Massimiliano Carrara

Circumstantialists already have a logical semantics for impossibilities. They expand their logical space of possible worlds by adding impossible worlds. These are impossible circumstances serving as indices of evaluation, at which impossibilities are true. A variant of circumstantialism, namely modal Meinongianism (noneism), adds impossible objects as well. These are so-called incomplete objects that are necessarily non-existent. The opposite of circumstantialism, namely structuralism, has some catching-up to do. What might a structuralist logical semantics for impossibilities without impossibilia look like? This paper makes a structuralist counterproposal. We present a semantics based on a procedural interpretation of the typed λ-calculus. The fundamental idea is that talk about impossibilities should be construed in terms of procedures: some yield as their product a condition that could not possibly have a satisfier, while the rest fail to yield a product altogether. Dispensing with a ‘bottom’ of impossibilia requires instead a ‘top’ consisting of structured hyperintensions, intensions, intensions defining other intensions, a typed universe, and dual (de dicto and de re) predication. We explain how the theory works by going through several examples.

Commonsense ontology often conflicts with the ontology of our best scientific and philosophical theories. However, commonsense ontology, and commonsense belief systems in general, seems to be remarkably efficient and cognitively fundamental. In cases of contrast, it is better to find a way to reconcile commonsense and ”theoretical” ontologies. Given that commonsense ontologies are typically expressed within natural language, a classical procedure of reconciliation is semantical. The strategy is that of individuating the ”ontologically problematic” expressions of natural language and paraphrasing the sentences in which they appear in a (formal) language whose commitments are compatible with those of our best theories. We believe that this strategy of reconciliation, though quite standard, especially in the philosophical literature, is problematic: for a start, it forces us to conclude that the ”real content” of our commonsense expressions and beliefs is different from what it appears. Commonsense ontology becomes just an illusion. We will thus propose an alternative approach: according to our view, a commonsense ontology is reconciled with a theoretical ontology in case it is shown that the explanation of why we believe in the existence of a problematic entity is compatible with our best theories. We will call this kind of reconciliation ”epistemic”. The advantage of an epistemic reconciliation is that commonsense ontology is treated in its own right and could be taken prima facie. Another advantage of the view is that epistemic reconciliation can be analysed through the notion of explaining away: a commonsense ontology is epistemically reconciled with a theoretical ontology if and only if the problematic entities of the commonsense ontology are explained away by ”respectable” entities of the theoretical ontology. In the final part of the paper, we sketch a formal analysis of explaining away.

The key-terms "language," "knowledge" and "metaphysics" arguably shape most of the recent researches in analytic philosophy. This volume aim to address some of the currently debated issues revolving around these three fundamental areas and, in particular: can the notion of "descriptive name" be extended to names of natural kinds? What does it mean for a belief to be justified? Is there a principled way to draw the distinction between causal and non causal relations? Do future contingent claims require us to employ a notion of relative truth? In what sense analytic sentences could be taken to be known a posteriori? The twelve papers collected in this volume arise from a selection of those presented during the First Graduate Conference of the Italian Society for Analytic Philosophy held at the University of Padua in September 2007. The authors are all young and brilliant scholars coming from some of the most prestigious universities in the world: University College, Nottingham, Princeton, Kentucky, Stanford, Eastern Piedmont, St. Andrews, Hebrew University of Jerusalem, Duhram, Catholic University of Leuven, London School of Economics.

A minimal constraint on normative reasons seems to be that if some fact is a reason for an agent to φ (act, believe, or feel), the agent could come to know that fact. This constraint is threatened by a well-known type of counterexamples. Self-effacing reasons are facts that intuitively constitute reasons for an agent to φ, but that if they were to become known, they would cease to be reasons for that agent. The challenge posed by self-effacing reasons bears important structural similarities with a range of epistemic paradoxes, most notably the Knowability Paradox. In this article, we investigate the similarities and differences between the two arguments. Moreover, we assess whether some of the approaches to the Knowability Paradox could help solve the challenge posed by self-effacing reasons. We argue that at least two popular approaches to the paradox can be turned into promising strategies for addressing the self-effacing reasons problem.

According to N. Goodman, the Carnapian notion of similarity is useless in science and without interest for philosophy. In our paper we suggest that, given the current role that the notion of similarity has in managing biomedical big data, this drastic position should be revised, and similarity should be provided a scientifically useful philosophical interpretation. With the advent of the new sequencing technologies, imaging technologies and with the improvements of health records, the number of genomics, post-genomics and clinical data has exponentially increased. The deluge of data has urged, among others, to devise a new way of stratifying patients. A solution has been found and it is based exactly on the notion of similarity. By discussing two examples focusing on similarity among breast cancer patients, in the paper we illustrate such a use, and analyze it from a philosophical standpoint by resorting to A. Tversky’s features matching approach. We believe that the latter can foster some better understanding of the meaning and current use of similarity in the context of biomedical big data, and that, therefore, be the focus of further reflections in the philosophy of science, in particular in the philosophy of biomedicine.

