I am professor of Philosophy in the University of Navarra where I took my PhD back in 2007 under the supervision of Prof. María Cerezo. My thesis is about vagueness and supervaluationism – the best bit was published in Studia Logica 2008. I spent one year, 2008, in UCL and the Institute of Philosophy London as a postdoc. I've been also visiting other places, recently the MCMP in LMU Munich with the support of the Humboldt Foundation. I am currently the coordinator of PLEXUS https://cordis.europa.eu/project/id/101086295
The supervaluationist theory of vagueness is committed to a particular notion of logical conseque... more The supervaluationist theory of vagueness is committed to a particular notion of logical consequence known as global validity. According to a recent objection, this notion of consequence is more problematic than is usually thought since i) it bears a commitment to some sort of bizarre inferences, ii) this commitment threatens the internal coherence of the theory and iii) we might find counterexamples to classically valid patterns of inference even in the absence of a definitely-operator (or similar device). As a consequence, the supervaluationist theory itself is in trouble. This paper discusses the objection.
Vagueness and Language Use. Palgrave McMillan, Oxford, 2010
This paper discusses Fara's so-called 'Paradox of Highe... more This paper discusses Fara's so-called 'Paradox of Higher-Order Vagueness' concerning supervaluationism. In the paper I argue that supervaluationism is not committed to global validity, as it is largely assumed in the literature, but to a weaker notion of logical consequence I call 'regional validity'. Then I show that the supervaluationist might solve Fara's paradox making use of this weaker notion of logical consequence. The paper is discussed by Delia Fara in the same volume.
In a recent paper, Barrio, Tajer and Rosenblatt establish a correspondence between metainferences... more In a recent paper, Barrio, Tajer and Rosenblatt establish a correspondence between metainferences holding in the strict-tolerant logic of transparent truth ST+ and inferences holding in the logic of paradox LP+. They argue that LP+ is ST+’s external logic and they question whether ST+’s solution to the semantic paradoxes is fundamentally different from LP+’s. Here we establish that by parity of reasoning, ST+ can be related to LP+’s dual logic K+. We clarify the distinction between internal and external logic and argue that while ST+’s nonclassicality can be granted, its self-dual character does not tie it to LP+ more closely than to K+.
The principle of tolerance characteristic of vague predicates is sometimes presented as a soft ru... more The principle of tolerance characteristic of vague predicates is sometimes presented as a soft rule, namely as a default which we can use in ordinary reasoning, but which requires care in order to avoid paradoxes. We focus on two ways in which the tolerance principle can be modeled in that spirit, using special consequence relations. The first approach relates tolerant reasoning to nontransitive reasoning; the second relates tolerant reasoning to nonmonotonic reasoning. We compare the two approaches and examine three specific consequence relations in relation to those, which we call: strict-to-tolerant entailment, pragmatic-to-tolerant entailment, and pragmatic-to-pragmatic entailment. The first two are nontransitive, whereas the latter two are nonmonotonic.
In his chapter ‘Non-transitive identity’ [8], Graham Priest develops a notion of non-transitive i... more In his chapter ‘Non-transitive identity’ [8], Graham Priest develops a notion of non-transitive identity based on a second-order version of \(LP\). Though we are sympathetic to Priest’s general approach to identity we think that the account can be refined in different ways. Here we present two such ways and discuss their appropriateness for a metaphysical reading of indefiniteness in connection to Evans’ argument.
This paper explores the relations between two logical approaches to vagueness: on the one hand th... more This paper explores the relations between two logical approaches to vagueness: on the one hand the fuzzy approach defended by Smith (2008), and on the other the strict-tolerant approach defended by Cobreros, Egré, Ripley and van Rooij (2012). Although the former approach uses continuum many values and the latter implicitly four, we show that both approaches can be subsumed under a common three-valued framework. In particular, we defend the claim that Smith's continuum many values are not needed to solve what Smith calls `the jolt problem', and we show that they are not needed for his account of logical consequence either. Not only are three values enough to satisfy Smith's central desiderata, but they also allow us to internalize Smith's closeness principle in the form of a tolerance principle at the object-language. The reduction, we argue, matters for the justification of many-valuedness in an adequate theory of vague language.
