This paper develops the idea that valid arguments are equivalent to true conditionals by combining Kripke’s theory of truth with the evidential account of conditionals offered by Crupi and Iacona. As will be shown, in a first-order language that contains a naïve truth predicate and a suitable conditional, one can define a validity predicate in accordance with the thesis that the inference from a conjunction of premises to a conclusion is valid when the corresponding conditional is true. The validity predicate (...) so defined significantly increases our expressive resources and provides a coherent formal treatment of paradoxical arguments. (shrink)

Since Saul Kripke’s influential work in the 1970s, the revisionary approach to semantic paradox—the idea that semantic paradoxes must be solved by weakening classical logic—has been increasingly popular. In this paper, we present a new revenge argument to the effect that the main revisionary approaches breed new paradoxes that they are unable to block.

We discuss the principles for a primitive, object-linguistic notion of consequence proposed by ) that yield a version of Curry’s paradox. We propose and study several strategies to weaken these principles and overcome paradox: all these strategies are based on the intuition that the object-linguistic consequence predicate internalizes whichever meta-linguistic notion of consequence we accept in the first place. To these solutions will correspond different conceptions of consequence. In one possible reading of these principles, they give rise to a notion (...) of logical consequence: we study the corresponding theory of validity by showing that it is conservative over a wide range of base theories: this result is achieved via a well-behaved form of local reduction. The theory of logical consequence is based on a restriction of the introduction rule for the consequence predicate. To unrestrictedly maintain this principle, we develop a conception of object-linguistic consequence, which we call grounded consequence, that displays a restriction of the structural rule of reflexivity. This construction is obtained by generalizing Saul Kripke’s inductive theory of truth. Grounded validity will be shown to satisfy several desirable principles for a naïve, self-applicable notion of consequence. (shrink)

This paper develops a trivalent semantics for indicative conditionals and extends it to a probabilistic theory of valid inference and inductive learning with conditionals. On this account, (i) all complex conditionals can be rephrased as simple conditionals, connecting our account to Adams's theory of p-valid inference; (ii) we obtain Stalnaker's Thesis as a theorem while avoiding the well-known triviality results; (iii) we generalize Bayesian conditionalization to an updating principle for conditional sentences. The final result is a unified semantic and probabilistic (...) theory of conditionals with attractive results and predictions. (shrink)

This paper develops a trivalent semantics for the truth conditions and the probability of the natural language indicative conditional. Our framework rests on trivalent truth conditions first proposed by Cooper (1968) and Belnap (1973) and it yields two logics of conditional reasoning: (i) a logic C of certainty-preserving inference; and (ii) a logic U for uncertain reasoning that preserves the probability of the premises. We show systematic correspondences between trivalent and probabilistic representations of inferences in either framework, and we use (...) the distinction between the two systems to cast light on the validity of inferences such as Modus Ponens, Or-To-If, and Conditional Excluded Middle. Specifically, the conditional behaves monotonically in C, but non-monotonically in U; Modus Ponens is valid in C, but valid in U only for non-nested conditionals. The result is a unified account of the semantics and epistemology of indicative conditionals that can be fruitfully applied to analyzing the validity of conditional inferences. (shrink)

Substructural logics and their application to logical and semantic paradoxes have been extensively studied. In the paper, we study theories of naïve consequence and truth based on a non-reflexive logic. We start by investigating the semantics and the proof-theory of a system based on schematic rules for object-linguistic consequence. We then develop a fully compositional theory of truth and consequence in our non-reflexive framework.

