In this study two strands of inferentialism are brought together: the philosophical doctrine of Brandom, according to which meanings are generally inferential roles, and the logical doctrine prioritizing proof-theory over model theory and approaching meaning in logical, especially proof-theoretical terms.

In this multi-disciplinary investigation we show how an evidence-based perspective of quantification---in terms of algorithmic verifiability and algorithmic computability---admits evidence-based definitions of well-definedness and effective computability, which yield two unarguably constructive interpretations of the first-order Peano Arithmetic PA---over the structure N of the natural numbers---that are complementary, not contradictory. The first yields the weak, standard, interpretation of PA over N, which is well-defined with respect to assignments of algorithmically verifiable Tarskian truth values to the formulas of PA under the interpretation. (...) The second yields a strong, finitary, interpretation of PA over N, which is well-defined with respect to assignments of algorithmically computable Tarskian truth values to the formulas of PA under the interpretation. We situate our investigation within a broad analysis of quantification vis a vis: * Hilbert's epsilon-calculus * Goedel's omega-consistency * The Law of the Excluded Middle * Hilbert's omega-Rule * An Algorithmic omega-Rule * Gentzen's Rule of Infinite Induction * Rosser's Rule C * Markov's Principle * The Church-Turing Thesis * Aristotle's particularisation * Wittgenstein's perspective of constructive mathematics * An evidence-based perspective of quantification. By showing how these are formally inter-related, we highlight the fragility of both the persisting, theistic, classical/Platonic interpretation of quantification grounded in Hilbert's epsilon-calculus; and the persisting, atheistic, constructive/Intuitionistic interpretation of quantification rooted in Brouwer's belief that the Law of the Excluded Middle is non-finitary. We then consider some consequences for mathematics, mathematics education, philosophy, and the natural sciences, of an agnostic, evidence-based, finitary interpretation of quantification that challenges classical paradigms in all these disciplines. (shrink)

Responding to the paradox of inference and the related problems in philosophy of logic, this paper argues for the necessity of distinguishing between two different objects of justification: logica utens and logica docens. Then, equipped with Peirce’s critical common-sensist conception of logica utens and his classification of sciences, I propose a diagnosis of and a solution to the problem of justification of logic. I argue that this alternative approach successfully avoids circularity in which most attempts in philosophy of logic have (...) been inescapably trapped. I also anticipate and respond to possible objections to taking a Peircean turn in justifying logic. (shrink)

Many contemporary logicians acknowledge a plurality of logical theories and accept that theory choice is in part motivated by logical evidence. However, just as there is no agreement on logical theories, there is also no consensus on what constitutes logical evidence. In this paper, I outline Jean Piaget’s psychological theory of reasoning and show how he used it to diagnose and solve one of the paradoxes of material implication. I assess Piaget’s use of psychology as a source of evidence for (...) logical theory in light of reservations raised by psychologism, and I highlight some ramifications for exceptionalism and anti-exceptionalism about logic by considering his use of psychology as logical evidence in the framework of genetic epistemology, Piaget’s research programme. I conclude that Piaget’s psychological theory of reasoning not only plausibly serves as a source of evidence for logical theory but also makes a strong case for anti-exceptionalism about logic. (shrink)

This paper is a study of debate practices as seen in the Nyāyasūtra and a number of commentaries. It concentrates on the ‘Points of Defeat ’, i.e., those occasions that if met in debate would entail defeat. The conditions under which a debater would meet with defeat were discussed widely in India and have also attracted considerable attention from modern scholars. In order to better understand this subject, use is made of some of the intuitions about language and conversation that (...) we owe to the philosopher H. P. Grice as well as of some recent theoretical advances in argumentation theory and informal logic, particularly of those most influenced by Grice’s thought. The Points of Defeat are studied both individually and as a group and it is shown that they point towards the practice of debating as being a rational, cooperative and goal-directed activity. (shrink)

De acuerdo con los principales enfoques al respecto la lógica de los estoicos es principalmente un sistema deductivo, lo que, en términos actuales, ha sido visto como un sistema de lógica proposicional. La obra de Crísipo acerca de los cinco argumentos indemostrables constituye la principal base de dicho sistema. En este artículo se examina la naturaleza de dichos cinco indemostrables así como el llamando teorema de Antipatro y los esquemas básicos de inferencia, o zemas. Por otra parte y en particular, (...) sostengo que dichos argumentos indemostrables tienen otro importante rol para la filosofía y la historia de la lógica, cual es el de constituirse en una justificación de la deducción, un problema central en el presente. Se analiza, primero, la justificación por los indemostrables y por el principio de condicionalización y, segundo, la justificación cognitiva de la lógica implícita en un sistema estoico. (shrink)

