This work proposes an understanding of deductive, default and abductive reasoning as different instances of the same phenomenon: epistemic dynamics. It discusses the main intuitions behind each one of these reasoning processes, and suggest how they can be understood as different epistemic actions that modify an agent’s knowledge and/or beliefs in a different way, making formal the discussion with the use of the dynamic epistemic logic framework. The ideas in this paper put the studied processes under the same umbrella, thus (...) highlighting their relationship and allowing a better understanding of how they interact together. (shrink)

This work proposes an understanding of deductive, default and abductive reasoning as different instances of the same phenomenon: epistemic dynamics. It discusses the main intuitions behind each one of these reasoning processes, and suggest how they can be understood as different epistemic actions that modify an agent’s knowledge and/or beliefs in a different way, making formal the discussion with the use of the dynamic epistemic logic framework. The ideas in this paper put the studied processes under the same umbrella, thus (...) highlighting their relationship and allowing a better understanding of how they interact together. (shrink)

Dans la philosophie de Hintikka la notion d'analyticité occupe une place particulière (e.g., [Hintikka 1973], [Hintikka 2007]) ; plus précisément, le philosophe finnois distingue deux notions d'analyticité : l'une qui est basée sur la notion d'information, l'autre sur la notion de preuve. Alors que ces deux notions ont été largement utilisées pour étudier la logique propositionnelle et la logique du premier ordre, aucun travail n'a été développé pour la logique modale. Cet article se propose de combler cette lacune et ainsi (...) d'examiner l'analyticité des validités de la logique modale. (shrink)

Classical propositional logic plays a prominent role in industrial applications, and yet the complexity of this logic is presumed to be non-feasible. Tractable systems such as depth-bounded boolean logics approximate classical logic and can be seen as a model for resource-bounded agents whose reasoning style is nonetheless classical. In this paper we first study a hierarchy of tractable logics that is not defined by depth. Then we extend it into a modal logic where modalities make explicit the assumptions discharged in (...) propositional proofs, thereby expressing blueprints for proofs. A natural deduction system is provided that permits to reason about and manage such proof blueprints. (shrink)

In the chapter “Information and Content” of their Impossible Worlds, Berto and Jago provide us with a semantic account of information in deductive reasoning such that we have an explanation for why some, but not all, logical deductions are informative. The framework Berto and Jago choose to make sense of the above-mentioned idea is a semantic interpretation of Sequent Calculus rules of inference for classical logic. I shall argue that although Berto and Jago’s idea and framework are hopeful, their definitions (...) do not capture what is intended. This is so because the definitions are solely based on the logical complexity of an argument and they fail to capture the richness of the non- logical content of that argument. Then I will suggest some amendments to address this problem. Finally, I will extend the application of the definitions to first-order logic. It shall be observed that in some classical deductions, applying contraction may lead to hiding some epistemic impossibilities. This happens when formulae which contribute different propositions to the proof get contracted at the quantified level. (shrink)

In consciousness science, theories often differ not only in the account of consciousness they arrive at, but also with respect to how they understand their starting point. Some approaches begin with experimentally gathered data, whereas others begin with phenomenologically gathered data. In this paper, I analyse how the most influential phenomenology-first approach, namely the Integrated Information Theory (IIT) of consciousness, fits its phenomenologically gathered data with explanatory hypotheses. First, I show that experimentally driven approaches hit an explanatory roadblock, since we (...) cannot tell, at the present stage, which model of consciousness is best. Then, I show that IIT’s phenomenology-first approach implies a self-evidencing explanation according to which consciousness can be explained by starting from consciousness itself. I claim that IIT can take advantage of the virtuous circularity of this reasoning, but it also faces a data-fitting issue that is somehow similar to that faced by experiment-driven approaches: we are not given enough information to decide whether the explanatory hypotheses IIT employs to explain its phenomenological data are in fact best. I call this problem “the self-evidencing problem” for IIT, and after introducing it, I propose a possible way for IIT to solve it. (shrink)

