Gideon Rosen, Brian Leiter, and Catarina Dutilh Novaes raise deep questions about the arguments in Morality and Mathematics (M&M). Their objections bear on practical deliberation, the formulation of mathematical pluralism, the problem of universals, the argument from moral disagreement, moral ‘perception’, the contingency of our mathematical practices, and the purpose of proof. In this response, I address their objections, and the broader issues that they raise.

According to Tarski's model-theoretic analysis of logical consequence, the sentence X is a logical consequence of a set of sentences Γ if and only if any model for Γ is also a model for X. Etchemendy, however, does not accept the analysis and critiques it. According to Etchemendy, Tarski’s analysis 1- involves a conceptual mistake: confusing the symptoms of logical consequence with their cause; 2- cannot properly explain the necessity of logical consequence; 3- faces the problem of overgeneration; and 4- (...) faces the problem of undergeneration. In the present article, by evaluating these critiques and examining the effectiveness of some of the answers presented in defense of Tarski's analysis, we try to show that among these critiques, only the problem of undergeneration is not acceptable. According to our common sense understanding, if an argument is valid, it is truth-preserving, and by assuming the truth of the premises, the conclusion will be true as well. But it does not mean that we can reduce the logical consequence relation to truth preservation. This flaw leads Tarski’s analysis to be an unacceptable analysis of logical consequence. (shrink)

In this paper, Graham Priest’s understanding of dialetheism, the view that there exist true contradictions, is discussed, and various kinds of metaphysical dialetheism are distinguished between. An alternative to dialetheism is presented, namely a thesis called ‘dimathematism’. It is pointed out that dimathematism enables one to escape a slippery slope argument for dialetheism that has been put forward by Priest. Moreover, dimathematism is presented as a thesis that is helpful in rejecting the claim that logic is a normative discipline.

In this paper I investigate how differences in approach to truth and logic (in particular, a deflationist vs. a substantivist approach to these fields) affect philosophers’ views concerning pluralism and normativity in these fields. My perspective on truth and logic is largely epistemic, focusing on the role of truth in knowledge (rather than on the use of the words “true” and “truth” in natural language), and my reference group includes Carnap (1934), Harman (1986), Horwich (1990), Wright (1992), Beall and Restall (...) (2006), Field (2009), Lynch (2009), and Sher (2016a).1 Whenever possible, I focus on positive rather than negative views on the issues involved, although in some cases this is not possible. (shrink)

The idea that logic is in some sense normative for thought and reasoning is a familiar one. Some of the most prominent figures in the history of philosophy including Kant and Frege have been among its defenders. The most natural way of spelling out this idea is to formulate wide-scope deductive requirements on belief which rule out certain states as irrational. But what can account for the truth of such deductive requirements of rationality? By far, the most prominent responses draw (...) in one way or another on the idea that belief aims at the truth. In this paper, I consider two ways of making this line of thought more precise and I argue that they both fail. In particular, I examine a recent attempt by Epistemic Utility Theory to give a veritist account of deductive coherence requirements. I argue that despite its proponents’ best efforts, Epistemic Utility Theory cannot vindicate such requirements. (shrink)

Logical pluralism is the view that there is more than one correct logic. This very general characterization gives rise to a whole family of positions. I argue that not all of them are stable. The main argument in the paper is inspired by considerations known as the “collapse problem”, and it aims at the most popular form of logical pluralism advocated by JC Beall and Greg Restall. I argue that there is a more general argument available that challenges all variants (...) of logical pluralism that meet the following three conditions: that there are at least two correct logical systems characterized in terms of different consequence relations, that there is some sort of rivalry among the correct logics, and that logical consequence is normative. The hypothesis I argue for amounts to conditional claim: If a position satisfies all these conditions, then that position is unstable in the sense that it collapses into competing positions. (shrink)

Logic arguably plays a role in the normativity of reasoning. In particular, there are plausible norms of belief/disbelief whose antecedents are constituted by claims about what follows from what. But is logic also relevant to the normativity of agnostic attitudes? The question here is whether logical entailment also puts constraints on what kinds of things one can suspend judgment about. In this paper I address that question and I give a positive answer to it. In particular, I advance two logical (...) norms of agnosticism, where the first one allows us to assess situations in which the subject is agnostic about the conclusion of a valid argument and the second one allows us to assess situations in which the subject is agnostic about one of the premises of a valid argument. (shrink)

In this paper I challenge two widespread convictions about unification in physics: unification is an aim of physics and unification is driven by metaphysical or metatheoretical presuppositions. I call these external explanations of why there is unification in physics. Against this, I claim that unification is a by-product of physical research and unification is driven by basic methodological strategies of physics alone. I call this an internal explanation of why there is unification in physics. To support my claims, I will (...) investigate the actual practice undertaken in physics in paradigmatic examples of unification. (shrink)

