Non‐classical logicians do not typically reject classically valid logical principles across the board. In fact, they sometimes suggest that their preferred logic recovers classical reasoning in most circumstances. This idea has come to be known in the literature as ‘classical recapture’. Recently, classical logicians have raised various doubts about it. The main problem is said to be that no rigorous explanation has been given of how is it exactly that classical logic can be recovered. The goal of the paper is (...) to address this problem. First, I discuss a number of different ways to characterize the idea of classical recapture and I examine how far it can be pushed. Secondly, I argue that a palatable form of classical recapture is given by the thought that classical logic can be retained for statements that are grounded (in Kripke’s sense). To substantiate this view I provide a formal fixed‐point semantics for a language containing a predicate standing for the concept of groundedness and I address a couple of objections that have been deployed against the claim that classical recapture can aid the non‐classical logician’s cause. (shrink)

Adding a transparent truth predicate to a language completely governed by classical logic is not possible. The trouble, as is well-known, comes from paradoxes such as the Liar and Curry. Recently, Cobreros, Egré, Ripley and van Rooij have put forward an approach based on a non-transitive notion of consequence which is suitable to deal with semantic paradoxes while having a transparent truth predicate together with classical logic. Nevertheless, there are some interesting issues concerning the set of metainferences validated by this (...) logic. In this paper, we show that this logic, once it is adequately understood, is weaker than classical logic. Moreover, the logic is in a way similar to the paraconsistent logic LP. (shrink)

It is not uncommon among theorists favoring a deviant logic on account of the semantic paradoxes to subscribe to an idea that has come to be known as ‘classical recapture’. The main thought underpinning it is that non-classical logicians are justified in endorsing many instances of the classically valid principles that they reject. Classical recapture promises to yield an appealing pair of views: one can attain naivety for semantic concepts while retaining classicality in ordinary domains such as mathematics. However, Julien (...) Murzi and Lorenzo Rossi have recently suggested that revisionary approaches to truth breed revenge paradoxes when they are coupled with the thought that classical reasoning can be recaptured in certain circumstances. What’s novel about the paradoxes they put forward is that they cannot be dismissed so easily. The concepts used to generate these paradoxes—those of paradoxicality and unparadoxicality—are concepts that non-classical theorists need in order to offer a diagnosis of the truth-theoretic paradoxes. My goal in this paper is to argue that non-classical theorists can represent the concept of paradoxicality without falling prey to revenge paradoxes. In particular, I will show how to provide a formal fixed-point semantics for a language extended with a paradoxicality predicate that adequately expresses the non-classical logician’s notion of paradoxicality. (shrink)

In the literature on self-referential paradoxes one of the hardest and most challenging problems is that of revenge. This problem can take many shapes, but, typically, it besets non-classical accounts of some semantic notion, such as truth, that depend on a set of classically defined meta-theoretic concepts, like validity, consistency, and so on. A particularly troubling form of revenge that has received a lot of attention lately involves the concept of validity. The difficulty lies in that the non-classical logician cannot (...) accept her own definition of validity because it is given in a classical meta-theory. It is often suggested that this mismatch between the consequence relation of the account being espoused and the consequence relation of the meta-theory is a serious embarrassment. The main goal of the paper is to explore whether certain substructural accounts of the paradoxes can avoid this sort of embarrassment. Typically, these accounts are expressively incomplete, since they cannot assert in the object language that certain invalid arguments are in fact invalid. To overcome this difficulty I develop a novel type of hybrid proof-procedure, one that takes invalidities to be just as fundamental as validities. I prove that this proof-procedure enjoys a number of interesting properties and I analyze the prospects of applying it to languages capable of expressing self-referential statements. (shrink)

The paper generalizes Van McGee's well-known result that there are many maximal consistent sets of instances of Tarski's schema to a number of non-classical theories of truth. It is shown that if a non-classical theory rejects some classically valid principle in order to avoid the truth-theoretic paradoxes, then there will be many maximal non-trivial sets of instances of that principle that the non-classical theorist could in principle endorse. On the basis of this it is argued that the idea of classical (...) recapture, which plays such an important role for non-classical logicians, can only be pushed so far. (shrink)

