Epistemology Of Logic Research Articles

A Contextual Account of Explanation in Logic

Recent approaches to the epistemology of logic, under the title of “anti-exceptionalism about logic”, explicitly adopt what is asserted to be the method of theory choice and the correct account of explanation in the sciences. Without embracing such a doctrine, but still keeping within a broad anti-exceptional trend, the current discussion proposes a contextual theory of explanation in logic, based on Bas van Fraassen’s framework of why-questions, which neither claims that logic is a science, nor relies on the metaphysical assumption of a validity-phenomenon to give account of the methodology of logic.

Peirce on the Normative Basis of Deductive Logic

Abstract: I analyze Peirce's reply in the 1903 Lowell Lectures to the "defendant argument" and show how his response provides a key to interpreting his later philosophy of logic and his views on the normative role of deductive logic in inquiry. I argue that in Peirce's discussion of self-control in reasoning and evaluation of reasoning, we find an underappreciated position on logical revision and how to understand rational choice between deductive theories. To defend this point, I reconstruct Peirce's reply by providing an interpretation of his comments on higher-order criticism and the soundness of our reasoning, arguing that the resulting position's ability to separate questions involving the role of logic in inquiry from questions better suited to the mathematical study of a logical theory provides a fruitful pragmatist reframing of problems in the epistemology of logic.

Reflective equilibrium in logic

Among the areas of knowledge that the method of reflective equilibrium (RE) has been applied to is that of logical validity. According to RE in logic, we come to be justified in believing a (deductive) logical theory in virtue of establishing some state of equilibrium between our initial judgements over the validity of specific (natural language) arguments and the logical principles which constitute our logical theory. Unfortunately, however, while relatively popular, RE with regards to logical theorizing is underspecified. In particular, it’s unclear what constitute: (1) the relevant logical “data”, (2) logical theories, so that they can be suitably tested, and (3) the mechanisms under which such theories are tested. Considering the various options for how to interpret the position, we argue that in order to be workable the advocate of RE about logic must embrace what we call an operationalised, wide and communal version of RE with a rich understanding of logical theories. Fortunately for the advocate of RE, there is an available account of logic’s epistemology which possesses just these properties, logical predictivism. However, equally unfortunately, logical predictivism commits the advocate of RE to certain further claims that they have historically been weary of holding. Consequently, it is unclear whether RE about logic itself is a viable proposal, or rather a similar but distinct epistemology of logic.

The Adoption Problem and the Epistemology of Logic

Abstract After introducing the adoption problem (AP) as the claim that certain basic logical principles cannot be adopted, I offer a characterization of this notion as a two-phase process consisting in (1) the acceptance of a basic logical principle, and (2) the development, in virtue of Phase 1, of a practice of inferring in accordance with that principle. The case of a subject who does not infer in accordance with universal instantiation is considered in detail. I argue that the AP has deep and wide implications for the epistemology of logic, extending well beyond Kripke’s original target, viz. Putnam’s proposal for the empirical revision of logic and its background Quinean epistemology. In particular, the AP questions whether basic logical principles could have a fundamental role in our inferential practices, drawing our attention to the nature of basic inferences and the need to have a clearer conception of them before taking a stand on the matter of the epistemic justification of the logical principles.

Countering Justification Holism in the Epistemology of Logic: The Argument from Pre-Theoretic Universality


 
 
 A key question in the philosophy of logic is how we have epistemic justification for claims about logical entailment (assuming we have such justification at all). Justification holism asserts that claims of logical entailment can only be justified in the context of an entire logical theory, e.g., classical, intuitionistic, paraconsistent, paracomplete etc. According to holism, claims of logical entailment cannot be atomistically justified as isolated statements, independently of theory choice. At present there is a developing interest in—and endorsement of—justification holism due to the revival of an abductivist approach to the epistemology of logic. This paper presents an argument against holism by establishing a foundational entailment-sentence of deduction which is justified independently of theory choice and outside the context of a whole logical theory.
 