Resumen En este trabajo analizo la crítica del psicologismo en las Investigaciones lógicas de Husserl. Para una reconstrucción adecuada del enfoque de este autor, vinculo las ideas centrales de su argumentación contra el psicologismo que se encuentran en el primer volumen con algunos análisis y tesis que introduce en el segundo volumen. Si bien no se presentan de manera explícita como críticas del psicologismo, estos análisis y tesis implican contribuciones para la superación de un enfoque empirista radical, vinculado en forma (...) estrecha con el subjetivismo y el psicologismo. Pongo atención especial en la crítica de las teorías de la abstracción en la Investigación Segunda, cuya vinculación con la crítica del psicologismo no suele reconocerse lo suficiente. También analizo el concepto de posibilidad ideal, fundamental para la comprensión del concepto husserliano de especie.In this paper I analyse the critique of psychologism advanced by Husserl in his Logical Investigations. In order to adequately rebuild the author's approach, I will link the central points of the argument against psychologism developed in the first volume with some analyses and theses introduced by Husserl in the second volume. These analyses and theses, although not explicitly presented as criticisms of psychologism, are clear contributions to overcoming a radical empiricist approach, closely linked to subjectivism and psychologism. I pay special attention to the critique of the theories of abstraction carried out in the Second Investigation, whose link with the critique of psychologism is not properly recognized. I also analyze the concept of ideal possibility, which is fundamental for the understanding of the Husserlian concept of species. (shrink)

Is logic, feasibly, a product of natural selection? In this paper we treat this question as dependent upon the prior question of where logic is founded. After excluding other possibilities, we conclude that logic resides in our language, in the shape of inferential rules governing the logical vocabulary of the language. This means that knowledge of (the laws of) logic is inseparable from the possession of the logical constants they govern. In this sense, logic may be seen as a product (...) of natural selection: the emergence of logic requires the development of creatures who can wield structured languages of a specific complexity, and who are capable of putting the languages to use within specific discursive practices. (shrink)

Psychologism in logic is the doctrine that the semantic content of logical terms is in some way a feature of human psychology. We consider the historically influential version of the doctrine, Psychological Individualism, and the many counter-arguments to it. We then propose and assess various modifications to the doctrine that might allow it to avoid the classical objections. We call these Psychological Descriptivism, Teleological Cognitive Architecture, and Ideal Cognizers. These characterizations give some order to the wide range of modern views (...) that are seen as psychologistic because of one or another feature. Although these can avoid some of the classic objections to psychologism, some still hold. (shrink)

This two-part paper reviews a scholarly debate on an alleged tension in Frege ’s philosophy of logic. In Section 1 of Part I, I discuss Frege ’s view that logic is concerned with establishing norms for correct thinking and is therefore a normative science. In Section 2, I explore a different understanding of the role of logic that Frege seems to advance: logic is constitutive of the very possibility of thought, because it sets forth necessary conditions for thought. Hence, the (...) tension the view according to which logic is normative for thought seems to be incompatible with the idea that abiding by the laws of logic forms a precondition for thought. In Section 1 of Part II, I survey a number of interpretations of Frege ’s conception of logic that deal with this question. I show that they are for the most part either normative readings or constitutive readings. Finally, in Section 2, I adjudicate the debate and aim at reconciling the normative and the constitutive strands in Frege ’s conception of logic. (shrink)

While anti-exceptionalism about logic is now a popular topic within the philosophy of logic, there’s still a lack of clarity over what the proposal amounts to. currently, it is most common to conceive of AEL as the proposal that logic is continuous with the sciences. Yet, as we show here, this conception of AEL is unhelpful due to both its lack of precision, and its distortion of the current debates. Rather, AEL is better understood as the rejection of certain traditional (...) properties of logic. The picture that results is not of one singular position, but rather a cluster of often connected positions with distinct motivations, understood in terms of their rejection of clusters of the various traditional properties. In order to show the fruitfulness of this new conception of AEL, we distinguish between two prominent versions of the position, metaphysical and epistemological AEL, and show how the two positions need not stand or fall together. (shrink)

The issue of the justification of the laws of logic has been under discussion since the end of the nineteenth century. However, in many works devoted to this problem Ajdukiewicz’s achievements are left unmentioned. It can be shown that in certain periods of the development of his views, he tried to present various attempts at solving the problem of the justification of the laws of logic.

