The article addresses the works of three 19th-century philosophers: Herbart, Bolzano and Lotze. Despite their differences, i will analyze two essential features they share: their refusal to psychologism as the radicalization of psychology as the ultimate source of philosophy , and the positing of an ideal ‘reality’, independent from both sensibility and the mental and linguistic dimensions, upon which the refusal to psychologism is founded . As a conclusion, i will show how, according to these authors, this platonic, ideal background (...) constitutes the very foundation of every meaningful thought. (shrink)

There is consensus among computer scientists, logicians, and philosophers that good reasoning with qualitative beliefs must have the structural property of cumulative transitivity or, for short, cut. This consensus is typically explicitly argued for partially on the basis of practical and mathematical considerations. But the consensus is also implicit in the approach philosophers take to almost every puzzle about reasoning that involves multiple steps: philosophers typically assume that if each step in reasoning is acceptable considered on its own, the whole (...) chain of reasoning must also acceptable. In this paper I focus on whether there are good philosophical reasons for thinking that the consensus that good reasoning must satisfy cut is true. My central claim is that we should not accept the consensus—good reasoning might not satisfy cut. In particular, I consider four arguments for the consensus and explain why they are unpersuasive. (§2-5). I then show that the issue of whether good reasoning is cut turns on a substantive yet until now unnoticed question in epistemology (§6). (shrink)

A comparison is given between two conditions used to define logical constants: Belnap's uniqueness and Hacking's deducibility of identicals. It is shown that, in spite of some surface similarities, there is a deep difference between them. On the one hand, deducibility of identicals turns out to be a weaker and less demanding condition than uniqueness. On the other hand, deducibility of identicals is shown to be more faithful to the inferentialist perspective, permitting definition of genuinely proof-theoretical concepts. This kind of (...) analysis is driven by exploiting the Curry–Howard correspondence. In particular, deducibility of identicals is shown to correspond to the computational property of eta expansion, which is essential in the characterization of propositional identity. (shrink)

The paper shows how ideas that explain the sense of an expression as a method or algorithm for finding its reference, preshadowed in Frege’s dictum that sense is the way in which a referent is given, can be formalized on the basis of the ideas in Thomason (1980). To this end, the function that sends propositions to truth values or sets of possible worlds in Thomason (1980) must be replaced by a relation and the meaning postulates governing the behaviour of (...) this relation must be given in the form of a logic program. The resulting system does not only throw light on the properties of sense and their relation to computation, but also shows circular behaviour if some ingredients of the Liar Paradox are added. The connection is natural, as algorithms can be inherently circular and the Liar is explained as expressing one of those. Many ideas in the present paper are closely related to those in Moschovakis (1994), but receive a considerably lighter formalization. (shrink)

Van Fraassen stresses two distinct but interrelated themes in The Scientific Image: the semantic view of theories and the epistemic status of unobservables. The first of these could easily be accepted by a scientific realist, and indeed realists like Giere have already adapted it to their purposes. So the specifically empiricist thread in van Fraassen’s philosophy stems from the second.Van Fraassen breaks from tradition in founding his empiricism not on the ontological status of unobservable entities but on the epistemic attitude (...) we take to them. The main points of his position are these:1)The claims of scientific theories, including claims about unobservable entities, are to be taken literally. Theories are not reconstructed so as to remove claims of the existence of unobservable objects.2)Observation is a matter of direct observation by accepted participants in the human scientific community. (shrink)