Contextualist approaches to the Liar Paradox postulate the occurrence of a context shift in the course of the Liar reasoning. In particular, according to the contextualist proposal advanced by Charles Parsons and Michael Glanzberg, the Liar sentence L doesn’t express a true proposition in the initial context of reasoning c, but expresses a true one in a new, richer context c', where more propositions are available for expression. On the further assumption that Liar sentences involve propositional quantifiers whose domains may (...) vary with context, the Liar reasoning is blocked. But why should context shift? We argue that the paradox involves principles of contextualist reflection that explain, by analogy with well-known reflection principles for arithmetic, why context must shift from c to c' in the course of the Liar reasoning. This provides a diagnosis of the Liar Paradox—one that equally applies to two revenge arguments against contextualist approaches, one recently advanced by Andrew Bacon, the other mentioned by Charles Parsons and more recently revived by Cory Juhl. (shrink)

This paper explores trivalent truth conditions for indicative conditionals, examining the “defective” truth table proposed by de Finetti and Reichenbach. On their approach, a conditional takes the value of its consequent whenever its antecedent is true, and the value Indeterminate otherwise. Here we deal with the problem of selecting an adequate notion of validity for this conditional. We show that all standard validity schemes based on de Finetti’s table come with some problems, and highlight two ways out of the predicament: (...) one pairs de Finetti’s conditional with validity as the preservation of non-false values, but at the expense of Modus Ponens; the other modifies de Finetti’s table to restore Modus Ponens. In Part I of this paper, we present both alternatives, with specific attention to a variant of de Finetti’s table proposed by Cooper and Cantwell. In Part II, we give an in-depth treatment of the proof theory of the resulting logics, DF/TT and CC/TT: both are connexive logics, but with significantly different algebraic properties. (shrink)

Beall and Murzi :143–165, 2013) introduce an object-linguistic predicate for naïve validity, governed by intuitive principles that are inconsistent with the classical structural rules. As a consequence, they suggest that revisionary approaches to semantic paradox must be substructural. In response to Beall and Murzi, Field :1–19, 2017) has argued that naïve validity principles do not admit of a coherent reading and that, for this reason, a non-classical solution to the semantic paradoxes need not be substructural. The aim of this paper (...) is to respond to Field’s objections and to point to a coherent notion of validity which underwrites a coherent reading of Beall and Murzi’s principles: grounded validity. The notion, first introduced by Nicolai and Rossi, is a generalisation of Kripke’s notion of grounded truth, and yields an irreflexive logic. While we do not advocate the adoption of a substructural logic, we take the notion of naïve validity to be a legitimate semantic notion that points to genuine expressive limitations of fully structural revisionary approaches. (shrink)

This paper develops the idea that valid arguments are equivalent to true conditionals by combining Kripke’s theory of truth with the evidential account of conditionals offered by Crupi and Iacona. As will be shown, in a first-order language that contains a naïve truth predicate and a suitable conditional, one can define a validity predicate in accordance with the thesis that the inference from a conjunction of premises to a conclusion is valid when the corresponding conditional is true. The validity predicate (...) so defined significantly increases our expressive resources and provides a coherent formal treatment of paradoxical arguments. (shrink)

We present a revenge argument for non-reflexive theories of semantic notions – theories which restrict the rule of assumption, or initial sequents of the form φ ⊩ φ. Our strategy follows the general template articulated in Murzi and Rossi [21]: we proceed via the definition of a notion of paradoxicality for non-reflexive theories which in turn breeds paradoxes that standard non-reflexive theories are unable to block.

Deflationists argue that ‘true’ is merely a logico-linguistic device for expressing blind ascriptions and infinite generalisations. For this reason, some authors have argued that deflationary truth must be conservative, i.e. that a deflationary theory of truth for a theory S must not entail sentences in S’s language that are not already entailed by S. However, it has been forcefully argued that any adequate theory of truth for S must be non-conservative and that, for this reason, truth cannot be deflationary :493–521, (...) 1998; Ketland in Mind 108:69–94, 1999). We consider two defences of conservative deflationism, respectively proposed by Waxman :429–463, 2017) and Tennant :551–582, 2002), and argue that they are both unsuccessful. In Waxman’s hands, deflationists are committed either to a non-purely expressive notion of truth, or to a conception of mathematics that does not allow them to justifiably exclude non-conservative theories of truth. Tennant’s conservative deflationism fares no better: if deflationist truth must be conservative over arithmetic, it can be shown to collapse into a non-conservative variety of deflationism. (shrink)

It is often argued that fully structural theories of truth and related notions are incapable of expressing a nonstratified notion of defectiveness. We argue that recently much-discussed non-contractive theories suffer from the same expressive limitation, provided they identify the defective sentences with the sentences that yield triviality if they are assumed to satisfy structural contraction.