 

Anti-exceptionalism and the justification of basic logical principles

Anti-exceptionalism about logic is the thesis that logic is not special. In this paper, I consider, and reject, a challenge to this thesis. According to this challenge, there are basic logical principles, and part of what makes such principles basic is that they are epistemically exceptional. Thus, according to this challenge, the existence of basic logical principles provides reason to reject anti-exceptionalism about logic. I argue that this challenge fails, and that the exceptionalist positions motivated by it are thus unfounded. I make this case by disambiguating two senses of ‘basic’ and showing that, once this disambiguation is taken into account, the best reason we have for thinking that there are basic principles actually implies that those principles do not require a special epistemology. Consequently, the existence of basic logical principles provides reason to accept, rather than reject, anti-exceptionalism concerning the epistemology of logic. I conclude by explaining how an abductivist, anti-exceptionalist approach to the epistemology of logic can accommodate the notion of basic logical principles.

Logical expressivism as a defense for the necessity of entailment of logical arguments

Introduction In his famous 1985 article “What the Tortoise Said to Achilles”, Lewis Carroll offers a regress that suggests we could never reach the conclusion of a deductive argument. In that story, logical rules are conditional propositions that adding them to an argument never provides enough reason to infer the conclusion. For example, when we are to use modus ponens, “if (if P then Q) and (P) then (Q)”, the rule itself does not justify us in a way that we could follow (Q) from (if P then Q) and (P) as the premises. Here, we follow a path that in Ethics is called non-cognitive moral expressivism. According to logical expressivism, logical inferences are not just mental states without any consequences, but we should consider logical facts and rules of logic as some dispositions that create capabilities for making inferences from premises. Methods and Material The method of research here is based on content analysis and logical inference. First, the main problem is established, and then I tried to apply the solution introduced in Ethics for the same problem in Logic. In the end, I concluded that disposition could serve as a good reason to reach the conclusion in arguments. Results and Discussion It seems as if we should have a principle that makes whoever faces an argument draw the conclusion. In the philosophy of Ethics, these principles are usually expressed by “ought”, so in logic, we should express inferential rules, such as MP, as follow: - Everyone that believes P and if P then Q ought to believes Q too. The normativity of logical rules is defended by some famous philosophers such as Wittgenstein and Ryle. Wittgenstein believes rules of inference cannot be true or false, since they are just like instructions or commands that we must follow like instructions in a handbook. What I added here is that these instructions themselves could make the mind move in a certain direction without any need for other reasons. Ryle believes that logical rules are not some sort of knowledge of facts, but actually, are “how-to-act” or knowledge of performance; in other words, we should explore the issue at hand in practical wisdom rather than theoretical wisdom. When we know a logical rule, we know how to act in a certain way, not that this knowledge is an extra premise that should be added to the argument. Boghossian suggests this idea that passing through one piece of information to another one does not need further belief to justify this move. Logical dispositions, when we try to have a valid inference, make the logical move from premises to the conclusion possible. As Wittgenstein put forward in his Philosophical Investigations, acting according to logic is like following some rules, and our knowledge about these rules is dispositional: “When I obey a rule, I do not choose. I obey the rule blindly”. In this way, logic is internally sufficient and justified. Logical internalism explains this idea as follow: - Beliefs, in their propositional form, do not motivate to act. - Logical rules motivate to act according to them. - Therefore, logical rules are not beliefs in propositional form. The conclusion introduces a simple form of logical non-cognitivism that suggests knowledge of logic is not knowledge about facts, but rather logic contains norms that lead agents to infer properly. Conclusion As the result, the solution for Carroll`s puzzle suggested here is that we should consider logical principles as dispositions that guide us in our mental movements; logical principles, in this way, are not some sort of beliefs that represents facts. In articulating this solution, we use a theory in the philosophy of ethics that considers moral judgments as non-cognitive mental states. In logical non-cognitivism, logic is a handbook for deducing. Also, according to logical internalism, non-propositional rules of logic are enough to entail the conclusion and there is no need to add other premises to the argument. Logical expressivism is an approach in the epistemology of logic that regards logic as a self-sufficient knowledge and as a prerequisite for any rational activity. Basic principles and rules of logic should not be presented as descriptive propositions. The justification of inferential rules is based on their normativity. All our knowledge is not objective and descriptive, but some part of it is normative and how-to-do norms. It is clear that this picture of logic is not realistic and logical expressivism should be considered an antirealist theory and must be interpreted in this way: logic is not trying to paint a picture of the word, rather it is the precondition for any objective knowledge about the world.