Some propositions add more information to bodies of propositions than do others. We start with intuitive considerations on qualitative comparisons of information added . Central to these are considerations bearing on conjunctions and on negations. We find that we can discern two distinct, incompatible, notions of information added. From the comparative notions we pass to quantitative measurement of information added. In this we borrow heavily from the literature on quantitative representations of qualitative, comparative conditional probability. We look at two ways (...) to obtain a quantitative conception of information added. One, the most direct, mirrors Bernard Koopman’s construction of conditional probability: by making a strong structural assumption, it leads to a measure that is, transparently, some function of a function P which is, formally, an assignment of conditional probability (in fact, a Popper function). P reverses the information added order and mislocates the natural zero of the scale so some transformation of this scale is needed but the derivation of P falls out so readily that no particular transformation suggests itself. The Cox–Good–Aczél method assumes the existence of a quantitative measure matching the qualitative relation, and builds on the structural constraints to obtain a measure of information that can be rescaled as, formally, an assignment of conditional probability. A classical result of Cantor’s, subsequently strengthened by Debreu, goes some way towards justifying the assumption of the existence of a quantitative scale. What the two approaches give us is a pointer towards a novel interpretation of probability as a rescaling of a measure of information added. (shrink)

In this paper I provide a theory of the speech act of assertion according to which assertion is a species of joint action. In doing so I rely on a theory of joint action developed in more detail elsewhere. Here we need to distinguish between the genus, joint action, and an important species of joint action, namely, what I call joint epistemic action. In the case of the latter, but not necessarily the former, participating agents have epistemic goals, e.g., the (...) acquisition of knowledge. It is joint epistemic action that assertion is a species of. (shrink)

Many claims about conceptual matters are often represented as, or inferred from, claims about the meaning, reference, or mastery, of words. But sometimes this has led to treating conceptual analysis as though it were nothing but linguistic analysis. We canvass the most promising justifications for moving from linguistic premises to substantive conclusions. We show that these justifications fail and argue against current practice (in metaethics and elsewhere), which confuses an investigation of a word’s meaning, reference, or competence conditions with an (...) analysis of some concept or property associated with that word. (shrink)

Berkeley’s ‘master argument’ for idealism has been the subject of extensive criticism. Two of his strongest critics, A.N. Prior and J.L. Mackie, argue that due to various logical confusions on the part of Berkeley, the master argument fails to establish his idealist conclusion. Prior argues that Berkeley’s argument ‘proves too little’ in its conclusion, while Mackie contends that Berkeley confuses two different kinds of self-refutation in his argument. This paper proposes a defence of the master argument based on intuitionistic argument. (...) It begins by giving a brief exposition of the master argument and Prior's and Mackie's criticism. The following section explains why we might read the master argument along intuitionistic lines. The final section demonstrates that, according to intuitionistic logic, Berkeley's argument withstands the criticisms of Prior and Mackie. (shrink)

Strictly intuitionistic inferences are employed to demonstrate that three conditions—the existence of Brouwerian weak counterexamples to _Test_, the recognition condition, and the _BHK_ interpretation of the logical signs—are together inconsistent. Therefore, if the logical signs in mathematical statements governed by the recognition condition are constructive in that they satisfy the clauses of the _BHK_, then every relevant instance of the classical principle _Test_ is true intuitionistically, and the antirealistic critique of conventional logic, once thought to yield such weak counterexamples, is (...) seen, in this instance, to fail. (shrink)

In this paper, I examine recent arguments for the widespread existence of simultaneous causation from Huemer & Kovitz and Mumford & Anjum, and conclude that they are mistaken. I argue that these arguments overlook two pictures of causation which are commonly assumed, which I call the Standard Modern Picture and the Contiguous Extended Picture.

Rejectivism is one of the most influential embodiments of pragmatism within contemporary philosophy of logic, advancing an explanation of the meaning of a logical notion, negation, in terms of the speech act of denial. This paper offers a challenge to rejectivism by proposing that in virtue of explaining negation in terms of denial, the rejectivist ought to be able to explain the concept of contradiction partially in terms of denial. It is argued that any failure to achieve this constitutes an (...) explanatory failure on the part of rejectivism, and reasons are then provided to doubt that the challenge can be successfully met. (shrink)

