In this paper I will explore the question whether the Trivialization construction of transparent intensional logic (TIL) can be understood in terms of the Execution construction, specifically, in terms of its degenerate case known as the 0-Execution. My answer will be positive and the apparent contrast between the intuitive understanding of Trivialization and 0-Execution will be explained as a matter of distinct yet related informal perspectives, not as a matter of technical or conceptual differences.

This paper clarifies the relationship between the Triviality Results for the conditional and the Restrictor Theory of the conditional. On the understanding of Triviality proposed here, it is implausible—pace many proponents of the Restrictor Theory—that Triviality rests on a syntactic error. As argued here, Triviality arises from simply mistaking the feature a claim has when that claim is logically unacceptable for the feature a claim has when that claim is unsatisfiable. Triviality rests on a semantic confusion—one which some semantic theories, (...) but not others, are prone to making. On the interpretation proposed here, Triviality Results thus play a theoretically constructive role in the project of natural language semantics. (shrink)

We present a new constructive proof of the following theorem: there exists a limit-computable function β_1:N→N which eventually dominates every computable function δ_1:N→N. We prove: (1) there exists a limit-computable function f:N→N of unknown computability which eventually dominates every function δ:N→N with a single-fold Diophantine representation, (2) statement (1) significantly strengthens a non-trivial mathematical theorem, (3) Martin Davis' conjecture on single-fold Diophantine representations disproves (1). We present both constructive and non-constructive proof of (1).

Art museums are built to elicit a wide variety of feelings, emotions, and moods from their visitors. While these effects are primarily achieved through the artworks on display, museums commonly deploy numerous other affect-inducing resources as well, including architectural solutions, audio guides, lighting fixtures, and informational texts. Art museums can thus be regarded as spaces that are designed to influence affective experiencing through multiple structures and mechanisms. At face value, this may seem like a somewhat self-evident and trivial statement to (...) make. However, in this article, I argue that niche construction theory enables us to make several illuminating observations about the ways in which art museums are engineered to influence our feelings. To expound on this claim, I single out for discussion the Museum of Non-Objective Painting, which for its entire lifespan (1939–52)—and prior to its evolution into the Solomon R. Guggenheim Museum—was expressly organized to kindle in its visitors a special, spiritual form of aesthetic experience: a liberating feeling of cosmic rhythm and order, no less. -/- The argument will proceed as follows: In Part 1, I introduce the basics of niche construction theory and specify the sense in which I apply it to museums and aesthetic affective experiencing. In Part 2, I outline the origins and ethos of the Museum of Non-Objective Painting, after which I pin down the type of affective experience it fostered by drawing from visitors’ self-reported reactions to the artworks on display. Then, in Part 3, I use niche construction theory to explain how the Museum consciously fashioned itself, by means of various mutually supportive resources and technologies, into a fertile setting for the specified feelings. Finally, in Part 4, I extend beyond the discussed case to assess the implications of niche construction theory for a broader understanding of how art museums make us feel. In other words, by tracing the early steps of the Museum of Non-Objective Painting towards the present-day Guggenheim, I call attention to the general variation in affective niches as regards their structure, technologies, and affective aims. Overall, the article elucidates the functioning of art museums as affective niches and furthers the conceptual development of niche construction theory in aesthetics. (shrink)

Revision operation is the consistent expansion of a theory by a new belief-representing sentence. We consider that in a paraconsistent setting this desideratum can be accomplished in at least three distinct ways: the output of a revision operation should be either non-trivial or non-contradictory (in general or relative to the new belief). In this paper those distinctions will be explored in the constructive level by showing how the remainder sets could be refined, capturing the key concepts of paraconsistency in a (...) dynamical scenario. These are preliminaries results of a wider project on Paraconsistent Belief Change conduced by the authors. (shrink)

Consider a set of shuffled observations drawn from a fixed probability distribution over some instance domain. What enables learning of inductive generalizations which proceed from such a set of observations? The scenario is worthwhile because it epistemically characterizes most of machine learning. This kind of learning from observations is also inverse and ill-posed. What reduces the non-uniqueness of its result and, thus, its problematic epistemic justification, which stems from a one-to-many relation between the observations and many learnable generalizations? The paper (...) argues that this role belongs to any complexity regularization which satisfies Norton’s Material Theory of Induction (MTI) by localizing the inductive risk to facts in the given domain. A prime example of the localization is the Lottery Ticket Hypothesis (LTH) about overparameterized neural networks. The explanation of MTI’s role in complexity regularization of neural networks is provided by analyzing the stability of Empirical Risk Minimization (ERM), an inductive rule that controls the learning process and leads to an inductive generalization on the given set of observations. In cases where ERM might become asymptotically unstable, making the justification of the generalization by uniform convergence unavailable, LTH and MTI can be used to define a local stability. A priori, overparameterized neural networks are such cases and the combination of LTH and MTI can block ERM’s trivialization caused by equalizing the strengths of its inductive support for risk minimization. We bring closer the investigation of generalization in artificial neural networks and the study of inductive inference and show the division of labor between MTI and the optimality justifications (developed by Gerhard Schurz) in machine learning. (shrink)

Internodons are a formalization of Hennig's concept of species. We present an alternative construction of internodons imposing a tree structure on the genealogical network. We prove that the segments (trivial unary trees) from this tree structure are precisely the internodons. We obtain the following spin-offs. First, the generated tree turns out to be an organismal tree of life. Second, this organismal tree is homeomorphic to the phylogenetic Hennigian species tree of life, implying the discovery of a multi-level tree of (...) life: this phylogenetic tree can be obtained by zooming out from the organismal tree, or conversely, the organismal tree of life can be generated by expanding the phylogenetic nodes into unary trees. Finally, the definition of the organismal tree allows an efficient algorithmic transformation of a given genealogical network into its corresponding phylogenetic species tree of life. The latter will be presented in a separate paper. (shrink)

