Ciro De Florio

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 model-theoretic 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.

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 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.

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 this paper, we will defend a particular version of the timeless solution to the problem of divine foreknowledge and human freedom. Our strategy is grounded on a particular temporal framework, which models the flow of time and a libertarian understanding of freedom. The propositions describing a certain act by an agent have an indeterminate truth value until the agent makes her choice; therefore, they become true or false when a decision is made. In order to account for this change of truth value, a multiple frame structure is introduced in which every frame presents a privileged time, with its past and the possible alternative futures, which are still open. God atemporally knows all the frames and the truth values of propositions with respect to each one. Since divine knowledge of what an agent decides in a certain temporal frame depends on the agent’s act itself, divine knowledge does not conflict with the agent’s free will

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.

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 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.

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.

Published in honor of Sergio Galvan, this collection concentrates on the application of logical and mathematical methods for the study of central issues in formal philosophy. The volume is subdivided into four sections, dedicated to logic and philosophy of logic, philosophy of mathematics, philosophy of science, metaphysics and philosophy of religion. The contributions adress, from a logical point of view, some of the main topics in these areas. The first two sections include formal treatments of: truth and paradoxes; definitions by abstraction; the status of abstract objects, such as mathematical objects and universal concepts; and the structure of explicit knowledge. The last two sections include papers on classical problems in philosophy of science, such as the status of subjective probability, the notion of verisimilitude, the notion of approximation, and the theory of mind and mental causation, and specific issues in metaphysics and philosophy of religion, such as the ontology of species, actions, and intelligible worlds, and the logic of religious belonging.

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, F F 1, which shows the existence of a satisfiable disjunction with unsatisfiable disjuncts in supervaluationist models. In reply, we show that formula 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, 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.

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. Specifically, 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 quantifier on histories. However, since natural language does not show this difference, one may conclude that there is no universal quantifier in the interpretation of these sentences. We show that this conclusion is premature. First, will has clear scope interactions with indefinite 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.

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 :264–281, 1970; Thomason, in: Gabbay, Guenthner Handbook of philosophical logic, Springer, Berlin, 1984), which preserves important logical principles. Recently, non-bivalent semantics are under attack from some pragmatics arguments: these semantics would be incompatible with our practices of asserting future contingents and with the probability we ascribe to such assertions :251–271, 2014; Cariani and Santorio in Mind 127:129–165, 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 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 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 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.

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 ontology and the logic of time. With a focus on three intertwined concepts - God's nature, the formal structure of time, and the metaphysics of 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.

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

In addressing the problem of the 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 ) seem to imply that conditionals of freedom are true or false, as Molinists maintain. Noting the resemblance between Molinism and \ models, Restall Molinism: the contemporary debate, pp 227–239, 2011) has advanced some criticisms of Molinism that have also been leveled against \ models. In particular, Restall believes that the implication \ is not true in \ 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 ) the implication \ 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 \ 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 or can be accounted for by these models and so is not a problem for Molinists either.

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.

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.

The pragmatic logic of assertions shows a connection between ignorance and 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 with scientific assertions.

In this paper, we have analyzed a number of solutions to the antinomy between divine foreknowledge and human freedom. If we assume that God is temporal, then a sort of backwards causation of past divine beliefs by future human acts must be acknowledged. Since this solution runs into difficulties, we consider the prospects of the view according to which God is outside time. A timeless and omniscient God seems to imply a B-theory of time and, at least at first glance, seems to jeopardize human freedom. Therefore, we have examined what happens when a non-standard A-theory of time like Fragmentalism is assumed. We demonstrate that in this case the prospects of a timeless view of God are much better: both human freedom and divine knowledge of the results of human choices are preserved if this metaphysics of time is adopted. The costs of this solution are, however, very high. From the logical point of view, it rejects bivalence; from the metaphysical point of view, the world is regarded as fragmentary and incoherent. However, if one is ready to accept these costs, this solution is one of the most successful in the search for a solution to the centuries-old problem of the conciliation between divine foreknowledge and human freedom.

Hume’s Principle 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 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 grounded by the fact that F and G can be paired one-to-one, 353–373, 2011, 362). HP is central to the neo-logicist program in the philosophy of mathematics ; 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.