Andrea Strollo

According to a traditional view, logical validity consists in necessary truth preservation. Such an account has been argued to carry an apparent commitment to a unique property of truth to be preserved from premises to conclusion. Recent discussions, however, have concluded that if the metaphor of truth preservation is carefully unpacked, no need for a unique property is there. All is needed is that certain structural relations among instantiations of truth properties hold. Against this view, we argue that a unique general truth property is indeed required by logical validity. We first show that the unpacking should be correctly understood since it imposes constraints on the concept and the properties of truth. We then demonstrate that, under such constraints, a general property is not imposed by truth preservation but by another feature of validity: its uniformity. Finally, some options that could be attempted to resist this result are discussed, showing that (strong) truth pluralism and deflationism are affected in different ways.

In contemporary philosophy, it is tempting to apply the metaphysics of properties to the specific case of truth, in the hope of making progress on the investigation of the latter. In this paper, I argue that a different approach, mostly independent from the metaphysics of properties and based on the naturalness, in Lewis’ sense, of semantic nations, is often a better alternative, both in general and in some specific cases. In particular, adopting the new perspective, I present a new problem of combining logical validity and strong truth pluralism, and offer a way to sharply distinguish deflationism and primitivism about truth. The main original upshot of the paper is offering a perspective on philosophy of truth that sheds new light on the general problem of truth and on some particular issues.

As for many other properties, to understand the nature of truth attention should be paid to the kind of entities that are apt to bear it. In particular, I argue that different kinds of truth bearers tend to support different properties of truth. After that, I show that there are reasons to admit a plurality of truth bearers. As a consequence of these two results, a plurality of truth properties may be naturally admitted. The general upshot of the paper is a new way to motivate alethic pluralism, which stems from considerations on the nature of representations rather than from considerations on what is represented. This new version of truth pluralism—truth (bearers) pluralism—is shown to be theoretically fertile and promising against some standard criticisms.

Belief, according to many philosophers, aims at truth. In this paper I discuss in what measure a pluralist conception of truth is compatible with this claim. In particular, I argue that if the idea is understood according to a teleological account, alethic pluralism can be adopted also in a strong form. I contend that while the teleological account of belief requires a generic concept of truth, it poses a few constraints on the property of truth. By contrast, at least a moderate version of alethic pluralism is commanded by a normativist interpretation of the aim.

In questo articolo sviluppiamo una Logica Dialeteista con Assunzioni e Conclusioni Esclusive, DLEAC. A questo scopo, verrà adottata la semantica della Logica del Paradosso (LP), estesa definendo una specifica nozione di modello. L’apparato deduttivo viene modificato specificando le nozioni di Assunzione e Conclusione, considerate come atti linguistici. Successivamente, introduciamo un nuovo paradosso — il paradosso del diniego —, sia informalmente che formalmente, derivandolo all’interno di un’estensione di DLEAC concepita apposta per esprimerlo. Un tale paradosso rappresenta un serio problema per il dialeteismo, nello specifico per la versione di Priest in cui si considerano gli atti linguistici di asserzione e diniego, e gli atteggiamenti proposizionali di accettazione e rifiuto, come esclusivi. Infine, discutiamo due proposte che Priest potrebbe avanzare per superare il paradosso: raffinare le nozioni pragmatiche in gioco e mostrare che il paradosso è un caso di dilemma razionale. Si mostra che entrambe le strategie non sono efficaci.

According to truth pluralism, sentences from different areas of discourse can be true in different ways. This view has been challenged to make sense of logical validity, understood as necessary truth preservation, when inferences involving different areas are considered. To solve this problem, a natural temptation is that of replicating the standard practice in many-valued logic by appealing to the notion of designated values. Such a simple approach, however, is usually considered a non-starter for strong versions of truth pluralism, since designation seems to embody nothing but a notion of generic truth. In this paper, I explore the analogy with many-valued logic by comparing the problem of mixed inferences with Suszko’s thesis, and argue that the strong pluralist has room to resist the commitment to a generic property of truth by undermining the semantic significance of Suszko’s reduction.

