Logics and Their Galaxies

This article introduces some concepts that help exploring the ontological import of universal logic. It studies the notions of an antilogic and counterlogic associated to each logic and shows some of their properties. It presents the notion of galaxy, as the class of possible worlds compatible with a given logic.We explore some consequences of these developments

Semantics and Ontology:\ud On the Modal Structure of an Epistemic Theory of Meaning

In this paper I shall confront three basic questions.\ud First, the relevance of epistemic structures, as formalized\ud and dealt with by current epistemic logics, for a\ud general Theory of meaning. Here I acknowledge M. Dummett"s\ud idea that a systematic account of what is meaning of\ud an arbitrary language subsystem must especially take into\ud account the inferential components of meaning itself. That\ud is, an analysis of meaning comprehension processes,\ud given in terms of epistemic logics and semantics for epistemic\ud notions.\ud The second and third questions relate to the ontological\ud and epistemological framework for this approach.\ud Concerning the epistemological aspects of an epistemic\ud theory of meaning, the question is: how epistemic logics\ud can eventually account for the informative character of\ud meaning comprehension processes. "Information� seems\ud to be built in the very formal structure of epistemic processes,\ud and should be exhibited in modal and possibleworld\ud semantics for propositional knowledge and belief.\ud However, it is not yet clear what is e.g. a possible world.\ud That is: how it can be defined semantically, other than by\ud accessibility rules which merely define it by considering its\ud set-theoretic relations with other sets-possible worlds.\ud Therefore, it is not clear which is the epistemological status\ud of propositional information contained in the structural\ud aspects of possible world semantics. The problem here\ud seems to be what kind of meaning one attributes to the\ud modal notion of possibility, thus allowing semantical and\ud synctactical selectors for possibilities. This is a typically\ud Dummett-style problem.\ud The third question is linked with this epistemological\ud problem, since it is its ontological counterpart. It concerns\ud the limits of the logical space and of logical semantics for a\ud of meaning. That is, it is concerned with the kind of\ud structure described by inferential processes, thought, in a\ud fregean perspective, as pre-conditions of estentional\ud treatment of meaning itself. The second and third questions\ud relate to some observations in Wittgenstein"s Tractatus.\ud I shall also try to show how their behaviour limits the\ud explicative power of some semantics for epistemic logics\ud (Konolige"s and Levesque"s for knowledge and belief)

Impossibility and Impossible Worlds

Possible worlds have found many applications in contemporary philosophy: from theories of possibility and necessity, to accounts of conditionals, to theories of mental and linguistic content, to understanding supervenience relationships, to theories of properties and propositions, among many other applications. Almost as soon as possible worlds started to be used in formal theories in logic, philosophy of language, philosophy of mind, metaphysics, and elsewhere, theorists started to wonder whether impossible worlds should be postulated as well. In many applications, possible worlds face limitations that can be dealt with through postulating impossible worlds as well. This chapter examines some of the uses of impossible worlds, and philosophical challenges theories of impossible worlds face

The Ontological Ground of the Alethic Modality

This paper is concerned with the wholly metaphysical question of whether necessity and possibility rest on nonmodal foundations—whether the truth conditions for modal statements are, in the final analysis, nonmodal. It is argued that Lewis’s modal realism is either arbitrary and stipulative or else it is circular. Even if there were Lewisean possible worlds, they could not provide the grounds for modality. D. M. Armstrong’s combinatorial approach to possibility suffers from similar defects. Since more traditional reductions to cognitive or linguistic facts suffer similar fates, the conclusion that the alethic modality is primitive and incapable of reduction is offered

Actuality and the a priori

We consider a natural-language sentence that cannot be formally represented in a first-order language for epistemic two-dimensional semantics. We also prove this claim in the “Appendix” section. It turns out, however, that the most natural ways to repair the expressive inadequacy of the first-order language render moot the original philosophical motivation of formalizing a priori knowability as necessity along the diagonal