This work studies some problems connected to the role of negation in logic, treating the positive fragments of propositional calculus in order to deal with two main questions: the proof of the completeness theorems in systems lacking negation, and the puzzle raised by positive paradoxes like the well-known argument of Haskel Curry. We study the constructive com- pleteness method proposed by Leon Henkin for classical fragments endowed with implication, and advance some reasons explaining what makes difficult to extend this constructive (...) method to non-classical fragments equipped with weaker implications (that avoid Curry's objection). This is the case, for example, of Jan Lukasiewicz's n-valued logics and Wilhelm Ackermann's logic of restricted implication. Besides such problems, both Henkin's method and the triviality phenomenon enable us to propose a new positive tableau proof system which uses only positive meta-linguistic resources, and to mo- tivate a new discussion concerning the role of negation in logic proposing the concept of paratriviality. In this way, some relations between positive reasoning and infinity, the possibilities to obtain a ¯first-order positive logic as well as the philosophical connection between truth and meaning are dis- cussed from a conceptual point of view. (shrink)

Amartya Sen has made a major contribution to the theory of social justice, and of gender justice, by arguing that capabilities are the relevant space of comparison when justice-related issues are considered. This article supports Sen's idea, arguing that capabilities supply guidance superior to that of utility and resources (the view's familiar opponents), but also to that of the social contract tradition, and at least some accounts of human rights. But I argue that capabilities can help us to construct a (...) normative conception of social justice, with critical potential for gender issues, only if we specify a definite set of capabilities as the most important ones to protect. Sen's "perspective of freedom" is too vague. Some freedoms limit others; some freedoms are important, some trivial, some good, and some positively bad. Before the approach can offer a valuable normative gender perspective, we must make commitments about substance. (shrink)

According to Bas van Fraassen, scientific realists and anti-realists disagree about whether accepting a scientific theory involves believing that the theory is true. On van Fraassen’s own anti-realist empiricist position, accepting a theory involves believing only that the theory is correct in its claims about observable aspects of the world. However, a number of philosophers have argued that acceptance and belief cannot be distinguished and thus that the debate is either confused or trivially settled in favor of the realist. In (...) addition, another set of philosophers have argued that van Fraassen’s empiricist position appeals to an unmotivated distinction between observable and unobservable aspects of the world. This paper aims to reconstruct a van Fraassen-style empiricism about scientific acceptance that avoids these two objections – reconstructed empiricism. (shrink)

In this paper, I investigate whether we can use a world-involving framework to model the epistemic states of non-ideal agents. The standard possible-world framework falters in this respect because of a commitment to logical omniscience. A familiar attempt to overcome this problem centers around the use of impossible worlds where the truths of logic can be false. As we shall see, if we admit impossible worlds where “anything goes” in modal space, it is easy to model extremely non-ideal agents that (...) are incapable of performing even the most elementary logical deductions. A much harder, and considerably less investigated challenge is to ensure that the resulting modal space can also be used to model moderately ideal agents that are not logically omniscient but nevertheless logically competent. Intuitively, while such agents may fail to rule out subtly impossible worlds that verify complex logical falsehoods, they are nevertheless able to rule out blatantly impossible worlds that verify obvious logical falsehoods. To model moderately ideal agents, I argue, the job is to construct a modal space that contains only possible and non-trivially impossible worlds where it is not the case that “anything goes”. But I prove that it is impossible to develop an impossible-world framework that can do this job and that satisfies certain standard conditions. Effectively, I show that attempts to model moderately ideal agents in a world-involving framework collapse to modeling either logical omniscient agents, or extremely non-ideal agents. (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)

In lieu of an abstract, here is a brief excerpt of the content:Spinoza and the Theory of Organism HANS JONAS I CARTESIANDUALISMlanded speculation on the nature of life in an impasse: intelligible as, on principles of mechanics, the correlation of structure and function became within the res extensa, that of structure-plus-function with feeling or experience (modes of the res cogitans) was lost in the bifurcation, and thereby the fact of life itself became unintelligible at the same time that the explanation (...) of its bodily performance seemed to be assured. The impasse became manifest in Occasionalism : its tour de force of an extraneous, divine "synchronization" of the outer and the inner world (the latter denied to animals) not only suffered from its extreme artificiality, the common failing of such ad hoc constructions, but even at so high a cost failed to accomplish its theoretical purpose by its own terms. For the animal machine, like any machine, raises beyond the question of the "how" that of the "what for" of its functioning---of the purpose for which it had thus been constructed by its maker.1 Its performance, however devoid of immanent teleology, must serve an end, and that end must be someone's end. This end may (directly) be itself, as indeed Descartes had implied when declaring self-preservation to be the effect of the functioning of the organic automaton. In that case the existence as such of the machine would be its end--either terminally, or in turn to benefit something else. In the former case, the machine would have to be more than a machine, for a mere machine cannot enioy its existence. But since, by the rigorous conception of the res extensa, it cannot be more than a machine, its function and/or existence must serve something other than itself. Automata in Descartes ' time were mainly for entertainment (rather than work). But the raison d'etre of the living kingdom could not well be seen in God's indulging his mechanical abilities or in the amusement of celestial spectators--especially since mere complexity of arrangement does not create new quality and thus add something to the unrelieved sameness of the simple substratum that might enrich the spectrum of being. For quality, beyond the primitive determinations of the extended per se, is the subjective creature of sensation, the confused representation of quantity in a mind; and thus organisms cannot harbor it because as mere machines they lack mentality, and pure spirits cannot because they lack sensuality, or the privilege of confusion and thereby of illusion with its possible enjoyment. And as to their intellectual enjoyment, even that, deprived of the thrill of discovery by the same token, would pale in the contemplation of what to sufficiently large The concept of "machine," adopted for its strict confinementto efficientcause, is still a finalisticconcept,even thoughthe final cause is no longer internal to the entity, as a mode of its own operation,but external to it as antecedent design. [43] 44 HISTORY OF PHILOSOPHY intellects is nothing but the ever-repeated exemplification of the same few, elementary (and ultimately trivial) truths. There remained, then, the time-honored--Stoic as well as Christian--idea that plants and animals are for the benefit of Man. Indeed, since the existence of a living world is the necessary condition for the existence of any of its members, the self-justifying nature of at least one such member (= species) would justify the existence of the whole. In Stoicism, Man provided this end by his possession of reason, which makes him the culmination of a terrestrial scale of being that is also self-justifying throughout all its grades (the end as the best of many that are good in degrees) ; in Christianity, by his possession of an immortal soul, which makes him the sole imago Dei in creation (the end as the sole issue at stake) ; and Cartesian dualism radicalized this latter position by making man even the sole possessor of inwardness or "soul" of any kind, thus the only one of whom "end" can meaningfully be predicated as he alone can entertain ends. All other life then, the product of physical necessity, can be considered his means. However, this traditional idea, in its anthropocentric vanity never a... (shrink)

