What is mathematics about? And if it is about some sort of mathematical reality, how can we have access to it? This is the problem raised by Plato, which still today is the subject of lively philosophical disputes. This book traces the history of the problem, from its origins to its contemporary treatment. It discusses the answers given by Aristotle, Proclus and Kant, through Frege's and Russell's versions of logicism, Hilbert's formalism, Gödel's platonism, up to the the current debate on (...) Benacerraf's dilemma and the indispensability argument. Through the considerations of themes in the philosophy of language, ontology, and the philosophy of science, the book aims at offering an historically-informed introduction to the philosophy of mathematics, approached through the lenses of its most fundamental problem. (shrink)

Donald Davidson contributed to the discussion of logical form in two ways. On the one hand, he made several influential suggestions on how to give the logical forms of certain constructions of natural language. His account of adverbial modification and so called action-sentences is nowadays, in some form or other, widely employed in linguistics (Harman (forthcoming) calls it "the standard view"). Davidson's approaches to indirect discourse and quotation, while not as influential, also still attract attention today. On the other hand, (...) Davidson provided a general account of what logical form is. This paper is concerned with this general account. Its foremost aim is to give a faithful and detailed picture of what, according to Davidson, it means to give the logical form of a sentence. The structure of the paper is as follows. (1) I will first informally introduce a notion of logical form as the form that matters in certain kinds of entailments, and indicate why philosophers have taken an interest in such a notion. (2) The second section develops constraints that we should arguably abide by in giving an account of logical form. (3) I then turn to Davidson’s view of what is involved in giving such an account. To this end, I will try to reconstruct Davidson’s view of the connection between an assignment of logical forms, a truth theory and a meaning theory. (4) Finally, I will briefly discuss possible problems of Davidson’s account as developed in this paper. (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)

I address a type of circularity threat that arises for the view that we employ general basic logical principles in deductive reasoning. This type of threat has been used to argue that whatever knowing such principles is, it cannot be a fully cognitive or propositional state, otherwise deductive reasoning would not be possible. I look at two versions of the circularity threat and answer them in a way that both challenges the view that we need to apply general logical principles (...) in deductive reasoning and defuses the threat to a cognitivist account of knowing basic logical principles. (shrink)

As analytic philosophy is becoming increasingly aware of and interested in its own history, the study of that field is broadening to include, not just its earliest beginnings, but also the mid-twentieth century. One of the towering figures of this epoch is W.V. Quine (1908-2000), champion of naturalism in philosophy of science, pioneer of mathematical logic, trying to unite an austerely physicalist theory of the world with the truths of mathematics, psychology, and linguistics. Quine's posthumous papers, notes, and drafts revealing (...) the development of his views in the forties have recently begun to be published, as well as careful philosophical studies of, for instance, the evolution of his key doctrine that mathematical and logical truth are continuous with, not divorced from, the truths of natural science. But one central text has remained unexplored: Quine's Portuguese-language book on logic, his 'farewell for now' to the discipline as he embarked on an assignment in the Navy in WWII. Anglophone philosophers have neglected this book because they could not read it. Jointly with colleagues, I have completed the first full English translation of this book. In this accompanying paper I draw out the main philosophical contributions Quine made in the book, placing them in their historical context and relating them to Quine's overall philosophical development during the period. Besides significant developments in the evolution of Quine's views on meaning and analyticity, I argue, this book is also driven by Quine's indebtedness to Russell and Whitehead, Tarski, and Frege, and contains crucial developments in his thinking on philosophy of logic and ontology. This includes early versions of some arguments from 'On What There Is', four-dimensionalism, and virtual set theory. (shrink)