In this paper we (i) identify the notion of ‘essentially non-conceptual content’ by critically analyzing the recent and contemporary debate about non-conceptual content, (ii) work out the basics of broadly Kantian theory of essentially non-conceptual content in relation to a corresponding theory of conceptual content, and then (iii) demonstrate one effective application of the Kantian theory of essentially non-conceptual content by using this theory to provide a ‘minimalist’ solution to the problem of perceptual self-knowledge which is raised by Strong Externalism.

There are perceptual states whose representational content cannot even in principle be conceptual. If that claim is true, then at least some perceptual states have content whose semantic structure and psychological function are essentially distinct from the structure and function of conceptual content. Furthermore the intrinsically “orientable” spatial character of essentially non-conceptual content entails not only that all perceptual states contain non-conceptual content in this essentially distinct sense, but also that consciousness goes all the way down into so-called unconscious or (...) subpersonal mental states. Both my argument for the existence of essentially non-conceptual content and my theory of its structure and function have a Kantian provenance. (shrink)

Popper emphasised both the problem-solving nature of human knowledge, and the need to criticise a scientific theory as strongly as possible. These aims seem to contradict each other, in that the former stresses the problems that motivate scientific theories while the one ignores the character of the problems that led to the formation of the theories against which the criticism is directed. A resolution is proposed in which problems as such are taken as prime in the search for knowledge, and (...) subject to discussion. This approach is then applied to the problem of induction. Popper set great stake to his solution of it, but others doubted its legitimacy, in ways that are clarified by changing the form of the induction problem itself. That change draws upon logic, which is the subject of another application: namely, in contrast to Popper’s adhesion to classical logic as the only welcome form (because of the maximal strength of criticism that it dispenses), can other logics be used without abandoning his philosophy of criticism? (shrink)

Semantic networks were developed in cognitive science and artificial intelligence studies as graphical knowledge representation and inference tools emulating human thought processes. Formal analysis of the representation and inference capabilities of the networks modeled them as subsets of standard first-order logic (FOL), restricted in the operations allowed in order to ensure the tractability that seemed to characterize human reasoning capabilities. The graphical network representations were modeled as providing a visual language for the logic. Sub-sets of FOL targeted on knowledge representation (...) came to be called description logics, and research on these logics has focused on issues of tractability of subsets with differing representation capabilities, and on the implementation of practical inference systems achieving the best possible performance. Semantic network research has kept pace with these developments, providing visual languages for knowledge entry, editing, and presenting the results of inference, that translate unambiguously to the underlying description logics. This paper discusses the design issues for such semantic network formalisms, and illustrates them through detailed examples of significant generic knowledge structures analyzed in the literature, including determinables, contrast sets, genus/differentiae, taxonomies, faceted taxonomies, cluster concepts, family resemblances, graded concepts, frames, definitions, rules, rules with exceptions, essence and state assertions, opposites and contraries, relevance, and so on. Such examples provide important test material for any visual language formalism for logic. (shrink)

Logical realism is a view about the metaphysical status of logic. Common to most if not all the views captured by the label ‘logical realism’ is that logical facts are mind- and language-independent. But that does not tell us anything about the nature of logical facts or about our epistemic access to them. The goal of this paper is to outline and systematize the different ways that logical realism could be entertained and to examine some of the challenges that these (...) views face. It will be suggested that logical realism is best understood as a metaphysical view about the logical structure of the world, but this raises an important question: does logical realism collapse into standard metaphysical realism? It will be argued that this result can be accommodated, even if it cannot be altogether avoided. (shrink)

Robert Hanna (Rationality and logic. MIT Press, Cambridge, 2006) articulates and defends the thesis of logical cognitivism, the claim that human logical competence is grounded in a cognitive faculty (in Chomsky’s sense) that is not naturalistically explicable. This position is intended to steer us between the Scylla of logical Platonism and the Charybdis of logical naturalism (/psychologism). The paper argues that Hanna’s interpretation of Chomsky is mistaken. Read aright, Chomsky’s position offers a defensible version of naturalism, one Hanna may accept (...) as far as his version of naturalism goes, although not one that supports the claim that cognitive science offers a place for logic that is somehow outside the natural, contingent order. (shrink)