Logical Predictivism

Motivated by weaknesses with traditional accounts of logical epistemology, considerable attention has been paid recently to the view, known as anti-exceptionalism about logic (AEL), that the subject matter and epistemology of logic may not be so different from that of the recognised sciences. One of the most prevalent claims made by advocates of AEL is that theory choice within logic is significantly similar to that within the sciences. This connection with scientific methodology highlights a considerable challenge for the anti-exceptionalist, as two uncontentious claims about scientific theories are that they attempt to explain a target phenomenon and (at least partially) prove their worth through successful predictions. Thus, if this methodological AEL is to be viable, the anti-exceptionalist will need a reasonable account of what phenomena logics are attempting to explain, how they can explain, and in what sense they can be said to issue predictions. This paper makes sense of the anti-exceptionalist proposal with a new account of logical theory choice, logical predictivism, according to which logics are engaged in both a process of prediction and explanation.

Identifying logical evidence

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.

Deviance and Vice: Strength as a Theoretical Virtue in the Epistemology of Logic

This paper is about the putative theoretical virtue ofstrength, as it might be used in abductive arguments to the correct logic in the epistemology of logic. It argues for three theses. The first is that the well‐defined property oflogical strengthis neither a virtue nor a vice, so that logically weaker theories are not—all other things being equal—worse or better theories than logically stronger ones. The second thesis is that logical strength does not entail the looser characteristic ofscientific strength, and the third is that many modern logics are on a par—or can be made to be on a par—with respect to scientific strength.

Sur la philosophie analytique de la logique et des mathématiques. À propos de Infini, logique, géométrie de Paolo Mancosu

Je propose dans cet article une analyse critique d’un ouvrage contemporain de philosophie analytique consacré aux questions d’épistémologie de la logique et des mathématiques. Je montre la portée et les limites du volume.

Logic and the Structure of the Web of Belief

In this paper, I examine Quine's views on the epistemology of logic. According to Quine's influential holistic account, logic is central in the “web of belief” that comprises our overall 
 theory of the world. Because of this, revisions to logic would have devastating systematic consequences, and this explains why we are loath to make such revisions. In section1, I clarify this idea and thereby show that Quine actually takes the web of belief to have asymmetrical internal structure. This raises two puzzles. First, as I show in section 2, Quine's mature thoroughly naturalized view has it that logic is simply obvious, and this is explains why we do not typically consider revising it. While Quine presents this naturalized view as a way to make good on his earlier metaphor of centrality in a web of belief, I argue that the resources of Quine's naturalized epistemology cannot adequately explain why we are reluctant to revise logic. And, Quine seems to recognize this point himself. In light of this, I explain in section 3 how Quine can allow that our overall scientific theory has systematic structure in a way that is consistent with his naturalistic strictures. Second, the asymmetrical internal structure of the web of belief seems to be inconsistent with its being a holistic web at all. I defuse this problem in section 4 by showing how Quine distinguishes between structural and confirmational considerations. I close by using this distinction to show how Quine's view can evade Michael Friedman’s criticisms, and allow for important methodological distinctions between areas of the web of belief.

What Do Deviant Logians Show About the Epistemology of Logic?

What I will call “the deviant logician objection” [DLO] is one line of attack against the common and compelling tenet that our justification for logical truths is grounded in our understanding of their constituent concepts. This objection seeks to undermine the possibility of any deep constitutive connection, in the epistemology of logic (and also beyond), between understanding and justification. I will consider varieties of the deviant logician objection developed by Horwich (2000, 2006) and by Williamson (2006, 2008). My thesis is that while the deviant logician objection falls short of proving that this traditional tenet must be rejected, nonetheless it serves to bolster some important refinements.

Metaphysical analyticity and the epistemology of logic

AbstractRecent work on analyticity distinguishes two kinds, metaphysical and epistemic. This paper argues that the distinction allows for a new view in the philosophy of logic according to which the claims of logic are metaphysically analytic and have distinctive modal profiles, even though their epistemology is holist and in many ways rather Quinean. It is argued that such a view combines some of the more attractive aspects of the Carnapian and Quinean approaches to logic, whilst avoiding some famous problems.

