My dissertation explores the ways in which Rudolf Carnap sought to make philosophy scientific by further developing recent interpretive efforts to explain Carnap’s mature philosophical work as a form of engineering. It does this by looking in detail at his philosophical practice in his most sustained mature project, his work on pure and applied inductive logic. I, first, specify the sort of engineering Carnap is engaged in as involving an engineering design problem and then draw out the complications of design (...) problems from current work in history of engineering and technology studies. I then model Carnap’s practice based on those lessons and uncover ways in which Carnap’s technical work in inductive logic takes some of these lessons on board. This shows ways in which Carnap’s philosophical project subtly changes right through his late work on induction, providing an important corrective to interpretations that ignore the work on inductive logic. Specifically, I show that paying attention to the historical details of Carnap’s attempt to apply his work in inductive logic to decision theory and theoretical statistics in the 1950s and 1960s helps us understand how Carnap develops and rearticulates the philosophical point of the practical/theoretical distinction in his late work, offering thus a new interpretation of Carnap’s technical work within the broader context of philosophy of science and analytical philosophy in general. (shrink)

This is the most comprehensive book ever published on philosophical methodology. A team of thirty-eight of the world's leading philosophers present original essays on various aspects of how philosophy should be and is done. The first part is devoted to broad traditions and approaches to philosophical methodology. The entries in the second part address topics in philosophical methodology, such as intuitions, conceptual analysis, and transcendental arguments. The third part of the book is devoted to essays about the interconnections between philosophy (...) and neighbouring fields, including those of mathematics, psychology, literature and film, and neuroscience. (shrink)

In this paper I examine the question of logic’s normative status in the light of Carnap’s Principle of Tolerance. I begin by contrasting Carnap’s conception of the normativity of logic with that of his teacher, Frege. I identify two core features of Frege’s position: first, the normative force of the logical laws is grounded in their descriptive adequacy; second, norms implied by logic are constitutive for thinking as such. While Carnap breaks with Frege’s absolutism about logic and hence with the (...) notion that any system of logic should have a privileged claim to correctness, I argue that there is a sense in which Carnap’s framework-relative conception of logical norms has a constitutive role to play: though they are not constitutive for the conceptual activity for thinking, they do nevertheless set the ground rules that make certain forms of scientific inquiry possible in the first place. I conclude that Carnap’s principle of tolerance is tamer than one might have thought and that, despite remaining differences, Frege’s and Carnap’s conceptions of logic have more in common than one might have thought. (shrink)

Carnap’s search for a criterion of empirical significance is usually considered a failure. I argue that the results from two out of his three different approaches are at the very least problematic, but that one approach led to success. Carnap’s criterion of translatability into logical syntax is too vague to allow for definite results. His criteria for terms—introducibility by chains of reduction sentences and his criterion from “The Methodological Character of Theoretical Concepts”—are almost trivial and have no clear relation to (...) the empirical significance of sentences. However, his criteria for sentences—translatability, verifiability, falsifiability, confirmability—are usable, and under the assumptions needed for the Carnap sentence approach, verifiability, falsifiability, and translatability become equivalent. As a result of the Carnap sentence approach, metaphysics is rendered analytic. (shrink)

This essay examines Friedman's recent approach to the analysis of physical theories. Friedman argues against Quine that the identification of certain principles as ‘constitutive’ is essential to a satisfactory methodological analysis of physics. I explicate Friedman's characterization of a constitutive principle, and I evaluate his account of the constitutive principles that Newtonian and Einsteinian gravitation presuppose for their formulation. I argue that something close to Friedman's thesis is defensible.

