Diversity Reading List

Abstract:

¿Seguimos reglas de inferencia al razonar? Por más intuitiva que resulte la respuesta positiva a esta pregunta, hay una serie de dificultades para vincular reglas lógicas y prácticas inferenciales. El Problema de la Adopción de Reglas de Inferencia constituye un desafío para todo aquel que proponga que podemos seguir nuevos patrones inferenciales a partir del reconocimiento de reglas. En esta sección temática se exploran diversos asuntos conectados a si podemos seguir un nuevo patrón inferencial en virtud de una regla.

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.

Abstract:

Abstract: In this paper, I take issue with a core commitment of logical conventionalism: that we impose a logic on ourselves by adopting general linguistic conventions governing our use of logical terms, thereby determining the meanings of the logical constants and which of our inferences are valid. Drawing on Kripke’s ‘adoption problem’, I argue that general logical principles cannot be adopted, either explicitly or implicitly. I go on to argue that the meanings of our logical terms, and the validity of our inferences, cannot depend on our adoption of logico-linguistic conventions.

Introduction: Though it is hardly uncontroversial, the thesis that logic is normative enjoys widespread agreement—probably just about as much agreement as one is ever likely to find in philosophy. There is far less agreement, however, on what exactly this thesis amounts to. To begin with, proponents of the
thesis can’t seem to agree on whether the normative authority of logic is robust or weak. If logic is robustly normative, it has a normative authority that is independent of our attitudes or conventions; if it is weakly normative, it has a normative au- thority that is entirely dependent on our attitudes or conventions. This fundamental disagreement about the normative authority of logic seems to leave little room for any point of agreement among the proponents of the thesis. Furthermore, some opponents of the thesis allow that logic is “entangled” with the normative to the extent that it has normative consequences that are instrumental to the achievement of our wider goals (Russell 2017). This makes it difficult to discern any daylight between the views of those who hold that logic is not normative and those who hold that it is only weakly so. In the next section, I will argue that the thesis that unites the proponents and excludes the opponents is that logical statements and the judgments they can be used to express—such as those concerning logical validity or logical entailment—are normative statements and judgments, in the sense that they analytically, semantically, or conceptually have normative consequences. In section 3, I will critically assess whether logical statements and judgments are indeed normative in this sense. I will consider the prospects of various accounts of what the normative consequences of logical statements or judgments might be, and find them all to be wanting. This, I claim, gives us good reason to deny that logic is normative.

Abstract:

This paper stresses the importance of identifying the nature of an author’s conception of logic when using terms from modern logic in order to avoid, as far as possible, injecting our own conception of logic in the author’s texts. Sundholm (2012) points out that inferences are staged at the epistemic level and are made out of judgments, not propositions. Since it is now standard to read Aristotelian sullogismoi as inferences, I have taken Alexander of Aphrodisias’s commentaries to Aristotle’s logical treatises as a basis for arguing that the premises and conclusions should be read as judgments rather than as propositions. Under this reading, when Alexander speaks of protaseis, we should not read the modern notion of proposition, but rather what we now call judgments. The point is not just a matter of terminology, it is about the conception of logic this terminology conveys. In this regard, insisting on judgments rather than on propositions helps bring to light Alexander’s epistemic conception of logic.

Abstract:

Recent works about ecumenical systems, where connectives from classical and intuitionistic logics can co-exist in peace, warmed the discussion on proof systems for combining logics. This discussion has been extended to alethic modalities using Simpson’s meta-logical characterization: necessity is independent of the viewer, while possibility can be either intuitionistic or classical. In this work, we propose a pure, label free calculus for ecumenical modalities, nEK, where exactly one logical operator figures in introduction rules and every basic object of the calculus can be read as a formula in the language of the ecumenical modal logic EK. We prove that nEK is sound and complete w.r.t. the ecumenical birelational semantics and discuss fragments and extensions.

Abstract:

Much has been said about intuitionistic and classical logical systems since Gentzen’s seminal work. Recently, Prawitz and others have been discussing how to put together Gentzen’s systems for classical and intuitionistic logic in a single unified system. We call Prawitz’ proposal the Ecumenical System, following the terminology introduced by Pereira and Rodriguez. In this work we present an Ecumenical sequent calculus, as opposed to the original natural deduction version, and state some proof theoretical properties of the system. We reason that sequent calculi are more amenable to extensive investigation using the tools of proof theory, such as cut-elimination and rule invertibility, hence allowing a full analysis of the notion of Ecumenical entailment. We then present some extensions of the Ecumenical sequent system and show that interesting systems arise when restricting such calculi to specific fragments. This approach of a unified system enabling both classical and intuitionistic features sheds some light not only on the logics themselves, but also on their semantical interpretations as well as on the proof theoretical properties that can arise from combining logical systems.

Publisher’s Note:

This book describes how logical reasoning works and puts it to the test in applications. It is self-contained and presupposes no more than elementary competence in mathematics.

Abstract:

In response to widespread use of automated decision-making technology, some have considered a right to explanation. In this paper I draw on insights from philosophical work on explanation to present a series of challenges to this idea, showing that the normative motivations for access to such explanations ask for something difficult, if not impossible, to extract from automated systems. I consider an alternative, outcomes-focused approach to the normative evaluation of automated decision-making, and recommend it as a way to pursue the goods originally associated with explainability.

Abstract:
Recent criticism of feminist philosophy poses a dilemma. Feminism is taken to be a substantive set of empirical claims and political commitments, whereas philosophy is taken to be a discipline of thought organized by the pursuit of truth, but uncommitted to any particular truth. This paper responds to this dilemma, and defends the project of feminist philosophy.The first task toward understanding the feminist critique of reason, Alcoff argues, is to historically situate it within the rather long tradition of critiquing reason that has existed within the mainstream of philosophy itself.