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Recent logic and linguistic literature suggest that certain forms of denial cannot be reduced to a simple assertion of negation. In particular, the existence of mathematical and empirical conjectures offers a basis for refuting Frege’s thesis of equivalence between denial and assertion of negation. Following this line of thought we develop a formal framework with two primitive illocutionary operators for assertion and denial, where denial is not as negation of assertion. We introduce a semantics for the operators mentioned above. Finally, we discuss the relations between asserted and denied contents.

In this essay, we discuss the relationship between God and the modal profile of the states of affairs. There is a well-known dilemma about this relationship: both the view that the necessity and the possibility of the states of affairs are dependent on God and the view that they are not dependent have unpalatable consequences. If the necessity of the states of affairs depends on God, then those states of affairs do not really seem necessary. By contrast, if the necessity of the states of affairs does not depend on God, then God is not the fundamental entity. However, the fundamentality of God is a cornerstone of classical theism. We present a bi-modal framework that solves the dilemma, by distinguishing between global and local necessities. This framework also proves useful for solving other dilemmas such as the problem whether God can or cannot do evil actions.

Lo scopo di questo articolo è quello di offrire un modello per il cosiddetto disaccordo religioso. Si tratta di un modello logico, ovvero di una struttura formale, in cui è possibile caratterizzare precisamente le zone di conflitto tra religioni e, analogamente, le zone di possibile accordo. L’implementazione di questo modello, come vedremo, è dipendente da quanto precise riusciranno a essere le descrizioni dei vari credi e questo è notoriamente un problema spinoso. Tuttavia, crediamo che non sia insormontabile e che un modello approssimato e difettoso sia sempre comunque meglio che lasciare intentata la strada per risolvere il conflitto.

In this chapter, we will analyze several philosophical issues related to the concept of the Metaverse. After having argued that the technological and conceptual propellant of the Metaverse is virtual reality, the fundamental properties characterizing virtual reality are illustrated, and the degree of reality possessed by virtual reality is questioned. In this regard, two different views exist: virtual realist and virtual irrealist. The former argues that virtual entities are real, while the latter argues that virtual entities are not real but are akin to characters in fiction. Virtual realists do not affirm, of course, that virtual entities are composed of atoms and molecules in the same manner as physical entities, but rather that they are made of bits, that is, ultimately, of information. However, this does not diminish their reality compared to the entities encountered in everyday life. No direct argument will be given here in favor of one position over the other, but an ethical dilemma regarding virtual reality will be proposed: are actions that are evil within the real world also evil within virtual reality? Since our responses to this question vary from case to case, depending on the level of realism of virtual reality, our conclusion will be that the reality of the virtual is a matter of degree.

Fragmentalism allows incompatible facts to constitute reality in an absolute manner, provided that they fail to obtain together. In recent years, the view has been extensively discussed, with a focus on its formalisation in modeltheoretic terms. This paper focuses on three formalisations: Lipman’s approach, the subvaluationist interpretation, and a novel view that has been so far overlooked. The aim of the paper is to explore the application of these formalisations to the alethic modal case. This logical exploration will allow us to study (i) cases of metaphysical incompatibility between modal facts and (ii) cases of modal dialetheias. In turn, this will enrich our understanding of the role of impossibility in the fragmentalist framework.

In this article, we take into consideration two semantics of the future tense: linearism, according to which future-tense sentences are interpreted on a single history, and universalism, according to which they are evaluated by universally quantifying on the plurality of future histories that radiate from the present instant. Specifcally, we focus on a objection advanced against universalism: if universalism were correct semantics of will, negated future-tense sentences of natural language should have two readings, depending on the scope of negation with respect to the universal quantifer on histories. However, since natural language does not show this difference, one may conclude that there is no universal quantifer in the interpretation of these sentences. We show that this conclusion is premature. First, will has clear scope interactions with indefnite nouns phrases, contrary to what linearism predicts. Second, it is possible to extend the treatment of vague predicates as partial predicates to will: Since partial predicates have no scope interactions with negation, this can account for the scopelessness of will. The partiality of truth conditions is not restricted to will but also pertains to counterfactuals and generics and probably is part of a general tendency to maximize contraries.