The supervaluationist theory of vagueness is committed to a particular notion of logical conseque... more The supervaluationist theory of vagueness is committed to a particular notion of logical consequence known as global validity. According to a recent objection, this notion of consequence is more problematic than is usually thought since i) it bears a commitment to some sort of bizarre inferences, ii) this commitment threatens the internal coherence of the theory and iii) we might find counterexamples to classically valid patterns of inference even in the absence of a definitely-operator (or similar device). As a consequence, the supervaluationist theory itself is in trouble. This paper discusses the objection.
Vagueness and Language Use. Palgrave McMillan, Oxford, 2010
This paper discusses Fara's so-called 'Paradox of Highe... more This paper discusses Fara's so-called 'Paradox of Higher-Order Vagueness' concerning supervaluationism. In the paper I argue that supervaluationism is not committed to global validity, as it is largely assumed in the literature, but to a weaker notion of logical consequence I call 'regional validity'. Then I show that the supervaluationist might solve Fara's paradox making use of this weaker notion of logical consequence. The paper is discussed by Delia Fara in the same volume.
In a recent paper, Barrio, Tajer and Rosenblatt establish a correspondence between metainferences... more In a recent paper, Barrio, Tajer and Rosenblatt establish a correspondence between metainferences holding in the strict-tolerant logic of transparent truth ST+ and inferences holding in the logic of paradox LP+. They argue that LP+ is ST+’s external logic and they question whether ST+’s solution to the semantic paradoxes is fundamentally different from LP+’s. Here we establish that by parity of reasoning, ST+ can be related to LP+’s dual logic K+. We clarify the distinction between internal and external logic and argue that while ST+’s nonclassicality can be granted, its self-dual character does not tie it to LP+ more closely than to K+.
The principle of tolerance characteristic of vague predicates is sometimes presented as a soft ru... more The principle of tolerance characteristic of vague predicates is sometimes presented as a soft rule, namely as a default which we can use in ordinary reasoning, but which requires care in order to avoid paradoxes. We focus on two ways in which the tolerance principle can be modeled in that spirit, using special consequence relations. The first approach relates tolerant reasoning to nontransitive reasoning; the second relates tolerant reasoning to nonmonotonic reasoning. We compare the two approaches and examine three specific consequence relations in relation to those, which we call: strict-to-tolerant entailment, pragmatic-to-tolerant entailment, and pragmatic-to-pragmatic entailment. The first two are nontransitive, whereas the latter two are nonmonotonic.
In his chapter ‘Non-transitive identity’ [8], Graham Priest develops a notion of non-transitive i... more In his chapter ‘Non-transitive identity’ [8], Graham Priest develops a notion of non-transitive identity based on a second-order version of \(LP\). Though we are sympathetic to Priest’s general approach to identity we think that the account can be refined in different ways. Here we present two such ways and discuss their appropriateness for a metaphysical reading of indefiniteness in connection to Evans’ argument.
This paper explores the relations between two logical approaches to vagueness: on the one hand th... more This paper explores the relations between two logical approaches to vagueness: on the one hand the fuzzy approach defended by Smith (2008), and on the other the strict-tolerant approach defended by Cobreros, Egré, Ripley and van Rooij (2012). Although the former approach uses continuum many values and the latter implicitly four, we show that both approaches can be subsumed under a common three-valued framework. In particular, we defend the claim that Smith's continuum many values are not needed to solve what Smith calls `the jolt problem', and we show that they are not needed for his account of logical consequence either. Not only are three values enough to satisfy Smith's central desiderata, but they also allow us to internalize Smith's closeness principle in the form of a tolerance principle at the object-language. The reduction, we argue, matters for the justification of many-valuedness in an adequate theory of vague language.