Alethic pluralism holds that there are many ways of being true. The view has been accused of being unable to do justice to the traditional account of logical validity, understood as necessary truth preservation. In this paper I reformulate the debate in terms of the naturalness of generic truth, and discuss some notable consequences of this more careful reformulation. I show not only that some alleged solutions, like the resort to plural quantification, are ineffective, but also that the problem is not really posed by mixed inferences, as usually thought. Finally, I argue that the traditional account of logical validity does carry a commitment to generic truth, so that a strong version of alethic pluralism can hardly vindicate it.

In this paper we first develop a Dialetheic Logic with Exclusive Assumptions and Conclusions, DLEAC. We adopt the semantics of the logic of paradox (LP) extended with a notion of model suitable for DLEAC, and we modify its proof theory by refining the notions of assumption and conclusion, which are understood as speech acts. We introduce a new paradox – the rejectability paradox – first informally, then formally. We then provide its derivation in an extension of DLEAC contanining the rejectability predicate.

Intervistati sul valore di questo testo, gli autori hanno dichiarato: «o questa affermazione è falsa, oppure questo è il miglior eserciziario di logica che sia mai stato scritto». Se la loro affermazione vi risulta poco comprensibile, ma avete intenzione di capirci qualcosa di più, questo eserciziario può fare al caso vostro! È uno strumento che integra ed estende un comune manuale di logica – ma che non si sostituisce ad esso, mancando la parte teorica –, ed è pensato per coloro che hanno intrapreso lo studio della logica per la prima volta e desiderano farne pratica. Il testo si rivolge principalmente agli studenti universitari che seguono un corso base di logica, ma anche a chi sta tentando di barcamenarsi con questa disciplina al di fuori dell’ambiente accademico. Se sarete disposti a mettervi in gioco e a spremervi un po’ le meningi, scoprirete che o l’affermazione degli autori è falsa o questo è davvero il miglior eserciziario di logica che sia mai stato scritto!

Philosophy, and analytic metaphysics in particular, is usually described as an armchair discipline, and exactly for such an armchair methodology it has been the target of ferocious criticisms. In this paper, I argue that the theoretical right to conduct metaphysics from the armchair can be defended understanding metaphysics as a form of Logic (broadly understood as including applied logics, philosophical logics and, especially, philosophy of logic). So characterized, the typical practice of metaphysics is not more problematic than the armchair methodology routinely employed in the study of Logic.

According to Naming and Necessity, proper names usually work referentially as rigid designators. In this paper, I argue that proper names have also attributive uses that systematically emerge in particular contexts. Attributive uses are then exploited to show that simple identity claims (such as “Hesperus is Phosphorus”) are open to a double interpretation. The main aim of the paper is arguing that the impression that certain true identities are a posteriori is mostly due to one of the two readings, a reading according to which, however, the expressed truth is only contingently true.

Recently, analytic metaphysics has been attacked from a scientist’s perspective. In Everything Must Go, James Ladyman and Don Ross argued that analytic metaphysics should be dismissed and replaced with a naturalized metaphysics. In this paper, I critically discuss the arguments proposed in the book in order to determine whether this critique of analytic metaphysics is successful. In particular, Ladyman and Ross elaborate on three main points: the role of intuitions and the ensuing misunderstanding of science, the demarcation of science from non science, and the exclusive theoretical authority of science. I argue that none of their arguments succeeds in excluding analytic metaphysics from the list of respectable theoretical disciplines.

