Logic is about reasoning, or so the story goes. This thesis looks at the concept of logic, what it is, and what claims of correctness of logics amount to. The concept of logic is not a settled matter, and has not been throughout the history of it as a notion. Tools from conceptual analysis aid in this historical venture. Once the unsettledness of logic is established we see the repercussions in current debates in the philosophy of logic. Much of the (...) battle over the ‘one true logic’ is conceptually talking past each other. The theory of logics-as-formalizations is presented as a conceptually open theory of logic which is Carnapian in flavour and grounding. Rudolf Carnap’s notions surrounding ‘external’ and ‘pseudo-questions’ about linguistic frameworks apply to formalizations, thus logics, as well. An account of what formalizations are, a more structured sub-set of modelling, is given to ground the claim that logics are formalizations. Finally, a novel account of correctness, the COFE framework, is developed which allows the notions of logical monism, pluralism and nihilism to be more precisely formulated than they currently are in the discourse. (shrink)

Gottlob Frege takes logic to be the science of truth throughout his career. However, the mature Frege makes remarks which seem to go against the idea that logic is the science of truth. This paper shows that we can explain away this tension in the mature Frege’s conception of logic if we accept that truth is an object, that is, the truth-vale True qua the reference of a sentence, for Frege. Even though the main thesis of this paper is a (...) conditional, I provide reasons why we ought to consider the possibility seriously that truth is an object for Frege. I also explain how we can make sense of Frege’s conception of logic as the science of truth while accepting truth is an object. (shrink)

This paper engages the question ‘Does the consistency of a set of axioms entail the existence of a model in which they are satisfied?’ within the frame of the Frege-Hilbert controversy. The question is related historically to the formulation, proof and reception of Gödel’s Completeness Theorem. Tools from mathematical logic are then used to argue that there are precise senses in which Frege was correct to maintain that demonstrating consistency is as difficult as it can be, but also in which (...) Hilbert was correct to maintain that demonstrating existence given consistency is as easy as it can be. (shrink)

Is logic normative for reasoning? In the wake of work by Gilbert Harman and John MacFarlane, this question has been reduced to: are there any adequate bridge principles which link logical facts to normative constraints on reasoning? Hitherto, defenders of the normativity of logic have exclusively focussed on identifying adequate validity bridge principles: principles linking validity facts—facts of the form 'gamma entails phi'—to normative constraints on reasoning. This paper argues for two claims. First, for the time being at least, Harman’s (...) challenge cannot be surmounted by articulating validity bridge principles. Second, Harman’s challenge can be met by articulating invalidity bridge principles: principles linking invalidity facts of the form 'gamma does not entail phi' to normative constraints on reasoning. In doing so, I provide a novel defence of the normativity of logic. (shrink)

According to a certain conception of language, any sentence can, when used on an occasion, have any of indefinitely many truth-conditions. Such a conception of language gives us reason to think that the question of whether the notion of truth has a distinctive content cannot be settled by looking solely at the predication of truth. By focusing on the predicate ‘true’ when trying to determine the significance of the notion of truth, we may have been looking in the wrong place.

In this article I explore some implications of the correspondence that went on between Ludwig Wittgenstein and the logician and mathematician Gottlob Frege. Part of this exchange was focused on the envisaged publication of Wittgenstein’s Tractatus Logico-Philosophicus, and on the philosophical or literary character of that work. The problem discussed concerned the question of whether the Tractatus should be seen not as a scientific but as an artistic achievement. My first goal is to present what, given Frege’s writings, his phrase (...) “an artistic rather than a scientific achievement” could be understood to mean in terms of the Tractatus itself. Secondly, I seek to determine the extent to which traces of Frege’s understanding of such terms as “mock thoughts,” “fiction,” “elucidation,” “paintings” and “colouring” are to be found in the language of the Tractatus. This should then make it possible to show how Wittgenstein’s work, viewed from a Fregean perspective, can be seen as furnishing a logic and semantics not only for the languages of logic and natural science, but also for something that is “an artistic rather than a scientific achievement”, while also indicating that the content of the Tractatus as a whole could not have been captured independently of the unified form Wittgenstein himself gave it. (shrink)