Logical pluralism is the view that there is more than one correct logic. Most logical pluralists think that logic is normative in the sense that you make a mistake if you accept the premisses of a valid argument but reject its conclusion. Some authors have argued that this combination is self-undermining: Suppose that L1 and L2 are correct logics that coincide except for the argument from Γ to φ, which is valid in L1 but invalid in L2. If you accept (...) all sentences in Γ, then, by normativity, you make a mistake if you reject φ. In order to avoid mistakes, you should accept φ or suspend judgment about φ. Both options are problematic for pluralism. Can pluralists avoid this worry by rejecting the normativity of logic? I argue that they cannot. All else being equal, the argument goes through even if logic is not normative. (shrink)

ABSTRACT My aim in this paper is to present a pluralist thesis about the inferential role of logical constants, which embraces classical, relevant, linear and ordered logic. That is, I defend that a logical constant c has more than one correct inferential role. The thesis depends on a particular interpretation of substructural logics' vocabulary, according to which classical logic captures the literal meaning of logical constants and substructural logics encode a pragmatically enriched sense of those connectives. The paper is divided (...) into four parts: first, I introduce the motivation for the pluralist thesis of the paper; second I introduce the calculus for the different logics endorsed in the pluralist thesis; third, I motivate how the different behaviors of the logical vocabulary of these logics can be pragmatically interpreted, and fourth, I motivate how the different inferential roles that each substructural logic attribute to logical constants can coexist, and how we should reason with a logical constant c given this plurality. (shrink)

Logical pluralism is the view that there is more than one logic. Logical normativism is the view that logic is normative. These positions have often been assumed to go hand-in-hand, but we show that one can be a logical pluralist without being a logical normativist. We begin by arguing directly against logical normativism. Then we reformulate one popular version of pluralism—due to Beall and Restall—to avoid a normativist commitment. We give three non-normativist pluralist views, the most promising of which depends (...) not on logic’s normativity but on epistemic goals. (shrink)

The paper is about the connection between logic and discrimination, with special focus on Plumwood’s ideas in her groundbreaking article ‘The Politics of Reason. Towards a Feminist Logic’ (1993). Although Plumwood’s paper is not focused on the notion of discrimination, what she writes is useful for illuminating some basic mechanisms of thought that are at the basis of discriminatory practices. After an introductory section about the concepts of logic and discrimination and their possible interconnections, I present Plumwood’s ideas in 1993 (...) with a special focus on their relevance for understanding the nature of discrimination. More specifically, I use examples of discriminatory practices that make the connection between logical operations and oppression envisaged by Plumwood clear. I focus especially on two questions: Can logic produce discrimination? Can logic contribute to the fight against discrimination? If so, how? (shrink)

The focus of the article is the notion of normativity in logic and politics and their possible intersections. The twentieth-century divide between the analytical and the continental idea of logic is explored, by noting that they both – with significant differences – can be seen as proposing a ‘bottom-up normativity’, which may have immediate political effects. Logical normativity postulates universality, and a connection between reality and reason able to orient actions universalistically. For a bottom-up conception (as specifically advanced by Deleuze’s (...) logic of sense), the universalistic approach does not descend from above on an elusive reality but is a self-organization of multiple processes occurring in a horizon which is typically affected by political facts and choices. (shrink)

How should we understand validity? A standard way to characterize validity is in terms of the preservation of truth (or truth in a model). But there are several problems facing such characterizations. An alternative approach is to characterize validity epistemically, for instance in terms of the preservation of an epistemic status. In this paper, I raise a problem for such views. First, I argue that if the relevant epistemic status is factive, such as being in a position to know or (...) having conclusive evidence for, then the account runs into trouble if we endorse certain familiar logical principles. Second, I argue that if the relevant epistemic status is non-factive, such as is rationally committed to or has justification for believing, then a similar problem arises if we endorse the logical principles as well as a sufficiently strong epistemic “level-bridging” principle. Finally, I argue that an analogous problem arises for the most natural characterization of validity in terms of rational credence. (shrink)

This paper argues that the traditional characterization of the notion of paradox — an apparently valid argument with apparently true premises and an apparently false conclusion — is too narrow; there are paradoxes that do not satisfy it. After discussing, and discarding, some alternatives, an outline of a new characterization of the notion of paradox is presented. A paradox is found to be an apparently valid argument such that, apparently, it does not present the kind of commitment to the conclusion (...) that should be implied by an acceptance of the truth of the premises and the validity of the argument. (shrink)

This paper aims to contribute to debates about the nature of philosophical inquiry and its relation to science. The starting point is the Discontinuity View (DV), which holds that philosophy is discontinuous with science. Upon critically engaging two lines of argument in favor of DV, the paper presents and defends the Continuity View (CV), according to which philosophy and science are continuous forms of inquiry. The critical engagement sheds light on continuities between philosophical and scientific inquiry while underlining special normative (...) competences of philosophical work. The final part of the paper uses these insights to offer a brief outline of a normative approach to philosophy of science. (shrink)

