von Fintel and Gillies : 329–360, 2007) have proposed a dynamic strict conditional account of counterfactuals as an alternative to the standard variably strict account due to Stalnaker and Lewis. Von Fintel’s view is motivated largely by so-called reverse Sobel sequences, about which the standard view seems to make the wrong predictions. More recently Moss :561–586, 2012) has offered a pragmatic/epistemic explanation that purports to explain the data without requiring abandonment of the standard view. So far the (...) small amount of subsequent literature has focused primarily on the original class of cases motivating the strict conditional view. What is needed in the debate is an examination of the predictions of the dynamic strict conditional account for a broader range of data. I undertake this task here, presenting a slew of cases that are problematic for the strict conditional view but not for Moss’s view, and considering some possible responses. Ultimately I take my contribution to constitute a significant blow to the dynamic strict conditional view, though not a decisive verdict against it. (shrink)

This paper extends Kripke’s theory of truth to a language with a variably strict conditional operator, of the kind that Stalnaker and others have used to represent ordinary indicative conditionals of English. It then shows how to combine this with a different and independently motivated conditional operator, to get a substantial logic of restricted quantification within naive truth theory.

Our understanding of subjunctive conditionals has been greatly enhanced through the use of possible world semantics and, more precisely, by the idea that they involve variably strict quantification over possible worlds. I propose to extend this treatment to ceteris paribus conditionals – that is, conditionals that incorporate a ceteris paribus or ‘other things being equal’ clause. Although such conditionals are commonly invoked in scientific theorising, they traditionally arouse suspicion and apprehensiveness amongst philosophers. By treating (...) ceteris paribus conditionals as a species of variably strict conditional I hope to shed new light upon their content and their logic. (shrink)

ABSTRACT The apparent consistency of Sobel sequences famously motivated David Lewis to defend a variably strict conditional semantics for counterfactuals. If Sophie had gone to the parade, she would have seen Pedro. If Sophie had gone to the parade and had been stuck behind someone tall, she would not have seen Pedro. But if the order of the counterfactuals in a Sobel sequence is reversed—in the example, if is asserted prior to —the second counterfactual asserted no longer rings (...) true. This is the Heim sequence problem. That the order of assertion makes this difference is surprising on the variably strict account. Some argue that this is reason to reject the Lewis-Stalnaker semantics outright. Others argue that the problem motivates a contextualist rendering of counterfactuals. Still others maintain that the explanation for the phenomenon is merely pragmatic. I argue that none of these is right, and I defend a novel way to understand the phenomenon. My proposal avoids the problems faced by the alternative analyses and enjoys independent support. There is, however, a difficulty for my view: it entails that many ordinarily accepted counterfactuals are not true. I argue that this cost is acceptable. (shrink)

According to existing accounts of indicative conditionals, any argument of the following form is valid: ϕ → ψ, ( ϕ ∧ ψ ) → χ ∴ ϕ → χ. Here, I present a set of counterexamples to show that there exist invalid arguments of this form. I argue that this data poses serious problems to variably strict accounts of conditionals, as such accounts are structurally unable to accommodate it. Dynamic strict accounts, however, are a different (...) story. While existing dynamic strict accounts do not accommodate the data, they are in principle able to, and I propose a modified dynamic strict account, drawing from von Fintel, that does. The key modification is this: whereas existing dynamic strict accounts take into account only the effects of conditional antecedents in changing the semantic context, the data shows that we must also take into account the effects of conditional consequents in changing the semantic context. (shrink)

Both Lowe and Tsai have presented their own versions of the theory that both indicative and subjunctive conditionals are strict conditionals. We critically discuss both versions and we find each version wanting.

Jonathan Lowe has argued that a particular variation on C.I. Lewis' notion of strict implication avoids the paradoxes of strict implication. We show that Lowe's notion of implication does not achieve this aim, and offer a general argument to demonstrate that no other variation on Lewis' notion of constantly strict implication describes the logical behaviour of natural-language conditionals in a satisfactory way.

This paper defends the thesis that counterfactuals are strict conditionals. Its purpose is to show that there is a coherent view according to which counterfactuals are strict conditionals whose antecedent is stated elliptically. Section 1 introduces the view. Section 2 outlines a response to the main argument against the thesis that counterfactuals are strict conditionals. Section 3 compares the view with a proposal due to Aqvist, which may be regarded as its direct predecessor. Sections (...) 4 and 5 explain how the view di ers from the theories of counterfactuals advocated by Stalnaker and Lewis, and from some contextualist strict conditional accounts of counterfactuals that have emerged recently. Finally, section 6 addresses the thorny issue of disjunctive antecedents. (shrink)

This paper is intended to show that, at least in a considerably wide class of cases, indicative conditionals are adequately formalized as strict conditionals. The first part of the paper outlines three arguments that support the strict conditional view, that is, three reasons for thinking that an indicative conditional is true just in case it is impossible that its antecedent is true and its consequent is false. The second part of the paper develops the strict (...) conditional view and defends it from some foreseeable objections. (shrink)