The idea of classical recapture has played a prominent role for non-classical logicians. In the specific case of non-classical theories of truth, although we know that it is not possible to retain classical logic for every statement involving the truth predicate, it is clear that for many such statements this is in principle feasible, and even desirable. What is not entirely obvious or well-known is how far this idea can be pushed. Can the non-classical theorist retain classical logic for every (...) non-paradoxical statement? If not, is she forced to settle for a very weak form of Classical Recapture, or are there robust versions of classical recapture available to her? These are the main questions that I will address in this paper. As a test case I will consider a paracomplete account of the truth-theoretic paradoxes and I will argue for two claims. First, that it is not possible to retain the law of excluded middle for every non-paradoxical statement. Secondly, that there are no robust versions of classical recapture available to the paracomplete logician. (shrink)

One of the most fruitful applications of substructural logics stems from their capacity to deal with self-referential paradoxes, especially truth-theoretic paradoxes. Both the structural rules of contraction and the rule of cut play a crucial role in typical paradoxical arguments. In this paper I address a number of difficulties affecting noncontractive approaches to paradox that have been discussed in the recent literature. The situation was roughly this: if you decide to go substructural, the nontransitive approach to truth offers a lot (...) of benefits that are not available in the noncontractive account. I sketch a noncontractive theory of truth that has these benefits. In particular, it has both a proof- and a model-theoretic presentation, it can be extended to a first-order language, and it retains every classically valid inference. (shrink)

Our main goal is to investigate whether the infinitary rules for the quantifiers endorsed by Elia Zardini in a recent paper are plausible. First, we will argue that they are problematic in several ways, especially due to their infinitary features. Secondly, we will show that even if these worries are somehow dealt with, there is another serious issue with them. They produce a truth-theoretic paradox that does not involve the structural rules of contraction.

The goal of the paper is to discuss whether substructural non-contractive accounts of the truth-theoretic paradoxes can be philosophically motivated. First, I consider a number of explanations that have been offered to justify the failure of contraction and I argue that they are not entirely compelling. I then present a non-contractive theory of truth that I’ve proposed elsewhere. After looking at some of its formal properties, I suggest an explanation of the failure of structural contraction that is compatible with it.

ABSTRACT There are many ways of understanding what it is for an argument to be valid. Although we usually identify the concept of validity with logical validity and, in turn, we typically take this to capture the notion of necessary preservation of truth in virtue of logical form, this is just one way in which validity can be explained. A different understanding of the notion of validity that has received some attention recently is based on the idea that an argument (...) is valid just in case accepting its premises is incoherent with rejecting its conclusion. The main claim of the paper will be that, under this understanding of the notion of validity, the usual reasons to privilege a treatment of validities over a treatment of invalidities loose much of their force. Validity and invalidity are on a par, which means that there are no strong reasons to treat validities primitively and to define invalidities in terms of them. (shrink)

Our main goal is to investigate whether the infinitary rules for the quantifiers endorsed by Elia Zardini in a recent paper are plausible. First, we will argue that they are problematic in several ways, especially due to their infinitary features. Secondly, we will show that even if these worries are somehow dealt with, there is another serious issue with them. They produce a truth-theoretic paradox that does not involve the structural rules of contraction.

It is part of the current wisdom that the Liar and similar semantic paradoxes can be taken care of by the use of certain non-classical multivalued logics. In this paper I want to suggest that bivalent logic can do just as well. This is accomplished by using a non-deterministic matrix to define the negation connective. I show that the systems obtained in this way support a transparent truth predicate. The paper also contains some remarks on the conceptual interest of such (...) systems. (shrink)

Rejecting the Cut rule has been proposed as a strategy to avoid both the usual semantic paradoxes and the so-called v-Curry paradox. In this paper we consider if a Cut-free theory is capable of accurately representing its own notion of validity. We claim that the standard rules governing the validity predicate are too weak for this purpose and we show that although it is possible to strengthen these rules, the most obvious way of doing so brings with it a serious (...) problem: an internalized version of Cut can be proved for a Curry-like sentence. We also evaluate a number of possible ways of escaping this difficulty. (shrink)

Thought: A Journal of Philosophy, EarlyView.