Recent years have seen a renewed interest in the philosophical study of information. In this paper a two-part analysis of information gain—objective and subjective—in the context of doxastic change is presented and discussed. Objective information gain is analyzed in terms of doxastic movement towards true belief, while subjective information gain is analyzed as an agent’s expectation value of her objective information gain for a given doxastic change. The resulting expression for subjective information gain turns out to be a familiar one (...) with well-known formal properties: the Kullback–Leibler divergence. The two notions of information are discussed and the suggested measure of subjective information gain is then compared with the widely held view that information gain equals uncertainty reduction. (shrink)

In a series of papers published in the sixties and seventies, Jaakko Hintikka, drawing upon Kant’s conception, defines an argument to be analytic whenever it does not introduce new individuals into the discussion and argues that there exists a class of arguments in polyadic first-order logic that are to be synthetic according to this sense. His work has been utterly overlooked in the literature. In this paper, I claim that the value of Hintikka’s contribution has been obscured by his formalisation (...) of the original definition. Therefore, I provide (i) a brief reconstruction of the historical framework of the problem and the revolutionary import of Hintikka’s contribution, (ii) a clarification of the most complicated steps of Hintikka’s elaboration of his insight, (iii) a criticism of several features that play a fundamental role in Hintikka’s formalisation and (iv) a selection from Hintikka’s own material of some valuable suggestions towards a clear and workable formalisation. As for the pars construens, I isolate in the approach of depth-bounded first-order logics (D'Agostino et al. 2021) an alternative formalisation of the notion of syntheticity as the introduction of new individuals in the reasoning, and I show that it is not affected by the same difficulties as Hintikka’s proposal. In so doing, I hope to have contributed to the realisation of the project of rehabilitating Kant’s analytic–synthetic distinction in the context of modern first-order logic with the purpose of showing, against the logical empiricist movement, that logic is not analytic. (shrink)

There are many ways of understanding the nature of philosophical questions. One may consider their morphology, semantics, relevance, or scope. This article introduces a different approach, based on the kind of informational resources required to answer them. The result is a definition of philosophical questions as questions whose answers are in principle open to informed, rational, and honest disagreement, ultimate but not absolute, closed under further questioning, possibly constrained by empirical and logico-mathematical resources, but requiring noetic resources to be answered. (...) The article concludes with a discussion of some of the consequences of this definition for a conception of philosophy as the study (or “science”) of open questions, which uses conceptual design to analyse and answer them. (shrink)

Three classic distinctions specify that truths can be necessary versus contingent,analytic versus synthetic, and a priori versus a posteriori. The philosopher reading this article knows very well both how useful and ordinary such distinctions are in our conceptual work and that they have been subject to many and detailed debates, especially the last two. In the following pages, I do not wish to discuss how far they may be tenable. I shall assume that, if they are reasonable and non problematic (...) in some ordinary cases, then they can be used in order to understand what kind of knowledge the maker’s knowledge is. By this I mean the sort of knowledge that Alice enjoys when she holds the information that Bob’s coffee is sweetened because she just put two spoons of sugar in it herself. The maker’s knowledge tradition is quite important but it is not mainstream in modern and analytic epistemology and lacks grounding in terms of exactly what sort of knowledge one is talking about. My suggestion is that this grounding can be provided by a minimalist approach, based on an information-theoretical analysis. In the article, I argue that we need to decouple a fourth distinction, namely informative versus uninformative, from the previous three and, in particular, from its implicit association with analytic versus synthetic and a priori versus a posteriori; such a decoupling facilitates, and is facilitated by, moving from a monoagent to a multiagent approach: the distinctions qualify a proposition, a message, or some information not just in themselves but relationally, with respect to an informational agent; the decoupling and the multiagent approach enable a re-mapping of currently available positions in epistemology on these four dichotomies; within such a re-mapping, two positions, capturing the nature of a witness’ knowledge and of a maker’s knowledge, can best be described as contingent, synthetic, a posteriori, and uninformative and as contingent, synthetic, weakly a priori, and uninformative respectively. In the conclusion, I indicate why the analysis of the maker’s knowledge has important consequences in all those cases in which the poietic intervention on a system determines the truth of the model of that system. (shrink)