This compelling reevaluation of the relationship between logic and knowledge affirms the key role that the notion of judgement must play in such a review. The commentary repatriates the concept of judgement in the discussion, banished in recent times by the logical positivism of Wittgenstein, Hilbert and Schlick, and the Platonism of Bolzano. The volume commences with the insights of Swedish philosopher Per Martin-Löf, the father of constructive type theory, for whom logic is a demonstrative science in which judgement is (...) a settled feature of the landscape. His paper opens the first of four sections that examine, in turn, historical philosophical assessments of judgement and reason; their place in early modern philosophy; the notion of judgement and logical theory in Wolff, Kant and Neo-Kantians like Windelband; their development in the Husserlian phenomenological paradigm; and the work of Bolzano, Russell and Frege. The papers, whose authors include Per Martin-Löf, Göran Sundholm, Michael Della Rocca and Robin Rollinger, represent a finely judged editorial selection highlighting work on philosophers exercised by the question of whether or not an epistemic notion of judgement has a role to play in logic. The volume will be of profound interest to students and academicians for its application of historical developments in philosophy to the solution of vexatious contemporary issues in the foundation of logic. ​. (shrink)

In this study two strands of inferentialism are brought together: the philosophical doctrine of Brandom, according to which meanings are generally inferential roles, and the logical doctrine prioritizing proof-theory over model theory and approaching meaning in logical, especially proof-theoretical terms.

Debates concerning the units and levels of selection have persisted for over fifty years. One major question in this literature is whether units and levels of selection are genuine, in the sense that they are objective features of the world, or merely reflect the interests and goals of an observer. Scientists and philosophers have proposed a range of answers to this question. This Element introduces this literature and proposes a novel contribution. It defends a realist stance and offers a way (...) of delineating genuine levels of selection by invoking the notion of a functional unit. (shrink)

What is the source of logical and mathematical truth? This book revitalizes conventionalism as an answer to this question. Conventionalism takes logical and mathematical truth to have their source in linguistic conventions. This was an extremely popular view in the early 20th century, but it was never worked out in detail and is now almost universally rejected in mainstream philosophical circles. Shadows of Syntax is the first book-length treatment and defense of a combined conventionalist theory of logic and mathematics. It (...) argues that our conventions, in the form of syntactic rules of language use, are perfectly suited to explain the truth, necessity, and a priority of logical and mathematical claims, as well as our logical and mathematical knowledge. (shrink)

Esta enciclopédia abrange, de uma forma introdutória mas desejavelmente rigorosa, uma diversidade de conceitos, temas, problemas, argumentos e teorias localizados numa área relativamente recente de estudos, os quais tem sido habitual qualificar como «estudos lógico-filosóficos». De uma forma apropriadamente genérica, e apesar de o território teórico abrangido ser extenso e de contornos por vezes difusos, podemos dizer que na área se investiga um conjunto de questões fundamentais acerca da natureza da linguagem, da mente, da cognição e do raciocínio humanos, bem (...) como questões acerca das conexões destes com a realidade não mental e extralinguística. A razão daquela qualificação é a seguinte: por um lado, a investigação em questão é qualificada como filosófica em virtude do elevado grau de generalidade e abstracção das questões examinadas (entre outras coisas); por outro, a investigação é qualificada como lógica em virtude de ser uma investigação logicamente disciplinada, no sentido de nela se fazer um uso intenso de conceitos, técnicas e métodos provenientes da disciplina de lógica. O agregado de tópicos que constitui a área de estudos lógico-filosóficos é já visível, pelo menos em parte, no Tractatus Logico-Philosophicus de Ludwig Wittgenstein, uma obra publicada em 1921. E uma boa maneira de ter uma ideia sinóptica do território disciplinar abrangido por esta enciclopédia, ou pelo menos de uma porção substancial dele, é extrair do Tractatus uma lista dos tópicos mais salientes aí discutidos; a lista incluirá certamente tópicos do seguinte género, muitos dos quais se podem encontrar ao longo desta enciclopédia: factos e estados de coisas; objectos; representação; crenças e estados mentais; pensamentos; a proposição; nomes próprios; valores de verdade e bivalência; quantificação; funções de verdade; verdade lógica; identidade; tautologia; o raciocínio matemático; a natureza da inferência; o cepticismo e o solipsismo; a indução; as constantes lógicas; a negação; a forma lógica; as leis da ciência; o número. (shrink)