Donald Davidson infamously claims that belief is in its nature veridical, and that skepticism is for this reason fundamentally incoherent. To those who take the issue of external world skepticism seriously, Davidson's arguments may seem to involve a conjuring trick. In particular, his invocation of an ‘omniscient interpreter’, whose intelligibility supposedly ensures that our beliefs must be largely true, has the air of incense and lantern-rubbing about it. Davidson's claim has received considerable critical response in the literature, almost all of (...) it negative. In my view, some commentators have indeed lit on a critical and controversial lemma in Davidson's argument, but this basic result has been obscured by being presented amidst an array of other criticisms that simply make no sense from a Davidsonian point of view. The aim of this paper is to clear away some of the confusion that stands in the way of a more productive evaluation of Davidson's important claim. (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.The irresistible metaphor is that pure abstract objects […] are no more than shadows cast by the syntax of our discourse. And the aptness of the metaphor is enhanced by the reflection that shadows are, after their own fashion, real. (Crispin Wright [1992], p. 181–2)But I feel conscious that many a reader will scarcely recognise in the shadowy forms which I bring before him his numbers which all his life long have accompanied him as faithful and familiar friends; (Richard Dedekind [1963], p. 33)1 Introduction2 Logical‐historical preliminaries3 The linguistic turn4 Reductionism5 Rejectionism6 The ‘Julius Caesar’ problem7 Second‐order logic8 Bad company objections9 Conclusion. (shrink)

Is the truthmaker principle a development of the correspondence theory of truth? So Armstrong introduced the truthmaker principle to us, but Lewis (2001. Forget about the ‘correspondence theory of truth’. Analysis 61: 275–80.) influentially argued that it is neither a correspondence theory nor a theory of truth. But the truthmaker principle can be correctly understood as a development of the correspondence theory if it’s conceived as incorporating the insight that truth is a relation between truth-bearers and something worldly. And we (...) strengthen rather than weaken the plausibility of the truthmaker principle if we conceive of truth as performing a substantial rather than deflationary role in the truthmaker principle. (shrink)

This paper aims to renew the “deflationary” interpretation of Ramsey’s theory of truth, with respect to his declared “pragmatist tendency,” which was not completely developed due to his premature death. This aim is not only historical-philosophical, but also exquisitely theoretical, since the mediation of pragmatism allowed Ramsey to achieve an original synthesis among different philosophical instances. In order to show this, I pay attention to the debate between Ramsey and some spokespeople of the leading British philosophical traditions at the beginning (...) of the twentieth century (especially Neo-idealism, Neo-empiricism, and Oxford Realism), through which it will stand out how Ramsey’s logical analysis of the truth predicate was embedded within a wider theoretical context, involving a pragmatic theory of knowledge and even a “general psychological theory.” Indeed, the truth of a belief will be defined in relation to mental factors, in so far as they involve a successful disposition to behave. (shrink)

Jaakko Hintikka points out the power of Skolem functions to affect both what there is and what we know. There is a tension in his presupposition that these functions actually extend the realm of logic. He claims to have resolved the tension by “reconstructing constructivism” along epistemological lines, instead of by a typical ontological construction; however, after the collapse of the distinction between first and second order, that resolution is not entirely satisfactory. Still, it does throw light on the conceptual (...) analysis Hintikka proposes. (shrink)

Dummett’s notion of indefinite extensibility is influential but obscure. The notion figures centrally in an alternative Dummettian argument for intuitionistic logic and anti-realism, distinct from his more famous, meaning-theoretic arguments to the same effect. Drawing on ideas from Dummett, a precise analysis of indefinite extensibility is proposed. This analysis is used to reconstruct the poorly understood alternative argument. The plausibility of the resulting argument is assessed.

The notion of potential infinity dominated in mathematical thinking about infinity from Aristotle until Cantor. The coherence and philosophical importance of the notion are defended. Particular attention is paid to the question of whether potential infinity is compatible with classical logic or requires a weaker logic, perhaps intuitionistic.