At the end of the nineties some authors (Leon Horsten, Stewart Shapiro and Jeffrey Ketland) worked out a fairly technical argument against deflationary theories of truth. In a nutshell, deflationism, it was argued, is committed to conservativeness by the the claim that truth is not a substantial notion, a conservative theory (under the light of certain logico-mathematical facts) can not be an adequate theory of truth, therefore deflationism is an inadequate theory of truth. Beside the apparent simplicity of this argument, it hides a lot of subtle questions and problems and it is a very sophisticated argument. Deflationists attempted to reply in different ways to the argument but the general impression is that, so far, they have not been able to find a good solution. Deflationism does really seem to be condemned to be an inadequate theory. This work is divided in three main parts. The first part is a very general survey where the study of the notion of truth is introduced. In Chapter One we sketch philosophical theories of truth comparing more traditional approaches to deflationism; we briefly survey the history of deflationism and then we try to find a general characterization of it. In the second Chapter the notion of truth is considered under a formal approach and some important and simple axiomatic theories of truth are sketched. The second part join the philosophical and the formal approach to truth together into the debate over deflationism and conservativeness. In Chapter Three we introduce the notion of conservativeness and we give some example of its application both to logical and to philosophical matters. Then we spell out the argument from conservativeness and we discuss it in order to get a precise requirement that deflationary theories are supposed to satisfy. In Chapter Four we focus on deflationist replies to the argument from conservativeness and we discuss each solution. The third and last part is the core of the work, it consists in a more technical study of some presuppositions of the debate: we want to take a step backward and to compare the two major claims of deflationism - the centrality of T-sentences and the logical function of the truth predicate - with conservativeness. Many of the results used here are due to other logicians and philosophers and are available in literature yet, the originality consists in a critical consideration of such results under the light of the conservativeness of truth. More original reflections can be found in Chapter Seven and in particular in the conclusive Chapter Eight, where the proposal is completely new, at least as far as I know. In Chapter Five we compare T-sentences with the empty base theory and in Chapter Six we analyse in what measure a deflationary theory can be really conservative over a theory of syntax. The result would be quite serious for a deflationist. In Chapter Seven we compare conservativeness with the logical function of the truth predicate. We will get the unpleasant result that the truth predicate is not able to serve the logical function in no sense without loosing conservativeness at the same time. In Chapter Eight we draw some conclusion and we sketch a reformulation of the conservativeness requirement. This new requirement, we will argue, makes justice to the claim of the unsubstantiality of truth and at the same time it does not condemn deflationism to death. In this way, we will be able also to clarify what is the exact role of truth in sentential quantification, showing that this role is really innocent and unsubstantial. The unsubstantiality of deflationary truth, though, will not force deflationism into an inadequate theory of truth.

One of the basic question we can ask about truth in a formal setting is what, if anything, we gain when we have a truth predicate at disposal. For example, does the expressive power of a language change or does the proof strength of a theory increase? Satisfaction classes are often described as complicated model theoretic constructions unable to give useful information toward the notion of truth from a general point of view. Their import is narrowed to a dimension of pure technical utility and curiosity. Here I offer an application of satisfaction classes in order to show that they can have a relevant role in confronting proof theoretical equivalent theories of truth.

In recent decades deflationary theories of truth have been challenged with a technical argument based on the notion of conservativeness. In this paper, I shall stress that conservative extensions of theories and expandability of their models are not equivalent notions. Then, I shall argue that the deflationary thesis of the unsubstantiality of truth is better understood as leveraging on the stronger notion of expandability of models. Once expandability is involved in the argument, some notable consequences follow: the strategy proposed by Hartry Field in response to the conservativeness objection is strongly undermined and even simpler proposals (such as theories based on standard t-sentences) are shown to be quite problematical

The notion of truth is a central subject both in Philosophy and Mathematical Logic. The logical approach on the one side and the philosophical one on the other, however, mostly deal with problems which, apparently, require different tools to be tackled. In this paper I argue that such a separation can and should be overcome, and, in order to build a bridge, I focus on the philosophical issue of the insubstantiality of truth, which is a crucial topic to distinguish inflationist from deflationist proposals. Elaborating on the interpretation of insubstantiality in terms of the sparse/abundant classification of properties, I put forward a refined version in which certain flaws afflicting other formulations are solved. Then, I show how, using this improved variant, the philosophical notion of abundance can be fruitfully related to the formal notion of expandability of models, if a logical framework is adopted. Among other virtues, the obtained link can shed new light on the debate of deflationism and conservativity.