In his 1927 Analysis of Matter and elsewhere, Russell argued that we can successfully infer the structure of the external world from that of our explanatory schemes. While nothing guarantees that the intrinsic qualities of experiences are shared by their objects, he held that the relations tying together those relata perforce mirror relations that actually obtain (these being expressible in the formal idiom of the Principia Mathematica). This claim was subsequently criticized by the Cambridge mathematician Max Newman as true but (...) trivial, insofar as from a closed body of observations (or “Ramsey sentence”) one can always generate other equally-satisfactory networks of relations, provided they respect the original set’s cardinality. Since any model thus generated will be empirically adequate, “[t]he defence is therefore driven back from the fairly safe fictitious-real classification to the much less tenable ‘trivial’ and ‘important’” (Newman 1928). Given the definitional rigour afforded by the initial appeal to isomorphism (via one-to-one correspondences in extension), the received assessment, shared by Russell himself, is that retreating to a pragmatic adjudication would betoken a fatal blow. However, I suggest that reliance on “importance” can be avoided if we incorporate an impersonal criterion of diachronic precedence. When collecting observations, an ordinality emerges alongside the cardinality which gives that underived structure an irrevocable epistemological privilege. Hence, I argue that, all other things being equal, any construct parasitic on an antecedent theory ought to be regarded as inferior/dispensable, since it was generated by an algorithm lacking the world-involving pedigree of its host structure. (shrink)

Husserl’s Logical Grammar is intended to explain how complex expressions can be constructed out of simple ones so that their meaning turns out to be determined by the meanings of their constituent parts and the way they are put together. Meanings are thus understood as structured contents and classified into formal categories to the effect that the logical properties of expressions reflect their grammatical properties. As long as linguistic meaning reduces to the intentional content of pre-linguistic representations, however, it is (...) not trivial to account for how semantics relates to syntax in this context. In this paper, I analyze Husserl’s Logical Grammar as a system of recursive rules operating on representations and suggest that the syntactic form of representations contributes to their semantics because it carries information about semantic role. I further discuss Husserl’s syntactic account of the unity of propositions and argue that, on this account, logical form supervenes on syntactic form. In the last section I draw some implications for the phenomenology of thought and conjecture that the structural features it displays are likely to convey the syntactic structures of an underlying language-like representational system. (shrink)

In order to reason in a non-trivializing way with contradictions, para- consistent logics reject some classically valid inferences. As a way of re- covering some of these inferences, Graham Priest ([Priest, 1991]) proposed to nonmonotonically strengthen the Logic of Paradox by allowing the se- lection of “less inconsistent” models via a comparison of their respective inconsistent parts. This move recaptures a good portion of classical logic in that it does not block, e.g., disjunctive syllogism, unless it is applied to contradictory (...) assumptions. In Priest’s approach the inconsistent parts of models are compared in an extensional way by considering their inconsis- tent objects. This distinguishes his system from the standard format of (inconsistency-)adaptive logics pioneered by Diderik Batens, according to which (atomic) contradictions validated in models form the basis of their comparison. A well-known problem for Priest’s extensional approach is its lack of the Strong Reassurance property, i.e., for specific settings there may be infinitely descending chains of less and less inconsistent models, thus never reaching a minimally inconsistent model. In this paper, we demonstrate that Strong Reassurance holds for the extensional approach under a cardinality-based comparison of the incon- sistent parts of models. Furthermore, we introduce and investigate the metatheory of the class of first-order nonmonotonic inconsistency-tolerant construct over the extensional or quantitative comparisons of their respec- tive models. Core model-theoretic properties for these logics, such as the Löwenheim-Skolem theorems, along with other nonmonotonic properties, are further studied. (shrink)

Cloud computing (ClC) has become a more popular computer paradigm in the preceding few years. Quality of Service (QoS) is becoming a crucial issue in service alteration because of the rapid growth in the number of cloud services. When evaluating cloud service functioning using several performance measures, the issue becomes more complex and non-trivial. It is therefore quite difficult and crucial for consumers to choose the best cloud service. The user's choices are provided in a quantifiable manner in the current (...) methods for choosing cloud services. Hence, this study attempts to achieve this objective through construction. decision-making framework so-called cloud services evaluator (CSsEv). The main indicator and its sub-indicators are formed as nodes at levels(n) in tree soft sets (TSSs). Thereafter Single Value Neutrosophic Sets (SVNSs) as branch of neutrosophic sets which conjunction with the Multi-Criteria Decision Making (MCDM) technique to facilitate analysis and evaluation process for the available Cloud services providers. Hence, entropy is employed to obtain indicators and sub_indicators weights and Complex Proportional Assessment utilizes these weights to facilitate the decision process of selecting optimal ClSPs. (shrink)

The folk Psychology frames propositional attitudes as fundamental theoretical entities for the construction of a model designed to predict the behavior of a subject. A trivial, such as grasping a pen and writing reveals - something complex - about the behavior. When I take a pen and start writing I do, trivially, because I believe that a certain object in front of me is a pen and who performs a specific function that is, in fact, that of writing. When (...) I believe that the object that stands before me is a pen, I am in relation to "believe" with the propositional content: that in front of me is a pen. Philosophers of the proposition, from Frege onwards, have dedicated their studies to the analysis of what kinds of entities are the propositional attitudes. Jerry Fodor says that now, the proper prediction of the psychology of common sense, can not be questioned and that the propositional attitudes represent the most effective way to describe our behavior. What Fodor says, however, is that propositional attitudes function, but not how they work. Most philosophers interested in the issue, we are dedicated to the search for a theory that can account consistently both a semantics for propositional attitudes, both of these entities that seem to cause the behavior of a rational subject. There are two main paradigms in the theory of the proposition that contributed to the discussion of the propositional attitudes. One is the one that begins with Gottlob Frege, the other with Bertrand Russell. Defenders of Frege argue that the paradigm scrub objects and properties can not be constituents of the propositional content which have a purely conceptual. In other words, the philosophers belonging to the paradigm of Frege, but not all, mean that you can test in a rigorous way the truth conditions of propositional attitudes. Who defends the russellian’s paradigm argues that the propositional content are made by the objects and properties on which propositional attitudes relate. The purpose of this article is not to rebuild - in detail - both paradigms, nor to reconstruct one but, in a sense, my work will be a completely partial objective is to demonstrate how the paradigm is more profitable russell not only to make a coherent semantic theory for propositional attitudes2 but also to predict the behavior of a rational subject thing, completely innovative, given the repeated objections in contemporary literature3. At the end of this paper will be drafted a proposal to build a consistent model to predict the behavior,of a rational agent, based on a referential theory of propositional attitudes. (shrink)