In this article we consider argumentation as an epistemic process performed by an agent to extend and revise her beliefs and gain knowledge, according to the information provided by the environment. Such a process can also generate the suspension of the claim under evaluation. How can we account for such a suspension phenomenon in argumentation process? We propose: (1) to distinguish two kinds of suspensions – critical suspension and non-critical suspension – in epistemic change processes; (2) to introduce a Paraconsistent Weak Kleene logic (PWK) based belief revision theory which makes use of the notion of topic to distinguish the two kinds of suspensions previously mentioned, and (3) to develop a PWK-style argumentation framework and its expansion. By doing that, we can distinguish two kinds of suspensions in an epistemic process by virtue of the notion of topic.

Beall (2016) proposes to read the middle-value of Weak Kleene logic as off-topic. This interpretation has recently drawn some attention: for instance, Francez has pointed out that Beall's interpretation does not meet some important requirements to count as a truth value. Moreover, Beall is silent about what a topic (or a subject matter) is. But arguably, what is a topic? is a crucial question, and an answer is really important to fully understand his proposal. Thus, our goal here is to help to remedy this deficiency, and show how Beall's interpretation of Weak Kleene truth-values interacts with the notion of topic. To do that, we formalize his motivating ideas and draw some consequences from them.

In Thin objects: an abstractionist account (Oxford University Press, 2018), Øystein Linnebo claims that ‘mathematical objects are thin in the sense that very little is required for their existence’. Linnebo articulates his view in an abstractionist manner: according to Linnebo, the truth of the right‐hand side of a Fregean abstraction principle, which states that two items stand in a given equivalence relation, is sufficient for the truth of its left‐hand side, which states that the same abstract object is associated to both items. This special issue contains nine articles discussing different aspects of Linnebo's book. In this introduction, we provide an opinionated introduction to the Special Issue and an overview of the contributions.

This paper offers a logico-algebraic investigation of AGM belief revision based on the logic of paradox ( \(\mathrm {LP}\) ). First, we define a concrete belief revision operator for \(\mathrm {LP}\), proving that it satisfies a generalised version of the traditional AGM postulates. Moreover, we investigate to what extent the Levi and Harper identities, in their classical formulation, can be applied to a paraconsistent account of revision. We show that a generalised Levi-type identity still yields paraconsistent-based revisions that are fully compatible with the AGM postulates. The main outcome is that, once the classical AGM framework is lifted up to an appropriate level of generality, it still appears as a regulative ideal for treating of paraconsistent-based epistemic operators.

Classical mereology seems unable to characterise the identity conditions of word types. For example, the same letter types ordered differently result in different word types; but mereological fusions of the same letters are identical, regardless of the order of the letters. We show, however, that by combining classical mereology with plural logic one can give a definition of word types that satisfies the identity criteria of word types. This means that it is not necessary to abandon classical mereology in order to give an analysis of the mereological structure of word types.

A.J. Cotnoir has argued that we should distinguish between two notions of proper parthood: outstripped part and non-identical part. Outstripped parthood is an asymmetric relation, but non-identical parthood is not. We argue, first, that the intuitions Cotnoir uses to motivate these notions do not always give the right verdict; and, second, that systematic reasons for distinguishing these two notions of parthood have further counter-intuitive consequences. This means the distinction between two notions of proper parthood currently lacks adequate motivation.

What kind of reference (if any) do terms such as “pencil,” “chair,” “television,” and so on have? On the matter, a de-bate between directly referential theorists and descriptiv-ist theorists is open. It is largely acknowledged that natural kind terms (such as “water,” “gold,” “tiger,” etc.) are directly referential expressions (cf. Putnam,1975). That is, they are expressions whose reference is determined by their refer-ents' nature, independent of whether we know or will ever know what this nature is. However, it does not seem like-wise convincing that all artifactual kind terms (like “pen-cil,” “chair,” “television,” etc.) semantically behave the same. Terms for artifactual kinds seem more likely to be subjected to a descriptivist view, that is, definable not by links to their extensions' nature but in terms of conjunctions or clusters of properties. In his celebrated “The Meaning of ‘Meaning’” (1975), Hilary Putnam originated the mentioned debate by arguing that artifactual kind terms also refer directly. Thus, the discussion ultimately revolves around establishing whether artifactual and natural kind terms are both directly referential expressions. The authors engaged in this debate have tried to argue in favor of (or against) Putnam's proposal by highlighting the similarities (or differences) between nat-ural vis-à-vis artifactual kind words and their respective ref-erents. This paper aims to provide a thorough and reasoned overview of the debate at stake, pointing out trends and problems associated with each proposed account.