In this paper I discuss a prevailing view by which logical terms determine forms of sentences and arguments and therefore the logical validity of arguments. This view is common to those who hold that there is a principled distinction between logical and nonlogical terms and those holding relativistic accounts. I adopt the Tarskian tradition by which logical validity is determined by form, but reject the centrality of logical terms. I propose an alternative framework for logic where logical terms no longer (...) play a distinctive role. This account employs a new notion of semantic. (shrink)

Scientific inquiry has led to immense explanatory and technological successes, partly as a result of the pervasiveness of scientific theories. Relativity theory, evolutionary theory, and plate tectonics were, and continue to be, wildly successful families of theories within physics, biology, and geology. Other powerful theory clusters inhabit comparatively recent disciplines such as cognitive science, climate science, molecular biology, microeconomics, and Geographic Information Science (GIS). Effective scientific theories magnify understanding, help supply legitimate explanations, and assist in formulating predictions. Moving from their (...) knowledge-producing representational functions to their interventional roles (Hacking 1983), theories are integral to building technologies used within consumer, industrial, and scientific milieus. -/- This entry explores the structure of scientific theories from the perspective of the Syntactic, Semantic, and Pragmatic Views. Each of these views answers questions such as the following in unique ways. What is the best characterization of the composition and function of scientific theory? How is theory linked with world? Which philosophical tools can and should be employed in describing and reconstructing scientific theory? Is an understanding of practice and application necessary for a comprehension of the core structure of a scientific theory? How are these three views ultimately related? (shrink)

Recent 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.

A critical notice of David J. Chalmers, Constructing the World (Oxford University Press,2012).

Inductive probability is the logical concept of probability in ordinary language. It is vague but it can be explicated by defining a clear and precise concept that can serve some of the same purposes. This paper presents a general method for doing such an explication and then a particular explication due to Carnap. Common criticisms of Carnap's inductive logic are examined; it is shown that most of them are spurious and the others are not fundamental.

Carnap’s work was instrumental to the liberalization of empiricism in the 1930s that transformed the logical positivism of the Vienna Circle to what came to be known as logical empiricism. A central feature of this liberalization was the deployment of the Principle of Tolerance, originally introduced in logic, but now invoked in an epistemological context in “Testability and Meaning”. Immediately afterwards, starting with Foundations of Logic and Mathematics, Carnap embraced semantics and turned to interpretation to guide the choice of a (...) theoretical language for science. The first thesis of this paper is that recourse to an intended interpretation led to a partial retrenchment of the conventionalism implied by the Principle of Tolerance. It required that the choice of a language be based on abstraction from a context; this procedure later became a component of the process of explication that was distinctive to Carnap’s mature views. The interpretive origin of formal systems also ensured their likely syntactic consistency, an issue on which Carnap was strongly criticized by figures such as Beth and Gödel. The second thesis of this paper is that this reliance on an intended interpretation enabled constructed formal systems to be relevant to the development of empirical science. (shrink)

G. Schiemer has recently ascribed to Carnap the so-called domains-as-fields conception of models, which he subsequently used to defend Carnap’s treatment of extremal axioms against J. Hintikka’s criticism that the number of tuples in a relation, and not the domain of discourse, is optimised in Carnap’s treatment. We will argue by a careful textual analysis, however, that this domains-as-fields conception cannot be applied to Carnap’s early semantics, because it includes a notion of submodel and subrelation that is not only absent (...) from Carnap’s work at that time, but even contradicts it. As a consequence, Schiemer’s defense of Carnap’s extremal axioms against Hintikka’s criticism fails. We will reconcile Carnap’s treatment of extremal axioms and Hintikka’s observation by taking into account the practice of axiomatics in the early twentieth century. If one realises that, in Carnap’s time, a predicate for the domain of discourse was often introduced in the formal theory, and that Carnap defined such predicates from the basic relations of an axiom system, the apparent disagreement between optimising relations and optimising domains disappears. (shrink)

Ontology is the philosophical discipline which aims to understand how things in the world are divided into categories and how these categories are related together. This is exactly what information scientists aim for in creating structured, automated representations, called 'ontologies,' for managing information in fields such as science, government, industry, and healthcare. Currently, these systems are designed in a variety of different ways, so they cannot share data with one another. They are often idiosyncratically structured, accessible only to those who (...) created them, and unable to serve as inputs for automated reasoning. This volume shows, in a nontechnical way and using examples from medicine and biology, how the rigorous application of theories and insights from philosophical ontology can improve the ontologies upon which information management depends. (shrink)