This essay calls attention to a set of linguistic interactions between counterfactual conditionals, on one hand, and possibility modals like could have and might have, on the other. These data present a challenge to the popular variably strict semantics for counterfactual conditionals. Instead, they support a version of the strict conditional semantics in which counterfactuals and possibility modals share a unified quantificational domain. I’ll argue that pragmatic explanations of this evidence are not available to the (...) variable analysis. And putative counterexamples to the unified strict analysis, on careful inspection, in fact support it. Ultimately, the semantics of conditionals and modals must be linked together more closely than has sometimes been recognized, and a unified strict semantics for conditionals and modals is the only way to fully achieve this. (shrink)

Entitlement is conceived as a kind of positive epistemic status, attaching to certain propositions, that involves no cognitive or intellectual accomplishment on the part of the beneficiary — a status that is in place by default. In this paper I will argue that the notion of entitlement — or something very like it — falls out of an idea that may at first blush seem rather disparate: that the evidential support relation can be understood as a kind of variably (...) strict conditional (in the sense of Lewis 1973). Lewis provided a general recipe for deriving what he termed inner modalities from any variably strict conditional governed by a logic meeting certain constraints. On my proposal, entitlement need be nothing more exotic than the inner necessity associated with evidential support. Understanding entitlement in this way helps to answer some common concerns — in particular, the concern that entitlement could only be a pragmatic, and not genuinely epistemic, status. (shrink)

This paper is about four inferences patterns governing conditionals: Transitivity, Simplification, Contraposition, and Antecedent Strengthening. Transitivity, Simplification, and Contraposition are intuitively compelling. Although Antecedent Strengthening may seem less attractive at first, close attention to the full range of data reveals that it too has considerable appeal. An adequate theory of conditionals should account for these facts. The strict theory does so by validating them. But the variably strict theory invalidates them. So the variably (...) class='Hi'>strict theorist faces a question: why do we find these inferences so compelling? In this paper, I suggest an answer on her behalf: that they are reasonable inferences in the sense introduced by Stalnaker (1975). -/- . (shrink)

In this paper it will be shown that when a conditional statement is understood or known to be true, a number of implicitly specified variables are given more or less concrete values. Each of the variables will be defined and examples will be employed to demonstrate their use in conditional evaluation. From time to time this analysis in terms of variables will be contrasted with a 'possible worlds' analysis of conditionals. The purpose of this paper is not to argue (...) against the possible worlds analysis but rather to provide an alternative to that analysis. (shrink)

Recent experimental work has shown that the truth-value judgments of color predications, i.e. utterances of the form “the leaves on my tree are green” or “these walls are brown,” are influenced by slight changes in the context of utterance (Hansen and Chemla 2013, Ziółkowski, 2021). Most explanations of this phenomenon focus on the semantics of color adjectives. However, it is not clear if these explanations do justice to the nuances of the empirical data on context-sensitivity of color predications (Ziółkowski, 2021). (...) In contrast to the adjectival explanations, Agustin Vicente (2015) has recently proposed that the context-sensitivity of color predications can be explained by invoking the polysemy of the noun. In this paper, we present the results of three studies designed to empirically test this hypothesis: a traditional survey experiment (Study 1), an exploratory correlational study inspired by the semantic integration paradigm (Study 2a), and a follow-up experiment (Study 2b) that was designed to mitigate possible shortcomings of Study 2a. The results of our studies present preliminary evidence against Vicente’s theory. (shrink)

.This paper discusses Aristotle’s thesis and Boethius’ thesis, the most distinctive theorems of connexive logic. Its aim is to show that, although there is something plausible in Aristotle’s thesis and Boethius’ thesis, the intuitions that may be invoked to motivate them are consistent with any account of indicative conditionals that validates a suitably restricted version of them. In particular, these intuitions are consistent with the view that indicative conditionals are adequately formalized as strict conditionals.

In this paper I try to show that semantics can explain word-to-world relations and that sentences can have meanings that determine truth-conditions. Critics like Chomsky typically maintain that only speakers denote, i.e., only speakers, by using words in one way or another, represent entities or events in the world. However, according to their view, individual acts of denotations are not explained just by virtue of speakers’ semantic knowledge. Against this view, I will hold that, in the typical cases considered, semantic (...) knowledge can account for the denotational uses of words of individual speakers. (shrink)

Modus ponens is the argument from premises of the form If A, then B and A to the conclusion B. Nearly all participants agree that the modus ponens conclusion logically follows when the argument appears in this Basic form. However, adding a further premise can lower participants’ rate of agreement—an effect called suppression. We propose a theory of suppression that draws on contemporary ideas about conditional sentences in linguistics and philosophy. Semantically, the theory assumes that people interpret an indicative conditional (...) as a context-sensitive strict conditional: true if and only if its consequent is true in each of a contextually determined set of situations in which its antecedent is true. Pragmatically, the theory claims that context changes in response to new assertions, including new conditional premises. Thus, the conclusion of a modus ponens argument may no longer be accepted in the changed context. Psychologically, the theory describes people as capable of reasoning about broad classes of possible situations, ordered by typicality, without having to reason about individual possible worlds. The theory accounts for the main suppression phenomena, and it generates some novel predictions that new experiments confirm. (shrink)