This paper aims to advance two claims. First, it aims to show that Hume's argument against the rationality of induction is sound. However, I claim that the conclusion does not follow merely from the self-defeating attempts to justify the rule of induction, unlike traditional readings of the argument. Rather, the skeptical conclusion must also take into account Hume's argument that the secret powers that are present in bodies and give rise to sensible qualities are unknowable. The paper's second aim is (...) to show that Newtonian induction escapes Hume's secret powers argument, given that it includes a transductive inference, from observable phenomena to the powers present in the ultimate parts of matter. Consequently Hume's argument against the rationality of induction does not demonstrate the non-rational nature of Newtonian induction. (shrink)

This article defends the view that having a language just is knowing how to engage in communication with it. It also argues that, despite claims to the contrary, this view is compatible and complementary with the Chomskyan conception of language on which humans have languages in virtue of being in brain states realizing tacit knowledge of grammars for those languages.

The representational nature of human cognition and thought in general has been a source of controversies. This is particularly so in the context of studies of unconscious cognition, in which representations tend to be ontologically and structurally segregated with regard to their conscious status. However, it appears evolutionarily and developmentally unwarranted to posit such segregations, as,otherwise, artifact structures and ontologies must be concocted to explain them from the viewpoint of the human cognitive architecture. Here, from a by-and-large Classical cognitivist viewpoint, (...) I show why this segregation is wrong, and elaborate on the need to postulate an ontological and structural continuity between unconscious and conscious representations. Specifically, I hypothesize that this continuity is to be found in the symbolic-based interplay between the syntax and the semantics of thought, and I propose a model of human information processing characterized by the integration of syntactic and semantic representations. (shrink)

The laws of logic and two of the broader theories of truth are fundamental components that are responsible for espousing an ontology and meaningfulness in matters of analytic philosophy. In this respect they have persisted as conventional attitudes or modes of thought which most, if not all, of analytic philosophy uses to philosophize. However, despite the conceptual productivity of these components they are unable to account for matters that are beyond them. These matters would include certain theological beliefs, for instance, (...) that transcend the purview of analytic ontology and the meaningfulness it ensues. Any attempt in making rational sense of such beliefs that are insusceptible to these methodological components would conventionally prohibit (restrict) us from rationally believing in them. This is because we would be unable to make sense of such beliefs with the aid of these methodological components. As a result of this, religious beliefs of this particular nature would be deemed irrational. I shall demonstrate this point by applying both of these components to an absolutely ineffable God of Islam. This would entail, attempting to make sense of an absolutely ineffable God of Islam in virtue of the laws of logic and two broad categories of truth theories, namely, substantive and insubstantive theories. I hope to establish that applying both of these methodological components in attempting to make sense of an absolutely ineffable God of Islam would not be conceptually viable. It would result in a contradictory notion which I shall allude to as the paradox of ineffability. (shrink)

In Rationality and Logic, Robert Hanna argues that logic is intrinsically psychological and that human psychology is intrinsically logical. He claims that logic is cognitively constructed by rational animals and that rational animals are essentially logical animals. In order to do so, he defends the broadly Kantian thesis that all rational animals possess an innate cognitive "logic faculty." Hanna 's claims challenge the conventional philosophical wisdom that sees logic as a fully formal or "topic-neutral" science irreconcilably separate from the species- (...) or individual-specific focus of empirical psychology.Logic and psychology went their separate ways after attacks by Frege and Husserl on logical psychologism--the explanatory reduction of logic to empirical psychology. Hanna argues, however, that--despite the fact that logical psychologism is false--there is an essential link between logic and psychology. Rational human animals constitute the basic class of cognizers or thinkers studied by cognitive psychology; given the connection between rationality and logic that Hanna claims, it follows that the nature of logic is significantly revealed to us by cognitive psychology. Hanna 's proposed "logical cognitivism" has two important consequences: the recognition by logically oriented philosophers that psychologists are their colleagues in the metadiscipline of cognitive science; and radical changes in cognitive science itself. Cognitive science, Hanna argues, is not at bottom a natural science; it is both an objective or truth-oriented science and a normative human science, as is logic itself. (shrink)

This volume aims to establish the starting point for the development, evaluation and appraisal of the phenomenology of mathematics.