Two parallelism hypotheses have been adopted and the third one on their relationship has been put forward. The illocutionary logic hypothesis states that the logic of linguistic commitments runs parallel to the logic of intentionality. The normative pragmatics hypothesis states that the logic of utterances runs parallel to the logic of linguistic commitments. According to the third stance or the logic projection hypothesis, the logic of utterances is the origin of all other logics used in describing psychological and social realities. (...) Consequently, the imperative logic or logic of utterances constitutes an independent but not self-sufficient research topic. The logic of utterances manifests itself in its meaning effects such as deontic and bouletic ones. It can be studied only in relation to deontic logics of the hearer’s obligation and the speaker’s linguistic commitments and in relation to logics of intentionality of the speaker’s expression and the hearer’s impression. Therefore, research in logic of imperative and other utterances must include investigation of relations between logics. (shrink)

In classical logic, a contradiction allows one to derive every other sentence of the underlying language; paraconsistent logics came relatively recently to subvert this explosive principle, by allowing for the subsistence of contradictory yet non-trivial theories. Therefore our surprise to find Wittgenstein, already at the 1930s, in comments and lectures delivered on the foundations of mathematics, as well as in other writings, counseling a certain tolerance on what concerns the presence of contradictions in a mathematical system. ‘Contradiction. Why just this (...) spectre? This is really very suspicious.’ ( Philosophical Remarks III–56) In the last decades, several authors (e.g. Arrington, Hintikka, Van Heijenoort, Wright, Wrigley) have been digging into Wittgenstein’s rather non-standard standpoint on what concerns the interpretation and import of contradiction in logic and mathematics, and many other authors (e.g. da Costa, Goldstein, Granger, Marconi) have been investigating the possibility of taking Wittgenstein seriously as one of the early forerunners of paraconsistency. While many advances have been made on the first front, the second set of investigations has led almost exclusively to negative results: no, no operational proposal about the construction of a logic in which (some) contradictions are made inoffensive can be read from Wittgenstein’s philosophical work; in fact, it appears that the most one can find there is the exhortation for mathematicians to alter their attitude with respect to contradictions and to consistency proofs. The play is done, and one looks for a resume of the opera. This paper fills that blank, as a thorough investigation of the possible relations between Wittgenstein and paraconsistency. DOI:10.5007/1808-1711.2010v14n1p135. (shrink)

Logical pluralism has been in vogue since JC Beall and Greg Restall 2006 articulated and defended a new pluralist thesis. Recent criticisms such as Priest 2006a and Field 2009 have suggested that there is a relationship between their type of logical pluralism and the meaning-variance thesis for logic. This is the claim, often associated with Quine 1970, that a change of logic entails a change of meaning. Here we explore the connection between logical pluralism and meaning-variance, both in general and (...) for Beall and Restall's theory specifically. We argue that contrary to what Beall and Restall claim, their type of pluralism is wedded to meaning-variance. We then develop an alternative form of logical pluralism that circumvents at least some forms of meaning-variance. (shrink)

In this paper, I critically discuss recent work on the role that the principle of tolerance plays in Rudolf Carnap's philosophy. Specifically, I consider how two prominent interpretations of Carnap's principle of tolerance can be used to argue for Carnap's anti-metaphysical views. I then argue that there are serious problems with these arguments, and I diagnose those problems as resulting, in part, from a tension between competing goals of Carnap's philosophical project.

Michael Friedman’s project both historically and systematically testifies to the importance of the relativized a priori. The importance of implicit definitions clearly emerges from Schlick’s General Theory of Knowledge . The main aim of this paper is to show the relationship between both and the relativized a priori through a detailed discussion of Friedman’s work. Succeeding with this will amount to a contribution to recent scholarship showing the importance of Hilbert for Logical Empiricism.

It has been argued that ethically correct robots should be able to reason about right and wrong. In order to do so, they must have a set of do’s and don’ts at their disposal. However, such a list may be inconsistent, incomplete or otherwise unsatisfactory, depending on the reasoning principles that one employs. For this reason, it might be desirable if robots were to some extent able to reason about their own reasoning—in other words, if they had some meta-ethical capacities. (...) In this paper, we sketch how one might go about designing robots that have such capacities. We show that the field of computational meta-ethics can profit from the same tools as have been used in computational metaphysics. (shrink)