It is usually accepted that deductions are non-informative and monotonic, inductions are informative and nonmonotonic, abductions create hypotheses but are epistemically irrelevant, and both deductions and inductions can’t provide new insights. In this article, I attempt to provide a more cohesive view of the subject with the following hypotheses: (1) the paradigmatic examples of deductions, such as modus ponens and hypothetical syllogism, are not inferential forms, but coherence requirements for inferences; (2) since any reasoner aims to be coherent, any inference (...) must be deductive; (3) a coherent inference is an intuitive process where the premises should be taken as sufficient evidence for the conclusion, which on its turn should be viewed as necessary evidence for the premises in some modal range; (4) inductions, properly understood, are abductions, but there are no abductions beyond the fact that in any inference the conclusion should be regarded as necessary evidence for the premises; (5) monotonicity is not only compatible with the retraction of past inferences given new information, but it is a requirement for it; (6) this explanation of inferences holds true for discovery processes, predictions and trivial inferences. (shrink)

This dissertation is about the structure of thought. Following Gottlob Frege, I define a thought as the sort of content relevant to determining whether an assertion is true or false. The historical component of the dissertation involves interpreting Frege’s actual views on the structure of thought. I argue that Frege did not think that a thought has a unique decomposition into its component senses, but rather the same thought can be decomposed into senses in a variety of distinct ways. I (...) extend Frege’s position and use it to develop an account of the hierarchy of senses, the senses expressed by indexicals and demonstratives, and the distinction between logical and non-logical structure. I also discuss various connections with the nature of meta-representation, our capacity for reflective judgment, some aspects of the structure of conscious experience, the way we perceive regions of space and durations of time, and our conscious awareness of our own perceptions and events of thinking. (shrink)

This paper asks whether a necessity can be the source of necessity. According to an influential argument due to Simon Blackburn, it cannot. This paper argues that although Blackburn fails to show that a necessity cannot be the source of necessity, extant accounts fail to establish that it is, with particular focus on Bob Hale’s essentialist theory and Christopher Peacocke’s ‘principle-based’ theory of modality. However, the paper makes some positive suggestions for what a satisfactory answer to the challenge must look (...) like. (shrink)

What is commonly referred to as the Adoption Problem is a challenge to the idea that the principles of logic can be rationally revised. The argument is based on a reconstruction of unpublished work by Saul Kripke. As the reconstruction has it, Kripke extends the scope of Willard van Orman Quine's regress argument against conventionalism to the possibility of adopting new logical principles. In this paper we want to discuss the scope of this challenge. Are all revisions of logic subject (...) to the Adoption Problem? If not, are there significant cases of logical revision that are subject to the Adoption Problem? We will argue that both questions should be answered negatively. (shrink)

In this talk I present the main results from Anta (2021), namely, that the theoretical division between Boltzmannian and Gibbsian statistical mechanics should be understood as a separation in the epistemic capabilities of this physical discipline. In particular, while from the Boltzmannian framework one can generate powerful explanations of thermal processes by appealing to their microdynamics, from the Gibbsian framework one can predict observable values in a computationally effective way. Finally, I argue that this statistical mechanical schism contradicts the Hempelian (...) (1958) thesis that the predictive power of a scientific theory is directly proportional to its explanatory potential, and vice versa. (shrink)

Lewis Carroll in “What the Tortoise Said to Achilles?” questioning one of the most important basis of logic and by narrating a fanciful dialog asks why we should move from premises to the conclusion. Is logic itself enough to justify the use of logic or we need something beyond logic to do that. In this article, two main approaches have been considered. First, the logical approach which Bertrand Russell is its most important member, and second, the social-internalism approach which Peter (...) Winch advocates. These two main philosophers have referred several times to Carroll’s article. According to Russell, analyzing logic is sufficient to explain why consequent will infer from premises, and on the other hand, Winch and his followers think every inference has a root in the historic understanding of life and if this understanding fails, logic will fall apart too. I will make some objections to both of these. In the end, I propose that the solution is to return to formal logic. If formal logic understood well, there won’t be any need to seek another logic to teach us how to use logic. Valid formal inferences are what logic consists of and if someone violates these inferences, he is out of the boundaries of logic. (shrink)