Given the plethora of competing logical theories of validity available, it’s understandable that there has been a marked increase in interest in logical epistemology within the literature. If we are to choose between these logical theories, we require a good understanding of the suitable criteria we ought to judge according to. However, so far there’s been a lack of appreciation of how logical practice could support an epistemology of logic. This paper aims to correct that error, by arguing for a (...) practice-based approach to logical epistemology. By looking at the types of evidence logicians actually appeal to in attempting to support their theories, we can provide a more detailed and realistic picture of logical epistemology. To demonstrate the fruitfulness of a practice-based approach, we look to a particular case of logical argumentation—the dialetheist’s arguments based upon the self-referential paradoxes—and show that the evidence appealed to support a particular theory of logical epistemology, logical abductivism. (shrink)

Frege claims that the laws of logic are characterized by their “generality,” but it is hard to see how this could identify a special feature of those laws. I argue that we must understand this talk of generality in normative terms, but that what Frege says provides a normative demarcation of the logical laws only once we connect it with his thinking about truth and science. He means to be identifying the laws of logic as those that appear in every (...) one of the scientific systems whose construction is the ultimate aim of science, and in which all truths have a place. Though an account of logic in terms of scientific systems might seem hopelessly antiquated, I argue that it is not: a basically Fregean account of the nature of logic still looks quite promising. (shrink)

The translation of both ‘bedeuten’ and ‘Bedeutung’ in Frege's works remains sufficiently problematic that some contemporary authors prefer to leave these words untranslated. Here a case is made for returning to Russell's initial choice of ‘to indicate’ and ‘indication’ as better alternatives than the more usual ‘meaning’, ‘reference’, or ‘denotation’. It is argued that this choice has the philosophical payoff that Frege's controversial doctrines concerning the semantic values of sentences and predicative expressions are rendered far more comprehensible by it, and (...) that this translational strategy fulfills the desiderata of offering a translation which is acceptable both before and after Frege introduced the distinction between sense and reference or, as this paper would have it, between the sense of an expression and what it indicates. (shrink)

Hourya Benis-Sinaceur, Marco Panza, and Gabriel Sandu. Functions and Generality of Logic: Reflections on Dedekind’s and Frege’s Logicisms. Logic, Epistemology, and the Unity of Science; 37. Springer, 2015. ISBN: 978-3-319-17108-1 ; 978-3-319-36782-8, 978-3-319-17109-8.. Pp. xxi + 125.

Bertrand Russell: Logic For Russell, Aristotelian syllogistic inference does not do justice to the subject of logic. This is surely not surprising. It may well be something of a surprise, however, to learn that in Russell’s view neither Boolean algebra nor modern quantification theory do justice to the subject. For Russell, logic is a synthetic … Continue reading Russell: Logic →.

Some writers object to logical pluralism on the grounds that logic is normative. The rough idea is that the relation of logical consequence has consequences for what we ought to think and h...

This paper identifies a tension in Frege’s philosophy and offers a diagnosis of its origins. Frege’s Context Principle can be used to dissolve the problem of propositional unity. However, Frege’s official response to the problem does not invoke the Context Principle, but the distinction between ‘saturated’ and ‘unsaturated’ propositional constituents. I argue that such a response involves assumptions that clash with the Context Principle. I suggest, however, that this tension is not generated by deep-seated philosophical commitments, but by Frege’s occasional (...) attempt to take a dubious shortcut in the justification of his conception of propositional structure. (shrink)

According to the Explanatory Problem with Frege's Platonism about Thoughts, the sharp separation between the psychological and the logical on which Frege famously insists is too sharp, leaving Frege no resources to show how it could be legitimate to invoke logical laws in an explanation of our activities of thinking. I argue that there is room in Frege's philosophy for such justificatory explanations. To see how, we need first to understand correctly the lesson of Frege's attack on psychologism as fundamentally (...) marking a contrast between justification and explanation, and, second, we must take Frege to be committed to the idea that the laws of truth are normatively constitutive for the process of thinking. (shrink)

Frege's philosophical writings, including the “logistic project,” acquire a new insight by being confronted with Kant's criticism and Wittgenstein's logical and grammatical investigations. Between these two points a non-formalist history of logic is just taking shape, a history emphasizing the Greek and Kantian inheritance and its aftermath. It allows us to understand the radical change in rationality introduced by Gottlob Frege's syntax. This syntax put an end to Greek categorization and opened the way to the multiplicity of expressions producing their (...) own intelligibility. This article is based on more technical analyses of Frege which Claude Imbert has previously offered in other writings. (shrink)