Boghossian and Casalegno on Understanding and Inference

In response to Paul Boghossian's objections in ‘Inferentialism and the epistemology of logic’, this paper defends counterexamples offered by Paolo Casalegno and the author to an inferentialist account of what it is to understand a logical constant, on which Boghossian had relied in his explanation of our entitlement to reason according to basic logical principles. The importance for understanding is stressed of non-inferential aspects of the use of logical constants. Boghossian's criteria for individuating concepts are also queried.

Inferentialism and the Epistemology of Logic: Reflections on Casalegno and Williamson

I defend an inferential account of the logical constants against objections made to it by Paolo Casalegno and Timothy Williamson.

Husserl’s Foundation of the Formal Sciences in his “Logical Investigations”

This article is composed of three sections that investigate the epistemological foundations of Husserl’s idea of logic from the Logical Investigations. First, it shows the general structure of this logic. Husserl conceives of logic as a comprehensive, multi-layered theory of possible theories that has its most fundamental level in a doctrine of meaning. This doctrine aims to determine the elementary categories that constitute every possible meaning (meaning-categories). The second section presents the main idea of Husserl’s search for an epistemological foundation for knowledge, science and logic. Their epistemological clarification can only be reached through a detailed analysis of the structure of those intentions that give us what is meant in our intentions. To reveal the intuitive giveness of logical forms is the ultimate aim of Husserl’s epistemology of logic. Logical forms and meaning-categories can only be given in a certain higher-order intuition that Husserl calls categorical intuition. The third section of this article distinguishes different kinds of categorical intuition and shows how the most basic logical categories and concepts are given to us in a categorical abstraction.

FREGE'S CONCEPT PARADOX AND THE MIRRORING PRINCIPLE

Frege held that singular terms can refer only to objects, not to concepts. I argue that the counter‐intuitive consequences of this claim (‘the concept paradox’) arise from Frege's mirroring principle that an incomplete expression can only express an incomplete sense and stand for an incomplete reference. This is not, as is sometimes thought, merely because predicates and singular terms cannot be intersubstituted salva veritate (congruitate). The concept paradox, properly understood, poses therefore a different, harder, challenge. An investigation of the foundations of the mirroring principle also sheds light on the role which language plays in Frege's epistemology of logic.

Piageten Epistemologia Genetikoa

The paper begins exposing the stages of the child's psychogenetic development: the sensory-motor stage, the preoperatory stage, the stage of concrete operations, and the stage of formal operations. In this exposition, we point to the parallels among the intellectual, affective and moral developments. Next, we introduce the guiding idea of Piaget's theory, according to which learning is based on construction and not on perception, and we distinguish deduction based on necessity from generalization. Then some cases of parallelism between the psychogenetic stages of the child and the stages of the history of the science —as the theory of the impetus— are exposed. The notions of time, simultaneity, speed and force are also analyzed. Some reflections are done on the epistemology of logic and of mathematics, and regarding the epistemology of space and of geometry, we emphasize the parallelisms found between the psychogenetic evolution and the history of sciences, in relation with the evolution of topologic, projective and Euclidean concepts. We analyze also the influence of paradigms or epistemic frames on the child's cognitive development and on the evolution of thought. The paper concludes with some remarks for the revision of Piaget's theory.

Intuition, Entitlement and the Epistemology of Logical Laws

The essay addresses the well-known idea that there has to be a place for intuition, thought of as a kind of non-inferential rational insight, in the epistemology of basic logic if our knowledge of its principles is non-empirical and is to allow of any finite, non-circular reconstruction. It is argued that the error in this idea consists in its overlooking the possibility that there is, properly speaking, no knowledge of the validity of principles of basic logic. When certain important distinctions are observed, for instance that between recognising that Modus Ponens is sound and recognising that it is proof against the competent discovery of basic counterexamples, the case for thinking that there is indeed no space for genuine recognition of the validity of Modus Ponens becomes increasingly impressive. It is argued however that, the impossibility of knowledge notwithstanding, we are, in an important sense, entitled to take it that Modus Ponens is sound and that this notion of entitlement can help break the trichotomy - intuition, inference, experience - which imprisons our ordinary thinking about logical knowledge.