A lot has been written on solutions to the semantic paradoxes, but very little on the topic of general theories of paradoxicality. The reason for this, we believe, is that it is not easy to disentangle a solution to the paradoxes from a specific conception of what those paradoxes consist in. This paper goes some way towards remedying this situation. We first address the question of what one should expect from an account of paradoxicality. We then present one conception of (...) paradoxicality that has been offered in the literature: the fixed-point conception. According to this conception, a statement is paradoxical if it cannot obtain a classical truth-value at any fixed-point model. In order to assess this proposal rigorously we provide a non-metalinguistic characterization of paradoxicality and we evaluate whether the resulting account satisfies a number of reasonable desiderata. (shrink)

In Kripke’s classic paper on truth it is argued that by adding a new semantic category different from truth and falsity it is possible to have a language with its own truth predicate. A substantial problem with this approach is that it lacks the expressive resources to characterize those sentences which fall under the new category. The main goal of this paper is to offer a refinement of Kripke’s approach in which this difficulty does not arise. We tackle this characterization (...) problem by letting certain sentences belong to more than one semantic category. We also consider the prospect of generalizing this framework to deal with languages containing vague predicates. (shrink)

My aim in this paper is to gather some evident in favor of the view that a general purge of self-reference is possible. I do this by considering a modal-epistemic version of the Liar Paradox introduced by Roy Cook. Using yabloesque techniques, I show that it is possible to transform this circular paradoxical construction (and other constructions as well) into an infinitary construction lacking any sort of circularity. Moreover, contrary to Cook’s approach, I think that this can be done without (...) using any controversial multimodal rules, i.e., the usual rules from normal epistemic and modal logic are enough to show the paradoxicality of the infinitary construction. Mi objetivo en este trabajo es ofrecer cierta evidencia a favor de la tesis según la cual una purga general de la autorreferencia es posible. Hago esto considerando una versión modal-epistémica de la Paradoja del mentiroso introducida por Roy Cook. usando técnicas yablescas, muestro que es posible transformar esta construcción paradójica circular (y también otras construcciones) en una construcción infinitaria que carece de cualquier forma de circularidad. más aún, en contra de la propuesta de Cook, muestro que esto puede hacerse sin utilizar ninguna regla multimodal controversial, esto es, las reglas usuales de la lógica modal y la lógica epistémica son suficientes para mostrar la paradojicidad de la construcción infinitaria. (shrink)

On July 31, 2017, a symposium on Ripley’s forthcoming book Uncut was held in Buenos Aires. Ripley presented the main ideas in the book and there were comments by some of the participants. After the symposium, many of us agreed that it would be a good idea to put together a volume to reflect some of the interesting discussions that took place there.

Some attempts have been made to block the Knowability Paradox and other modal paradoxes by adopting a type-theoretic framework in which knowledge and necessity are regarded as typed predicates. The main problem with this approach is that when these notions are simultaneously treated as predicates, a new kind of paradox appears. I claim that avoiding this paradox either by weakening the Knowability Principle or by introducing types for both predicates is rather messy and unattractive. I also consider the prospect of (...) using the truth predicate to emulate other modal notions. It turns out that this idea works quite well. (shrink)