Hilbert’s choice operators τ and ε, when added to intuitionistic logic, strengthen it. In the presence of certain extensionality axioms they produce classical logic, while in the presence of weaker decidability conditions for terms they produce various superintuitionistic intermediate logics. In this thesis, I argue that there are important philosophical lessons to be learned from these results. To make the case, I begin with a historical discussion situating the development of Hilbert’s operators in relation to his evolving program in the (...) foundations of mathematics and in relation to philosophical motivations leading to the development of intuitionistic logic. This sets the stage for a brief description of the relevant part of Dummett’s program to recast debates in metaphysics, and in particular disputes about realism and anti-realism, as closely intertwined with issues in philosophical logic, with the acceptance of classical logic for a domain reflecting a commitment to realism for that domain. Then I review extant results about what is provable and what is not when one adds epsilon to intuitionistic logic, largely due to Bell and DeVidi, and I give several new proofs of intermediate logics from intuitionistic logic+ε without identity. With all this in hand, I turn to a discussion of the philosophical significance of choice operators. Among the conclusions I defend are that these results provide a finer-grained basis for Dummett’s contention that commitment to classically valid but intuitionistically invalid principles reflect metaphysical commitments by showing those principles to be derivable from certain existence assumptions; that Dummett’s framework is improved by these results as they show that questions of realism and anti-realism are not an “all or nothing” matter, but that there are plausibly metaphysical stances between the poles of anti-realism and realism, because different sorts of ontological assumptions yield intermediate rather than classical logic; and that these intermediate positions between classical and intuitionistic logic link up in interesting ways with our intuitions about issues of objectivity and reality, and do so usefully by linking to questions around intriguing everyday concepts such as “is smart,” which I suggest involve a number of distinct dimensions which might themselves be objective, but because of their multivalent structure are themselves intermediate between being objective and not. Finally, I discuss the implications of these results for ongoing debates about the status of arbitrary and ideal objects in the foundations of logic, showing among other things that much of the discussion is flawed because it does not recognize the degree to which the claims being made depend on the presumption that one is working with a very strong logic. (shrink)

Despite its importance for early analytic philosophy, Gottlob Frege's account of existence statements, according to which they classify concepts, has been thought to succumb to a number of well-worn criticisms. This article does two things. First, it argues that, by remaining faithful to the letter of Frege's claim that concepts are functions, the Fregean account can be saved from many of the standard criticisms. Second, it examines the problem that Frege's account fails to generalize to cases which involve definite descriptions (...) and proper names. To deal with this the proffered analysis deviates from the letter of Frege's views, while remaining within its spirit. It proposes, in opposition to Frege, that expressions which grammatically look like singular terms should not always be read as referring to objects, but are sometimes best analysed as indicating functions. (shrink)

This paper argues that Carnap both did not view and should not have viewed Frege's project in the foundations of mathematics as misguided metaphysics. The reason for this is that Frege's project was to give an explication of number in a very Carnapian sense — something that was not lost on Carnap. Furthermore, Frege gives pragmatic justification for the basic features of his system, especially where there are ontological considerations. It will be argued that even on the question of the (...) independent existence of abstract objects, Frege and Carnap held remarkably similar views. I close with a discussion of why, despite all this, Frege would not accept the principle of tolerance. (shrink)

This paper offers a new interpretation for Wittgenstein`s treatment of mathematical identities. As it is widely known, Wittgenstein`s mature philosophy of mathematics includes a general rejection of abstract objects. On the other hand, the traditional interpretation of mathematical identities involves precisely the idea of a single abstract object – usually a number –named by both sides of an equation.

We see no grounds for insisting that, because the concept natural number is abstract, its foundations must be innate. It is possible to specify domain general learning processes that feed into more abstract concepts of numerical infinity. By neglecting the messiness of children's slow acquisition of arithmetical concepts, Rips et al. present an idealized, unnecessarily insular, view of number development.