This thesis investigates the metaphysical nature of necessity. My study focuses primarily on the reduction of metaphysical necessity and the question of whether a necessary truth can be reductively defined. Theodore Sider develops a new reductive account of metaphysical necessity. Unfortunately, the multiple realizability problem posed by Jonathan Schaffer undermines the credibility of Sider’s account. This underlies my motivation to search for a revised Siderian account of necessity. On this basis, I propose a modified version of Sider’s account and argue (...) that analytic, natural-kind and micro-reduction truths are necessary truths if and only if they express the same states of affairs as logical truths. Since logical truths are necessary truths, analytic, natural-kind and micro-reduction truths are necessary truths as well. In this thesis, I will proceed as follows. Chapter 1 introduces Sider’s account of necessity. In particular, I focus on his analysis of the necessity of a micro-reduction truth. His analysis is largely constitutive of the notion of a metaphysical semantics and some associated notions. I reconstruct his analysis and articulate his metaphysical semantics and the associated notions. Chapter 2 presents and clarifies the multiple realizability problem of Schaffer. His critique shows that Sider’s metaphysical semantics cannot handle multiple realizability. Sider refutes this claim by arguing that the multiple realizability problem is a problem for his analysis of the necessity of a micro-reduction truth, not for his metaphysical semantics itself. This is a good starting point to propound a modified account of necessity. Chapter 3 proposes and articulates my modified analysis of the necessity of a micro-reduction, where I show that the necessity of a micro-reduction truth can be reductively defined without appeal to Sider’s metaphysical semantics. I argue that analytic, natural-kind and microreduction truths are necessary truths if and only if they express the same states of affairs as logical truths. Logical truths are necessary and so are they. After that, I consider a potential objection to my modified account and attempt to respond to it. (shrink)

This project is an investigation into the prospects for an antirealist theory of essence. Essentialism is the claim that at least some things have some of their properties essentially. Essentialist discourse includes claims such as “Socrates is essentially human”, and “Socrates is accidentally bearded”. Historically, there are two ways of interpreting essentialist discourse. I call these positions ‘modal essentialism’ and ‘neo-Aristotelian essentialism’. According to modal essentialism, for Socrates to be essentially human is for it to be necessary that he be (...) a human if he exists, and for Socrates to accidentally have a beard is for it to be contingent that Socrates has a beard if he exists. According to neo-Aristotelian essentialism, objects have definitions in something like the way words do. For Socrates to be essentially human but accidentally bearded is for it to be part of the definition of Socrates that he is human, but not part of that definition that he is bearded. I argue that both are susceptible to antirealist interpretation. This thesis sets about showing that this is the case. In Chapters One and Two I investigate neo-conventionalist theories of modality, in the hope of using such a position to develop an antirealist modal essentialism. In Chapter Three I discuss the debate between modal and neo-Aristotelian essentialism and conclude that it is by no means settled. In Chapter Four I develop an antirealist neo-Aristotelian essentialism based on the mechanism of one of the neo-conventionalist accounts of modality. In Chapter Five I argue that this account is in a better position to give an essentialist theory of necessity than its realist counterparts. I conclude that, regardless of whether one is a modal or neo-Aristotelian essentialist, antirealist essentialism is a viable theory of essence that is worthy of consideration in contemporary debate. (shrink)