Formal symptoms of relevance usually concern the propositional variables shared between the antecedent and the consequent of provable conditionals. Among the most famous results about such symptoms are Belnap’s early results showing that for sublogics of the strong relevant logic R, provable conditionals share a signed variable between antecedent and consequent. For logics weaker than R stronger variable sharing results are available. In 1984, Ross Brady gave one well-known example of such a result. As a corollary to the (...) main result of the paper, we give a very simple proof of a related but strictly stronger result. (shrink)

Polysemy seems to be a relatively neglected phenomenon within philosophy of language as well as in many quarters in linguistic semantics. Not all variations in a word’s contribution to truth-conditional contents are to be thought as expressions of the phenomenon of polysemy, but it can be argued that many are. Polysemous terms are said to contribute senses or aspects to truth-conditional contents. In this paper, I will make use of the notion of aspect to argue that some apparently wild variations (...) in an utterance’s truth conditions are instead quite systematic. In particular, I will focus on Travis’ much debated green leaves case and explain it in terms of the polysemy of the noun; and in particular, in terms of the as-it-is and the as-it-looks aspects associated with kind words. (shrink)

In natural language, conditionals are frequently used for giving explanations. Thus the antecedent of a conditional is typically understood as being connected to, being relevant for, or providing evidential support for the conditional's consequent. This aspect has not been adequately mirrored by the logics that are usually offered for the reasoning with conditionals: neither in the logic of the material conditional or the strict conditional, nor in the plethora of logics for suppositional conditionals that have been (...) produced over the past 50 years. In this paper I survey some recent attempts to come to terms with the problem of encoding evidential support or relevance in the logic of conditionals. I present models in a qualitative-modal and in a quantitative-probabilistic setting. Focussing on some particular examples, I show that no perfect match between the two kinds of settings has been achieved yet. (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.

Variable-Value axiologies avoid Parfit’s Repugnant Conclusion while satisfying some weak instances of the Mere Addition principle. We apply calibration methods to two leading members of the family of Variable-Value views conditional upon: first, a very weak instance of Mere Addition and, second, some plausible empirical assumptions about the size and welfare of the intertemporal world population. We find that such facts calibrate these two Variable-Value views to be nearly totalist, and therefore imply conclusions that should seem repugnant to anyone who (...) opposes Total Utilitarianism only due to the Repugnant Conclusion. (shrink)

This paper presents a new system of conditional logic B2, which is strictly intermediate in strength between the existing systems B1 and B3 from John Burgess (1981) and David Lewis (1973a). After presenting and motivating the new system, we will show that it is characterized by a natural class of frames. These frames correspond to the idea that conditionals are about which worlds are nearly closest, rather than which worlds are closest. Along the way, we will also give new (...) characterization results for B1 and B3, along with two other new systems B1.1 and B1.2. (shrink)

In this article I define a strong conditional for classical sentential logic, and then extend it to three non-classical sentential logics. It is stronger than the material conditional and is not subject to the standard paradoxes of material implication, nor is it subject to some of the standard paradoxes of C. I. Lewis’s strict implication. My conditional has some counterintuitive consequences of its own, but I think its pros outweigh its cons. In any case, one can always augment one’s (...) language with more than one conditional, and it may be that no single conditional will satisfy all of our intuitions about how a conditional should behave. Finally, I suspect the strong conditional will be of more use for logic rather than the philosophy of language, and I will make no claim that the strong conditional is a good model for any particular use of the indicative conditional in English or other natural languages. Still, it would certainly be a nice bonus if some modified version of the strong conditional could serve as one. -/- I begin by exploring some of the disadvantages of the material conditional, the strict conditional, and some relevant conditionals. I proceed to define a strong conditional for classical sentential logic. I go on to adapt this account to Graham Priest’s Logic of Paradox, to S. C. Kleene’s logic K3, and then to J. Łukasiewicz’s logic Ł, a standard version of fuzzy logic. (shrink)

This paper aims to examine Kant’s views on evolution of organized beings and to show that Kant’s antievolutionary conclusions stem from his study of natural history and variability of organisms. Accordingly, I discuss Kant’s study of natural history and consider whether his conclusion about impossibility of knowledge about such history expands on the research of history of organized beings. Moving forward, I examine the notion of variability in Kant’s philosophy, and show that his theory of organized beings relies on the (...) preformationist conception of variability that provides limited insight into the history of organisms. I explain that Kant’s endorsement of preformationism is conditioned by a lack of knowledge about the mechanism that successfully explains adaptation and transmutation of organisms leading towards the creation of new species. Finally, I sumarize the following reasons for Kant’s rejection of the hypothesis of evolution: lack of cognitive ability to discover all changes of natural phenomena in different periods of time and adoption of preformationist conception of variability of organized beings. I finish off with a discussion about mechanical inexplicability of organisms and find a third reason Kant believes that the idea of evolution is only “a daring adventure on the part of reason”. (shrink)