Nous publions sous ce titre la traduction française de l'essai philosophique de Kurt Gödel intitulé: «Is Mathematics Syntax of Language?» Inédit jusqu'à présent, l'original paraîtra dans le 3e volume des Collected Works de Gödel, dont la publication est imminente. Nous savons par Hao Wang que, le 15 mai 1953, Paul Arthur Schilpp avait invité Gödel à apporter sa contribution au volume consacré à Carnap dans The Library of Living Philosophers. Le manuscrit de Gödel «Carnap and the Ontology of Mathematics», devait (...) être remis au plus tard le 2 avril 1954. Dés le 2 juillet 1953, Gödel donnait son accord à Schilpp pour la rédaction d'un article intitulé «Some Observations on the Nominalistic View of the Nature of Mathematics.» Cependant, le volume consacré à Carnap paraîtra en 1963 sans qu'y figure la contribution de Gödel. En effet — toujours selon Wang — Gödel avait informé Schilpp, le 2 février 1959, qu'il renonçait à l'envoi de l'article, dont il avait composé, surtout en 1954–1955, plusieur s versions sous le titre «Is Mathematics Syntax of Language?» Pour expliquer cet abandon, Wang avance les raisons suivantes: En premier lieu, Gödel était bien convaincu d'avoir réfuté la thése syntaxique, mais il n'était pas satisfait de son argumentation en faveur du platonisme. Deuxiémement, les critiques de Gödel s'adressent aux théses soutenues par Carnap en 1934 plutôt qu'à celles que ce dernier défendra vingt ans aprés, et qui paraissent moins hostiles au platonisme de son interlocuteur. II pouvait paraître douteux, en troisieme lieu, que Carnap ait eu le temps de rédiger, en 1959, la réponse qu'il aurait du faire, conformément aux régies de la collection, à Gödel. Or, en 1943 déjà, Gödel avait voulu retirer sa contribution au volume consacré à Russell dans la même serie, parce que ce dernier n'avait pu répondre à l'article de Gödel dont la rédaction lui avait été communiquée trop tardivement. (shrink)

The ?no???no? paradox (so-called by Sorensen) consists of a pair of propositions each of which says of the other that it is false. It is not immediately paradoxical, since it has a solution in which one proposition is true, the other false. However, that is itself paradoxical, since there is no clear ground for determining which is which. The two propositions should have the same truth-value. The paper shows how a proposal by the medieval thinker Thomas Bradwardine solves not only (...) the Liar paradox, but also symmetric paradoxes like the ?no???no?, the descending ?no???no?, and the Truth-teller paradoxes. (shrink)

Four distinguished authors have been brought together to produce this elegant study of a much-neglected figure. The book is divided into three sections: Neurath's biographical background and the economic and social context of his ideas; his theory of science; and the development of his role in debates on Marxist concepts of history and his own conception of science. Coinciding with the emerging serious interest in logical positivism, this timely publication will redress a current imbalance in the history and philosophy of (...) science. (shrink)

Logical pluralism is the view that there is more than one correct logic. In this article, I explore what logical pluralism is, and what it entails, by: (i) distinguishing clearly between relativism about a particular domain and pluralism about that domain; (ii) distinguishing between a number of forms logical pluralism might take; (iii) attempting to distinguish between those versions of pluralism that are clearly true and those that are might be controversial; and (iv) surveying three prominent attempts to argue for (...) logical pluralism and evaluating them along the criteria provided by (ii) and (iii). (shrink)

Whereas an inference (deductive as well as inductive) is usually viewed as being valid in virtue of its argument form, the present paper argues that scientific reasoning is material inference, i.e., justified in virtue of its content. A material inference is licensed by the empirical content embodied in the concepts contained in the premises and conclusion. Understanding scientific reasoning as material inference has the advantage of combining different aspects of scientific reasoning, such as confirmation, discovery, and explanation. This approach explains (...) why these different aspects (including discovery) can be rational without conforming to formal schemes, and why scientific reasoning is local, i.e., justified only in certain domains and contingent on particular empirical facts. The notion of material inference also fruitfully interacts with accounts of conceptual change and psychological theories of concepts. (shrink)

In this paper, I consider an argument for the claim that any satisfactory epistemology of mathematics will violate core tenets of naturalism, i.e. that mathematics cannot be naturalized. I find little reason for optimism that the argument can be effectively answered.