This chapter distinguishes between several senses of “normativity”. For example, that we ought to abstain from causing unnecessary suffering is a normative, not descriptive, claim. And so is the claim that we have good reason, and ought to drive on the right, or left, side of the road because the law requires us to do that. Reasons and oughts are normative, by definition. Indeed, it may be that “[t]he normativity of all that is normative consists in the way it is, (...) or provides, or is otherwise related to reasons” (Raz 1999, 67) . That is what the “reasons-first” view holds, but there are also other views, and what is by definition a normative statement, or a normative fact if you like, depends on how we define normativity. -/- It may seem that requirements are also by definition normative. But it seems that there can also be requirements that one has no reason to meet: it is less clear whether such requirements are normative in the same sense that reasons and oughts are normative. This paper will go through various further phenomena, which are candidates for being normative in some other sense than normative reasons and oughts, defending however the view that not all of them are. But arguably four or so different senses of normativity can be distinguished. -/- The paper will accept the view that the normativity of reasons and oughts, which is here called normativity1, is central. It is an open question whether all requirements or expectations or socially constructed norms are normative in that sense. Arguably it depends on the contents and content-independent authority of the legislators, whether we have good reasons, or ought, to meet the requirements, obey the law, or to follow the etiquette, or to conform to others’ interpersonal expectations, requests, demands or prescriptions. Whether and when we do have such reasons is a difficult and important substantive question, which concerns the normativity1 of requirements of law. -/- In another sense, norms (intended to guide behavior) are trivially or by definition normative, and constitute normativity: some forms of behavior are ruled as acceptable (e.g. driving on the right) and others as unacceptable (e.g. driving on the left) in light of the norm. Even in the case of a bad norm (that we have no reason to follow, and which ought to be changed, and ought not prevail) classifies behaviours as acceptable or unacceptable in light of the norm. Surely norms are by definition normative? Call this conformity to social norms and actual expectations normativity2. It is not an open question whether social norms are normative in that sense – they are by definition normative2. But importantly, it is an open question whether one has good reasons, or sufficient reason, or ought, to follow any social norm – that is, whether the norm in question is normative1. -/- The first section of the article characterizes further the difference between these two senses of normativity, and additionally introduces various other candidate senses of “normativity”. These possible senses of “normativity” may be at stake in the debates about normative requirements of rationality , about so called ought-to-be -rules , about normativity of linguistic meaning , about “directions of fit” of beliefs and desires , about subjective authority of intentions and decisions and interpersonal authority or co-authority of concrete others. -/- In later sections these cases are discussed. Do they constitute separate senses of normativity? And are the later phenomena such that they give agents good reasons: do they include normativity1 – the core sense? A “normative power -model” is suggested as a framework for examining whether actual social norms, laws, expectations provide good reasons and oughts or not. Once we understand the relation between the first two senses of normativity, do the later phenomena follow the same pattern – is the “normative powers – model” relevant for them as well? (shrink)

The standard, foundationalist reading of Our Knowledge of the External World requires Russell to have a view of perceptual acquaintance that he demonstrably does not have. Russell’s actual purpose in “constructing” physical bodies out of sense-data is instead to show that psychology and physics are consistent. But how seriously engaged was Russell with actual psychology? I show that OKEW makes some non-trivial assumptions about the character of visual space, and I argue that he drew those assumptions from William James’s Principles. (...) This point helps us take a fresh look at the complex relationship between the two men. In light of this surprising background of agreement, I highlight ways their more general approaches to perception finally diverged in ways that put the two at epistemological odds. (shrink)

The aim of the paper is to analyze the expressive power of the square operator of Łukasiewicz logic: ∗x=x⊙x⁠, where ⊙ is the strong Łukasiewicz conjunction. In particular, we aim at understanding and characterizing those cases in which the square operator is enough to construct a finite MV-chain from a finite totally ordered set endowed with an involutive negation. The first of our main results shows that, indeed, the whole structure of MV-chain can be reconstructed from the involution and the (...) Łukasiewicz square operator if and only if the obtained structure has only trivial subalgebras and, equivalently, if and only if the cardinality of the starting chain is of the form n+1 where n belongs to a class of prime numbers that we fully characterize. Secondly, we axiomatize the algebraizable matrix logic whose semantics is given by the variety generated by a finite totally ordered set endowed with an involutive negation and Łukasiewicz square operator. Finally, we propose an alternative way to account for Łukasiewicz square operator on involutive Gödel chains. In this setting, we show that such an operator can be captured by a rather intuitive set of equations. (shrink)

In a possible world framework, an agent can be said to know a proposition just in case the proposition is true at all worlds that are epistemically possible for the agent. Roughly, a world is epistemically possible for an agent just in case the world is not ruled out by anything the agent knows. If a proposition is true at some epistemically possible world for an agent, the proposition is epistemically possible for the agent. If a proposition is true at (...) all epistemically possible worlds for an agent, the proposition is epistemically necessary for the agent, and as such, the agent knows the proposition. -/- This framework presupposes an underlying space of worlds that we can call epistemic space. Traditionally, worlds in epistemic space are identified with possible worlds, where possible worlds are the kinds of entities that at least verify all logical truths. If so, given that epistemic space consists solely of possible worlds, it follows that any world that may remain epistemically possible for an agent verifies all logical truths. As a result, all logical truths are epistemically necessary for any agent, and the corresponding framework only allows us to model logically omniscient agents. This is a well-known consequence of the standard possible world framework, and it is generally taken to imply that the framework cannot be used to model non-ideal agents that fall short of logical omniscience. -/- A familiar attempt to model non-ideal agents within a broadly world involving framework centers around the use of impossible worlds where the truths of logic can be false. As we shall see, if we admit impossible worlds where “anything goes” in epistemic space, it is easy to avoid logical omniscience. If any logical falsehood is true at some impossible world, then any logical falsehood may remain epistemically possible for some agent. As a result, we can use an impossible world involving framework to model extremely non-ideal agents that do not know any logical truths. -/- A much harder, and considerably less investigated challenge is to ensure that the resulting epistemic space can also be used to model moderately ideal agents that are not logically omniscient but nevertheless logically competent. Intuitively, while such agents may fail to rule out impossible worlds that verify complex logical falsehoods, they are nevertheless able to rule out impossible worlds that verify obvious logical falsehoods. To model such agents, we need a construction of a non-trivial epistemic space that partly consists of impossible worlds where not "anything goes". This involves imposing substantive constraints on impossible worlds to eliminate from epistemic space, say, trivially impossible worlds that verify obvious logical falsehoods. -/- The central aim of this dissertation is to investigate the nature of such non-trivially impossible worlds and the corresponding epistemic spaces. To flag my conclusions, I argue that successful constructions of epistemic spaces that can safely navigate between the Charybdis of logical omniscience and the Scylla of of “anything goes” are hard, if not impossible to find. (shrink)

