Concha Martínez-Vidal

In our daily lives, we often make claims about what is possible or necessary, prompting the question of how we come to acquire these modal claims. In this paper we examine what Vaidya and Wallner have called the "problem of modal epistemic friction." According to this problem, some accounts of modal knowledge presuppose essentialist theses, thereby making the epistemology of modality a special case of the epistemology of essences. Vaidya advances an essence-based account centered on the method of “variation in imagination” (VIM), wherein the essential properties of an object are those that remain constant across imaginative variations over time. However, since this method is closed under logical consequence, it identifies what—in Finean terms—constitutes consequential rather than constitutive essences. In this paper, we aim to refine Vaidya's proposal by offering a way to capture constitutive essences, starting from a consequential perspective. To do so, we will draw on the notion of web consequence (WC), as developed by Schnieder, which helps distinguish constitutive essences from those which are merely consequential.

In philosophy, it is common for a concept to be modified according to the author and the role this concept will play in a theory. This is the case with the term “naturalism.” Various naturalistic approaches have emerged from disagreements on how the inquiry underlying the term “naturalism” should be understood. Consider the approach to naturalism designed in the early days of “institutional” philosophy of science (Hanna 2006) versus proposals such as Putnam’s liberal naturalism or Price’s subject naturalism. Our intuition is that the latter two positions defend reformulations of the meaning of the term and of the underlying inquiry that go so far that it is difficult to see any naturalism in them beyond the minimal demand that explanations or inquiries are to be compatible with science. The purpose of this paper is to see whether conceptual engineering can be useful to argue for the abovementioned intuition. Our tenet is that the case of liberal naturalism involves not just a change of meaning, but also a change of subject. To this purpose, we rely on Belleri’s (2021) notion of Progressive Semantic Inquiry and what counts as going too far in that change. The paper serves two objectives: on one hand, it helps to understand what is going on with the versions of naturalism mentioned above; on the other, it assesses Belleri’s solution to the change of subject objection.

The question of the existence of putative abstract objects has prompted a range of deflationist responses both ontological and metaontological in nature. Many of these draw inspiration from Carnap’s influential essay “Empiricism, Semantics, and Ontology”, as seen in the work of Putnam, Schiffer, Hirsch, Price, and Thomasson, among others. However, there are also notable deflationist approaches that diverge from Carnap’s framework—for instance, Jody Azzouni’s “pure deflationary metaphysics,” Otá vio Bueno’s “agnostic nominalism” and his more recent argument for the contingent nature of mathematical objects, as well as forms of metaontological minimalism advanced by figures like Øystein Linnebo and Agustı́n Rayo. This chapter introduces the central issues explored in the volume and offers a concise overview of the individual contributions that follow.

Drawing on the notions of deep disagreement and metalinguistic negotiation, we develop a new interpretation of the debate between scientific naturalism and liberal naturalism over the idea of naturalism. We argue that recent revisions of the debate suggest that the common perception of this as a case of metalinguistic negotiation is misleading. We trace this misperception back to the different ways in which scientific naturalism and liberal naturalism use the term ‘naturalism.’ Once this difference is considered, their seemingly contradictory claims on this issue can apparently be reconciled. It turns out to be a remarkably consequential metalinguistic negotiation over whether the term ‘naturalism’ should be reinterpreted or replaced for the purposes of positive philosophical theorizing. This interpretation explains the genuine disagreement that led scientific naturalism and liberal naturalism to engage in this debate and illuminates the broader meta-philosophical convictions that underlie each of their positions. Finally, we analyze how the development of the principle of charity acts as a mediating argumentative tool in disagreements.

Logical anti-exceptionalism, that is the idea that logic is not fundamentally different from other forms of inquiry such as science or mathematics, can be broadly characterized as being contrary to paradigmatic examples of exceptionalism about logic, such as the rationalist and semanticist conceptions. Logical inferentialism asserts that the meanings of logical expressions are determined by the basic rules prescribed for their correct application, such that comprehension of a logical expression is achieved through its use in accordance with the appropriate logical rule Brandom (Making it explicit: Reasoning, representing, and discursive commitment. Cambridge, 1994); Boghossian (Blind Reasoning. Proceedings of the Aristotelian Society, Supplementary Volume 77(1), 225–248, 2003a), Boghossian (Epistemic Analyticity: A Defence. Grazer Philosophische Studien 66(1), 15–35, 2003b). Despite the fact that inferentialism may appear to be an exceptionalist theory given its semanticist approach, not all inferentialists keep to the exceptionalist tenets of logic. This paper scrutinizes the recent moderate anti-exceptionalist proposal of naturalized inferentialism by Peregrin and Svoboda (Moderate anti-exceptionalism and earthborn logic. Synthese 199 (3–4), 8781–8806, 2021). To contextualize Peregrin and Svoboda’s proposal, the paper presents a series of issues concerning the various anti-exceptionalist and exceptionalist theories; this discussion shows that naturalized inferentialism can resolve the adoption problem identified by Kripke, and Boghossian and Wright (Kripke, Quine, the “Adoption Problem” and the Empirical Conception of Logic. Mind, 133(529), 86–116, 2024) while remaining faithful to the anti-exceptionalism it seeks to advance, except for its adherence to the fundamental nature of logical human practice. Moreover, it illustrates that as anti-exceptionalist proposals reduce their aspirations, the distinction from exceptionalist positions progressively diminishes in clarity and precision.