The sentences employed in semantic paradoxes display a wide range of semantic behaviours. However, the main theories of truth currently available either fail to provide a theory of paradox altogether, or can only account for some paradoxical phenomena by resorting to multiple interpretations of the language. In this paper, I explore the wide range of semantic behaviours displayed by paradoxical sentences, and I develop a unified theory of truth and paradox, that is a theory of truth that also provides a (...) unified account of paradoxical sentences. The theory I propose here yields a threefold classification of paradoxical sentences – liar-like sentences, truth-teller-like sentences, and revenge sentences. Unlike existing treatments of semantic paradox, the theory put forward in this paper yields a way of interpreting all three kinds of paradoxical sentences, as well as unparadoxical sentences, within a single model. (shrink)

Revenge arguments purport to show that any proposed solution to the semantic paradoxes generates new paradoxes that prove that solution to be inadequate. In this paper, I focus on revenge arguments that employ the model-theoretic semantics of a target theory and I argue, contra the current revenge-theoretic wisdom, that they can constitute genuine expressive limitations. I consider the anti-revenge strategy elaborated by Field and argue that it does not offer a way out of the revenge problem. More generally, I argue (...) that the difference between ‘standard’ and ‘revenge’ paradoxes is ill-conceived and should be abandoned. This will contribute to show that the theories that provide a uniform account of truth and other semantic notions are the ones best equipped to avoid the paradoxes altogether—‘standard’ and ‘revenge’ alike. (shrink)

Substructural logics and their application to logical and semantic paradoxes have been extensively studied, but non-reflexive systems have been somewhat neglected. Here, we aim to fill this lacuna, at least in part, by presenting a non-reflexive logic and theory of naive consequence (and truth). We also investigate the semantics and the proof-theory of the system. Finally, we develop a compositional theory of truth (and consequence) in our non-reflexive framework.

Kripke’s theory of truth, 690–716; 1975) has been very successful but shows well-known expressive difficulties; recently, Field has proposed to overcome them by adding a new conditional connective to it. In Field’s theories, desirable conditional and truth-theoretic principles are validated that Kripke’s theory does not yield. Some authors, however, are dissatisfied with certain aspects of Field’s theories, in particular the high complexity. I analyze Field’s models and pin down some reasons for discontent with them, focusing on the meaning of the (...) new conditional and on the status of the principles so successfully recovered. Subsequently, I develop a semantics that improves on Kripke’s theory following Field’s program of adding a conditional to it, using some inductive constructions that include Kripke’s one and feature a strong evaluation for conditionals. The new theory overcomes several problems of Kripke’s one and, although weaker than Field’s proposals, it avoids the difficulties that affect them; at the same time, the new theory turns out to be quite simple. Moreover, the new construction can be used to model various conceptions of what a conditional connective is, in ways that are precluded to both Kripke’s and Field’s theories. (shrink)

Semantic and soritical paradoxes display remarkable family resemblances. For one thing, several non-classical logics have been independently applied to both kinds of paradoxes. For another, revenge paradoxes and higher-order vagueness—among the most serious problems targeting solutions to semantic and soritical paradoxes—exhibit a rather similar dynamics. Some authors have taken these facts to suggest that truth and vagueness require a unified logical framework, or perhaps that the truth predicate is itself vague. However, a common core of semantic and soritical paradoxes has (...) not been identified yet, and no explanation of their relationships has been provided. Here we aim at filling this lacuna, in the framework of many-valued logics. We provide a unified diagnosis of semantic and soritical paradoxes, identifying their source in a general form of indiscernibility. We then develop our diagnosis into a theory of paradoxicality, which formalizes both semantic and soritical paradoxes as arguments involving specific instances of our generalized indiscernibility principle, and correctly predicts which logics can non-trivially solve them. (shrink)