In this paper, I develop a new defense of logicism: one that combines logicism and nominalism. First, I defend the logicist approach from recent criticisms; in particular from the charge that a cruciai principie in the logicist reconstruction of arithmetic, Hume's Principle, is not analytic. In order to do that, I argue, it is crucial to understand the overall logicist approach as a nominalist view. I then indicate a way of extending the nominalist logicist approach beyond arithmetic. Finally, I argue (...) that a nominalist can use the resulting approach to provide a nominalization strategy for mathematics. In this way, mathematical structures can be introduced without ontological costs. And so, if this proposal is correct, we can say that ultimately all the nominalist needs is logic (and, rather loosely, ali the logicist needs is nominalism). (shrink)

I aim to stand the received view about verificationism on its head. It is commonly thought that verificationism is a powerful philosophical tool, which we could deploy very effectively if only it weren’t so hopelessly implausible. On the contrary, I argue. Verificationism - if properly construed - may well be true. But its philosophical applications are chimerical.

In this paper, elementary but hitherto overlooked connections are established between Wittgenstein's remarks on mathematics, written during his transitional period, and free-variable finitism. After giving a brief description of theTractatus Logico-Philosophicus on quantifiers and generality, I present in the first section Wittgenstein's rejection of quantification theory and his account of general arithmetical propositions, to use modern jargon, as claims (as opposed to statements). As in Skolem's primitive recursive arithmetic and Goodstein's equational calculus, Wittgenstein represented generality by the use of free (...) variables. This has the effect that negation of unbounded universal and existential propositions cannot be expressed. This is claimed in the second section to be the basis for Wittgenstein's criticism of the universal validity of the law of excluded middle. In the last section, there is a brief discussion of Wittgenstein's remarks on real numbers. These show a preference, in line with finitism, for a recursive version of the continuum. (shrink)

Recent Carnap scholarship suggests that the received view of the Carnap-Quine analyticity debate is importantly mistaken. It has been suggested that Carnap’s analyticity distinction is immune from Quine’s criticisms. This is either because Quine did not understand Carnap’s use of analytic-ity, or because Quine did not appreciate that, rather than dispelling dog-mas, he was merely offering an alternate framework for philosophy. It has also been suggested that ultimately nothing of substance turns on this dis-pute. I am sympathetic to these reassessments (...) and their rejection of the re-ceived view, but argue that they fail to pay proper attention to Carnap’s metaphysical deflationism. For it is there that Quine’s arguments ultimately make contact with Carnap, undermining his metaphysical deflationism. Moreover, the viability of deflationism is directly related to the viability of Carnap’s view of philosophy as methodologically distinct from science. Hence, Quine’s criticisms make contact with the deepest aspects of Carnap’s views. (shrink)

Michael Dummett and Dag Prawitz have argued that a constructivist theory of meaning depends on explicating the meaning of logical constants in terms of the theory of valid inference, imposing a constraint of harmony on acceptable connectives. They argue further that classical logic, in particular, classical negation, breaks these constraints, so that classical negation, if a cogent notion at all, has a meaning going beyond what can be exhibited in its inferential use. I argue that Dummett gives a mistaken elaboration (...) of the notion of harmony, an idea stemming from a remark of Gerhard Gentzen's. The introduction-rules are autonomous if they are taken fully to specify the meaning of the logical constants, and the rules are harmonious if the elimination-rule draws its conclusion from just the grounds stated in the introduction-rule. The key to harmony in classical logic then lies in strengthening the theory of the conditional so that the positive logic contains the full classical theory of the conditional. This is achieved by allowing parametric formulae in the natural deduction proofs, a form of multiple-conclusion logic. (shrink)