"Language and its Public Features: Reorganizing the Trivium in Locke's Essay and Port-Royal Logic" The new theory of language in the 17th century coincides with the end the traditional order of disciplines in the trivium (grammar, logic and rhetoric), which in the mediaeval times provided a comprehensive view of the problems of discourse. The article focuses on some key passages in Port-Royal Logic and Locke's Essay that provide us with a typical early modern scheme of linguistic representation, characterised by heavily (...) emphasized dualism of ideas and words. Since ideas are also the meanings of words and are ontologically essentially private, one can raise the question, where in this analysis of language is it even possible to locate its public features. The article tries to show that private language is not only possible for Locke and the Port-Royalists, but that it is even a necessary and primary character of language. Language becomes a public medium of communication only on the junctures of private meanings constituted by the “common use” of words. The article then focuses on almost complete marginalisation in the two works of the theory of public speech. Rhetoric, in the 17th century often reduced to mere eloquence, has no place in philosophy, and the duties of making speeches persuasive are taken over by reason alone. To show how the domains of jurisdiction of the trivial disciplines had been transformed in the linguistic theories proposed by the Port-Royal Logic and Locke, one can construct a hypothetical early modern trivium in the light of the following order: idea – word – figure, or, logic – grammar – rhetoric. Rhetoric is found to have kept its structural place only to be singled out as dangerous. (shrink)

Library information science (LIS) should develop its foundation in terms of a philosophy of information (PI). This seems a rather harmless suggestion. Where else could information science look for its conceptual foundations if not in PI? However, accepting this proposal means moving away from one of the few solid alternatives currently available in the field, namely, providing LIS with a foundation in terms of social epistemology (SE). This is no trivial move, so some reasonable reluctance is to be expected. To (...) overcome it, the proposal needs to be more than just acceptable; it must be convincing. In Floridi (2002a), I have articulated some of the reasons why I believe that PI can fulfill the foundationalist needs better than SE can. I won’t rehearse them here. I find them compelling, but I am ready to change my mind if counterarguments become available. Rather, in this contribution, I wish to clarify some aspects of my proposal (Floridi, 2002a) in favor of the interpretation of LIS as applied PI. I won’t try to show you that I am right in suggesting that PI may provide a foundation for LIS better than SE. My more modest goal is to remove some ambiguities and possible misunderstandings that might prevent the correct evaluation of my position, so that disagreement can become more constructive. (shrink)

In the domain of ontology design as well as in Knowledge Representation, modeling universals is a challenging problem.Most approaches that have addressed this problem rely on Description Logics (DLs) but many difficulties remain, due to under-constrained representation which reduces the inferences that can be drawn and further causes problems in expressiveness. In mathematical logic and program checking, type theories have proved to be appealing but, so far they have not been applied in the formalization of ontologies. To bridge this gap, (...) we present in this paper a theory for representing ontologies in a dependently typed framework which relies on strong formal foundations including both a constructive logic and a functional type system. The language of this theory defines in a precise way what ontological primitives such as classes, relations, properties, etc., and thereof roles, are. The first part of the paper details how these primitives are defined and used within the theory. In a second part, we focus on the formalization of the role primitive. A review of significant role properties leads to the specification of a role profile and most of the remaining work details through numerous examples, how the proposed theory is able to fully satisfy this profile. It is demonstrated that dependent types can model several non-trivial aspects of roles including a formal solution for generalization hierarchies, identity criteria for roles and other contributions. A discussion is given on how the theory is able to cope with many of the constraints inherent in a good role representation. (shrink)

Corcoran, J. 2005. Counterexamples and proexamples. Bulletin of Symbolic Logic 11(2005) 460. -/- John Corcoran, Counterexamples and Proexamples. Philosophy, University at Buffalo, Buffalo, NY 14260-4150 E-mail: [email protected] Every perfect number that is not even is a counterexample for the universal proposition that every perfect number is even. Conversely, every counterexample for the proposition “every perfect number is even” is a perfect number that is not even. Every perfect number that is odd is a proexample for the existential proposition that some (...) perfect number is odd. Conversely, every proexample for the proposition “some perfect number is odd” is a perfect number that is odd. As trivial these remarks may seem, they can not be taken for granted, even in mathematical and logical texts designed to introduce their respective subjects. One well-reviewed book on counterexamples in analysis says that in order to demonstrate that a universal proposition is false it is necessary and sufficient to construct a counterexample. It is easy to see that it is not necessary to construct a counterexample to demonstrate that the proposition “every true proposition is known to be true” is false–necessity fails. Moreover the mere construction of an object that happens to be a counterexample does not by itself demonstrate that it is a counterexample–sufficiency fails. In order to demonstrate that a universal proposition is false it is neither necessary nor sufficient to construct a counterexample. Likewise, of course, in order to demonstrate that an existential proposition is true it is neither necessary nor sufficient to construct a proexample. This article defines the above relational concepts of counterexample and of proexample, it discusses their surprising history and philosophy, it gives many examples of uses of these and related concepts in the literature and it discusses some of the many errors that have been made as a result of overlooking the challenging subtlety of the proper use of these two basic and indispensable concepts. (shrink)