Cogency is the central normative concept of informal logic. But it is a loose evaluative concept and I argue that a generic notion covering all of the qualities of a well-reasoned argument is the most plausible conception. It is best captured by the standard RSA criterion: in a good argument acceptable (A) and relevant (R) premises provide sufficient (S) grounds for the conclusion. Logical qualities in a broad sense are affected by the epistemic qualities of the premises and “consequence” in (...) a broad sense exhibits an interplay of form and content. There are four proposals for the premise—conclusion relation: (i) no strictly logical connection (“non-logical” consequence); (ii) one type of connection only (deductivism); (iii) a few types of connection (deduction, induction, perhaps conduction and analogical reasoning); (iv) many types of connection (argumentation schemes). Deductivism is a serious option but in its strong version, as the discussion about petitio shows, it fails to establish that arguments which are not cogent are thereby invalid. And weak deductivism, very attractive from the pedagogical point of view, has some deficiencies (implausible hidden premises; preservation of truth, not probability). I argue that the idea of a counterexample, when we regard certain components of the argument as fixed and others as variable, is the best approach to the analysis of the illative core of every-day arguments (the approach of David Hitchcock on material consequence). (shrink)

According to received wisdom, Kant takes the laws of logic to be normative laws of thought. This has been challenged by Tolley (2006). In this paper, I defend the received wisdom, but with an important modification: Kant's logical laws are constitutive norms for thought. The laws of logic do tell us what thinking is, not because all thoughts are in conformity with logical laws, but because all thoughts are, by nature, subject to the standard of logic.

Starting from the sixties of the past century theory change has become a main concern of philosophy of science. Two of the best known formal accounts of theory change are the post-Popperian theories of verisimilitude (PPV for short) and the AGM theory of belief change (AGM for short). In this paper, we will investigate the conceptual relations between PPV and AGM and, in particular, we will ask whether the AGM rules for theory change are effective means for approaching the truth, (...) i.e., for achieving the cognitive aim of science pointed out by PPV. First, the key ideas of PPV and AGM and their application to a particular kind of propositional theories - the so called "conjunctive propositions" - will be illustrated. Afterwards, we will prove that, as far as conjunctive propositions are concerned, AGM belief change is an effective tool for approaching the truth. (shrink)

This paper is divided in five sections. Section 11.1 sketches the history of the distinction between speech act with negative content and negated speech act, and gives a general dynamic interpretation for negated speech act. “Downdate semantics” for AGM contraction is introduced in Section 11.2. Relying on semantically interpreted contraction, Section 11.3 develops the dynamic semantics for constative and directive speech acts, and their external negations. The expressive completeness for the formal variants of natural language utterances, none of which is (...) a retraction, has been proved in Section 11.4. The last section gives a laconic answer to the question posed in the title of the paper. (shrink)

Philosophers love a priori knowledge: we delight in truths that can be known from the comfort of our armchairs, without the need to venture out in the world for confirmation. This is due not to laziness, but to two different considerations. First, it seems that many philosophical issues aren’t settled by our experience of the world — the nature of morality; the way concepts pick out objects; the structure of our experience of the world in which we find ourselves — (...) these issues seem to be decided not on the basis of our experience, but in some manner by things prior to (or independently of) that experience. Second, even when we are deeply interested in how our experience lends credence to our claims about the world, the matter remains of the remainder: we learn more about how experience contributes to knowledge when we see what knowledge is available independent of that experience. (shrink)

A traditional pastime of philosophers is the analysis of rhetoric and the repudiation of sophistry. Nevertheless, some of what philosophers call sophistry might rather be a subtle repudiation of the traditional principles of rationality. In this paper I start by granting the Sophist his repudiation and outline some of the obstacles to settling the dispute between Sophists and Rationalists. I then suggest that we should distinguish pragmatic Sophism from nihilistic Sophism. In the hope of driving a wedge between these two (...) I illustrate the way in which the two are confounded when Sophism is advanced by use of a particular rhetorical manoeuvre and then give an argument against nihilistic Sophism which even a nihilistic Sophist should be persuaded by. (shrink)