En este trabajo presento un problema que afecta al programa neologicista que han defendido en varias ocasiones Crispin Wright y Bob Hale. En particular, argumento que Wright y Hale no han dado suficientes condiciones para separar las definiciones implícitas apropiadas como el principio de Hume de otras definiciones implícitas rivales como la aritmética de Peano de segundo orden. Sugiero, además, que esa tarea sólo puede realizarse adecuadamente si una de las condiciones propuestas es la condición de que toda definición implícita (...) sea unívoca. In this paper I consider a problem affecting the Neologicist Program advocated on many occasions by Bob Hale and Crispin Wright. In particular, I argue that Hale and Wright have not given enough conditions to separate appropriate implicit definitions such as Hume's Principle from rival implicit definitions like Second-Order Peano Arithmetic. I also suggest that this task can only be performed adequately if one of the proposed conditions is that every implicit definition be univocal. (shrink)

An old and well-known objection to non-classical logics is that they are too weak; in particular, they cannot prove a number of important mathematical results. A promising strategy to deal with this objection consists in proving so-called recapture results. Roughly, these results show that classical logic can be used in mathematics and other unproblematic contexts. However, the strategy faces some potential problems. First, typical recapture results are formulated in a purely logical language, and do not generalize nicely to languages containing (...) the kind of vocabulary that usually motivates non-classical theories—for example, a language containing a naïve truth predicate. Second, proofs of recapture results typically employ classical principles that are not valid in the targeted non-classical system; hence, non-classical theorists do not seem entitled to those results. In this paper, we analyze these problems and provide solutions on behalf of non-classical theorists. To address the first problem, we provide a novel kind of recapture result, which generalizes nicely to a truth-theoretic language. As for the second problem, we argue that it relies on an ambiguity and that, once the ambiguity is removed, there are no reasons to think that non-classical logicians are not entitled to their recapture results. (shrink)

Theories where truth is a naive concept fall under the following dilemma: either the theory is subject to Curry’s Paradox, which engenders triviality, or the theory is not trivial but the resulting conditional is too weak. In this paper we explore a number of theories which arguably do not fall under this dilemma. In these theories the conditional is characterized in terms of non-deterministic matrices. These non-deterministic theories are similar to infinitely-valued Łukasiewicz logic in that they are consistent and their (...) conditionals are quite strong. The difference is the following: while Łukasiewicz logic is \-inconsistent, the non-deterministic theories might turn out to be \-consistent. (shrink)

Recently, it has been observed that the usual type-theoretic restrictions are not enough to block certain paradoxes involving two or more predicates. In particular, when we have a self-referential language containing modal predicates, new paradoxes might appear even if there are type restrictions for the principles governing those predicates. In this article we consider two type-theoretic solutions to multimodal paradoxes. The first one adds types for each of the modal predicates. We argue that there are a number of problems with (...) most versions of this approach. The second one, which we favour, represents modal notions by using the truth predicate together with the corresponding modal operator. This way of doing things is not only useful because it avoids multimodal paradoxes, but also because it preserves the expressive capacity of the language. As an example of the sort of theory we have in mind, we provide a type-theoretic axiomatization that combines truth with necessity and knowledge. (shrink)

The goal of this paper is to review and critically discuss the philosophical aspects of probabilistic seismic hazard analysis (PSHA). Given that estimates of seismic hazard are typically riddled with uncertainty, diferent epistemic values (related to the pursuit of scientifc knowledge) compete in the selection of seismic hazard models, in a context infuenced by non-epistemic values (related to practical goals and aims) as well. We frst distinguish between the diferent types of uncertainty in PSHA. We claim that epistemic and nonepistemic (...) considerations are closely related in the selection of the appropriate estimate of seismic hazard by the experts. Finally, we argue that the division of scientifc responsibility among the experts can lead to responsibility gaps. This raises a problem for the ownership of the results (“no one’s model” problem) similar to the “problem of many hands” in the ethics of technology. We conclude with a plea for a close collaboration between philosophy and engineering. (shrink)