Many experiments with infants suggest that they possess quantitative abilities, and many experimentalists believe that these abilities set the stage for later mathematics: natural numbers and arithmetic. However, the connection between these early and later skills is far from obvious. We evaluate two possible routes to mathematics and argue that neither is sufficient: (1) We first sketch what we think is the most likely model for infant abilities in this domain, and we examine proposals for extrapolating the natural number concept (...) from these beginnings. Proposals for arriving at natural number by (empirical) induction presuppose the mathematical concepts they seek to explain. Moreover, standard experimental tests for children's understanding of number terms do not necessarily tap these concepts. (2) True concepts of number do appear, however, when children are able to understand generalizations over all numbers; for example, the principle of additive commutativity (a+b=b+a). Theories of how children learn such principles usually rely on a process of mapping from physical object groupings. But both experimental results and theoretical considerations imply that direct mapping is insufficient for acquiring these principles. We suggest instead that children may arrive at natural numbers and arithmetic in a more top-down way, by constructing mathematical schemas. (shrink)

It is well known that the circumflex notation used by Russell and Whitehead to form complex function names in Principia Mathematica played a role in inspiring Alonzo Church's “lambda calculus” for functional logic developed in the 1920s and 1930s. Interestingly, earlier unpublished manuscripts written by Russell between 1903–1905—surely unknown to Church—contain a more extensive anticipation of the essential details of the lambda calculus. Russell also anticipated Schönfinkel's combinatory logic approach of treating multiargument functions as functions having other functions as value. (...) Russell’s work in this regard seems to have been largely inspired by Frege’s theory of functions and “value-ranges”. This system was discarded by Russell due to his abandonment of propositional functions as genuine entities as part of a new tack for solving Russell’s paradox. In this article, I explore the genesis and demise of Russell’s early anticipation of the lambda calculus. (shrink)

In the past few years, a number of philosophers ; Horgan and Tienson 2002; Pitt 2004) have maintained the following three theses: there is a distinctive sort of phenomenology characteristic of conscious thought, as opposed to other sorts of conscious mental states; different conscious thoughts have different phenomenologies; and thoughts with the same phenomenology have the same intentional content. The last of these three claims is open to at least two different interpretations. It might mean that the phenomenology of a (...) thought expresses its intentional content, where intentional content is understood as propositional, and propositions are understood as mind-and language-independent abstract entities. And it might mean that the phenomenology of a thought is its intentional content—that is, that the phenomenology of a thought, like the phenomenology of a sensation, constitutes its content. The second sort of view is a kind of psychologism. Psychologistic views hold that one or another sort of thing—numbers, sentences, propositions, etc.—that we can think or know about is in fact a kind of mental thing. Since Frege, psychologism has been in bad repute among analytic philosophers. It is widely held that Frege showed that such views are untenable, since, among other things, they subjectivize what is in fact objective, and, hence, relativize such things as consistency and truth to the peculiarities of human psychology. The purpose of this paper is to explore the consequences of the thesis that intentional mental content is phenomenological and to try to reach a conclusion about whether it yields a tenable view of mind, thought and meaning. I believe the thesis is not so obviously wrong as it will strike many philosophers of mind and language. In fact, it can be defended against the standard objections to psychologism, and it can provide the basis for a novel and interesting account of mentality. (shrink)

The paper is the Part IV of the large research, dedicated to both revision of the system of basic logical categories and generalization of modern predicate logic to functional logic. The topic of the paper is consideration of graphs of functions and relations as a derivative and definable category of ultra-Fregean logistics. There are two types of function specification: an operational specification, in which a function is first applied to arguments and then the value of the function is entered as (...) the result of such application, and a grammar specification, in which an object is first entered and then represented as a value of the function on the given arguments. Since function specifications are relations themselves (which was shown in the previous article of the series), this means that each function forms two relations: the obverse (for an operational specification) and the reverse one (for a grammatical specification). Hence, the definitions introduce two types of graphs: the obverse graph of a function, or a graph of the obverse relation formed by this function, is a set of sequences of such objects, the last of which is a value of this function on the sequence of other of these objects as arguments of the same function. Similarly, the reverse graph of a function, or the graph of the reverse relation formed by this function, is called a set of sequences of such objects, the first of which is the value of this function on the sequence of other of these objects as arguments of the same function. In the limiting case of 0-ary functions, both graphs of any such function coincide. Gottlob Frege discovered obverse graphs of functions and called them function value-ranges. He fundamentally emphasized the non-identity of functions and their graphs. Unfortunately, in set theory under the influence of Giuseppe Peano, an alternative approach was adopted, according to which functions and relations are identical to their graphs and, ultimately, to each other. We show that this approach leads to two unacceptable and, at the same time, mutually contradictory conclusions, and must therefore be rejected. (shrink)

The Caesar problem arises for abstractionist views, which seek to secure reference for terms such as ‘the number of Xs’ or #X by stipulating the content of ‘unmixed’ identity contexts like ‘#X = #Y’. Frege objects that this stipulation says nothing about ‘mixed’ contexts such as ‘# X = Julius Caesar’. This article defends a neglected response to the Caesar problem: the content of mixed contexts is just as open to stipulation as that of unmixed contexts.