Behaviorism was a peculiarly American phenomenon. As a school of psychology it was founded by John B. Watson (1878-1958) and grew into the neobehaviorisms of the 1920s, 30s and 40s. Philosophers were involved from the start, prefiguring the movement and endeavoring to define or redefine its tenets. Behaviorism expressed the naturalistic bent in American thought, which came in response to the prevailing philosophical idealism and was inspired by developments in natural science itself. There were several versions of naturalism in American (...) philosophy, and also several behaviorisms. Most behaviorists paid homage to Darwinian functionalism; all forswore introspection and made learned changes in behavior the primary subject matter and explanatory domain of psychology. They differed in their descriptions of behavior, modes of explanation, and attitudes toward mentalistic concepts. Watson was a strict materialist who wanted to eliminate all mentalistic talk from psychology. Edward Chace Tolman (1886-1959) regarded mind as a biological function of the organism. He permitted mentalistic terms such as 'purpose' in behavioral description, and posited intervening processes that included 'representations' of the environment, while requiring such processes be studied only as expressed in behavior. Clark L. Hull (1884-1952) developed a hypothetical-deductive version of behaviorism, akin to Tolman's functionalism in positing intervening variables but without his cognitivist constructs. B. F. Skinner (1904-90) rejected intervening variables and developed his own account of the behavior of the whole organism, based on the laws of operant conditioning. The naturalism in American philosophy of the early twentieth century showed respect for the natural sciences, especially biology and psychology. John Dewey (1896, 1911), George Santayana (1905, 1920), and F. J. E. Woodbridge (1909, 1913) expressed this attitude. It animated the neorealism of E. B. Holt and Ralph Barton Perry, who gave special attention to psychology, and the evolutionary naturalism and critical realism of Roy Wood Sellars. This naturalism differed from Watson's in regarding mind as part of nature from a Darwinian and functionalist perspective, and treating behavior as the product of the mental functioning. It fed Tolman's version of behaviorism. It was not materialistic or physical-reductionist. Only later, with Quine and logical empiricism, was behaviorism seen as essentially physicalistic. (shrink)

Relatively few authors attempt to assess individuals’ moral responsibility for collective action within organizations. I draw on fairly technical recent work by Seamus Miller, Christopher Kutz, and Tracy Isaacs in the field of collective responsibility to see what normative lessons can be prepared for people considering entry into large hierarchical, compartmentalized organizations like businesses or the military. I will defend a view shared by Isaacs that group members’ responsibility for collective action depends on intentions to contribute to particular collective actions, (...) against Miller and Kutz’s more inculpating standards. Miller and Kutz fail to achieve their goal of articulating a variable standard for measuring individual responsibility within organizations, for reasons suggesting we might not be able to do better with their theoretical commitments than a threshold warning for all potential entrants to be wary of the groups they enter. Isaacs sketches an approach that is more successful at creating a variable standard for assessing high echelon actors; I build on and refine her theory to argue that organization members can be held responsible for their unique interpretations of the organization mission and unique contributions to their role duties. High echelon actors may share personal responsibility for their subordinates’ behavior when they have created the conditions for those actions through their unique orders. (shrink)

Tarski’s Convention T—presenting his notion of adequate definition of truth (sic)—contains two conditions: alpha and beta. Alpha requires that all instances of a certain T Schema be provable. Beta requires in effect the provability of ‘every truth is a sentence’. Beta formally recognizes the fact, repeatedly emphasized by Tarski, that sentences (devoid of free variable occurrences)—as opposed to pre-sentences (having free occurrences of variables)—exhaust the range of significance of is true. In Tarski’s preferred usage, it is part of the meaning (...) of true that attribution of being true to a given thing presupposes the thing is a sentence. Beta’s importance is further highlighted by the fact that alpha can be satisfied using the recursively definable concept of being satisfied by every infinite sequence, which Tarski explicitly rejects. Moreover, in Definition 23, the famous truth-definition, Tarski supplements “being satisfied by every infinite sequence” by adding the condition “being a sentence”. Even where truth is undefinable and treated by Tarski axiomatically, he adds as an explicit axiom a sentence to the effect that every truth is a sentence. Surprisingly, the sentence just before the presentation of Convention T seems to imply that alpha alone might be sufficient. Even more surprising is the sentence just after Convention T saying beta “is not essential”. Why include a condition if it is not essential? Tarski says nothing about this dissonance. Considering the broader context, the Polish original, the German translation from which the English was derived, and other sources, we attempt to determine what Tarski might have intended by the two troubling sentences which, as they stand, are contrary to the spirit, if not the letter, of several other passages in Tarski’s corpus. (shrink)