A prominent objection against the logicality of second-order logic is the so-called Overgeneration Argument. However, it is far from clear how this argument is to be understood. In the first part of the article, we examine the argument and locate its main source, namely, the alleged entanglement of second-order logic and mathematics. We then identify various reasons why the entanglement may be thought to be problematic. In the second part of the article, we take a metatheoretic perspective on the matter. (...) We prove a number of results establishing that the entanglement is sensitive to the kind of semantics used for second-order logic. These results provide evidence that by moving from the standard set-theoretic semantics for second-order logic to a semantics which makes use of higher-order resources, the entanglement either disappears or may no longer be in conflict with the logicality of second-order logic. (shrink)

The article investigates the sceptical challenge from an informationtheoretic perspective. Its main goal is to articulate and defend the view that either informational scepticism is radical, but then it is epistemologically innocuous because redundant; or it is moderate, but then epistemologically beneficial because useful. In order to pursue this cooptation strategy, the article is divided into seven sections. Section 1 sets up the problem. Section 2 introduces Borei numbers as a convenient way to refer uniformly to (the data that individuate) (...) different possible worlds. Section 3 adopts the Hamming distance between Borei numbers as a metric to calculate the distance between possible worlds. In Sects. 4 and 5, radical and moderate informational scepticism are analysed using Borei numbers and Hamming distances, and shown to be either harmless (extreme form) or actually fruitful (moderate form). Section 6 further clarifies the approach by replying to some potential objections. In the conclusion, the Peircean nature of the overall approach is briefly discussed. (shrink)

In this article, I define and then defend the principle of information closure (pic) against a sceptical objection similar to the one discussed by Dretske in relation to the principle of epistemic closure. If I am successful, given that pic is equivalent to the axiom of distribution and that the latter is one of the conditions that discriminate between normal and non-normal modal logics, a main result of such a defence is that one potentially good reason to look for a (...) formalization of the logic of “ $S$ is informed that $p$ ” among the non-normal modal logics, which reject the axiom, is also removed. This is not to argue that the logic of “ $S$ is informed that $p$ ” should be a normal modal logic, but that it could still be insofar as the objection that it could not be, based on the sceptical objection against pic, has been removed. In other word, I shall argue that the sceptical objection against pic fails, so such an objection provides no ground to abandon the normal modal logic B (also known as KTB) as a formalization of “ $S$ is informed that $p$ ”, which remains plausible insofar as this specific obstacle is concerned. (shrink)

Contemporary science seems to be caught in a strange predicament. On the one hand, it holds a firm and reasonable commitment to a healthy naturalistic methodology, according to which explanations of natural phenomena should never overstep the limits of the natural itself. On the other hand, contemporary science is also inextricably and now inevitably dependent on ever more complex technologies, especially Information and Communication Technologies, which it exploits as well as fosters. Yet such technologies are increasingly “artificialising” or “denaturalising” the (...) world, human experiences and interactions, as well as what qualifies as real. So the search for the ultimate explanation of the natural seems to rely upon, and promote, the development of the artificial, seen here as an instantiation of the non-natural. In this article, I would like to try and find a way out of this apparently strange predicament. I shall argue that the naturalisation of our knowledge of the world is either philosophically trivial, or mistaken. First, I shall distinguish between different kinds of naturalism. Second, I shall remind the reader that the kinds of naturalism that are justified today need to be protected and supported pragmatically, but they are no longer very interesting conceptually. We know how to win the argument. We just have to keep winning it. Whereas the kind of naturalism that is still interesting today is now in need of revision in order to remain acceptable. Such a kind of naturalism may be revised on the basis of a realistic philosophy of information, according to which knowing is a constructive activity, through which we do not merely represent the phenomena we investigate passively, but create more or less correct informational models of them, proactively and interactively. I shall conclude that the natural is in itself artefactual, and that the information revolution is disclosing a tension not between the natural and the non-natural, but a deeper one between a user’s and a producer’s interpretation of knowledge. The outcome is a philosophical view of knowledge and science in the information age that may be called constructionist and a revival of philosophy as a classic, foundationalist enterprise. (shrink)