The aim of this paper is to clarify under what conditions a philosophical problem arises. I will describe two ways in which we might perceive a question as a problem. First, when we fnd ourselves inclined to believe in propositions that appear incompatible with each other. Second, when we fnd ourselves inclined to believe in propositions that seem incompatible with our desires. I will discuss both of these cases and articulate a didactic strategy – the Clash Strategy – which can (...) be used in order to plan and facilitate dialogic inquiry in the classroom. This strategy suggests introducing stimuli that will help students appreciate the clash that drives the philosophical question to be explored during the dialogue. In summary, this paper aims to ofer insights to all teachers interested in promoting dialogic inquiry, whether philosophical or otherwise, in education. (shrink)

This book discusses Aristotle’s notions of essence and substance as they are developed in Metaphysics ZH. I examine Aristotle's argument at length and defends an unorthodox interpretation according to which his motivation is to provide an answer against a conflation between criteria for existential priority (delivering substances as primary beings) and criteria for explanatory priority (delivering essences as primary principles).

Translation of Aristotle's Physics I-II into Portuguese, with commentaries. Tradução para o português dos livros I e II da Física de Aristóteles, com comentários.

This is an introductory handbook for some of the main themes around the notion of predication in Aristotle. It does not aim at being exhaustive, but only sketches some important lines about the subject; it contains an introductory essay, besides the translation (into Portuguese) and commentary of basic texts (such as Posterior Analytics I-22, Categories 1-5, Interpretation 1-6 etc.).

Translation of Aristotle's Posterior Analytics I into Portuguese, with a few notes, experimental glossary and introduction. The translation, which was made at 2003/4, was preliminary and its publication was intended to provide a didactic tool for courses as well as a provisional resource in research seminars. It needs some revision. I am currently working (slowly...) on the revision of the translation and a new revised one will surely appear at some point.

Translation of Aristotle's Metaphysics IV and VI, with notes. The translation is preliminary and intended as a provisional teaching tool to be also used in seminars and discussions with peers in order to reach a more elaborated version.

Translation of Aristotle's Posterior Analytics II into Portuguese, with a few notes, experimental glossary and introduction. The translation, which was made at 2002 (with a new printing in 2004), was preliminary and its publication was intended to provide a didactic tool for courses as well as a provisional resource in research seminars. It needs some revision. I am currently working (slowly...) on the revision of the translation and a new revised one will surely appear at some point.

Translation of Aristotle's Metaphysics I-III into Portuguese, with a few notes and introduction. The translation, which was made at 2007, is preliminary and its publication was intended to provide a didactic tool for courses as well as a provisional resource in research seminars. It needs some revision. I am currently working (slowly...) on the revision of the translation and a new revised one will surely appear at some point.

This book uses mathematical models of language to explain why there are certain gaps in language: things that we might expect to be able to say but can't. For instance, why can we say I ran for five minutes but not *I ran to the store for five minutes? Why is five pounds of books acceptable, but *five pounds of book not acceptable? What prevents us from saying *sixty degrees of water to express the temperature of the water in a (...) swimming pool when sixty inches of water can express its depth? And why can we not say *all the ants in my kitchen are numerous? The constraints on these constructions involve concepts that are generally studied separately: aspect, plural and mass reference, measurement, and distributivity. In this book, Lucas Champollion provides a unified perspective on these domains, connects them formally within the framework of algebraic semantics and mereology, and uses this connection to transfer insights across unrelated bodies of literature and formulate a single constraint that explains each of the judgments above. (shrink)

This note reproduces a brief article by Thomas Nixon Carver, a leading Progressive Era American economist on what was then called the ‘Negro Question’. This virtually unknown piece represents a striking in-stance of blaming the victim for her/his condition which is to be found in the economic literature of the period.

Translation of Aristotle’s Metaphysics IX and X (Theta & Iota) into Portuguese, with a few notes, experimental glossary and introduction. The translation, which was made at 2004, is preliminary and its publication was intended to provide a didactic tool for courses as well as a provisional resource in research seminars. It needs some revision. I am currently working (slowly...) on the revision of the translation and a new revised one will surely appear at some point.