In this paper, we discuss the coherence and the stability of three rather plausible philosophical intuitions: the idea that all that exists is present (Presentism); the idea that there exists a true future, although it is just a contingent future (Thin Red Line); and the idea that a proposition depends on (or is grounded in) a truthmaker (Truthmaking). We will not show that assuming these three ideas together is logically incoherent; however, their combination seems to be very difficult to hold and, ultimately, it should be discarded. As a consequence, some of these assumptions must be rejected. We will analyze in detail one of the most promising strategies that can be pursed to reconcile Truthmaking and Presentism: adopting a liberalized version of Truthmaking, for which not only what exists but also what will exist and what existed can ground the truth of a proposition. However, as for the future, this strategy works only if the future is historically closed. If there are future contingents, this line of defense is flawed.

Todd and Rabern (2021) have argued that if we assume that future contingents are untrue and if we accept the Retro-closure principle (p → PF(p)), then the existence of a temporal omniscient entity becomes metaphysically impossible. Since the truth of a metaphysical and theological theory should not be dependent on questions of temporal semantics, Todd and Rabern conclude that, if one wishes to maintain that future contingents are untrue, one must abandon the Retro-closure principle. The aim of this paper is to propose a temporal semantics system in which future contingents are untrue, the Retro-closure principle is valid, and the possibility of the existence of an omniscient and temporal being is guaranteed.

In this short paper we consider Linnebo's thin/thick dichotomy: first, we show that it does not overlap with the very common one between abstract/concrete objects; second, on the basis of some difficulties with the distinction, we propose, as a possible way out, to move from thin/thick objects to thin/thick concepts.

In this paper, we aim to examine the relationships between four solutions to the dilemma of divine foreknowledge and human freedom— theological determinism, Molinism, simple foreknowledge and open theism—and divine providence and theodicy. Some of these solutions— theological determinism and Molinism, in particular—highlight God’s government of the world. Some others—simple foreknowledge and open theism—highlight human autonomy and freedom. In general, the more libertarian human freedom is highlighted, the less God’s government of the history of the world seems possible. However, the task of theodicy becomes easier because humans are fully responsible for the evil they do. Conversely, the more God’s government is highlighted, the more human freedom seems to be restricted. Moreover, God seems to be directly or indirectly responsible for evil in the world. Because of the trade–off between control and freedom, each solution finds itself at ease with some problems, while on other fronts, it must adopt a defensive position. As we will see, no solution can solve all problems; thus, the pros and cons of each solution should be weighed carefully.

In questo saggio vengono analizzate alcune caratteristiche metateoriche della filosofia analitica della religione.

Non-bivalent semantics of the future tense assert that propositions regarding future contingents are neither true nor false. One of the most relevant non-bivalent semantics is supervaluationism (Thomason in Theoria 36(3):264–281, 1970; Thomason, in: Gabbay, Guenthner (eds) Handbook of philosophical logic, Springer, Berlin, 1984), which preserves important logical principles. Recently, non-bivalent semantics are under attack from some pragmatics arguments: these semanticswould be incompatible with our practices of asserting future contingents and with the probability we ascribe to such assertions (Besson and Hattiangadi in Philosophical Studies 167(2):251–271, 2014; Cariani and Santorio in Mind 127(505):129–165, 2018). The aim of this paper is to defend supervaluationism against this kind of criticism.We argue that, if probability is interpreted as the subjective belief in a proposition and if a semantic contextualism is adopted, supervaluationism makes correct predictions concerning the norms that govern our practices of asserting future contingents. Obviously, other arguments can be proposed against supervaluationism, but they must be of a different kind, such as metaphysical arguments.