The classical theory of semantic information (ESI), as formulated by Bar-Hillel and Carnap in 1952, does not give a satisfactory account of the problem of what information, if any, analytically and/or logically true sentences have to offer. According to ESI, analytically true sentences lack informational content, and any two analytically equivalent sentences convey the same piece of information. This problem is connected with Cohen and Nagel's paradox of inference: Since the conclusion of a valid argument is contained in the premises, (...) it fails to provide any novel information. Again, ESI does not give a satisfactory account of the paradox. In this paper I propose a solution based on the distinction between empirical information and analytic information. Declarative sentences are informative due to their meanings. I construe meanings as structured hyperintensions, modelled in Transparent Intensional Logic as so-called constructions. These are abstract, algorithmically structured procedures whose constituents are sub-procedures. My main thesis is that constructions are the vehicles of information. Hence, although analytically true sentences provide no empirical information about the state of the world, they convey analytic information, in the shape of constructions prescribing how to arrive at the truths in question. Moreover, even though analytically equivalent sentences have equal empirical content, their analytic content may be different. Finally, though the empirical content of the conclusion of a valid argument is contained in the premises, its analytic content may be different from the analytic content of the premises and thus convey a new piece of information. (shrink)

(1) If a deductive argument is valid, then the conclusion is not novel. (2) If the conclusion of an argument is not novel, the argument is not useful. So, (3) if a deductive argument is valid, it is not useful. This conclusion, (3), is unacceptable. Since the argument is valid, we must reject at least one premise. So, should we reject (1) or (2)? This puzzle is usually known as the ‘scandal of deduction’. Analytic philosophers have tried to reject (1) (...) but have assumed premise (2). I argue here that Aristotle would deny (2). Aristotle thinks that at least some deductive arguments are useful, even though they present no new conclusions. Thus, Aristotle’s view contrasts with analytic philosophers of logic, who assume that all useful deductive arguments present novel conclusions. I don’t claim that Aristotle ‘solves’ the problem: it was never posed in Aristotle’s time. Rather, I suggest that Aristotle does not face the problem because he assumes deductions can be useful, without presenting novel conclusions. Aristotle’s view of deduction tames the scandal. (shrink)

In this paper we provide a detailed proof-theoretical analysis of a natural deduction system for classical propositional logic that (i) represents classical proofs in a more natural way than standard Gentzen-style natural deduction, (ii) admits of a simple normalization procedure such that normal proofs enjoy the Weak Subformula Property, (iii) provides the means to prove a Non-contamination Property of normal proofs that is not satisfied by normal proofs in the Gentzen tradition and is useful for applications, especially in formal argumentation, (...) (iv) naturally leads to defining a notion of depth of a proof, to the effect that, for every fixed natural k, normal k-depth deducibility is a tractable problem and converges to classical deducibility as k tends to infinity. (shrink)

This volume presents recent advances in philosophical logic with chapters focusing on non-classical logics, including paraconsistent logics, substructural logics, modal logics of agency and other modal logics. The authors cover themes such as the knowability paradox, tableaux and sequent calculi, natural deduction, definite descriptions, identity, truth, dialetheism and possible worlds semantics. The developments presented here focus on challenging problems in the specification of fundamental philosophical notions, as well as presenting new techniques and tools, thereby contributing to the development of the (...) field. Each chapter contains a bibliography, to assist the reader in making connections in the specific areas covered. Thus this work provides both a starting point for further investigations into philosophical logic and an update on advances, techniques and applications in a dynamic field. The chapters originate from papers presented during the Trends in Logic XI conference at the Ruhr University Bochum, June 2012. (shrink)

Rational agents base their actions on information from observation, inference, introspection, or other sources. But this information comes in different kinds, and it is usually handled by different logical mechanisms. We discuss how to integrate external ‘updating information’ and internal ‘elucidating information’ into one system of dynamic epistemic logic, by distinguishing two basic informational actions: ‘bare seeing’ versus ‘conscious realization’.