This collection of papers, celebrating the contributions of Swedish logician Dag Prawitz to Proof Theory, has been assembled from those presented at the Natural Deduction conference organized in Rio de Janeiro to honour his seminal research. Dag Prawitz’s work forms the basis of intuitionistic type theory and his inversion principle constitutes the foundation of most modern accounts of proof-theoretic semantics in Logic, Linguistics and Theoretical Computer Science. The range of contributions includes material on the extension of natural deduction with higher-order (...) rules, as opposed to higher-order connectives, and a paper discussing the application of natural deduction rules to dealing with equality in predicate calculus. The volume continues with a key chapter summarizing work on the extension of the Curry-Howard isomorphism, via methods of category theory that have been successfully applied to linear logic, as well as many other contributions from highly regarded authorities. With an illustrious group of contributors addressing a wealth of topics and applications, this volume is a valuable addition to the libraries of academics in the multiple disciplines whose development has been given added scope by the methodologies supplied by natural deduction. The volume is representative of the rich and varied directions that Prawitz work has inspired in the area of natural deduction. (shrink)

This article claims that events, facts and states of affairs need to be differentiated. It takes as a starting point Chisholm’s claim that only his ontology of states of affairs explains effectively thirteen sentences related to propositions and events. He does this by reducing propositions and events to states of affairs. We argue that our ontology also solves those problems. We defend a hierarchized Platonist ontology that has concrete entities and abstract entities. The distinctions we propose allow us to explain (...) the pre-analytic data analyzed by Chisholm without reducing entities. We claim that our ontology provides a different way of explaining that data, and is, thus, promissory. (shrink)

Neo-Fregeans such as Bob Hale and Crispin Wright seek a foundation of mathematics based on abstraction principles. These are sentences involving a relation called the abstraction relation. It is usually assumed that abstraction relations must be equivalence relations, so reflexive, symmetric and transitive. In this article I argue that abstraction relations need not be reflexive. I furthermore give an application of non-reflexive abstraction relations to restricted abstraction principles.

It is argued that the finitist interpretation of wittgenstein fails to take seriously his claim that philosophy is a descriptive activity. Wittgenstein's concentration on relatively simple mathematical examples is not to be explained in terms of finitism, But rather in terms of the fact that with them the central philosophical task of a clear 'ubersicht' of its subject matter is more tractable than with more complex mathematics. Other aspects of wittgenstein's philosophy of mathematics are touched on: his view that mathematical (...) propositions are 'grammatical propositions' (and so, Strictly speaking, Not genuine propositions at all) and his view that in mathematics 'everything is algorithm, Nothing meaning'. His views on consistency and his anti-Foundationalism are linked with this central thesis. (shrink)

In “Truth and Probability” Ramsey claimed that the logic of consistency for probability is not a logic of truth. After supporting this claim, he proceeded to explore the possibilities for a logic of truth for probability. An examination of Ramsey's intent reveals that Ramsey was far from being an orthodox Bayesian when it comes to statistical reasoning. The relations between Ramsey's thought and the ideas of Keynes and Peirce are discussed.

Simon Blackburn has shown that there is an analogy between the problem of moral motivation in ethics (how can moral reasons move us?) and the problem of what we might call the power of logical reasons (how can logical reasons move us, what is the force of the 'logical must?'). In this paper, I explore further the parallel between the internalism problem in ethics and the problem of the power of logical reasons, and defend a version of psychologism about reasons, (...) although not one of the Humean form. I discuss two forms of cognitivism: (i) a pure cognitivism and 'hard' realism modelled after Dancy's parallel conception in ethics: when we grasp logical reasons we grasp facts, which are directly known to us; (ii) a Kantian form of cognitivism, based on the idea that compulsion by reason goes with the capacity of reflection. I argue that (i) is implausible, and that (ii) fails to meet the internalist requirement. One would then seem to be left with what Dancy calls, about practical reasoning, psychologism about reasons. I sketch what might be such a psychologism. But it fails to account for the objectivity of logical reasons. I argue that the relevant state here is a form of dispositional knowledge of logical reasons. (shrink)