In this paper, we deal with the relationships among libertarian human freedom, divine omniscience and providence. Several models try to reconcile human freedom and divine prescience. However, we show that most of these models are defective in accounting for the providential aspect of the divine action. Moreover, the models that hypothesize a meticulous providence tend to restrict human freedom. We show that the Molinist solution can account for both divine prescience and providence without harming human freedom. However, Molinists are able to do so only on the basis of very expensive metaphysical assumptions.

The aim of this entry is to provide an overview of the most important philosophical issues concerning the Artificial Intelligence. The introduction is devoted to shortly analyze the meaning of the term “Artificial Intelligence” and its history; the first section presents Turing’s test and its philosophical significance for the question whether the machines can think. Then, it is discussed John Searle’s Chinese room argument with the exploration of the topics of consciousness and intentionality. The last section is devoted to Catholic Church’s view on these matters.

Supervaluationism is one of the most discussed approaches to the semantics of future tense sentences in a branching time. In this paper, we consider the criticism advanced by Malpass against Supervaluationism. This criticism relies on the fact that supervaluationists must accept as supertrue disjunctions whose disjuncts are not only supertrue-which supervaluationists are ready to acknowledge-but also not satisfiable. In order to show this, Malpass proposes a formula, FF1$$ F{F}_1 $$, which shows the existence of a satisfiable disjunction with unsatisfiable disjuncts in supervaluationist models. In reply, we show that formula FF1$$ F{F}_1 $$ cannot be expressed within a model (whether Ockhamist or supervaluationist) because it quantifies on models. It can be correctly characterised only within a meta-model that has the resources to quantify on various models. However, once that is done, FF1$$ F{F}_1 $$ is, for the advocates of Supervaluationism, no more demanding than other disjunctions because it just generalises at the meta-theoretical level what supervaluationists already acknowledge at the theoretical level.

According to some scholars, universalist semantics of the future are incompatible with classical ascriptions of probability. This alleged fact is used as an argument for the linearist semantics of the future. In this paper, we show that, on the contrary, universalist semantics of the future are in harmony with the theory of probability, while the advocates of linearist semantics have to pay high theoretical costs to maintain the coherence with the classical theory of probability.

The concept of autonomy is crucial for the theoretical characterization of robots and, more in general, complex technological artifacts. The aim of this paper is to provide a conceptual and logical framework in which it is possible to define two concepts of autonomy: autonomy of performance and autonomy of process. The analysis is carried out exploiting the logical resources of the counterfactual semantics – developed by Lewis’ and Stalnaker’s seminal works – and branching structures of the possible courses of actions. It allows to differentiate the autonomy of a robotic arm from the autonomy of a highly complex machine- like rovers for the explorations of the planets. The clarification of the concept of autonomy is, moreover, an essential precondition for the investigation concerning the ethics of artificial agents.

In this paper, we aim to examine the relationships between four solutions to the dilemma of divine foreknowledge and human freedom—theological determinism, Molinism, simple foreknowledge and open theism—and divine providence and theodicy. Some of these solutions—theological determinism and Molinism, in particular—highlight God’s government of the world. Some others—simple foreknowledge and open theism—highlight human autonomy and freedom. In general, the more libertarian human freedom is highlighted, the less God’s government of the history of the world seems possible. However, the task of theodicy becomes easier because humans are fully responsible for the evil they do. Conversely, the more God’s government is highlighted, the more human freedom seems to be restricted. Moreover, God seems to be directly or indirectly responsible for evil in the world. Because of the trade–off between control and freedom, each solution finds itself at ease with some problems, while on other fronts, it must adopt a defensive position. As we will see, no solution can solve all problems; thus, the pros and cons of each solution should be weighed carefully.

The present paper is devoted to present two pragmatic logics and their corresponding intended interpretations according to which an illocutionary act of (scientific) hypothesis-making is justified by a scintilla of evidence. The paper first introduces a general pragmatic frame for assertions, expanded to hypotheses, AH and a hypothetical pragmatic logic for evidence HLP. Both AH and HLP are extensions of the Logic for Pragmatics, LP. We compare AH and HLP. Then, we underline the expressive and inferential richness of both systems in dealing with hypothetical judgements, especially when based on different, sometimes conflicting, evidence.