Counting Incompossibles

We often speak as if there are merely possible people—for example, when we make such claims as that most possible people are never going to be born. Yet most metaphysicians deny that anything is both possibly a person and never born. Since our unreflective talk of merely possible people serves to draw non-trivial distinctions, these metaphysicians owe us some paraphrase by which we can draw those distinctions without committing ourselves to there being merely possible people. We show that such paraphrases are unavailable if we limit ourselves to the expressive resources of even highly infinitary first-order modal languages. We then argue that such paraphrases are available in higher-order modal languages only given certain strong assumptions concerning the metaphysics of properties. We then consider alternative paraphrase strategies, and argue that none of them are tenable. If talk of merely possible people cannot be paraphrased, then it must be taken at face value, in which case it is necessary what individuals there are. Therefore, if it is contingent what individuals there are, then the demands of paraphrase place tight constraints on the metaphysics of properties: either (i) it is necessary what properties there are, or (ii) necessarily equivalent properties are identical, and having properties does not entail even possibly being anything at all

The Quinean Roots of Lewis's Humeanism

An odd dissensus between confident metaphysicians and neopragmatist antimetaphysicians pervades early twenty-first century analytic philosophy. Each faction is convinced their side has won the day, but both are mistaken about the philosophical legacy of the twentieth century. More historical awareness is needed to overcome the current dissensus. Lewis and his possible-world system are lionised by metaphysicians; Quine’s pragmatist scruples about heavy-duty metaphysics inspire antimetaphysicians. But Lewis developed his system under the influence of his teacher Quine, inheriting from him his empiricism, his physicalism, his metaontology, and, I will show in this paper, also his Humeanism. Using published as well as never-before-seen unpublished sources, I will make apparent that both heavy-duty metaphysicians and neopragmatist antimetaphysicians are wrong about the roles Quine and Lewis played in the development of twentieth-century philosophy. The two are much more alike than is commonly supposed, and Quine much more instrumental to the pedigree of current metaphysics

Being Metaphysically Unsettled: Barnes and Williams on Metaphysical Indeterminacy and Vagueness

This chapter discusses the defence of metaphysical indeterminacy by Elizabeth Barnes and Robert Williams and discusses a classical and bivalent theory of such indeterminacy. Even if metaphysical indeterminacy arguably is intelligible, Barnes and Williams argue in favour of it being so and this faces important problems. As for classical logic and bivalence, the chapter problematizes what exactly is at issue in this debate. Can reality not be adequately described using different languages, some classical and some not? Moreover, it is argued that the classical and bivalent theory of Barnes and Williams does not avoid the problems that arise for rival theories

Moderate Modal Skepticism

This paper examines "moderate modal skepticism", a form of skepticism about metaphysical modality defended by Peter van Inwagen in order to blunt the force of certain modal arguments in the philosophy of religion. Van Inwagen’s argument for moderate modal skepticism assumes Yablo's (1993) influential world-based epistemology of possibility. We raise two problems for this epistemology of possibility, which undermine van Inwagen's argument. We then consider how one might motivate moderate modal skepticism by relying on a different epistemology of possibility, which does not face these problems: Williamson’s (2007: ch. 5) counterfactual-based epistemology. Two ways of motivating moderate modal skepticism within that framework are found unpromising. Nevertheless, we also find a way of vindicating an epistemological thesis that, while weaker than moderate modal skepticism, is strong enough to support the methodological moral van Inwagen wishes to draw

Agency and fictional truth: a formal study on fiction-making

Fictional truth, or truth in fiction/pretense, has been the object of extended scrutiny among philosophers and logicians in recent decades. Comparatively little attention, however, has been paid to its inferential relationships with time and with certain deliberate and contingent human activities, namely, the creation of fictional works. The aim of the paper is to contribute to filling the gap. Toward this goal, a formal framework is outlined that is consistent with a variety of conceptions of fictional truth and based upon a specific formal treatment of time and agency, that of so-called stit logics. Moreover, a complete axiomatic theory of fiction-making TFM is defined, where fiction-making is understood as the exercise of agency and choice in time over what is fictionally true. The language L of TFM is an extension of the language of propositional logic, with the addition of temporal and modal operators. A distinctive feature of L with respect to other modal languages is a variety of operators having to do with fictional truth, including a \u2018fictionality\u2019 operator M (to be read as \u201cit is a fictional truth that\u201d). Some applications of TFM are outlined, and some interesting linguistic and inferential phenomena, which are not so easily dealt with in other frameworks, are accounted for