Recent work in contemporary compatibilist theory displays considerable sophistication and subtlety when compared with the earlier theories of classical compatibilism. Two distinct lines of thought have proved especially influential and illuminating. The first developed around the general hypothesis that moral sentiments or reactive attitudes are fundamental for understanding the nature and conditions of moral responsibility. The other important development is found in recent compatibilist accounts of rational self-control or reason responsiveness. Strictly speaking, these two lines of thought have developed independent (...) of each other. However, in the past decade or so they have been fused together in several prominent statements of compatibilist theory. I will refer to theories that combine these two elements in this way as RS theories. RS theories face a number of familiar difficulties that relate to each of their two components. Beyond this, they also face a distinct set of problems concerning how these two main components relate or should be integrated. My concerns in this paper focus primarily on this set of problems. According to one version of RS compatibilism, the role of moral sentiments is limited to explaining what is required for holding an agent responsible. In contrast with this, the role of reason responsiveness is to explain what moral capacities are required for an agent to be responsible, one who is a legitimate or fair target of our moral sentiments. More specifically, according to this view, moral sense is not required for rational selfcontrol or reason responsiveness. There is, therefore, no requirement that the responsible agent has some capacity to feel moral sentiment. Contrary to this view, I argue that a responsible agent must be capable of holding herself and others responsible. Failing this, an agent’s powers of rational self-control will be both limited and impaired. In so far as holding responsible requires moral sense, it follows that being responsible also requires moral sense. (shrink)

The explicit history of the “hidden variables” problem is well-known and established. The main events of its chronology are traced. An implicit context of that history is suggested. It links the problem with the “conservation of energy conservation” in quantum mechanics. Bohr, Kramers, and Slaters (1924) admitted its violation being due to the “fourth Heisenberg uncertainty”, that of energy in relation to time. Wolfgang Pauli rejected the conjecture and even forecast the existence of a new and unknown then elementary particle, (...) neutrino, on the ground of energy conservation in quantum mechanics, afterwards confirmed experimentally. Bohr recognized his defeat and Pauli’s truth: the paradigm of elementary particles (furthermore underlying the Standard model) dominates nowadays. However, the reason of energy conservation in quantum mechanics is quite different from that in classical mechanics (the Lie group of all translations in time). Even more, if the reason was the latter, Bohr, Cramers, and Slatters’s argument would be valid. The link between the “conservation of energy conservation” and the problem of hidden variables is the following: the former is equivalent to their absence. The same can be verified historically by the unification of Heisenberg’s matrix mechanics and Schrödinger’s wave mechanics in the contemporary quantum mechanics by means of the separable complex Hilbert space. The Heisenberg version relies on the vector interpretation of Hilbert space, and the Schrödinger one, on the wave-function interpretation. However the both are equivalent to each other only under the additional condition that a certain well-ordering is equivalent to the corresponding ordinal number (as in Neumann’s definition of “ordinal number”). The same condition interpreted in the proper terms of quantum mechanics means its “unitarity”, therefore the “conservation of energy conservation”. In other words, the “conservation of energy conservation” is postulated in the foundations of quantum mechanics by means of the concept of the separable complex Hilbert space, which furthermore is equivalent to postulating the absence of hidden variables in quantum mechanics (directly deducible from the properties of that Hilbert space). Further, the lesson of that unification (of Heisenberg’s approach and Schrödinger’s version) can be directly interpreted in terms of the unification of general relativity and quantum mechanics in the cherished “quantum gravity” as well as a “manual” of how one can do this considering them as isomorphic to each other in a new mathematical structure corresponding to quantum information. Even more, the condition of the unification is analogical to that in the historical precedent of the unifying mathematical structure (namely the separable complex Hilbert space of quantum mechanics) and consists in the class of equivalence of any smooth deformations of the pseudo-Riemannian space of general relativity: each element of that class is a wave function and vice versa as well. Thus, quantum mechanics can be considered as a “thermodynamic version” of general relativity, after which the universe is observed as if “outside” (similarly to a phenomenological thermodynamic system observable only “outside” as a whole). The statistical approach to that “phenomenological thermodynamics” of quantum mechanics implies Gibbs classes of equivalence of all states of the universe, furthermore re-presentable in Boltzmann’s manner implying general relativity properly … The meta-lesson is that the historical lesson can serve for future discoveries. (shrink)