Among the many fundamental problems Wittgenstein discussed, two are especially relevant for evolutionary theory. The first one is the problem of negation and its relation to the intentionality of thought. Its resolution answers the question of how thought can anticipate reality though what is thought may not exist, and explains how empirical propositions are distinguishable from mathematical, logical, and conceptual (or what are traditionally called metaphysical) propositions. The second is the problem of the grounds of sensory experience. Wittgenstein’s resolution of (...) this problem is revolutionary since he showed that first-person, present-tense expressions (these are sentences by which we express what goes on in our mind) have no grounds at all, clarifying why we should abandon (all variants of) representative idealism. In combination with the resolution of the first problem, it enables us to develop new explanations about how during the course of development and evolution the mind evolves and evolved. (shrink)

According to Øystein Linnebo's account of abstractionism, abstraction principles, received as Fregean criteria of identity, can be used to reduce facts about singular reference to objects such as directions and numbers to facts that do not involve such objects. In this article, first I show how the resources of Linnebo's metasemantics successfully handle Dummett's challenge against the referentiality of the singular terms formed by abstraction principles. Then, I argue that Linnebo's metasemantic commitments do not provide us with tools for dispelling (...) the threat of a version of referential indeterminacy, according to which nothing in our use of a singular term, even when it is guided by an associated criterion of identity, could determine which particular object it refers to. I end by examining the bearing of the indeterminacy challenge to Linnebo's treatment of Frege's Caesar Problem: in the absence of an argument against the indeterminacy of reference, it is unclear how numerical expressions could qualify as genuine singular terms. (shrink)

In ontological debates, realists typically argue for their view via one of two approaches. The _Quinean approach_ employs naturalistic arguments that say our scientific practices give us reason to affirm the existence of a kind of entity. The _Fregean approach_ employs linguistic arguments that say we should affirm the existence of a kind of entity because our discourse contains reference to those entities. These two approaches are often seen as distinct, with _indispensability arguments_ typically associated with the former, but not (...) the latter, approach. This paper argues for a connection between the two approaches on the grounds that the typical arguments of the Fregean approach can be reformulated as indispensability arguments. This connection is significant in at least two ways. First, it implies that indispensability arguments provide a common framework within which to compare the Quinean and Fregean approaches, which allows for a more precise delineation of the two approaches. Second, it implies the possibility of analogical relations that allow proponents and opponents of each approach to draw upon the ideas that have been developed regarding the other. (shrink)

The investigations on higher-order type theories and on the related notion of parametric polymorphism constitute the technical counterpart of the old foundational problem of the circularity of second and higher-order logic. However, the epistemological significance of such investigations has not received much attention in the contemporary foundational debate.We discuss Girard’s normalization proof for second order type theory or System F and compare it with two faulty consistency arguments: the one given by Frege for the logical system of the Grundgesetze and (...) the one given by Martin-Löf for the intuitionistic type theory with a type of all types.The comparison suggests that the question of the circularity of second order logic cannot be reduced to Russell’s and Poincaré’s 1906 “vicious circle” diagnosis. Rather, it reveals a bunch of mathematical and logical ideas hidden behind the hazardous idea of impredicative quantification, constituting a vast domain for foundational research. (shrink)

Let me start with the enigmatic dictum of Blaise Pascal: ‘l'homme passe l'homme’ – ‘man goes beyond himself’; ‘humanity transcends itself’. What does this mean? On one plausible interpretation, Pascal is adverting to that strange restlessness of the human spirit which so many philosophers have pondered on, from Augustine before him, to Kierkegaard and many subsequent writers since. To be human is to recognize that we are, in a certain sense, incomplete beings. We are on a journey to a horizon (...) that always seems to recede from view. Unlike all the other animals, who need nothing further for their thriving and flourishing once the appropriate environmental conditions are provided, human beings, even when all their needs are catered for – physical, biological, social, cultural – and even when they enjoy a maximally secure and enriching environment, still have a certain resistance to resting content with existence defined within a given set of parameters. They still have the restless drive to reach forward to something more. (shrink)