In his recent book, "The Metaphysicians of Meaning" (2000), Gideon Makin argues that in the so-called "Gray's Elegy" argument (the GEA) in "On Denoting", Russell provides decisive arguments against not only his own theory of denoting concepts but also Frege's theory of sense. I argue that by failing to recognize fundamental differences between the two theories, Makin fails to recognize that the GEA has less force against Frege's theory than against Russell's own earlier theory. While I agree with many aspects (...) of Makin's interpretation of the GEA, I differ with him regarding some significant details and present an interpretation according to which the GEA emerges as simpler, stronger, and more integrated. (shrink)

On the background of the later opposition between realism and anti-realism, and with special attention to the overlapping of reality and logos, an examination of Aristotle’s way of answering to the...

In this paper we address the question of how it can be possible for a non-expert to acquire justified true belief from expert testimony. We discuss reductionism and epistemic trust as theoretical approaches to answer this question and present a novel solution that avoids major problems of both theoretical options: Performative Expert Testimony. PET draws on a functional account of expertise insofar as it takes the expert’s visibility as a good informant capable to satisfy informational needs as equally important as (...) her specific skills and knowledge. We explain how PET generates justification for testimonial belief, which is at once assessable for non-experts and maintains the division of epistemic labor between them and the experts. Thereafter we defend PET against two objections. First, we point out that the non-expert’s interest in acquiring widely assertable true beliefs and the expert’s interest in maintaining her status as a good informant counterbalances the relativist account of justification at work in PET. Second, we show that with regard to the interests at work in testimonial exchanges between experts and non-experts, PET yields a better explanation of knowledge-acquisition from expert testimony than externalist accounts of justification such as reliabilism. As our arguments ground in a conception of knowledge, which conceives of belief-justification as a declarative speech act, throughout the rearmost sections of this paper we also indicate to how such a conception is operationalized in PET. (shrink)

This paper puts forward and defends an account of mathematical truth, and in particular an account of the truth of mathematical axioms. The proposal attempts to be completely nonrevisionist. In this connection, it seeks to satisfy simultaneously both horns of Benacerrafs work on informal rigour. Kreisel defends the view that axioms are arrived at by a rigorous examination of our informal notions, as opposed to being stipulated or arrived at by trial and error. This view is then supplemented by a (...) Fregean account of the objectivity and our knowledge of abstract objects. It is then argued that the resulting view faces no insurmountable metaphysical or epistemic obstacles. (shrink)

Abstract: Chomsky (1986) has claimed that the prima facie incompatibility between descriptive linguistics and semantic externalism proves that an externalist semantics is impossible. Although it is true that a strong form of externalism does not cohere with descriptive linguistics, sociolinguistic theory can unify the two approaches. The resulting two-level theory reconciles descriptivism, mentalism, and externalism by construing community languages as a function of social identification. This approach allows a fresh look at names and definite descriptions while also responding to Chomsky's (...) (1993, 1995) challenge to articulate an externalist theory of meaning that can be used in the scientific investigation of language. (shrink)

A situated agent is one which operates within an environment. In most cases, the environment in which the agent exists will be more complex than the agent itself. This means that an agent, human or artificial, which wishes to carry out non-trivial operations in its environment must use techniques which allow an unbounded world to be represented within a cognitively bounded agent. We present a brief description of some important theories within the fields of epistemology and metaphysics. We then discuss (...) ways in which philosophical problems of scepticism are related to the problems faced by knowledge representation. We suggest that some of the methods that philosophers have developed to address the problems of epistemology may be relevant to the problems of representing knowledge within artificial agents. (shrink)

Wittgenstein's paradoxical theses that unproved propositions are meaningless, proofs form new concepts and rules, and contradictions are of limited concern, led to a variety of interpretations, most of them centered on rule-following skepticism. We argue, with the help of C. S. Peirce's distinction between corollarial and theorematic proofs, that his intuitions are better explained by resistance to what we call conceptual omniscience, treating meaning as fixed content specified in advance. We interpret the distinction in the context of modern epistemic logic (...) and semantic information theory, and show how removing conceptual omniscience helps resolve Wittgenstein's paradoxes and explain the puzzle of deduction, its ability to generate new knowledge and meaning. (shrink)