The semantic paradoxes and the paradoxes of vagueness display remarkable family resemblances. In particular, the same non-classical logics have been applied to both kinds of paradoxes. These facts have been taken by some authors to suggest that truth and vagueness require a unified logical framework. Some authors go further, and argue that truth is itself a vague or indeterminate concept. Importantly, however, there currently is no identification of what the common features of semantic and soritical paradoxes exactly consist in. This (...) is what we aim to do in this work: we analyze semantic and soritical paradoxes, and develop our analysis into a theory of paradoxicality. The unification of the paradoxes of truth and vagueness we propose here has a wide scope, but for the sake of concreteness we focus on four three-valued logics. (shrink)

In Part I of this paper, we identified and compared various schemes for trivalent truth conditions for indicative conditionals, most notably the proposals by de Finetti and Reichenbach on the one hand, and by Cooper and Cantwell on the other. Here we provide the proof theory for the resulting logics DF/TT and CC/TT, using tableau calculi and sequent calculi, and proving soundness and completeness results. Then we turn to the algebraic semantics, where both logics have substantive limitations: DF/TT allows for (...) algebraic completeness, but not for the construction of a canonical model, while CC/TT fails the construction of a Lindenbaum-Tarski algebra. With these results in mind, we draw up the balance and sketch future research projects. (shrink)

Can one quantify over absolutely everything? Absolutists answer positively, while relativists answer negatively. Here, I focus on the absolutism versus relativism debate in the framework of theories of truth, where relativism becomes a form of contextualism about truth predications. Contextualist theories of truth provide elegant and uniform solutions to the semantic paradoxes while preserving classical logic. However, they interpret harmless generalizations (such as “everything is self-identical”) in less than absolutely comprehensive domains, thus systematically misconstruing them. In this article, I show (...) that contextualism is broadly compatible with absolute generality. More specifically, I develop a bipartite contextualist semantics, or “bicontextualism,” on which sentences are split in two groups: the unproblematic sentences, which are compatible with absolute generality, and the problematic ones, which are given a relativist semantics. I then argue that bicontextualism retains the advantages of (orthodox) contextualism and does not give rise to new revenge paradoxes. (shrink)

IntroductionDuring the COVID-19 pandemic, healthcare workers in Italy have been exposed to an unprecedented pressure and traumatic events. However, no direct comparison with the general population is available so far. The aim of this study is to detail mental health outcomes in healthcare workers compared to the general population.Methods24050 respondents completed an on-line questionnaire during the contagion peak, 21342 general population, 1295 second-line healthcare workers, and 1411 front-line healthcare workers. Depressive, anxious, post-traumatic symptoms and insomnia were assessed. Specific COVID-19 related (...) potential risk factors were also considered in healthcare workers.ResultsDepressive symptoms were more frequent in the general population and front-line healthcare workers compared to the second-line healthcare workers groups. Anxiety symptoms showed a prevalence of 21.25% in the general population, 18.05% for second-line healthcare workers, and 20.55% for front-line healthcare workers. Insomnia showed a prevalence of 7.82, 6.58, and 9.92% for the general population, second-line healthcare workers, and front-line healthcare workers, respectively. Compared to the general population, front-line healthcare workers had higher odds of endorsing total trauma-related symptoms. Both second-line healthcare workers and front-line healthcare workers had higher odds of endorsing core post-traumatic symptoms compared to the general population, while second-line healthcare workers had lower odds of endorsing negative affect and dissociative symptoms. Higher total traumatic symptom score was associated with being a front-line healthcare worker, having a colleague infected, hospitalized, or deceased, being a nurse, female gender, and younger age.ConclusionThis study suggests a significant psychological impact of the COVID-19 pandemic on the Italian general population and healthcare workers. Front-line healthcare workers represent a specific at-risk population for post-traumatic symptoms. These findings underline the importance of monitoring and intervention strategies. (shrink)