The pragmatic logic of assertions shows a connection between ignorance and (informal) decidability. In it, we can express pragmatic factual ignorance and first-order ignorance as well as some of their variants. We also show how some pragmatic versions of second-order ignorance and of Rumsfeld-ignorance may be formulated. A specific variant of second-order ignorance is particularly relevant. This indicates a strong pragmatic version of ignorance of ignorance, irreducible to any previous form of ignorance, which defines limits to what can justifiably be asserted about higher-order ignorance. Finally, we relate the justified assertion of second-order ignorance (that cannot be known) with scientific assertions.

Hume’s Principle (HP) states that the cardinal number of the concept F is identical with the cardinal number of G if and only if F and G can be put into one-to-one correspondence. The Schwartzkopff-Rosen Principle (SR Principle) is a modification of HP in terms of metaphysical grounding: it states that if the number of F is identical with the number of G, then this identity is (strictly, fully, and immediately) grounded by the fact that F and G can be paired one-to-one (Rosen 2010, 117; Schwartzkopff Grazer Philosophische Studien, 82(1), 353–373, 2011, 362). HP is central to the neologicist program in the philosophy of mathematics (Wright 1983; Hale and Wright 2001); in this paper we submit that, even if the neo-logicists wish to venture into the metaphysics of grounding, they can avoid the SR Principle. In Section 1 we introduce neo-logicism. In Sections 2 and 3 we examine the SR Principle. We then formulate an account of arithmetical facts which does not rest on the SR Principle; we finally argue that the neo-logicists should avoid the SR Principle in favour of this alternative proposal.

This article aims to show that the simple foreknowledge model does not provide an adequate explanation of God’s providential action. In order to do that, we advance two arguments: the first argument emphasizes the difficulties surrounding the very concept of God’s intervention within history; the second argument advocates the view according to which, for the providence, it seems unavoidable some form of counterfactual reasoning. This suggests the departure for simple foreknowledge in favour of some kind of molinist account.

In our introduction we make some remarks on the main topics of this issue: assertion and proof. We briefly describe how each of the papers in the present publication has contributed from either different or complementary perspectives to the logical reflection on assertion and proof, while also specifying the relation between them.

The aim of this paper is to develop and extend a framework of pragmatic logic for assertions. The base system has been developed by Dalla Pozza and Garola; here, we want to improve the analysis of the justification conditions of the act of assertion. Furthermore, we explore the possibility of a pragmatic logic of denial. We analyse the relationships between denial, negation, and assertion.

The aim of this paper is to investigate some proposals about the possibility of metaphysics. In particular, we want to focus on the relationships between the justification procedures used in empirical sciences and in metaphysics. We develop three models of meta-metaphysics, that is Metaphysics Through Physics, (MTP); Metaphysics Through Physics or Logic, (MTPL); and Metaphysics Constrained by Physics or Logic, (MCPL) and we argue that the latter is able to guarantee an autonomous field of enquiry for metaphysics.

La prima introduzione sistematica alla metafisica analitica contemporanea in Italia.

Are identity criteria grounding principles? A prima facie answer to this question is positive. Specifically, two-level identity criteria can be taken as principles related to issues of identity among objects of a given kind compared with objects of a more basic kind. Moreover, they are grounding metaphysical principles of some objects with regard to others. In the first part of the paper we criticise this prima facie natural reading of identity criteria. This result does not mean that identity criteria could not be taken as grounding principles. In the second part, we propose some basic steps towards a conceptual reading of grounding. Such a way of understanding it goes along with an epistemic reading of identity criteria.

Our aim is to overcome some counterexamples to the classical criteria of abstractness; this can be done, we argue, by considering another fundamental metaphysical distinction, that is, the distinction between dependent and independent entities. By including it in the framework we are able to cast some light on the relationship between abstractness criteria based on the negation of some features of concrete objects (metaphysical criteria) and abstractness criteria based on Frege’s Abstraction Principles (logico-semantical criteria).

