege's concern in GGI §10 is neither with the epistemological issue of how we come to know about value-ranges, nor with the semantic-metaphysical issue of whether we have said enough about such objects in order to ensure that any kind of reference to them is possible. The problem which occupies Frege in GGI §10 is the general problem according to which we ‘cannot yet decide’, for any arbitrary function, what value ‘’ has if ‘ℵ’ is a canonical value-range name. This (...) is a problem with the ‘reference’ of value-range names, but only in the weak sense that, if we do not exercise care, value-range terms might become ‘bedeutungslos’ for purely formal reasons. Frege addresses the general problem only for the primitive function- and object-names he has already introduced into his concept-script. I argue that this methodology was perfectly intentional: his intention for GG in general, on display in GGI §10, is to check, for each primitive function- and object-name, as it is introduced into concept-script, whether it interacts with the other primitive names which have already been introduced in such a way that these atomic combinations of primitive names do not become bedeutungslos. If there is a risk of producing a bedeutungslos combination, Frege will make an arbitrary stipulation to ensure that logical hygiene is maintained. I argue that this interpretation does not violate some of the other principal commitments of GG. (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)

The period in the foundations of mathematics that started in 1879 with the publication of Frege's Begriffsschrift and ended in 1931 with Gödel's Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I can reasonably be called the classical period. It saw the development of three major foundational programmes: the logicism of Frege, Russell and Whitehead, the intuitionism of Brouwer, and Hilbert's formalist and proof-theoretic programme. In this period, there were also lively exchanges between the various schools culminating in (...) the famous Hilbert-Brouwer controversy in the 1920s. -/- The purpose of this anthology is to review the programmes in the foundations of mathematics from the classical period and to assess their possible relevance for contemporary philosophy of mathematics. What can we say, in retrospect, about the various foundational programmes of the classical period and the disputes that took place between them? To what extent do the classical programmes of logicism, intuitionism and formalism represent options that are still alive today? These questions are addressed in this volume by leading mathematical logicians and philosophers of mathematics. (shrink)

According to the so-called metaphysical conception of analyticity, analytic truths are true in virtue of meaning (or content) alone and independently of (extralinguistic) facts. Quine and Boghossian have tried to present a conclusive argument against the metaphysical conception of analyticity. In effect, they tried to show that the metaphysical conception inevitably leads into a highly implausible view about the truthmakers of analytic truths. We would like to show that their argument fails, since it relies on an ambiguity of the notion (...) of 'independence of (extralinguistic) facts'. If one distinguishes between variation independence and existence independence, the unwelcome view about the truthmakers of analytic truths no longer follows. Thus, there is at best a challenge, but no conclusive argument. The door to the metaphysical conception of analyticity is still open. (shrink)

In this paper I will argue that Boghossian's explanation of how we can acquire a priori knowledge of logical principles through implicit definitions commits a transmission of warrant-failure. To this end, I will briefly outline Boghossian's account, followed by an explanation of what a transmission of warrant-failure consists in. I will also show that this charge is independent of the worry of rule-circularity which has been raised concerning the justification of logical principles and of which Boghossian is fully aware. My (...) argument comes in two steps: firstly, I will argue for the insufficiency of Boghossian's template which is meant to explain how a subject can acquire a warrant for logical principles. I will show however that this insufficiency of his template can be remedied by adopting what I call the Disquotational Step. Secondly, I will argue that incorporating this further step makes his template subject to a transmission of warrant-failure, assuming that certain rather basic and individually motivated principles hold. Thus, Boghossian's account faces a dilemma: either he adopts the Disquotational Step and subjects his account to the charge of a transmission of warrant-failure, or he drops this additional step leaving the account confronted with explaining the gap that has previously been highlighted. I will then suggest various rejoinders that Boghossian might adopt but none of which - I will argue - can resolve the dilemma. Lastly, I will raise and briefly discuss the question whether this worry generalizes to other accounts, such as Hale and Wright's that aim to explain our knowledge of logic and/or mathematics in virtue of implicit definitions. (shrink)

Kim's argument appears to render causally efficacious emergence impossible: Hume's argument appears to render normative emergence impossible, and, in its general form, it precludes any emergence at all. I argue that both of these barriers can be overcome, and, in fact, that they each constitute reductions of their respective underlying presuppositions. In particular, causally efficacious ontological emergence can be modeled, but only within a process metaphysics, thus avoiding Kim's argument, and making use of non-abbreviatory forms of definition, thus avoiding Hume's (...) argument. I illustrate these points with models of the emergent nature of normative function and of representation. (shrink)

An interactive process model of the nature of representation intrinsically accounts for multiple emergent properties of consciousness, such as being a contentful experiential flow, from a situated and embodied point of view. A crucial characteristic of this model is that content is an internally related property of interactive process, rather than an externally related property as in all other contemporary models. Externally related content requires an interpreter, yielding the familiar regress of interpreters, along with a host of additional fatal problems. (...) Further properties of consciousness, such as differentiated qualities of experience, including qualia, emerge with conscious reflection. In particular, qualia are not constituents or direct properties of consciousness per se. Assuming that they are so is a common and ultimately disastrous misconstrual of the problems of consciousness. (shrink)