Logic is widely held to be a normative discipline. Various claims have been offered in support of this view, but they all revolve around the idea that logic is concerned with how one ought to reason. I argue that most of these claims—while perhaps correct—only entail that logic is normative in a way that many, if not all, intellectual disciplines are normative. I also identify some claims whose correctness would make logic normative in a way that sets it apart from (...) other disciplines. I argue that we have no reason think that these claims are correct. In other words, logic is not a distinctively normative discipline. (shrink)

Saul Kripke proposed a skeptical challenge that Romina Padró defended and popularized by the name of the Adoption Problem. The challenge is that, given a certain definition of adoption, there are some logical principles that cannot be adopted—paradigmatic cases being Universal Instantiation and Modus Ponens. Kripke has used the Adoption Problem to argue that there is an important sense in which logic is not revisable. In this essay, I defend two independent claims. First, that the Adoption Problem does not entail (...) that logic is never revisable in the sense that Kripke addresses. Second, that, to assess whether an agent can revise their logic in the sense that Kripke addresses, it is best to consider a different definition of adoption, according to which Universal Instantiation and Modus Ponens are sometimes adoptable. (shrink)

How does rationality bind the agnostic, that is, the one who suspends judgment about whether a given proposition is true? In this paper I explore two alternative ways of establishing what the rational requirements of agnosticism are: the Lockean–Bayesian framework and the doxastic logic framework. Each of these proposals faces strong objections. Fortunately, however, there is a rich kernel of requirements of agnosticism that are vindicated by both of them. One can then endorse the requirements that belong to that kernel (...) without thereby committing oneself to the problematic implications that stem from either of the aforementioned proposals. (shrink)

The orthodox view of logic takes for granted the central importance of logical principles. Logic, and thus logical reasoning, is to be understood as a system of rules or principles with universal application. Let us call this orthodox view logical generalism. In this paper we argue that logical generalism, whether monist or pluralist, is wrong. We then outline an account of logical consequence in the absence of general logical principles, which we call logical particularism.

Actualmente estamos viviendo una situación de pandemia que está dando pie a diferentes explicaciones. Cabe preguntarse, ¿hay que confiar ciegamente en los expertos o es cierto que el gobierno no es totalmente transparente? Para ello, un análisis Latourniano de las posibles explicaciones de la pandemia puede arrojar una respuesta a nuestras preguntas.

This paper presents a counterexample to the principle that all epistemic reasons for doxastic attitudes towards p are provided by evidence concerning p. I begin by motivating and clarifying the principle and the associated picture of epistemic reasons, including the notion of evidence concerning a proposition, which comprises both first- and second-order evidence. I then introduce the counterexample from incoherent doxastic attitudes by presenting three example cases. In each case, the fact that the subject’s doxastic attitudes are incoherent is an (...) epistemic reason to suspend, which is not provided by evidence. I argue that this incoherence fact is a reason for the subject to take a step back and reassess her evidence for her conflicting attitudes, and thus a reason to suspend all of them. Suspending judgment enables the subject to revise attitudes where appropriate and thus (typically) to arrive at a set of coherent and well-supported attitudes. I then address a dilemma for my proposal and, in conclusion, briefly suggest a picture of epistemic reasons on which they are to be understood against the background of the subject’s virtuous intellectual conduct. (shrink)

Starting from a proof-theoretic perspective, where meaning is determined by the inference rules governing logical operators, in this paper we primarily aim at developing a proof-theoretic alternative to the model-theoretic meaning-invariant logical pluralism discussed in Beall and Restall. We will also outline how this framework can be easily extended to include a form of meaning-variant logical pluralism. In this respect, the framework developed in this paper—which we label two-level proof-theoretic pluralism—is much broader in scope than the one discussed in Beall (...) and Restall’s book. (shrink)

ABSTRACTThis paper discusses the normativity of truth and logic. The paper has three objectives. First, I argue that logic is normative for thought in the sense of underwriting instrumental rationality. Logic is a good instrument for achieving truth, the goal of cognition. In recent work, Filippo Ferrari has argued that the normative nature of truth may vary across domains. My second aim is to extend this idea to logic, against the background of the idea that logic serves to underwrite instrumental (...) rationality. The third objective is to further develop Ferrari’s framework of normative alethic variability. I do so through a discussion of the normative problem of mixed compounds: the challenge of providing a principled account of the normativity of compounds with constituents whose respective normative profiles differ. I argue that the challenge can be met. Besides offering a solution to a major challenge, the response offered sheds new light on the normative variability framework: the truth of a single mixed compound may have different normative profiles across different ‘disagreement-realizers’. This feature of the view is rooted in a key commitment of the normative variability framework – namely, that disagreement and alethic normativity are intimately connected. (shrink)