The notion of grounding is usually conceived as an objective and explanatory relation. It connects two relata if one—the ground—determines or explains the other—the consequence. In the contemporary literature on grounding, much effort has been devoted to logically characterize the formal aspects of grounding, but a major hard problem remains: defining suitable grounding principles for universal and existential formulae. Indeed, several grounding principles for quantified formulae have been proposed, but all of them are exposed to paradoxes in some very natural (...) contexts of application. We introduce in this paper a first-order formal system that captures the notion of grounding and avoids the paradoxes in a novel and non-trivial way. The system we present formally develops Bolzano’s ideas on grounding by employing Hilbert’s ε-terms and an adapted version of Fine’s theory of arbitrary objects. (shrink)

Theoretical and manipulative abduction conjectures and manipulations : the extra-theoretical dimension of scientific discovery. -- Non-explanatory and instrumental abduction : plausibility, implausibility, ignorance preservation. -- Semiotic brains and artificial minds : how brains make up material cognitive systems. -- Neuromultimodal abduction : pre-wired brains, embidiment, neurospaces. -- Animal abduction : from mindless organisms to srtifactual mediators. -- Abduction, affordances, and cognitive niches : sharing representations and creating chances through cognitive niche construction. -- Abduction in human and logical agents : hasty (...) generalizers, hybrid abducers, fallacies. -- Morphodynamical abduction : causation of hypotheses by attractors dynamics. (shrink)

Drawing on empirical evidence from history and anthropology, we aim to demonstrate that there is room for genealogical ideology critique within normative political theory. The test case is some libertarians’ use of folk notions of private property rights in defence of the legitimacy of capitalist states. Our genealogy of the notion of private property shows that asking whether a capitalist state can emerge without violations of self-ownership cannot help settling the question of its legitimacy, because the notion of private property (...) presupposed by that question is a product of the entity it is supposed to help legitimise: the state. We anchor our genealogical critique in recent work on ideology in epistemology and philosophy of language, and in current debates on the methodology of political theory. But, unlike more traditional approaches that aim to debunk whole concepts or even belief systems, we propose a more targeted, argument-specific form of ideology critique. (shrink)

Ensayos-homenaje en el primer centenario del nacimiento del fil sofo espa ol, que abordan diversos aspectos de la obra de Ortega. Los cuatro trabajos dibujan con rigor algunos de los horizontes planteados por el maestro y respetan la debida modernidad conceptual. la compilaci n estuvo a cargo de Fernando Salmer n, Alejandro Rossi, Luis Villoro y Ram n Xirau.

According to most interpreters, Aristotle explains death as the result of material processes of the body going against the nature of the living being. Yet, this description is incomplete, for it does not clarify the relationship between the process of decay and the teleological system in which it occurs: this makes it impossible to distinguish between natural and violent death. In this paper, I try to fill this gap by looking at his so-called ‘biological works’ and mainly at the De (...) Juventute. I first introduce the specific concept of life at play in this treatise and prove its complementarity with the framework of the De Anima. Then, I illustrate in detail the process of dying and the reasons why a merely material description is insufficient to account for the distinction between natural and violent death. Finally, I show that for Aristotle natural death is a by-product of teleologically directed life activities: only against the background of this teleological structure is natural death fully explained in terms of essence and causes. To support this claim, I compare death to two analogous cases in Aristotle’s biology, namely dreams and the features of GA V. (shrink)