The best known and most widely discussed aspect of Kurt Gödel's philosophy of mathematics is undoubtedly his robust realism or platonism about mathematical objects and mathematical knowledge. This has scandalized many philosophers but probably has done so less in recent years than earlier. Bertrand Russell's report in his autobiography of one or more encounters with Gödel is well known:Gödel turned out to be an unadulterated Platonist, and apparently believed that an eternal “not” was laid up in heaven, where virtuous logicians (...) might hope to meet it hereafter.On this Gödel commented:Concerning my “unadulterated” Platonism, it is no more unadulterated than Russell's own in 1921 when in the Introduction to Mathematical Philosophy … he said, “Logic is concerned with the real world just as truly as zoology, though with its more abstract and general features.” At that time evidently Russell had met the “not” even in this world, but later on under the infuence of Wittgenstein he chose to overlook it.One of the tasks I shall undertake here is to say something about what Gödel's platonism is and why he held it.A feature of Gödel's view is the manner in which he connects it with a strong conception of mathematical intuition, strong in the sense that it appears to be a basic epistemological factor in knowledge of highly abstract mathematics, in particular higher set theory. Other defenders of intuition in the foundations of mathematics, such as Brouwer and the traditional intuitionists, have a much more modest conception of what mathematical intuition will accomplish. (shrink)

This paper will deal with three questions regarding Carnap's transition from the position he held at the time of writing Syntax to the doctrines he held during his semantic phase: (1) What was Carnap's attitude towards truth at the time of writing Syntax? (2) What was Carnap's position regarding questions of reference and ontology at the time of writing Syntax? (3) Was Carnap's acceptance of Tarski's analysis of truth and reference detrimental to his philosophical project? Section 1 of this paper (...) will deal with the first of these questions. Special attention will be paid to identifying what it was that prevented Carnap from defining a truth predicate for descriptive languages in Syntax. Section 2 of this paper will deal with the question of Carnap's attitude towards reference and ontology in Syntax. It will be shown that the attempt in Syntax to address ontological questions is seriously defective. Section 3 of this paper addresses the last of the questions posed above. It is argued that in the light of what is established in Sections 1 and 2, Carnap could not have retained the position of Syntax with respect to truth and reference. (shrink)

An overview of the following three related papers in this issue presents the Emergence of Highly Complex Systems such as living organisms, man, society and the human mind from the viewpoint of the current Ontological Theory of Levels. The ontology of spacetime structures in the Universe is discussed beginning with the quantum level; then, the striking emergence of the higher levels of reality is examined from a categorical—relational and logical viewpoint. The ontological problems and methodology aspects discussed in the first (...) two papers are followed by a rigorous paper based on Category Theory, Algebraic Topology and Logic that provides a conceptual and mathematical basis for a Categorical Ontology Theory of Levels. The essential links and relationships between the following three papers of this issue are pointed out, and further possible developments are being considered. (shrink)

The aim of this article is to show that the prospects for intentional irrealism are much brighter than it is generally thought. In the first section, I provide a general haracterization of some of the various forms that the realism/irrealism debates might take. In the second, I ask whether there is any defensible form of realism about intentional states. I show that most candidates are nearly trivially false, and that the only form of intentional realism which is not, is a (...) restricted one which is prima facie no more plausible than the corresponding form of irrealism. In the third and last section, I defend my interpretation of what intentional irrealism amounts to against some possible misunderstandings, give some reasons why it should be taken seriously and argue that it could plausibly be attributed to Davidson. (shrink)

What is reasoning? What is logic? What is math? Common sense tells us that concepts such as numbers, relations, and logical structures feel inherently familiar—almost intuitive. They seem so obvious, but why? Do they have deeper origins? What is the number? What is addition? Why do they work in this way? Basic axioms of math, their foundation seems to be very intuitive, but absolutely mysteriously appear to the human mind out of nowhere. In a way their true essence magically slips (...) away unnoticed from the consciousness, in an attempt to pinpoint its foundation. This paper delves into the fundamental nature of mathematics, logic, and rational reasoning, examining their "unreasonable effectiveness" in understanding and shaping the world. By drawing parallels between advancements in artificial neural networks and human cognition, the work introduces a novel perspective on intuition as the cornerstone of higher cognitive systems. Intuition is presented not only as a tool for pattern recognition but as the foundation upon which complex reasoning processes, such as mathematical abstraction and logical frameworks are constructed. This perspective redefines the role of consciousness, highlighting its capacity for innovation and exploration within abstract domains. Beyond theoretical insights, the paper outlines potential pathways for advancing artificial general intelligence by leveraging the interplay between intuition and conscious reasoning. (shrink)

We argue that (1) a purported example of an infinite inference we humans can actually perform admits a faithful, finitary description, and (2) infinite inference contravenes any view which does not grant our minds uncomputable powers. These arguments block the strategy, dating back to Carnap's Logical Syntax of Language, of using infinitary inference rules to secure the determinacy of arithmetical truth on conventionalist grounds.