Philosophy of mathematics of last fifty years has been dominated by the metaontological stance according to which one fundamental problem of the ontology of mathematical theories is the existence of mathematical objects and the related epistemic access to them. But during the last ten years another fecund and promising metaphysical framework has been developed: the key idea (which goes back to Aristotle) is that the main problem of metaphysics is about the relation of grounding among various levels of reality. Although this approach should be relevant for almost all the metaphysical questions, however, there are few attempts to extend these intuitions to the debate in philosophy of mathematics. The aim of this, preliminary, work is analysing some possible outcomes of the grounding approach in metaphysics of mathematics.

In this paper, we argue that Williamson’s arguments against luminosity and the KK principle do not work, at least in a scientific context. Both of these arguments are based on the presence of a so-called “buffer zone” between situations in which one is in a position to know p and situations in which one is in a position to know ¬p. In those positions belonging to the buffer zone ¬p holds, but one is not in a position to know ¬p. The presence of this buffer zone triggers two types of sorites arguments. We show that this kind of argument does not hold in a scientific context, where the buffer zone is controlled by a quantitative measurement of the experimental error.

In the first part of this paper, we analyze the concept of open future. Our main thesis is that the indeterminateness of the future crucially depends on the perspective from which the propositions containing the future operator are evaluated. For this reason, we offer a perspectival temporal semantics, in which propositions are evaluated with respect to two indexes: the time of evaluation and the time of the perspective. This demonstrates the compatibility of this semantics with both a tensed and a tenseless metaphysics of time. In the second part, we apply the theoretical device of perspectival semantics to the problem of divine foreknowledge, demonstrating that this semantics proves to be promising in the solution of the foreknowledge problem. Finally, we discuss this solution from the point of view of both a tenseless and a tensed conception of the universe.

The aim of this paper is twofold: on the one hand, to provide a conceptual analysis of the so called moving spotlight theory of time, highlighting its underlying metaphysical assumptions; on the other hand, to develop a semantics for a temporal logic which allows us to grasp the philosophical background of this theory.

In addressing the problem of the (in)compatibility of divine foreknowledge and human freedom, philosophers of religion encounter problems regarding the metaphysics and structure of time. Some models of temporal logic developed for completely independent reasons have proved especially appropriate for representing the temporal structure of the world as Molinism conceives it. In particular, some models of the Thin Red Line (TRL) seem to imply that conditionals of freedom are true or false, as Molinists maintain. Noting the resemblance between Molinism and TRL models, Restall (2011) has advanced some criticisms of Molinism that have also been leveled against TRL models. In particular, Restall believes that the implication p --> HFp is not true in TRL models. Because Molinists must also accept that this implication is not true, this is a problem for them. We will show that Restall’s criticism is wide of the mark. Firstly, it will be demonstrated that in many open future models (not just TRL) the implication p --> HFp is invalid. Secondly, while it is possible to account for this implication, some modifications are required in respect of the branching time semantics. In proposing one such modification, we show that this new semantics can be adopted by advocates of the TRL and, as a consequence, by Molinists as well. We conclude that the principle stated by Restall is either a problem for many open future models (not just for Molinists) or can be accounted for by these models and so is not a problem for Molinists either.

The aim of this paper is to discuss Bergmann’s method of ideal language. According to Bergmann, philosophical questions – and, particularly, metaphysical ones – have to be solved by reflecting on the syntactical structure of the ideal language. This procedure should guarantee rigour and coherence to philosophy; however, this proposal seems to be puzzling. After shortly retracing Bergmann’s position, we argue that within it there seem to be conceptual tensions and that it is internally instable.

This is a special Issue of Logique et Analyse devoted to the logic of speech acts.