Future Logic is an original, and wide-ranging treatise of formal logic. It deals with deduction and induction, of categorical and conditional propositions, involving the natural, temporal, extensional, and logical modalities. Traditional and Modern logic have covered in detail only formal deduction from actual categoricals, or from logical conditionals (conjunctives, hypotheticals, and disjunctives). Deduction from modal categoricals has also been considered, though very vaguely and roughly; whereas deduction from natural, temporal and extensional forms of conditioning has been all but totally (...) ignored. As for induction, apart from the elucidation of adductive processes (the scientific method), almost no formal work has been done. This is the first work ever to strictly formalize the inductive processes of generalization and particularization, through the novel methods of factorial analysis, factor selection and formula revision. This is the first work ever to develop a formal logic of the natural, temporal and extensional types of conditioning (as distinct from logical conditioning), including their production from modal categorical premises. Future Logic contains a great many other new discoveries, organized into a unified, consistent and empirical system, with precise definitions of the various categories and types of modality (including logical modality), and full awareness of the epistemological and ontological issues involved. Though strictly formal, it uses ordinary language, wherever symbols can be avoided. Among its other contributions: a full list of the valid modal syllogisms (which is more restrictive than previous lists); the main formalities of the logic of change (which introduces a dynamic instead of merely static approach to classification); the first formal definitions of the modal types of causality; a new theory of class logic, free of the Russell Paradox; as well as a critical review of modern metalogic. But it is impossible to list briefly all the innovations in logical science — and therefore, epistemology and ontology — this book presents; it has to be read for its scope to be appreciated. (shrink)

Neural activity varies continually from moment to moment. Such temporal variability (TV) has been highlighted as a functionally specific brain property playing a fundamental role in cognition. We sought to investigate the mechanisms involved in TV changes between two basic behavioral states, namely having the eyes open (EO) or eyes closed (EC) in vivo in humans. To these ends we acquired BOLD fMRI, ASL, and [18F]-fluoro-deoxyglucose PET in a group of healthy participants (n = 15), along with BOLD fMRI and (...) [18F]-flumazenil PET in a separate group (n = 19). Focusing on an EO- vs EC-sensitive region in the occipital cortex (identified in an independent sample), we show that TV is constrained in the EO condition compared to EC. This reduction is correlated with an increase in energy consumption and with regional GABAA receptor density. This suggests that the modulation of TV by behavioral state involves an increase in overall neural activity that is related to an increased effect from GABAergic inhibition in addition to any excitatory changes. These findings contribute to our understanding of the mechanisms underlying activity variability in the human brain and its control. (shrink)

Conditional independence tests have received special attention lately in machine learning and computational intelligence related literature as an important indicator of the relationship among the variables used by their models. In the field of probabilistic graphical models, which includes Bayesian network models, conditional independence tests are especially important for the task of learning the probabilistic graphical model structure from data. In this paper, we propose the full Bayesian significance test for tests of conditional independence for discrete datasets. The full Bayesian (...) significance test is a powerful Bayesian test for precise hypothesis, as an alternative to the frequentist’s significance tests (characterized by the calculation of the p-value). (shrink)

The literature on counterfactuals is dominated by strict accounts and variably strict accounts. Counterexamples to the principle of Antecedent Strengthening were thought to be fatal to SA; but it has been shown that by adding dynamic resources to the view, such examples can be accounted for. We broaden the debate between VSA and SA by focusing on a new strengthening principle, Strengthening with a Possibility. We show dynamic SA classically validates this principle. We give a counterexample to (...) it and show that extra dynamic resources cannot help SA. We then show VSA accounts for the counterexample if it allows for orderings on worlds that are not almost-connected, and that such an ordering naturally falls out of a Kratzerian ordering source semantics. We conclude that the failure of Strengthening with a Possibility tells strongly against Dynamic SA and in favor of an ordering source-based version of VSA. (shrink)

The currently used humanity model is chaotic, devoid of logic or coherence. In Part 1 of this two-part paper, we examined human traits of a scientific model in absence of ‘born sinner’ starting point. We demonstrated that the so-called ‘viceroy model’ that is characterized as scientifically sustainable can replace the existing models that are based on fear and scarcity. Part Two of the paper deals with adequate definition of moral campus that conforms to the viceroy model. In this paper, it (...) is shown that the talk of morality or a moral compass is aphenomenal in absence of strict necessary and sufficient conditions. It also follows that natural justice can only be followed after defining the term ‘natural’ with the same scientific rigor as that of the viceroy model. Once these terms are consistently defined, one is well poised to talk about inalienable rights, moral compass, environmental sustainability, and humanity. The immediate consequence of this model is the demonstration that currently used governance models, such as democracy, is inherently implosive and must be replaced with a new model that is in conformance with the scientific definition of ‘natural’. This emerging model is free from inconsistencies and will remain effective as a governance tool that optimizes individual rights and balances with the right of the state as well as a Creator. It is concluded that this model offers the only hope of maximizing individual liberty without compromising universal peace and natural justice. At this point, morality and legality become equivalent to each. The implications of this paper are overwhelming, making all current judicial actions immoral, in essence repudiating the entire Establishment as little more than a mafia entity, bringing back ‘might is right’ mantra, packaged as ‘social progress’. The paper finally shows how a standard that is necessarily and sufficiently universal can become impetus for a true knowledge. (shrink)

This paper develops a probabilistic analysis of conditionals which hinges on a quantitative measure of evidential support. In order to spell out the interpreta- tion of ‘if’ suggested, we will compare it with two more familiar interpretations, the suppositional interpretation and the strict interpretation, within a formal framework which rests on fairly uncontroversial assumptions. As it will emerge, each of the three interpretations considered exhibits specific logical features that deserve separate consideration.