This chapter addresses two questions. First, if knowledge is accounted information, how are we supposed (to apply this analysis in order) to understand perceptual knowledge and knowledge by testimony? In the first part of the chapter, I articulate an answer in terms of a re-interpretation of perception and testimony as data providers rather than full-blown cases of knowledge. Second, if perception and testimony are correctly understood as data providers, how are we supposed (to apply this analysis in order) to understand (...) the semantic value of the data provided by such processes? In the second part of the chapter, I argue in favour of a constructionist hypothesis about how data may become meaningful for human cognitive agents through a process of repurposing of natural data/signals. The conclusion of the chapter is that human agents are natural-born data hackers. (shrink)

The topic of this paper may be introduced by fast zooming in and out of the philosophy of information. In recent years, philosophical interest in the nature of information has been increasing steadily. This has led to a focus on semantic information, and then on the logic of being informed, which has attracted analyses concentrating both on the statal sense in which S holds the information that p (this is what I mean by logic of being informed in the rest (...) of this article) and on the actional sense in which S becomes informed that p. One of the consequences of the logic debate has been a renewed epistemological interest in the principle of information closure (henceforth PIC), which finally has motivated a revival of a skeptical objection against its tenability first made popular by Dretske. This is the topic of the paper, in which I seek to defend PIC against the skeptical objection. If I am successful, this means – and we are now zooming out – that the plausibility of PIC is not undermined by the skeptical objection, and therefore that a major epistemological argument against the formalization of the logic of being informed based on the axiom of distribution in modal logic is removed. But since the axiom of distribution discriminates between normal and non-normal modal logics, this means that a potentially good reason to look for a formalization of the logic of being informed among the non-normal modal logics, which reject the axiom, is also removed. And this in turn means that a formalization of the logic of being informed in terms of the normal modal logic B (also known as KTB) is still very plausible, at least insofar as this specific obstacle is concerned. In short, I shall argue that the skeptical objection against PIC fails, so it is not a good reason to abandon the normal modal logic B as a good formalization of the logic of being informed. (shrink)

Philosophers of information, according to Luciano Floridi (The philosophy of information. Oxford University Press, Oxford, 2010, p 32), study how information should be “adequately created, processed, managed, and used.” A small number of epistemologists have employed the concept of information as a cornerstone of their theoretical framework. How this concept can be used to make sense of seemingly intractable epistemological problems, however, has not been widely explored. This paper examines Fred Dretske’s information-based epistemology, in particular his response to radical epistemological (...) skepticism. We discuss the relationship between information, evidence and knowledge in relation to the problem of skepticism and the options available to an information-based epistemology for dealing with it. (shrink)

This special issue collects together nine new essays on logical consequence :the relation obtaining between the premises and the conclusion of a logically valid argument. The present paper is a partial, and opinionated,introduction to the contemporary debate on the topic. We focus on two influential accounts of consequence, the model-theoretic and the proof-theoretic, and on the seeming platitude that valid arguments necessarilypreserve truth. We briefly discuss the main objections these accounts face, as well as Hartry Field’s contention that such objections (...) show consequenceto be a primitive, indefinable notion, and that we must reject the claim that valid arguments necessarily preserve truth. We suggest that the accountsin question have the resources to meet the objections standardly thought to herald their demise and make two main claims: (i) that consequence, as opposed to logical consequence, is the epistemologically significant relation philosophers should be mainly interested in; and (ii) that consequence is a paradoxical notion if truth is. (shrink)

In this paper I use the distinction between hard and soft information from the dynamic epistemic logic tradition to extend prior work on informational conceptions of logic to include non-monotonic consequence-relations. In particular, I defend the claim that at least some non-monotonic logics can be understood on the basis of soft or “belief-like” logical information, and thereby question the orthodox view that all logical information is hard, “knowledge-like”, information.