This is a three-week course on logic and paradoxes: classical logic, K3 and LP and also a bit of ... more This is a three-week course on logic and paradoxes: classical logic, K3 and LP and also a bit of ST. With Tableaux.
It's a second edition of a course I prepared three years ago. All materials have been revised and exercises where reformulated to provide instant feedback after submission.
The logic ST has been proposed to deal with paradoxes of vagueness and with the semantic paradoxe... more The logic ST has been proposed to deal with paradoxes of vagueness and with the semantic paradoxes. There is something very distinctive about ST: namely, it is classical logic for a classical language, but it provides ways of strengthening classical logic to deal with paradoxes. For example, the logic ST + (ST for a language with a transparent truth predicate and self-referential sentences) is a conservative extension of classical logic. That is, ST + is not only non-trivial, but it has exactly the same valid inferences as classical logic for the T-free fragment. How is this possible? Well, because ST + preserves all classically valid inferences but not some classical metainferences. The question then arises of exactly which are the metainferences of ST +. In a recent paper, Eduardo Barrio, Lucas Rosenblatt and Diego Tajer show that ST + metainferences are closely related to LP inferences. In this paper we review their result and put the connection in a broader context.
The logic ST has been proposed to deal with paradoxes of vagueness and with the semantic paradoxe... more The logic ST has been proposed to deal with paradoxes of vagueness and with the semantic paradoxes. There is something very distinctive about ST: namely, it is classical logic for a classical language, but it provides ways of strengthening classical logic to deal with paradoxes. For example, the logic ST + (ST for a language with a transparent truth predicate and self-referential sentences) is a conservative extension of classical logic. That is, ST + is not only non-trivial, but it has exactly the same valid inferences as classical logic for the T-free fragment. How is this possible? Well, because ST + preserves all classically valid inferences but not some classical metainferences. The question then arises of exactly which are the metainferences of ST +. In a recent paper, Eduardo Barrio, Lucas Rosenblatt and Diego Tajer show that ST + metainferences are closely related to LP inferences. In this paper we review their result and put the connection in a broader context.
Perhaps it's peacefully accepted that there must be finitely many sentences in natural language. ... more Perhaps it's peacefully accepted that there must be finitely many sentences in natural language. But still I find it puzzling, because the question, how many sentence are then? seems to have no definite answer. And this time this sort of indefiniteness can hardly be counted as "semantic".
I believe it can be easily shown that there are finitely many sentences in natural language. This... more I believe it can be easily shown that there are finitely many sentences in natural language. This is puzzling because the next question is: what is then that number? And to this question there seems to be no reasonable answer.
If God knew I were going to write this paper, was I able to refrain from writing it this morning?... more If God knew I were going to write this paper, was I able to refrain from writing it this morning? One possible response to this question is that God's knowledge does not take place in time and therefore He does not properly fore-know. According to this response, God knows absolutely everything, it's just that He knows everything outside of time. The so-called timeless solution was one of the influential responses to the foreknowledge problem in classical Christian Theology. This solution, however, seemed to lose support in the recent debate. For example, Pike claims that "the doctrine of God's timelessness entered Christian Theology (only) because Platonic thought was stylish at the time" (Pike, 1970, 190) and Hasker (2001) catalogues this as one of the minor solutions to the problem. One possible source for this general attitude towards timelessness is the thought that the very idea of timelessness is incoherent. In this paper I argue that that the timeless solution to the foreknowledge problem is congenial with the supervaluationist theory of branching time and that this formal framework provides, in fact, a precise characterization of the timeless solution to the foreknowledge problem. The views presented in this paper are in line with those of Kretzmann and Stump (1981), Leftow (1991) and De Florio and Frigerio (2015).
Se trata de una introducción en español a algunos temas de la filosofía de la lógica y las lógica... more Se trata de una introducción en español a algunos temas de la filosofía de la lógica y las lógicas no-clásicas.
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Papers by Pablo Cobreros
It's a second edition of a course I prepared three years ago. All materials have been revised and exercises where reformulated to provide instant feedback after submission.