This thesis is about how deduction is analytic and, at the same time, informative. In the first two chapters I am after the question of the justification of deduction. This justification is circular in the sense that to explain how deduction works we use some basic deductive rules. However, this circularity is not trivial as not every rule can be justified circularly. Moreover, deductive rules may not need suasive justification because they are not ampliative. Deduction preserves meaning, that is, the (...) meaning of non-logical vocabulary of any theory which is developed by deductive reasoning remains unchanged. It means that deduction adds no information to what we already had in our premises. This is why deduction is analytic. -/- However, there are many ways deduction can be informative. In the next three chapters, I will pick a specific kind of deductive reasoning, namely arithmetical reasoning, and will attempt to understand the nature of information we obtain by this kind of reasoning. There is a difference between simple deductive moves such as inferring `Socrates is mortal' from `All human are mortal' and `Socrates is human', and inferring that a relation is reflexive given that it is directed, symmetric and transitive. The latter is more complicated and not as easy to prove as the former. Therefore it is informative and the proof we construct to prove it puts us in an epistemic position that we were not in before having the proof. To be more specific, I show that concepts we need to confirm the conclusion are made in the process of proving the conclusion. (shrink)

Tichý’s Transparent Intensional Logic (TIL) is an overarching logical framework apt for the analysis of all sorts of discourse, whether colloquial, scientific, mathematical or logical. The theory is a procedural (as opposed to denotational) one, according to which the meaning of an expression is an abstract, extra-linguistic procedure detailing what operations to apply to what procedural constituents to arrive at the product (if any) of the procedure that is the object denoted by the expression. Such procedures are rigorously defined as (...) TIL constructions. Though TIL analytical potential is very large, deduction in TIL has been rather neglected. Tichý defined a sequent calculus for pre-1988 TIL, that is TIL based on the simple theory of types. Since then no other attempt to define a proof calculus for TIL has been presented. The goal of this paper is to propose a generalization and adjustment of Tichý’s calculus to TIL 2010. First, I briefly recapitulate the rules of simple-typed calculus as presented by Tichý. Then, I propose the adjustments of the calculus so that it be applicable to hyperintensions within the ramified hierarchy of types. TIL operates with a single procedural semantics for all kinds of logical-semantic context, be it extensional, intensional or hyperintensional. I show that operating in a hyperintensional context is far from being technically trivial. Yet, it is feasible. To this end, we introduce a substitution method that operates on hyperintensions. It makes use of a four-place substitution function (called Sub) defined over hyperintensions. (shrink)

Our investigative question is what part of the human psyche is active when we are sleeping. We use the single-counter-example method, extracted from Classical Logic, to prove that it could not be the case that one of our existing models for the human psyche could explain the human sleep. The models of the human psyche that we consider are the Freudian, the Jungian, and our own. By proving that no known part could be active whilst we sleep, and we prove (...) all by presenting known facts, we reach the conclusion that we need a new model of psyche to account for the entire complexity of our beings. We associate sleep with dreams. Upon discussing the human dreams in more details, we end up applying the principles of the inference to the best explanation to explain the human dreams by means of references to the spiritual world. That makes us think about how the spiritists would describe our psyche, and we then present a new model. The new model is obviously a fruit of speculation. This time, the model involves all Freudian elements, our extensional elements, body, and soul. We use the synthetic method to construct our new model. Since our sleep time is so important, to the point of obliging us to build a new model for the human psyche, we worry about protecting it. We then use studies on the impact of noise on humans to talk about how bad the consequences of having a person speaking to us during sleep are. This trivially extends to people that are in hypnotic state. We try to make a case against hypnosis and interference with the sleep of human beings by referring to health, spiritual, and world consequences. Our main result is then a new model for the human psyche, and this time a model that has to do with what is beyond what has already been formally acknowledged by us. A secondary result is that we should not allow people to hypnotize others or to speak to them as they sleep. Our conclusions are that there is definitely something beyond our rationality that happens during our sleep time and this something has not been identified by Freud, Jung or us this far. Besides, that we should not allow people to hypnotize others or speak to them as they sleep. (shrink)

There are at least three interpretations that attempt to read from the Sense-Certainty Chapter a Hegelian theory of indexicals. First, the Impossibility of Singular Reference Reading understands Hegel as excluding in principle the possibility of any linguistic cognition of individuals. Second, the Theory of Reference Reading criticizes the first reading and interprets from Hegel the classical idea of direct reference theory. Third, Brandom’s Anaphoric Theory Reading suggests an alternative explanation while still defending the possibility of knowledge of individuals in Hegel. (...) I criticize the first two readings and argue that the third is the most exegetically and philosophically adequate interpretation. The first interpretation attempts to ascribe to Hegel a sort of skepticism, but this can be at most in a very restricted sense successful and the skepticism constructed in such a way is too trivial to refute Hegel’s position. The second reading is more adequate in that it does not fall into the error that the first one committed, but is still flawed because it introduces a subject-object or mind-world dualism that Hegel denies. The third reading has great advantages compared to the first two readings in terms that it provides a suitable account of indexical knowledge on individuals while avoiding skepticism and dualism which arise in the former readings. (shrink)

I present two Triviality results for Kratzer's standard “restrictor” analysis of indicative conditionals. I both refine and undermine the common claim that problems of Triviality do not arise for Kratzer conditionals since they are not strictly conditionals at all.

Inquiry into the meaning of logical terms in natural language (‘and’, ‘or’, ‘not’, ‘if’) has generally proceeded along two dimensions. On the one hand, semantic theories aim to predict native speaker intuitions about the natural language sentences involving those logical terms. On the other hand, logical theories explore the formal properties of the translations of those terms into formal languages. Sometimes, these two lines of inquiry appear to be in tension: for instance, our best logical investigation into conditional connectives may (...) show that there is no conditional operator that has all the properties native speaker intuitions suggest if has. Indicative conditionals have famously been the source of one such tension, ever since the triviality proofs of both Lewis (1976) and Gibbard (1981) established conclusions which are in prima facie tension with ordinary judgments about natural language indicative conditionals. In a recent series of papers, Branden Fitelson has strengthened both triviality results (Fitelson 2013, 2015, 2016), revealing a common culprit: a logical schema known as IMPORT-EXPORT. Fitelson’s results focus the tension between the logical results and ordinary judgments, since IMPORT-EXPORT seems to be supported by intuitions about natural language. In this paper, we argue that the intuitions which have been taken to support IMPORT-EXPORT are really evidence for a closely related, but subtly different, principle. We show that the two principles are independent by showing how, given a standard assumption about the conditional operator in the formal language in which IMPORT-EXPORT is stated, many existing theories of indicative conditionals validate one, but not the other. Moreover, we argue that once we clearly distinguish these principles, we can use propositional anaphora to show that IMPORT-EXPORT is in fact not valid for natural language indicative conditionals (given this assumption about the formal conditional operator). This gives us a principled and independently motivated way of rejecting a crucial premise in many triviality results, while still making sense of the speaker intuitions which appeared to motivate that premise. We suggest that this strategy has broad application and an important lesson: in theorizing about the logic of natural language, we must pay careful attention to the translation between the formal languages in which logical results are typically proved, and natural languages which are the subject matter of semantic theory. (shrink)