Causal theory of knowledge has been used by some theoreticians who, dealing with the philosophy of mathematics, touched the subject of mathematical knowledge. Some of them discuss the necessity of the causal condition for justification, which creates the grounds for renewing the old conflict between empiricists and rationalists. Emphasizing the condition of causality as necessary for justifiability, causal theory has provided stimulus for the contemporary empiricists to venture on the so far unquestioned cognitive foundations of mathematics. However, in what sense (...) can we speak about the justifiability as causality when it comes to mathematical knowledge? Can we justify the mathematical statement 2+2=4 by means of causality-perceptibility? Do we need perceptibility, a visual image of apples and marbles we add up in our first mathematics lesson, in order to know that statement? Does the same go with the statement that any two points can be joined by a straight line, and that the sum of angles in any triangle is the angle the measure of which equals the sum of the measures of the two right angles? Even though the major part of this article offers a review of the attitudes of various authors who endeavor to discuss the application of the causal theory to the problem of understanding of mathematical knowledge, it advocates the idea that knowledge expressed in a mathematical statement is acquired and transmitted by evidence. Evidence is by itself a guarantee of truth. It convinces us of the accuracy of mathematical truths. Proving, we find out. The greatest part of what we know is based on evidence of the previous knowledge . Due to the previous knowledge, we can say that knowledge in mathematics is in itself different from the knowledge in empirical sciences, i.e. it does not require causal relation that is considered necessary condition of knowing in those sciences.Uzročna teorija znanja iskorištena je od strane nekih teoretičara koji su se, baveći se filozofijom matematike, dotakli teme matematičkog znanja. Neki od njih govore o nužnosti uzročnog uvjeta za opravdanje, čime se stvaraju uvjeti za obnavljanje starog sukoba empirista i racionalista. Uzročna teorija je, isticanjem uvjeta uzročnosti kao nužnog za opravdanost, dala poticaj suvremenim empiristima da krenu čak i na do tada nedodirljive spoznajne temelje matematike. Međutim, u kom smislu možemo govoriti o opravdanosti kao uzročnosti kad je riječ o matematičkom znanju? Da li uzročnošću-čulnošću možemo opravdati matematički iskaz 2+2=4? Je li nam za znanje tog iskaza neophodna čulnost, vizualna predodžba jabuka ili klikera koje zbrajamo na našim prvim satovima matematike u školi? Stoje li stvari isto i s iskazom da se kroz bilo koje dvije točke može povući točno jedan pravac, ili da je zbroj kutova bilo kojeg trokuta kut čija je mjera jednaka zbroju mjera dvaju pravih kutova? Iako je u ovom radu, uglavnom, dan pregled stavova autora koji pokušavaju govoriti o primjeni uzročne teorije u shvaćanju matematičkog znanja, ideja koja se podržava u njemu jest da je znanje, iskazano matematičkim tvrđenjem, dobiveno i preneseno dokazom. Dokaz, sam po sebi, jamac je istine. On nas uvjerava u točnost matematičkih tvrdnji. Dokazujući spoznajemo. Najveći dio onoga što znamo zasnovano je dokazom na prethodnim znanjima . Zbog prethodnog možemo reći da je znanje u matematici po svojoj prirodi drugačije od znanja u empirijskim znanostima, to jest da ne iziskuje uzročnu vezu koja se smatra nužnim uvjetom za znanje u tim znanostima. (shrink)

Christine Korsgaard has attempted to defend a distinct approach to metaethics – Neo-Kantian Constructivism. Not only does she present a positive case for her own view, she also attacks existing metaethical positions and even the disctinctions that metaethics has traditionally relied on. This thesis is a sustained examination of this position. I consider whether Korsgaard can legitimately claim to be offering a metaethical position at all, providing her with some defence against the scepticism of some metaethicists. I also examine her (...) attacks on traditional metaethical positions. I argue that her attack on moral realism can be avoided if the realism on offer takes a particular form. In the case of expressivism I claim that Korsgaard’s attack, though not fully developed in her work, motivates an examination of contemporary hybrid-expressivist theories. I argue that these are, as of yet, no advance over their non-hybrid cousins. Finally I examine Korsgaard’s own position, attempting to make it clearer by combining her claims with a framework developed by Crispin Wright for judgement-dependent qualities. This gives Korsgaard her best chance of a distinctive metaethical position. Ultimately, though, the Neo-Kantian approach to morality fails. (shrink)