I outline the theoretical framework of, and three research programs within American speculative philosophy of science during the period 1900-1931. One program applies verificationism to research in psychology, one investigates the methodology of research programs, and one analyses scientific explanation and other scientific concepts. The primary sources for my outline are works by Morris Raphael Cohen, Grace Andrus de Laguna, Theodore de Laguna, Edgar Arthur Singer Jr., Harold Robert Smart, and Marie Collins Swabey. I also use my outline to provide (...) a partial comparison of American speculative philosophy of science and 1930s logical positivism. My comparison suggests that logical positivism was a proposal for substantially narrowing down and winding back American philosophy of science and was based on positions that were already problematized in the American context. -/- . (shrink)

In the language of second-order logic, first- and second-order variables are distinguished syntactically and cannot be grammatically substituted. According to a prominent argument for the deployment of these languages, these substitution failures are necessary to block the derivation of paradoxes that result from attempts to generalize over predicate interpretations. I first examine previous approaches which interpret second-order sentences using expressions of natural language and argue that these approaches undermine these syntactic restrictions. I then examine Williamson’s primitivist approach according to which (...) second-order sentences are not offered readings in a previously understood language. I argue that the syntactic restrictions alone do not block the derivation of the paradox, unless they are backed by a principled reason that the language cannot be expanded to allow the grammatical substitution of first- and second- order variables. I argue that there is neither a syntactic nor a semantic principle that prohibits such an expansion. (shrink)

Although mathematical philosophy is flourishing today, it remains subject to criticism, especially from non-analytical philosophers. The main concern is that even if formal tools serve to clarify reasoning, they themselves contribute nothing new or relevant to philosophy. We defend mathematical philosophy against such concerns here by appealing to its metaphysical foundations. Our thesis is that mathematical philosophy can be founded on the phenomenological theory of ideas as developed by Roman Ingarden. From this platonist perspective, the “unreasonable effectiveness of mathematics in (...) philosophy”—to adapt Wigner’s phrase—is analogous to that of mathematical explanations in science. As success-criteria for mathematical philosophy, we propose that it should be correct, responsive, illuminating, promising, relevant, and adequate. (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)

The historical consensus is that logical evidence is special. Whereas empirical evidence is used to support theories within both the natural and social sciences, logic answers solely to a priori evidence. Further, unlike other areas of research that rely upon a priori evidence, such as mathematics, logical evidence is basic. While we can assume the validity of certain inferences in order to establish truths within mathematics and test scientifi c theories, logicians cannot use results from mathematics or the empirical sciences (...) without seemingly begging the question. Appeals to rational intuition and analyticity in order to account for logical knowledge are symptomatic of these commitments to the apriority and basicness of logical evidence. This chapter argues that these historically prevalent accounts of logical evidence are mistaken, and that if we take logical practice seriously we fi nd that logical evidence is rather unexceptional, sharing many similarities to the types of evidence appealed to within other research areas. (shrink)

European Journal of Philosophy, Volume 29, Issue 4, Page 864-886, December 2021.

In this paper, I defend Rudolf Carnap's Principle of Tolerance from an accusation, due to Michael Friedman, that it is self-defeating by prejudicing any debate towards the logically stronger theory. In particular, Friedman attempts to show that Carnap's reconstruction of the debate between classicists and intuitionists over the foundations of mathematics in his book The Logical Syntax of Language, is biased towards the classical standpoint since the metalanguage he constructs to adjudicate between the rival positions is fully classical. I argue (...) that this criticism is mistaken on two counts: (1) it fails to fully appreciate the freedom with regard to the construction of linguistic frameworks that Carnap intended his Principle to embody, and (2) Friedman's objection underestimates the extent to which the evaluation of a framework is task-relative. I conclude that Tolerance is not self-undermining in the way that Friedman claims it is. While this is a restricted conclusion -- and is not a vindication of Carnap's views on logic and mathematics tout court -- it nonetheless suggests that his tolerant perspective has been dismissed too quickly, even by his supporters. (shrink)