I present a formal theory of the logic and aboutness of imagination. Aboutness is understood as the relation between meaningful items and what they concern, as per Yablo and Fine’s works on the notion. Imagination is understood as per Chalmers’ positive conceivability: the intentional state of a subject who conceives that p by imagining a situation—a configuration of objects and properties—verifying p. So far aboutness theory has been developed mainly for linguistic representation, but it is natural to extend it to (...) intentional states. The proposed framework combines a modal semantics with a mereology of contents: imagination operators are understood as variably strict quantifiers over worlds with a content-preservation constraint. (shrink)

We present a formal semantics for epistemic logic, capturing the notion of knowability relative to information (KRI). Like Dretske, we move from the platitude that what an agent can know depends on her (empirical) information. We treat operators of the form K_AB (‘B is knowable on the basis of information A’) as variably strict quantifiers over worlds with a topic- or aboutness- preservation constraint. Variable strictness models the non-monotonicity of knowledge acquisition while allowing knowledge to be intrinsically stable. (...) Aboutness-preservation models the topic-sensitivity of information, allowing us to invalidate controversial forms of epistemic closure while validating less controversial ones. Thus, unlike the standard modal framework for epistemic logic, KRI accommodates plausible approaches to the Kripke-Harman dogmatism paradox, which bear on non-monotonicity, or on topic-sensitivity. KRI also strikes a better balance between agent idealization and a non-trivial logic of knowledge ascriptions. (shrink)

I want to model a finite, fallible cognitive agent who imagines that p in the sense of mentally representing a scenario—a configuration of objects and properties—correctly described by p. I propose to capture imagination, so understood, via variably strict world quantifiers, in a modal framework including both possible and so-called impossible worlds. The latter secure lack of classical logical closure for the relevant mental states, while the variability of strictness captures how the agent imports information from actuality in (...) the imagined non-actual scenarios. Imagination turns out to be highly hyperintensional, but not logically anarchic. Section 1 sets the stage and impossible worlds are quickly introduced in Sect. 2. Section 3 proposes to model imagination via variably strict world quantifiers. Section 4 introduces the formal semantics. Section 5 argues that imagination has a minimal mereological structure validating some logical inferences. Section 6 deals with how imagination under-determines the represented contents. Section 7 proposes additional constraints on the semantics, validating further inferences. Section 8 describes some welcome invalidities. Section 9 examines the effects of importing false beliefs into the imagined scenarios. Finally, Sect. 10 hints at possible developments of the theory in the direction of two-dimensional semantics. (shrink)

Our aim is to provide a sequent calculus whose external consequence relation coincides with the three-valued paracomplete logic `of nonsense' introduced by Dmitry Bochvar and, independently, presented as the weak Kleene logic K3W by Stephen C. Kleene. The main features of this calculus are (i) that it is non-reflexive, i.e., Identity is not included as an explicit rule (although a restricted form of it with premises is derivable); (ii) that it includes rules where no variable-inclusion conditions are attached; and (iii) (...) that it is hybrid, insofar as it includes both left and right operational introduction as well as elimination rules. (shrink)

A widely accepted claim about counterfactuals is that they differ from strict conditionals, that is, there is no adequate representation of them as sentences of the form   . To justify this claim, Stalnaker and Lewis have argued that some fallacious inferences would turn out valid if counterfactuals were so represented. However, their argument has a flaw, as it rests on a questionable assumption about the relation between surface grammar and logical form. Without that assumption, no consequence (...) of the alleged kind is obtained, hence the claim may be rejected. (shrink)

The main disciples of Socrates criticise the use of city walls. However, their attacks are less grounded in a deep strategic reflexion than related to the traumatic consequences of Pericles’ strategy at the beginning of the Peloponnesian war. The Lacedemonians’ opposition to the erection of surrounding walls is more likely linked to their aristo- cratic ideology and interests than to moral imperatives. Though Plato and Xenophon’s motives are to avoid political divisions in the city, their positions on fortifications reveal their (...) aristocratic bias and the question of the walls appears to be part of a more general questioning on the spatial and political organisation of the city. On that issue, Aristotle criticises Plato from a pragmatic point of view and defends the use of walls, but under strict conditions only. The Spartan and Socratic critique of the building of the walls, as well as Aristotle reluctance to fully accept them, could be traced back to a common Greek archaic ideal. (shrink)

Assessment of those with whom one finds oneself in dispute is indispensable in the epistemology of disagreement. The assessment of one’s opponents is necessary in order to determine whether a particular disagreement constitutes evidence of a likely error in one’s own understanding. However, assessment of an opponent’s capacity to know the matter in dispute is only possible when the conditions for knowledge are not themselves open to debate. Consequently, epistemic significance can only be recognised in disagreements among those who are (...) in tacit or explicit agreement about what constitutes justification in a given case. The result is that the epistemic significance that disagreement possesses is always strictly conditional upon prior assumptions. The difference between a peer disagreement and a non-peer disagreement cannot indicate whether one is or is not more likely to be right than one’s opponent in an absolute sense, only whether one is or is not more likely to be right given the presupposed conditions. (shrink)