The chapter aims to clarify the metaphysical picture underlying the so-called Quine-Putnam Indispensability Argument (IA) by proposing an alternative reading that allows for minimal notions of object and existence (in Linnebo’s 2013 sense). In such a framework, the conclusion of the revised IA is not that mathematical entities exist, as existence comes with reference and objecthood and is, therefore, quite easy to establish. Rather, this revised version of the argument claims that mathematical entities make a demand on the world, thus asserting that mathematical entities are heavyweight entities.The chapter begins by introducing the debate over the metaphysical picture underlying the IA and goes on to present Linnebo’s notions of minimal object, existence, and the distinction between thick versus thin objects. It then shows that it is possible to take some of Quine’s theses on ontological commitment, existence, and reference to formulate a notion of existence that is minimal in nature. Furthermore, the chapter explores what is required to characterize light and heavyweight objects in a Quinean manner. Finally, the Quine-Putnam IA is reformulated in terms of the light versus heavy distinction, with the aim of uncovering the metaphysical assumptions underpinning the original argument and demonstrating that its conclusion is implausible by Quine’s naturalistic standards.

Putnam rejects having argued in the terms of the argument known in the literature as “the Quine-Putnam indispensability argument”. He considers that mathematics contribution to physics does not have to be interpreted in platonist terms but in his favorite modal variety (Putnam 1975; Putnam 2012). The purpose of this paper is to consider Putnam’s acknowledged argument and philosophical position against contemporary so called in the literature ‘fictionalist’ views about applied mathematics. The conclusion will be that the account of the applicability of mathematics that stems from Putnam‘s acknowledged argument can be assimilated to so-called ‘fictionalist’ views about applied mathematics.

Physical laws are irresistible. Logical rules are not. That is why logic is said to be normative. Given a system of logic we have a Norma, a standard of correctness. The problem is that we need another Norma to establish when the standard of correctness is to be applied. Subsequently we start by clarifying the senses in which the term ‘Iogic’ and the term ‘normativity’ are being used. Then we explore two different epistemologies for logic to see the sort of defence of the normativity of logic they allow for; if any. The analysis concentrates on the case of classical logic. In particular the issue will be appraised from the perspective put forward by the epistemology based on the methodology of wide reflective equilibrium and the scientific one underlying the view of logic as model

Fitch´s problem and the "knowability paradox" involve a couple of argumentations that are to each other in the same relation as Cantor´s uncollected multitudes theorem and Russell´s paradox. The authors exhibit the logical nature of the theorem and of the paradox and show their philosophical import, both from an anti-realist and from a realist perspective. In particular, the authors discuss an anti-realist solution to Fitch´s problem and provide an anti-realist interpretation of the problematic statement "It is knowable that r is known and yet unknown". Then, it is argued that the knowability paradox has a solution even if one adopts a realist point of view. The authors provide a solution that takes into account the ambiguity of the term 'knowability' by deploying a temporal possible world semantics for epistemic modalities

This paper aims to answer several epistemological questions raised by the use of computers in mathematical practice; for this purpose, it uses the template for a conceptual engineering project proposed in Isaac, Koch, and Nedft 2022. Some interesting theoretical questions raised by this change in the methodology of mathematics are whether proofs continue to be accessible to human mathematicians, whether computers are reliable and therefore should be trusted by mathematicians, and whether proof is still an a priori methodology even though the use of computers is essential for some of them. The paper begins by introducing the project, which is to assess the “functionality” of the notion of proof and apriority in relation to the novelty that the use of computers in proof has brought to mathematical practice. The paper suggests that there has been a development of the methodology that conveys an “improvement of the functionality” and enforces reasons to adopt a certain notion of apriority.