Il existe un lien intuitif entre le bien-être et le bonheur. Nous souhaitons proposer une nouvelle théorie selon laquelle le bien-être consiste en un bonheur approprié. Notre théorie peut être considérée comme la combinaison de quatre thèses. La première thèse est que le bonheur psychologique consiste en une balance largement positive d’états affectifs tels que les émotions, les humeurs et les plaisirs sensoriels. La seconde est que les émotions, les humeurs et les plaisirs sensoriels sont différents types d’expériences perceptuelles de (...) propriétés évaluatives. Il s’ensuit que le bonheur consiste en une balance largement positive d’expériences perceptuelles de propriétés évaluatives. La troisième thèse est que, dans la mesure où le bonheur est constitué par des états qui ont des conditions d’adéquation, alors le bonheur aussi peut être évalué comme étant approprié ou inapproprié. La quatrième thèse est une thèse concernant le bien-être : elle affirme que le bien-être consiste en un bonheur approprié ainsi défini. (shrink)

What do we talk about when we talk about ethical diversity as a challenge to the normative justifiability of liberal democracy? Many theorists claim that liberal democracy ought to be reformed or rejected for not being sufficiently ‘inclusive’ towards diversity; others argue that, on the contrary, liberalism is desirable because it accommodates (some level of) diversity. Moreover, it has been argued that concern for diversity should lead us to favour (say) neutralistic over perfectionist, universalistic over particularistic, participative over representative versions (...) of liberal democracy. This paper provides a conceptual framework to situate those debates, and argues that there are two fundamental ways in which diversity constitutes a challenge to the justificatory status of liberal democracy: consistency (whereby diversity causes clashes between the prescriptions generated by normative political theories), and adequacy (whereby diversity generates a rift between our experience of what is considered valuable and what the theory treats as such). (shrink)

This is the first dedicated commentary to Sextus Empiricus’ treatise _Against the Arithmeticians_, dealing with crucial issues in the history of the sceptical, Platonic and Pythagorean traditions and in the ancient philosophy of mathematics.

Lorenzo Valla (1407–1457) ranks among the greatest scholars and thinkers of the Renaissance. He secured lasting fame for his brilliant critical skills, most famously in his exposure of the “Donation of Constantine,” the forged document upon which the papacy based claims to political power. Lesser known in the English-speaking world is Valla's work in the philosophy of language—the basis of his reputation as the greatest philosopher of the humanist movement. Dialectical Disputations, translated here for the first time into any (...) modern language, is his principal contribution to the philosophy of language and logic. With this savage attack on the scholastic tradition of Aristotelian logic, Valla aimed to supersede it with a new logic based on the actual historical usage of classical Latin and on a commonsense approach to semantics and argument. Valla provides a logic that could be used by lawyers, preachers, statesmen, and others who needed to succeed in public debate—one that was stylistically correct and rhetorically elegant, and thus could dispense with the technical language of the scholastics, a “tribe of Peripatetics, perverters of natural meanings.” Valla's reformed dialectic became a milestone in the development of humanist logic and contains startling anticipations of modern theories of semantics and language. Volume 1 contains Book I, in which Valla refutes Aristotle's logical works on the categories, transcendentals, and predicables, with excursions into natural and moral philosophy and theology. (shrink)

In this paper, we embark on the complicated discussion about the nature of vice in Virtue Ethics through a twofold approach: first, by taking seriously the claim that virtues (and certain flavours of vices) are genuinely dispositional features possessed by agents, and secondly, by employing a pluralistic attitude borrowed from Battaly’s pluralism (2008). Through these lenses, we identify three varieties of viciousness: incontinence, indifference, and malevolence. The upshot is that the notion of vice is not as categorically homogeneous as that (...) of virtue: some states of viciousness consist in interference of present virtuous dispositions, or mimicking of absent vicious ones, whereas others can be considered genuine dispositions themselves. Furthermore, this set-up can provide an interesting, albeit highly idealized story as to how, through the interference in one’s environment, one gets acquainted with vice in various degrees. Finally, this approach can be illuminating vis-à-vis Virtue Ethics in general; e.g. we can employ it to discuss more productively Johnston’s (2003) objection to Hursthouse’s (1999) account of moral conduct. Finally, this approach can be illuminating vis-a-vis Virtue Ethics in general; e.g. we can employ it to discuss more productively Johnston’s (2003) objection to Hursthouse’s (1999) account of moral conduct. (shrink)