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.

Per il dialeteismo ci sono contraddizioni vere. Questa concezione filosofica ha assunto una forma chiara e definita a partire dal lavoro del filosofo e logico Graham Priest – uno dei suoi padri fondatori, nonché uno dei suoi più strenui difensori. Questo libro intende portare il dialeteismo all’attenzione di un ampio pubblico, che non sia solo quello degli addetti ai lavori. Il volume è suddiviso in due parti. La prima include le cinque lezioni su "Dialeteismo e storia della filosofia" tenute da Priest e Filippo Casati a Padova nel 2016, in occasione del Corso di Eccellenza per il dottorato in filosofia dell’Università di Padova. La seconda contiene quattro contributi sul dialeteismo di autori italiani.

A popular stance amongst philosophers is one according to which, in Lewis’ words, “identity is utterly simple and unproblematic”. Building from Lewis’ famous passage on the matter, we reconstruct, and then criticize, an argument to the conclusion that identities cannot be grounded. With the help of relatively uncontroversial assumption concerning identity facts, we show that not all identities are equi-fundamental, and, on the contrary, some appear to be provided potential grounding bases using two-level identity criteria. Further potential grounding bases for identities are presented. Identity might be utterly simple and unproblematic, but this is not sufficient to conclude that identities are ungrounded, or fundamental.

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!

Conflicts between our best philosophical theories (BPTs) and our common beliefs are widespread. For example, if eliminativism is our BPT, then our BPT conflicts with common beliefs about the existence of middle-sized composite artifacts. “Compatibilism” is the name usually given to a theoretical attitude, according to which, in the case of a conflict between BPT and a common belief P, we should try to find a reconciliation. The two major variants of compatibilism are “semantic compatibilism” (SC) and “cognitive compatibilism” (CC). According to SC, to be reconciled with BPT is the “real” version of the content of our ordinary assertions; according to CC, to be reconciled with BPT is the mental state we are “really” in while thinking P. In this paper, we present a new kind of compatibilism, epistemic compatibilism (EC). According to EC, to be reconciled with BPT is the explanation of why we believe that P. After presenting EC, we will argue that it fares better than SC and CC for at least two related reasons: EC does not rely on any form of what we call semantic or cognitive “recarving”; thus, EC avoids some sceptical problems that aect the other two versions of compatibilism.

In this paper we introduce some logical and philosophical refinements to OntoClean, first by developing some formal constraints on identity criteria, secondly by specifying a kind of identity criteria, two level identity criteria, whose role is to explain an identity among some entities referring to some other, more basic, entities. Using such refinement we add a formal constraint to the stock of OntoClean meta-constraints (OC+). We, then, observe that two level identity criteria have an intuitive reading in terms of dependence of a kind of entities on some other entities, possibly specified in terms of a grounding relation. Are identity criteria grounding principles? In the second part of the paper we discuss this option.

In the 1951 Gibbs lecture, Gödel asserted his famous dichotomy, where the notion of informal proof is at work. G. Priest developed an argument, grounded on the notion of naïve proof, to the effect that Gödel’s first incompleteness theorem suggests the presence of dialetheias. In this paper, we adopt a plausible ideal notion of naïve proof, in agreement with Gödel’s conception, superseding the criticisms against the usual notion of naïve proof used by real working mathematicians. We explore the connection between Gödel’s theorem and naïve proof so understood, both from a classical and a dialetheic perspective.

Can an identity be the proper subject of an explanation? A popular stance, albeit not one often argued for, gives a negative answer to this question. Building from a contentious passage from Jaegwon Kim in this direction, we reconstruct an argument to the conclusion that identities, to the extent in which they are necessary, cannot be explained. The notion of contrastive explanation, characterized as difference-seeking, will be crucial for this argument; however, we will eventually find the argument to be unsatisfactory. On the contrary, the discussion provides enough resource to sketch a very simple framework for a non-causal contrastive explanation of identities. Many instances will be provided, with different varieties of explanans, ultimately suggesting that certain entailment or biconditional principles involving identities (first and foremost, so-called two-level identity criteria) may indeed be taken to have an inherent explanatory value.

The pragmatic notion of assertion has an important inferential role in logic. There are also many notational forms to express assertions in logical systems. This paper reviews, compares and analyses languages with signs for assertions, including explicit signs such as Frege’s and Dalla Pozza’s logical systems and implicit signs with no specific sign for assertion, such as Peirce’s algebraic and graphical logics and the recent modification of the latter termed Assertive Graphs. We identify and discuss the main ‘points’ of these notations on the logical representation of assertions, and evaluate their systems from the perspective of the philosophy of logical notations. Pragmatic assertions turn out to be useful in providing intended interpretations of a variety of logical systems.