The aim of this paper is to provide an example for each extension strategy of the pragmatic logic. Firstly, we analytically introduce the logic for pragmatics LP as a logic for assertions. Then, in section 3, we embrace the first strategy in an attempt to show that the speech act of denial can be reduced to the act of assertion (we are assuming, indeed, the equivalence thesis). However, we will see that this attempt fails: the act of denying A cannot be reduced to the act of asserting ¬ A. In section 4 and section 5, we propose two extensions of LP: the first one, which follows the first sub-strategy, previously cited, permits the treatment of the hypotheses, the second one, which is in harmony with the second sub-strategy, is such that the act of proving is formalisable.

This book deals with an old conundrum: if God knows what we will choose tomorrow, how can we be free to choose otherwise? If all our choices are already written, is our freedom simply an illusion? This book provides a precise analysis of this dilemma using the tools of modern metaphysics and logic of time. With a focus on three intertwined concepts - God’s nature, the formal structure of time, and the metaphysics time, including the relationship between temporal entities and a timeless God - the chapters analyse various solutions to the problem of foreknowledge and freedom, revealing the advantages and drawbacks of each. Building on this analysis, the authors advance constructive solutions, showing under what conditions an entity can be omniscient in the presence of free agents, and whether an eternal entity can know the tensed futures of the world. The metaphysics of time, its topology and the semantics of future tensed sentences are shown to be invaluable topics in dealing with this issue. Combining investigations into the metaphysics of time with the discipline of temporal logic this monograph brings about important advancements in the philosophical understanding of an ancient and fascinating problem. The answer, if any, is hidden in the folds of time, in the elusive nature of this feature of reality and in the infinite branching of our lives.

This is the book of abstracts for the International Conference held at Lecce University Assertion and Proof

The species concept is one of the central concepts in biological science. Although modern systematics speculates about the existence of a complex hierarchy of nested taxa, biological species are considered particularly important for the active role they play in evolution. However, neither theoretical biologists nor philosophers of biology have come to an agreement about what a species is. In this chapter, we address two questions pertaining to biological species: (1) are they individuals or universals? and (2) are they bona fide or fiat entities? In section The Species-as-Individuals View, we illustrate the reasons that have led many scholars to support the view that species are individuals. In the next two sections, we show that the relational concepts of species – on which the species-as-individuals view is based – provide neither necessary nor sufficient conditions for species membership. This seriously undermines the species-as-individuals view. In the section A Conceptualist Model for the Metaphysics of Species, we advance the proposal that species are fiat concepts (and thus, universal entities partially dependent on the human mind) carved in a multi-dimensional space representing the properties that the biological organisms possess. The final section concludes.

How to Say 'Yes' or 'No': Logical Approaches to Modes of Assertion and Denial. Book of Abstracts.

Com’è possibile conciliare l’onniscienza di Dio con la libertà degli esseri umani? In fondo, se Dio conosce fin dall’eternità l’esito della storia, non è forse tutto già scritto, immutabile e quindi vana la nostra pretesa di essere protagonisti del nostro destino? Domande simili hanno assillato teologi, filosofi e credenti di tutti i tempi – anche al di fuori della fede cristiana. La questione è cruciale e tocca due cardini di quella che, un po’ sbrigativamente, potremmo chiamare concezione religiosa del mondo: l’esistenza di un’entità suprema che conosce ogni cosa e la possibilità da parte degli esseri umani (ma anche di altre entità personali) di autodeterminare le loro esistenze. Scopo di questo lavoro è fornire una rassegna sintetica, ma aggiornata, circa le trattazioni filosofiche del problema dell’onniscienza divina e della libertà umana.

Following the speech act theory, we take hypotheses and assertions as linguistic acts with different illocutionary forces. We assume that a hypothesis is justified if there is at least a scintilla of evidence for the truth of its propositional content, while an assertion is justified when there is conclusive evidence that its propositional content is true. Here we extend the logical treatment for assertions given by Dalla Pozza and Garola (1995, Erkenntnis, 43, 81–109) by outlining a pragmatic logic for assertions and hypotheses. On the basis of this extension we analyse the standard logical opposition relations for assertions and hypotheses. We formulate a pragmatic square of oppositions for assertions and a hexagon of oppositions for hypotheses. Finally, we give a mixed hexagon of oppositions to point out the opposition relations for assertions and hypotheses

This paper has a twofold aim. The first is to offer a precise definition of soft fact. Without such definition it is impossible to assess the Ockhamist solution to the problem of divine foreknowledge and human freedom in an accurate way. The second purpose is to identify the costs of such a solution, distinguishing them from some of the other costs usually ascribed to Ockhamism, which Ockhamism does not actually need to pay. In particular, it is argued that Ockhamism is committed to the view that a true future exists and to a form of backward causation.