A noção de analiticidade teve um papel central em vários debates filosóficos, em particular durante a primeira metade do século XX. Na sequência do influente artigo de W. V. Quine “Dois Dogmas do empirismo” (1951), a noção passou a ser vista com grande cepticismo. Mais recentemente, Paul Boghossian, no artigo “Analiticidade Reconsiderada” (1996), propôs uma forma de compreender a noção que é, putativamente, imune às críticas de Quine. O interesse na noção de analiticidade ficou desta forma renovado, assim como a (...) sua centralidade no debate acerca da possibilidade do conhecimento a priori. O principal objectivo deste artigo consiste em introduzir a noção de analiticidade e os principais problemas que esta enfrenta. (shrink)

Within his overarching program aiming to defend an epistemic conception of analyticity, Boghossian (1996 and 1997) has offered a clear-cut explanation of how we can acquire a priori knowledge of logical truths and logical rules through implicit definition. The explanation is based on a special template or general form of argument. Ebert (2005) has argued that an enhanced version of this template is flawed because a segment of it is unable to transmit warrant from its premises to the conclusion. This (...) article aims to defend the template from this objection. We provide an accurate description of the type of non-transmissivity that Ebert attributes to the template and clarify why this is a novel type of non-transmissivity. Then, we argue that Jenkins (2008)’s response to Ebert fails because it focuses on doxastic rather than propositional warrant. Finally, we rebut Ebert’s objection on Boghossian’s behalf by showing that it rests on an unwarranted assumption and is internally incoherent. (shrink)

I argue that Quine’s early critique of Carnap’s conventionalism is in serious tension with the holism of "Two Dogmas of Empiricism", since his critique of convention- alism makes a compelling case for a privileged status either for logic, or for some other principle by means of which to derive consequences. Based on this, I call for a modification of Quinean holism, on grounds internal to Quine’s views. The result motivates a rehabilitation of Carnap’s notion of framework principles, and a rethinking (...) of logic as a kind of relativised a priori. (shrink)

The following study aims to articulate the key problems, doctrines, concepts and contributions of the conventionalist philosophers. Following the preliminary clarifications, the main body of this dissertation will proceed to a critical and analytical survey of key conventionalist philosophers and their contribution to the development of the convention­ alist outlook. This study will conclude with a brief statement about some of the important contributions to epistemology that can be traced to the work of conventionalists.

Recently, game theory and evolutionary game theory - mathematical frameworks from economics and biology designed to model and explain interactive behavior - have proved fruitful tools for philosophers in areas such as ethics, philosophy of language, social epistemology, and political philosophy. This methodological osmosis is part of a trend where philosophers have blurred disciplinary lines to import the best epistemic tools available. In this vein, experimental philosophers have drawn on practices from the social sciences, and especially from psychology, to expand (...) philosophy's grasp on issues from morality to consciousness. We argue that the recent prevalence of formal work on human interaction in philosophy opens the door for new methods in experimental philosophy. In particular, we discuss methods from experimental economics, focusing on a small literature we have been developing investigating signaling and communication in humans. We describe results from a novel experiment showing how environmental structure can shape signaling behavior. (shrink)

This paper describes a class of idealized models that illuminate minimal conditions for inequity. Some such models will track the actual causal factors that generate real world inequity. Others may not. Whether or not these models do track these real-world factors is irrelevant to the epistemic role they play in showing that minimal commonplace factors are enough to generate inequity. In such cases, it is the fact that the model does not fit the world that makes it a particularly powerful (...) argumentative tool. As I will argue, this epistemic role is a particularly important one when it comes to modeling inequity, because such models are often also aimed at interventions to stop it. Given this, it is crucial to know if we intervene on the current causes of inequity, what other, common social factors might continue to contribute to it. (shrink)