Joseph Rouse has drawn from Heidegger’s early philosophy to develop what he calls a “practical hermeneutics of science.” With this, he has not only become an important player in the recent trend towards practice-based conceptualisations of science, he has also emerged as the predominant expositor of Heidegger’s philosophy of science. Yet, there are serious shortcomings in both Rouse’s theory of science and his interpretation of Heidegger. In the first instance, Rouse’s practical hermeneutics appears confused on the topic of realism. In (...) the second instance, Rouse suppresses Heidegger’s distinction between existence and essence, and hence fails to grasp the latter’s corollary distinction between scientic research and everyday practice. I argue that, by accepting a correction in his interpretation of Heidegger, Rouse would find the means to resolve the debilitating tensions in his stance towards realism. (shrink)

While it is common in social epistemology, philosophy of education and sociology to speak of theoretical knowledge, the concept of theoretical knowledge used in ordinary discourse has not been properly examined, and its relations to other types of knowledge remain unclear. This article argues that this ordinary language notion of theoretical knowledge has a distinct meaning different from the meanings of terms for other knowledge types, for example, knowledge‐that, and meta‐cognitive knowledge, and provides an analysis that characterizes theoretical knowledge as (...) distinguished by its indirectness. The article then discusses the implications of this view for the practical role of theoretical knowledge and suggests that a reappraisal of its epistemic significance is due. (shrink)

We are logical pluralists who hold that the right logic is dependent on the domain of investigation; different logics for different mathematical theories. The purpose of this article is to explore the ramifications for our pluralism concerning normativity. Is there any normative role for logic, once we give up its universality? We discuss Florian Steingerger’s “Frege and Carnap on the Normativity of Logic” as a source for possible types of normativity, and then turn to our own proposal, which postulates that (...) various logics are constitutive for thought within particular practices, but none are constitutive for thought as such. (shrink)

European Journal of Philosophy, Volume 30, Issue 3, Page 1010-1027, September 2022.

According to the communication desideratum (CD), a notion of semantic content must be adequately related to communication. In the recent debate on indexical reference, (CD) has been invoked in arguments against the view that intentions determine the semantic content of indexicals and demonstratives (intentionalism). In this paper, I argue that the interpretations of (CD) that these arguments rely on are questionable, and suggest an alternative interpretation, which is compatible with (strong) intentionalism. Moreover, I suggest an approach that combines elements of (...) intentionalism with other subjectivist approaches, and discuss the role of intuitions in developing and evaluating theories of indexical reference. (shrink)

An "overview article" that (a) clarifies the nature of theological anti-realism and how that thesis should be formulated, and (b) negatively assesses some of the most common arguments for being a theological anti-realist.

Different versions of moral projectivism are delineated: minimal, metaphysical, nihilistic, and noncognitivist. Minimal projectivism (the focus of this paper) is the conjunction of two subtheses: (1) that we experience morality as an objective aspect of the world and (2) that this experience has its origin in an affective attitude (e.g., an emotion) rather than in perceptual faculties. Both are empirical claims and must be tested as such. This paper does not offer ideas on any specific test procedures, but rather undertakes (...) the important preliminary task of clarifying the content of these subtheses (e.g., what is meant by "objective"? what is meant by "experience"?). Finally, attention is given to the relation between (a) acknowledging that the projectivist account might be true of a token moral judgment and (b) maintaining moral projectivism to be true as a general thesis. (shrink)

This is a review of 'The Facts in Logical Space' by Jason Turner.