A pervasive and influential argument appeals to trivial truths to demonstrate that the aim of inquiry is not the acquisition of truth. But the argument fails, for it neglects to distinguish between the complexity of the sentence used to express a truth and the complexity of the truth expressed by a sentence.

I defend a new account of constitutive essence on which an entity’s constitutively essential properties are its most fundamental, nontrivial necessary properties. I argue that this account accommodates the Finean counterexamples to classic modalism about essence, provides an independently plausible account of constitutive essence, and does not run into clear counterexamples. I conclude that this theory provides a promising way forward for attempts to produce an adequate nonprimitivist, modalist account of essence. As both triviality and fundamentality in the account are (...) understood in terms of grounding, the theory also potentially has important implications for the relation between essence and grounding. (shrink)

The Equation (TE) states that the probability of A → B is the probability of B given A. Lewis (1976) has shown that the acceptance of TE implies that the probability of A → B is the probability of B, which is implausible: the probability of a conditional cannot plausibly be the same as the probability of its consequent, e.g., the probability that the match will light given that is struck is not intuitively the same as the probability that it (...) will light. Here I want to counter Lewis’ claim. My aim is to argue that: (1) TE express the coherence requirements implicit in the probability distributions of a modus ponens inference (MP); (2) the triviality result is not implausible because it is a result from these requirements; (3) these coherence requirements measure MP employability, so TE significance is tied to it; (4) MP employability doesn’t provide either the acceptability or the truth conditions of conditionals, since MP employability depends on previous independent reasons to accept the conditional and some acceptable conditionals are not MP friendly. Consequently, TE doesn’t have the logical significance that is usually attributed to it. (shrink)

Conditional probability is often used to represent the probability of the conditional. However, triviality results suggest that the thesis that the probability of the conditional always equals conditional probability leads to untenable conclusions. In this paper, I offer an interpretation of this thesis in a possible worlds framework, arguing that the triviality results make assumptions at odds with the use of conditional probability. I argue that these assumptions come from a theory called the operator theory and that the rival restrictor (...) theory can avoid these problematic assumptions. In doing so, I argue that recent extensions of the triviality arguments to restrictor conditionals fail, making assumptions which are only justified on the operator theory. (shrink)

The Good Regulator Theorem and the Internal Model Principle are sometimes cited as mathematical proofs that an agent needs an internal model of the world in order to have an optimal policy. However, these principles rely on a definition of “internal model" that is far too permissive, applying even to cases of systems that do not use an internal model. As a result, these principles do not provide evidence (let alone a proof) that internal models are necessary. The paper also (...) diagnoses what is missing in the GRT and IMP definitions of internal model, which is that models need to make predictions that represent variables in the target system (and these representations need to be usable by an agent so as to guide behavior). (shrink)

Opponents of the computational theory of mind have held that the theory is devoid of explanatory content, since whatever computational procedures are said to account for our cognitive attributes will also be realized by a host of other ‘deviant’ physical systems, such as buckets of water and possibly even stones. Such ‘triviality’ claims rely on a simple mapping account of physical implementation. Hence defenders of CTM traditionally attempt to block the trivialization critique by advocating additional constraints on the implementation (...) relation. However, instead of attempting to ‘save’ CTM by constraining the account of physical implementation, I argue that the general form of the triviality argument is invalid. I provide a counterexample scenario, and show that SMA is in fact consistent with empirically rich and theoretically plausible versions of CTM. This move requires rejection of the computational sufficiency thesis, which I argue is scientifically unjustified in any case. By shifting the ‘burden of explanatory force’ away from the concept of physical implementation, and instead placing it on salient aspects of the target phenomenon to be explained, it’s possible to retain a maximally liberal and unfettered view of physical implementation, and at the same time defuse the triviality arguments that have motivated defenders of CTM to impose various theory-laden constraints on SMA. (shrink)

In recent years, a number of theorists have claimed that beliefs about probability are transparent. To believe probably p is simply to have a high credence that p. In this paper, I prove a variety of triviality results for theses like the above. I show that such claims are inconsistent with the thesis that probabilistic modal sentences have propositions or sets of worlds as their meaning. Then I consider the extent to which a dynamic semantics for probabilistic modals can capture (...) theses connecting belief, certainty, credence, and probability. I show that although a dynamic semantics for probabilistic modals does allow one to validate such theses, it can only do so at a cost. I prove that such theses can only be valid if probabilistic modals do not satisfy the axioms of the probability calculus. (shrink)

I formulate a counterfactual version of the notorious 'Ramsey Test'. Whereas the Ramsey Test for indicative conditionals links credence in indicatives to conditional credences, the counterfactual version links credence in counterfactuals to expected conditional chance. I outline two forms: a Ramsey Identity on which the probability of the conditional should be identical to the corresponding conditional probabihty/expectation of chance; and a Ramsey Bound on which credence in the conditional should never exceed the latter.Even in the weaker, bound, form, the counterfactual (...) Ramsey Test makes counterfactuals subject to the very argument that Lewis used to argue against the indicative version of the Ramsey Test. I compare the assumptions needed to run each, pointing to assumptions about the time-evolution of chances that can replace the appeal to Bayesian assumptions about credence update in motivating the assumptions of the argument.I finish by outlining two reactions to the discussion: to indicativize the debate on counterfactuals; or to counterfactualize the debate on indicatives. (shrink)