In recent years, a new dispute has risen to prominence: the dispute between realists and anti-realists about causal powers. Albeit sometimes overlooked, the meta-ontological features of this “question of realism for powers” are quite peculiar. For friends and foes of causal powers have characterized their contrasting views in a variety of different ways; as existence claims, as semantic or truth-making claims, as fundamentality claims, as claims about the nature of certain properties. Not only does this multiplicity of interpretations make it (...) unclear what the genuine bone of contention is, if there is one; some of them appear to be mutually exclusive. Some light can be shed on this apparent yet widespread confusion by distinguishing three degrees of ontological involvement in dispositional truths; viz., three ways, of increasing robustness, to read ontological commitments from dispositional truths. Relatedly, by exploring the literature, and focusing on some selected examples of power realism and anti-realism, we can observe that power realists vastly disagree over the intrinsic nature ad make-up of dispositional properties. Such examples furthermore invite the thought that the question of realism for powers is best understood not as the debate around the existence of properties with a distinctive identity, but rather as a debate about metaphysical hierarchy. Finally, some anti-realists positions are indistinguishable from realist ones, using merely intensional resources: power realism is best appreciated by going hyperintensional. (shrink)

This paper attempts a reconstruction of reason’s contribution to empirical truth in connection with Kant’s definition of truth as the agreement of cognition with its object. I argue that Kant’s treatment of truth in the Transcendental Analytic gets completed in the Appendix to the Transcendental Dialectic with an often neglected but compelling argument (what I shall call the Variety Argument). This argument postulates such a variety in the appearances as to undermine any attempt at formulating empirical truths. Crucially, I argue (...) that this variety does not depict an extreme-case scenario, but our own epistemic situation without reason. Reason completes Kant’s theory of truth by allowing the understanding (i.) to form empirical concepts and (ii.) approximate to empirical truth. (shrink)

Philosophers have debated at length the epistemological status of scientific thought experiments. I contend that the literature on this topic still lacks a common conceptual framework, a lacuna that produces radical disagreement among the participants in this debate. To remedy this problem, I suggest focusing on the distinction between the internal and the external validity of an experiment, which is also crucial for thought experiments. I then develop an account of both kinds of validity in the context of thought experiments. (...) I show that we can naturally conceptualise internal validity in terms of games of make-believe. Then, I argue that external validity is best defined as accurate representation of a target system. Finally, I turn back to the current debate on thought experiments and show that my diarchic account provides a general framework that can be shared by the competing philosophical views, as well as a fruitful guide for their reconciliation. (shrink)

We present an elementary system of axioms for the geometry of Minkowski spacetime. It strikes a balance between a simple and streamlined set of axioms and the attempt to give a direct formalization in first-order logic of the standard account of Minkowski spacetime in [Maudlin 2012] and [Malament, unpublished]. It is intended for future use in the formalization of physical theories in Minkowski spacetime. The choice of primitives is in the spirit of [Tarski 1959]: a predicate of betwenness and a (...) four place predicate to compare the square of the relativistic intervals. Minkowski spacetime is described as a four dimensional ‘vector space’ that can be decomposed everywhere into a spacelike hyperplane - which obeys the Euclidean axioms in [Tarski and Givant, 1999] - and an orthogonal timelike line. The length of other ‘vectors’ are calculated according to Pythagora’s theorem. We conclude with a Representation Theorem relating models of our system that satisfy second order continuity to the mathematical structure called ‘Minkowski spacetime’ in physics textbooks. (shrink)