The timeless solution to the problem of divine foreknowledge and human freedom has many advantages. Still, the relationship between a timeless God and temporal beings is problematic in a number of ways. In this paper, we focus on the specific problems the timeless view has to deal with when certain assumptions on the metaphysics of time are taken on board. It is shown that on static conception of time God’s omniscience is easily accounted for, but human freedom is threatened, while a dynamic conception has no problems with human freedom, but, on this view, some truths seem not to be knowable by a timeless God. We propose Fragmentalism as a metaphysics of time in which the divine timeless knowledge of temporal events and human freedom can be reconciled.

Linnebo argues that Boolos' interpretation of second order monadic logic (MSOL) is not logic. His argument starts by proposing some conditions for logicality (ontological innocence, cognitive primacy, and universal applicability) and goes on arguing that Boolos' proposal does not satisfy them. The problem is that, in our view, Linnebo's conditions for logicality meet some general difficulties on the very same notion. His formulation cannot be considered a good test for demarcating what is logic at all. Take first order logic (F OL ): either it does not satisfy the conditions proposed or it satisfies them trivially. A positive result of our analysis is that an account of logicality based on independency is better evaluable in a relational setting.

This is a review of Evandro Agazzi's book "Ragioni e limiti del formalismo"

L'articolo difende una concezione aprioristica del sapere matematico che fa appello a una forma di intuizione intellettiva delle entità matematiche.

The aim of this work is to provide a sufficiently reliable criterion for distinguishing abstract entities from concrete entities. The two mail candidates are the non spatio-temporal collocation and the abstraction principles à la Frege. We suggest that these criteria have to be considered as complementary and not opposite; this fact is explained by the metaphysical framework of the abstract entities taken into account, namely if they are dependent or independent entities. Since each criterion has an intended background metaphysical framework, the adoption of both will make more complex the description of the domain of abstracta.

The idea of omnipotence plays a crucial role within the framework of classical theism. God is typically considered omnipotent, that is, able to perform any action. Sometimes, it is said that for God there is no difference between will and action; everything he wishes happens. However, as one reflects on the concept of omnipotence, some rather complex questions arise; the range of God’s possible “actions” is not clear. What are the boundaries of the power of an omnipotent being, if these boundaries exist at all? In this paper, we will examine an interesting question: is it possible that two omnipotent beings exist? Or, does the property of omnipotence necessarily imply the uniqueness of its instantiation? Intuitively, the existence of more than one omnipotent being seems to be contradictory. However, we will demonstrate that under some conditions the existence of two omnipotent beings is possible.

In a classical theory of denial to deny A is equivalent to asserting ¬A. Glut theorists reject the right-to-left direction of the Classical denial: asserting ¬A must not commit one to denying A, i.e. denial must not be reducible to the assertion of ¬A. In particular, the paraconsistent denial of A is stronger than the assertion of ¬A. Unlike paraconsistent negation, which allows for overlap between truthand falsity, denial is assumed to be exclusive: assertion and denial are mutually incompatible speech acts. Starting from this basic idea, i.e. that assertion and denial are mutually incompatible speech acts, we outline a logic for denial. We first consider a logic for assertion, i.e. the logic for pragmatics (LP), proposed by DallaPozza and Garola in Dalla Pozza and Garola (1995) and ask: Is it possibile to extend LP so to include also the speech act of denial? First, we defend a negative answer to the question, then we outline a new pragmatic logicthat should be considered as a logic of denial LPD.