If we are eventually to understand the capability of higher organisms for perceptual recognition, generalization, recall, and thinking, we must first have answers to three fundamental questions: 1. How is information about the physical world sensed, or detected, by the biological system? 2. In what form is information stored, or remembered? 3. How does information contained in storage, or in memory, influence recognition and behavior? The first of these questions is in the.

In this monograph we contrast two prominent models of education, Competence-Based Education (CBE), more recent and currently dominant in most school systems of the world, and Bildung-Oriented Education (BOE), once the basis of school systems of Northern Europe. CBE interprets learning as the acquisition of clearly definable and allegedly measurable competences, and is supported by supranational organisations, such as the OECD, which approach education from the perspective of the human capital theory. BOE instead characterises learning holistically as aimed at the (...) progressive articulation of a meaningful ‘big picture’ in the student’s mind. Emerged in Northern Europe under the influence of the ideals of the Enlightenment and Neo-Humanism of individual and collective autonomy and responsibility, BOE was subsequently enriched with a hermeneutical approach to teaching and socio-political objectives of emancipation and solidarity originating within Critical Theory. We argue that, in spite of its celebrated ‘scientificity’, CBE is internally incoherent and unreliable, contributes to structural forms of oppression and injustice, fosters social pathologies, and fails to provide students with the kind of intellectual autonomy they need as both human beings and citizens of our complex post-industrial societies. We also defend BOE from objections made by critical theorists, poststructuralists and postcolonial thinkers, and argue that it is a coherent and flexible model of education that endows students with autonomy and responsibility, and can help heal social pathologies. (shrink)

This article uses social dominance theory (SDT) to explore the dynamic and systemic nature of the initiation and maintenance of organizational corruption. Rooted in the definition of organizational corruption as misuse of power or position for personal or organizational gain, this work suggests that organizational corruption is driven by the individual and institutional tendency to structure societies as group-based social hierarchies. SDT describes a series of factors and processes across multiple levels of analysis that systemically contribute to the initiation and (...) maintenance of social hierarchies and associated power inequalities, favoritism, and discrimination. I posit that the same factors and processes also contribute to individuals’ lower awareness of the misuse of power and position within the social hierarchies, leading to the initiation and maintenance of organizational corruption. Specifically, individuals high in social dominance orientation, believing that they belong to superior groups, are likely to be less aware of corruption because of their feeling of entitlement to greater power and their desire to maintain dominance even if that requires exploiting others. Members of subordinate groups are also likely to have lower awareness of corruption if they show more favoritism toward dominant group members to enhance their sense of worth and preserve social order. Institutions contribute to lower awareness of corruption by developing and enforcing structures, norms, and practices that promote informational ambiguity and maximize focus on dominance and promotion. Dynamic coordination among individuals and institutions is ensured through the processes of person-environment fit and legitimizing beliefs, ideologies, or rationalizations. (shrink)

In this paper I discuss a new kind of hinge epistemology which is called transcendental hinge epistemology. According to this view, hinges are immune from doubt because it is impossible to doubt them coherently, and this impossibility arises because any attempt to doubt them will presuppose their truth. Such an immunity is possessed only by inescapable hinges, that is, hinges that must be presupposed in every inquiry. I will argue that current hinge epistemologies fail to provide a satisfactory anti-sceptical strategy (...) because they focus on escapable hinges, that is, hinges with respect to which one can entertain coherent doubts. (shrink)

Translation of Aristotle's Metaphysics V.1-8 with a few notes.

Tradução preliminar em pré-print. A Tradução definitiva é a de 2009.

In Posterior Analytics 71b9 12, we find Aristotle’s definition of scientific knowledge. The definiens is taken to have only two informative parts: scientific knowledge must be knowledge of the cause and its object must be necessary. However, there is also a contrast between the definiendum and a sophistic way of knowing, which is marked by the expression “kata sumbebekos”. Not much attention has been paid to this contrast. In this paper, I discuss Aristotle’s definition paying due attention to this contrast (...) and to the way it interacts with the two conditions presented in the definiens. I claim that the “necessity” condition ammounts to explanatory appropriateness of the cause. (shrink)