Several philosophers have argued that the logic of set theory should be intuitionistic on the grounds that the open-endedness of the set concept demands the adoption of a nonclassical semantics. This paper examines to what extent adopting such a semantics has revisionary consequences for the logic of our set-theoretic reasoning. It is shown that in the context of the axioms of standard set theory, an intuitionistic semantics sanctions a classical logic. A Kripke semantics in the context of a weaker axiomatization (...) is then considered. It is argued that this semantics vindicates an intuitionistic logic only insofar as certain constraints are put on its interpretation. Wider morals are drawn about the restrictions that this places on the shape of arguments for an intuitionistic revision of the logic of set theory. (shrink)

In 'General Propositions and Causality' Ramsey rejects his earlier view that universal generalizations are infinite conjunctions, arguing that they are not genuine propositions at all. We argue that his new position is unstable. The issues about infinity that lead Ramsey to the new view are essentially those underlying Wittgenstein's rule-following considerations. If they show that generalizations are not genuine propositions, they show that there are no genuine propositions. The connection raises interesting historical questions about the direction of influence between Ramsey (...) and Wittgenstein, the origin of the rule-following argument, and the influence of writers such as Brouwer. (shrink)

Can it ever be rational to revise one's own logic by one's own lights? In this paper I argue that logic is never rationally revisable, even if one's own logic gives rise to paradoxes and allows one to derive any conclusion whatsoever. Instead of revising logic, we need to revise a certain widely held position in the philosophy of logic, one tied to the standard conception of validity and to the alleged monotonicity of deductive reasoning. I develop the alternative conception (...) of validity and of deductive reasoning, which explains why we are generally entitled to the conclusions of deductive reasoning, even though we rationally do not accept them in certain circumstances tied to paradoxes. (shrink)

I argue that the implementation of theDummettian program of an ``anti-realist'' semanticsrequires quite different conceptions of the technicalmeaning-theoretic terms used than those presupposed byDummett. Starting from obvious incoherences in anattempt to conceive truth conditions as assertibilityconditions, I argue that for anti-realist purposesnon-epistemic semantic notions are more usefully kept apart from epistemic ones rather than beingreduced to them. Embedding an anti-realist theory ofmeaning in Martin-Löf's Intuitionistic Type Theory(ITT) takes care, however, of many notorious problemsthat have arisen in trying to specify suitableintuitionistic (...) notions of semantic value,truth-conditions, and validity, taking into accountthe so-called ``defeasibility of evidence'' forassertions in empirical discourses. (shrink)

Michael Dummett offered a semantic characterisation of a variety of realism-antirealism debates. This approach has fallen out of fashion. This has been to the detriment of metaphysics. This paper offers an accurate characterisation of Dummett’s view, often lacking in the literature, and then defends it against a range of attacks (from Devitt, Miller and Williamson). This understanding of realism debates is resilient, and if we take it seriously the philosophical terrain looks importantly different. In particular, the philosophy of language has (...) a foundational role with respect to metaphysics. (shrink)

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

Realism takes many forms. The aim of this paper is to show that the “Critique of pure Reason” is the founding document of realism and that to the present-day Kant’s discussion of realism has shaped the theoretical landscape of the debates over realism. Kant not only invents the now common philosophical term ‘realism’. He also lays out the theoretical topography of the forms of realism that still frames our understanding of philosophical questions concerning reality. The paper explores this by analysis (...) of Kant’s methodological procedure to distinguish between empirical and transcendental realism. This methodological procedure is still of great help in contemporary philosophy, although it has its limits. (shrink)

A remembrance of Dummett's work on philosophy of mathematcis.

Many people claim that semantic content is normative, and that therefore naturalistic theories of content face a potentially insuperable difficulty. The normativity of content allegedly undermines naturalism by introducing a gap between semantic 'ought's and the explanatory resources of naturalism. I argue here that this problem is not ultimately pressing for naturalists. The normativity thesis, I maintain, is ambiguous; it could mean either that the content of a term prescribes a pattern of use, or that it merely determines which pattern (...) of use can be described as 'correct'. For the antinaturalist argument to go forward, content must be prescriptive. I argue, however, that it is not. Moreover, the thesis that content supplies standards for correct use is insufficient to supply a similar, a priori objection to naturalism. (shrink)