At several points in his later writings Wittgenstein discusses imaginary forms of life and ways of thinking that appear queer or alien from our point of view; concepts so different from ours that those who think from within them seem to be alternatives to us. In this paper I argue that reflection on the notions of difference and possibility in play here shows that imaginary cases of alien conceptual schemes or forms of life such as those considered by Wittgenstein are (...) not all cases of concepts that are entirely unintelligible for us; rather they may represent possible, albeit distant, ways of thinking for us. Such cases serve to aid imaginative reflection on our own case(s). By making us appreciate the possibility of the strange, they help us better to appreciate the arbitrariness of the familiar. I end the paper by considering what the implications of this reading of Wittgenstein’s position might be for Donald Davidson’s rejection of conceptual relativism. (shrink)

I shall compare two views of legal concepts: as nodes in inferential nets and as categories in an ontology (a conceptual architecture). Firstly, I shall introduce the inferential approach, consider its implications, and distinguish the mere possession of an inferentially defined concept from the belief in the concept’s applicability, which also involves the acceptance of the concept’s constitutive inferences. For making this distinction, the inferential and eliminative analysis of legal concepts proposed by Alf Ross will be connected to the views (...) on theoretical concepts in science advanced by Frank Ramsey and Rudolf Carnap. Consequently, the mere comprehension of a legal concept will be distinguished from the application of the concept to a particular legal system, since application presupposes a doctrinal commitment, namely, the belief that the inferences constituting the concept hold in that system. Then, I shall consider how concepts can be characterised by defining the corresponding terms and placing them within an ontology. Finally, I shall argue that there is a tension between the inferential and the ontological approach, but that both need to be taken into account, to capture the meaning and the cognitive function of legal concepts. (shrink)

In the explanations of logical laws and inference rules of the mature version of Begriffsschrift in Grundgesetze, Frege uses the predicate “… is the True.” Scholars like Greimann maintain that this predicate is a metalinguistic truth-predicate for Frege. This paper examines an argument for this claim that is based on the “nominal reading” of Frege’s conception of sentences—the claim that for Frege a sentence “p” is equivalent to a nonsentential phrase like “the truth-value of the thought that p.” In particular, (...) this paper attempts to establish two points concerning this argument based on the nominal reading. First, the argument implies a claim about the nature of assertion which Frege repeatedly denies in his mature works. Secondly, the nominal reading on which the argument depends is false. A sentence “p” is not equivalent to a nonsentential phrase like “the truth-value of the thought that p” for Frege. Our discussion will lead to an important lesson about Frege’s conception of sentences and of assertion. (shrink)

ABSTRACT Is it possible to effect singular reference to mathematical objects in the abstractionist framework? I will argue that even if mathematical expressions pass the relevant syntactic and inferential tests to qualify as singular terms, that does not mean that their semantic function is to refer to a particular object. I will defend two arguments leading to this claim: the permutation argument for the referential indeterminacy of mathematical terms, and the argument from the semantic idleness of the terms introduced by (...) abstraction principles. (shrink)

Extensionalism, as I understand it here, is the view that physical reality consists exclusively of extensional entities. On this view, intensional entitities must either be eliminated in favor of an ontology of extensional entities, or be reduced to such an ontology, or otherwise be admitted as non-physical. In this paper I argue that extensionalism is a misguided philosophical doctrine. First, I argue that intensional phenomena are not confined to the realm of language and thought. Rather, the ontology of such phenomena (...) is intimately entwined with the ontology of properties. After providing some evidence to the popularity of extensionalism in contemporary analytic philosophy, I investigate the motivating reasons behind it. Considering several explanations, I argue that the main motivating reason is rooted in the identification of matter with extension, an identification which is one of the hallmarks of the mechanistic conception of nature inherited from the founding fathers of our modern scientific outlook. I then argue that such a conception is not only at odds with a robust ontology of properties but is also at odds with our best contemporary physics. Rather than vindicating extensionalism contemporary science undermines the position, and the lesson to be drawn from this surprising fact is that extensionalism needs no longer be espoused as a regulative ideal of naturalistic philosophy. I conclude by showing that the ontological approach to intensional phenomena advocated throughout the paper also gains support from an examination of the historical context within which ‘intension’ was first introduced as a semantic notion. (shrink)