I here present and defend what I call the Triviality Theory of Truth, to be understood in analogy with Matti Eklund’s Inconsistency Theory of Truth. A specific formulation of is defended and compared with alternatives found in the literature. A number of objections against the proposed notion of meaning-constitutivity are discussed and held inconclusive. The main focus, however, is on the problem, discussed at length by Gupta and Belnap, that speakers do not accept epistemically neutral conclusions of Curry derivations. I (...) first argue that the facts about speakers’ reactions to such Curry derivations do not constitute a problem for the Triviality Theory specifically. Rather, they follow from independent, uncontroversial facts. I then propose a solution which coheres with the theory as I understand it. Finally, I consider a normative reading of their objection and offer a response. (shrink)

Suppose that you're certain that a certain sentence, e.g. "Frida is tall", lacks a determinate truth value. What cognitive attitude should you take towards it—reject it, suspend judgment, or what else? We show that, by adopting a seemingly plausible principle connecting credence in A and Determinately A, we can prove a very implausible answer to this question: i.e., all indeterminate claims should be assigned credence zero. The result is striking similar to so-called triviality results in the literature on modals and (...) conditionals. (shrink)

The aim of this paper is to bring recent work on metaphysical grounding to bear on the phenomenon of social construction. It is argued that grounding can be used to analyze social construction and that the grounding framework is helpful for articulating various claims and commitments of social constructionists, especially about social identities, e.g., gender and race. The paper also responds to a number of objections that have been leveled against the application of grounding to social construction (...) from Elizabeth Barnes, Mari Mikkola, and Jessica Wilson. (shrink)

Niche construction theory highlights the active role of organisms in modifying their environment. A subset of these modifications is the developmental niche, which concerns ecological, epistemic, social and symbolic legacies inherited by organisms as resources that scaffold their developmental processes. Since in this theory development is a situated process that takes place in a culturally structured environment, we may reasonably ask if implicit cultural biases may, in some cases, be responsible for maladaptive developmental niches. In this paper we wish (...) to argue for an affirmative answer. In order to do so, we first propose to conceptualize implicit bias as embodied perceptual habits, and then proceed to show that these habits are at least partially responsible for maladaptive developmental niches of children with Down syndrome and autism. With this framework we thus hope to bring together two fields of research that haven’t been explicitly connected: implicit bias and niche construction theory. Linking these two theories may bring benefits both to implicit bias researchers, who can extend this concept to characterize other sets of processes as biased, as well as to niche construction theorists, who will have a useful theoretical tool to diagnose maladaptive features of niches brought about by sociocultural biases. (shrink)

The Identity of Indiscernibles is the principle that objects cannot differ only numerically. It is widely held that one interpretation of this principle is trivially true: the claim that objects that bear all of the same properties are identical. This triviality ostensibly arises from haecceities (properties like \textit{is identical to a}). I argue that this is not the case; we do not trivialize the Identity of Indiscernibles with haecceities, because it is impossible to express the haecceities of indiscernible objects. I (...) then argue that this inexpressibility generalizes to all of their trivializing properties. Whether the Identity of Indiscernibles is trivially true ultimately turns on whether we can quantify over properties that we cannot express. (shrink)

This paper presents a range of new triviality proofs pertaining to naïve truth theory formulated in paraconsistent relevant logics. It is shown that excluded middle together with various permutation principles such as A → (B → C)⊩B → (A → C) trivialize naïve truth theory. The paper also provides some new triviality proofs which utilize the axioms ((A → B)∧ (B → C)) → (A → C) and (A → ¬A) → ¬A, the fusion connective and the Ackermann constant. An (...) overview over various ways to formulate Leibniz’s law in non-classical logics and two new triviality proofs for naïve set theory are also provided. (shrink)

Constructive empiricism implies that if van Fraassen does not believe that scientific theories and his positive philosophical theories, including his contextual theory of explanation, are empirically adequate, he cannot accept them, and hence he cannot use them for scientific and philosophical purposes. Moreover, his epistemic colleagues, who embrace epistemic reciprocalism, would not believe that his positive philosophical theories are empirically adequate. This epistemic disadvantage comes with practical disadvantages in a social world.

This paper looks at the question of what it means for a psychological test to have construct validity. I approach this topic by way of an analysis of recent debates about the measurement of implicit social cognition. After showing that there is little theoretical agreement about implicit social cognition, and that the predictive validity of implicit tests appears to be low, I turn to a debate about their construct validity. I show that there are two questions at stake: First, what (...) level of detail and precision does a construct have to possess such that a test can in principle be valid relative to it? And second, what kind of evidence needs to be in place such that a test can be regarded as validated relative to a given construct? I argue that construct validity is not an all-or-nothing affair. It can come in degrees, because both our constructs and our knowledge of the explanatory relation between constructs and data can vary in accuracy and level of detail, and a test can fail to measure all of the features associated with a construct. I conclude by arguing in favor of greater philosophical attention to processes of construct development. (shrink)

This paper discusses and relates two puzzles for indicative conditionals: a puzzle about indeterminacy and a puzzle about triviality. Both puzzles arise because of Ramsey's Observation, which states that the probability of a conditional is equal to the conditional probability of its consequent given its antecedent. The puzzle of indeterminacy is the problem of reconciling this fact about conditionals with the fact that they seem to lack truth values at worlds where their antecedents are false. The puzzle of triviality is (...) the problem of reconciling Ramsey's Observation with various triviality proofs which establish that Ramsey's Observation cannot hold in full generality. In the paper, I argue for a solution to the indeterminacy puzzle and then apply the resulting theory to the triviality puzzle. On the theory I defend, the truth conditions of indicative conditionals are highly context dependent and such that an indicative conditional may be indeterminate in truth value at each possible world throughout some region of logical space and yet still have a nonzero probability throughout that region. (shrink)

On an influential line of thinking tracing back to Ramsey, conditionals are closely linked to the attitude of supposition. When applied to counterfactuals, this view suggests a subjunctive version of the so-called Ramsey test: the probability of a counterfactual If A, would B ought to be equivalent to the probability of B, under the subjunctive supposition that A. I present a collapse result for any view that endorses the subjunctive version of the Ramsey test. Starting from plausible assumptions, the result (...) shows that one’s rational credence in a would-counterfactual and in the corresponding might-counterfactual have to be identical. (shrink)