We argue that the extant evidence for Stoic logic provides all the elements required for a variable-free theory of multiple generality, including a number of remarkably modern features that straddle logic and semantics, such as the understanding of one- and two-place predicates as functions, the canonical formulation of universals as quantified conditionals, a straightforward relation between elements of propositional and first-order logic, and the roles of anaphora and rigid order in the regimented sentences that express multiply general propositions. We (...) consider and reinterpret some ancient texts that have been neglected in the context of Stoic universal and existential propositions and offer new explanations of some puzzling features in Stoic logic. Our results confirm that Stoic logic surpasses Aristotle’s with regard to multiple generality, and are a reminder that focusing on multiple generality through the lens of Frege-inspired variable-binding quantifier theory may hamper our understanding and appreciation of pre-Fregean theories of multiple generality. (shrink)

The practice of screening potential users of reproductive services is of profound social and political significance. Access screening is inconsistent with the principles of equality and self-determination, and violates individual and group human rights. Communities that strive to function in accord with those principles should not permit access screening, even screening that purports to be a benign exercise of professional discretion. Because reproductive choice is controversial, regulation by law may be required in most jurisdictions to provide effective protection for reproductive (...) rights. In Canada, for example, equal access can, and should be, guaranteed by federal regulations imposing strict conditions on the licences of fertility clinics. (shrink)

Recent revelations of Iran’s hitherto undisclosed uranium enrichment programs have once again incited western fears that Tehran seeks nuclear weapons’ capability. Their fears seem motivated by more than the concern for compliance with the Nuclear Nonproliferation Treaty (NPT). Rather, they seem strongly connected to the western moral assumptions about what kind of government or people can be trusted with a nuclear arsenal. In this paper, I critically examine the western assumptions of the immorality of contemporary nuclear proliferation from an international (...) ethical stance that otherwise might be expected to give it unequivocal support – the stance of Kantian nonideal theory. In contrast to the uses of Kant that were prominent during the Cold War, I advance and apply a sketch of a Kantian nonideal theory that specifies the conditions (although strict conditions) under which nuclear proliferation for states like Iran is morally permissible even though the NPT forbids it. (shrink)

Population axiology is the study of the conditions under which one state of affairs is better than another, when the states of affairs in ques- tion may differ over the numbers and the identities of the persons who ever live. Extant theories include totalism, averagism, variable value theories, critical level theories, and “person-affecting” theories. Each of these the- ories is open to objections that are at least prima facie serious. A series of impossibility theorems shows that this is no coincidence: (...) it can be proved, for various sets of prima facie intuitively compelling desiderata, that no axiology can simultaneously satisfy all the desiderata on the list. One’s choice of population axiology appears to be a choice of which intuition one is least unwilling to give up. (shrink)

Relevant logics infamously have the property that they only validate a conditional when some propositional variable is shared between its antecedent and consequent. This property has been strengthened in a variety of ways over the last half-century. Two of the more famous of these strengthenings are the strong variable sharing property and the depth relevance property. In this paper I demonstrate that an appropriate class of relevant logics has a property that might naturally be characterized as the supremum of these (...) two properties. I also show how to use this fact to demonstrate that these logics seem to be constructive in previously unknown ways. (shrink)

We give two social aggregation theorems under conditions of risk, one for constant population cases, the other an extension to variable populations. Intra and interpersonal welfare comparisons are encoded in a single ‘individual preorder’. The theorems give axioms that uniquely determine a social preorder in terms of this individual preorder. The social preorders described by these theorems have features that may be considered characteristic of Harsanyi-style utilitarianism, such as indifference to ex ante and ex post equality. However, the theorems are (...) also consistent with the rejection of all of the expected utility axioms, completeness, continuity, and independence, at both the individual and social levels. In that sense, expected utility is inessential to Harsanyi-style utilitarianism. In fact, the variable population theorem imposes only a mild constraint on the individual preorder, while the constant population theorem imposes no constraint at all. We then derive further results under the assumption of our basic axioms. First, the individual preorder satisfies the main expected utility axiom of strong independence if and only if the social preorder has a vector-valued expected total utility representation, covering Harsanyi’s utilitarian theorem as a special case. Second, stronger utilitarian-friendly assumptions, like Pareto or strong separability, are essentially equivalent to strong independence. Third, if the individual preorder satisfies a ‘local expected utility’ condition popular in non-expected utility theory, then the social preorder has a ‘local expected total utility’ representation. Fourth, a wide range of non-expected utility theories nevertheless lead to social preorders of outcomes that have been seen as canonically egalitarian, such as rank-dependent social preorders. Although our aggregation theorems are stated under conditions of risk, they are valid in more general frameworks for representing uncertainty or ambiguity. (shrink)