Since it was presented in 1963, Chisholm’s paradox has attracted constant attention in the deontic logic literature, but without the emergence of any definitive solution. We claim this is due to its having no single solution. The paradox actually presents many challenges to the formalization of deontic statements, including (1) context sensitivity of unconditional oughts, (2) formalizing conditional oughts, and (3) distinguishing generic from nongeneric oughts. Using the practical interpretation of ‘ought’ as a guideline, we propose a linguistically motivated logical (...) solution to each of these problems, and explain the relation of the solution to the problem of contrary-to-duty obligations. (shrink)

Possible worlds semantics for conditionals leave open the problem of how to construct models for realistic domains. In this paper, we show how to adapt logics of action and change such as John McCarthy’s Situation Calculus to conditional logics. We illustrate the idea by presenting models for conditionals whose antecedents combine a declarative condition with a hypothetical action.

I argue that a counterexample proposed by donald nute shows only that past tenses involve indexical restriction to a limited domain of times. The purpose of this note is to defend the thesis that there is a single conditional connective figuring in both indicative and 'had'--'would' connectives, And that the differences in logical form between the two sorts of english conditional expressions have to do with tense.

Although moral philosophers have argued that shame is a valuable moral emotion, feminist philosophers have been skeptical. From the feminist perspective, shame appears to be an emotion more mediated by social circumstances than moral philosophers acknowledge. It is, they will argue, not an accident that shame occurs more frequently in people with marginalized identities. If who I am is a social subordinate, this would explain why women feel more shame. This argument relies on the assumption that the reason women feel (...) more shame is because they internalize negative social judgments about themselves. Although this explanation is tempting, in this chapter I want to evince a skeptical position against it. I want to put pressure on the claim that women internalize their oppression and that this process explains their shame. Instead, I argue that their shame can be explained by the difficulties of navigating one’s identity under conditions of oppression. (shrink)

We relate the theory of presupposition accommodation to a computational framework for reasoning in conversation. We understand presuppositions as private commitments the speaker makes in using an utterance but expects the listener to recognize based on mutual information. On this understanding, the conversation can move forward not just through the positive effects of interlocutors’ utterances but also from the retrospective insight interlocutors gain about one anothers’ mental states from observing what they do. Our title, ENLIGHTENED UPDATE, highlights such cases. Our (...) approach fleshes out two key principles: that interpretation is a form of intention recognition; and that intentions are complex informational structures, which specify commitments to conditions and to outcomes as well as to actions. We present a formalization and implementation of these principles for a simple conversational agent, and draw on this case study to argue that pragmatic reasoning is holistic in character, continuous with common-sense reasoning about collaborative activities, and most effectively characterized by associating specific, reliable interpretive constraints directly with grammatical forms. In showing how to make such claims precise and to develop theories that respect them, we illustrate the general place of computation in the cognitive science of language. (shrink)

Following the pioneer work of Bruno De Finetti [12], conditional probability spaces (allowing for conditioning with events of measure zero) have been studied since (at least) the 1950's. Perhaps the most salient axiomatizations are Karl Popper's in [31], and Alfred Renyi's in [33]. Nonstandard probability spaces [34] are a well know alternative to this approach. Vann McGee proposed in [30] a result relating both approaches by showing that the standard values of infinitesimal probability functions are representable as Popper functions, and (...) that every Popper function is representable in terms of the standard real values of some infinitesimal measure. Our main goal in this article is to study the constraints on (qualitative and probabilistic) change imposed by an extended version of McGee's result. We focus on an extension capable of allowing for iterated changes of view. Such extension, we argue, seems to be needed in almost all considered applications. Since most of the available axiomatizations stipulate (definitionally) important constraints on iterated change, we propose a non-questionbegging framework, Iterative Probability Systems (IPS) and we show that every Popper function can be regarded as a Bayesian IPS. A generalized version of McGee's result is then proved and several of its consequences considered. In particular we note that our proof requires the imposition of Cumulativity, i.e. the principle that a proposition that is accepted at any stage of an iterative process of acceptance will continue to be accepted at any later stage. The plausibility and range of applicability of Cumulativity is then studied. In particular we appeal to a method for defining belief from conditional probability (first proposed in [42] and then slightly modified in [6] and [3]) in order to characterize the notion of qualitative change induced by Cumulative models of probability kinematics. The resulting cumulative notion is then compared with existing axiomatizations of belief change and probabilistic supposition. We also consider applications in the probabilistic accounts of conditionals [1] and [30]. (shrink)

In applying Bayes’s theorem to the history of science, Bayesians sometimes assume – often without argument – that they can safely ignore very implausible theories. This assumption is false, both in that it can seriously distort the history of science as well as the mathematics and the applicability of Bayes’s theorem. There are intuitively very plausible counter-examples. In fact, one can ignore very implausible or unknown theories only if at least one of two conditions is satisfied: (i) one is certain (...) that there are no unknown theories which explain the phenomenon in question, or (ii) the likelihood of at least one of the known theories used in the calculation of the posterior is reasonably large. Often in the history of science, a very surprising phenomenon is observed, and neither of these criteria is satisfied. (shrink)

Spite is typically considered a vicious emotion that causes us to engage in petty, vindictive, and sometimes self-destructive behavior. Even though it has this bad reputation, I will argue that spite is a reactive attitude. Spite is emotional defiance of another’s command: to spite you, I will do something exactly because you told me not to. Our liability to feelings of spite presupposes that we recognize others as having practical authority, which is why it qualifies as a reactive attitude. I (...) conclude by offering conditions under which spite can be justified and unjustified. (shrink)

In Lowe (1995), instead of endorsing a Stalnaker/Lewis-style account of counterfactuals, E. J. Lowe claims that a variation of C. I. Lewis’s strict implication alone captures the essence of everyday conditionals and avoids the paradoxes of strict implication. However, Lowe’s approach fails to account for the validity of simple and straightforward arguments such as ‘if 2=3 then 2+1=3+1’, and Heylen & Horsten (2006) even claims that no variation of strict implication can successfully describe the logical behavior of natural language (...) conditionals. By incorporating the German logician O. Becker’s modal intuition with the insight of Ramsey’s Test, we show that there does exist a unified, strict-conditional based account of everyday conditionals, which withstands all attacks previously raised against truth-conditional accounts of conditionals. Furthermore, a subtle distinction between autistic and realistic readings of the indexical ‘I’ involved in a conditional helps us resolve a recent debate concerning the Thomason conditionals. (shrink)

Temporal necessity and the subjunctive conditional appear to be related by the principle of Past Predominance, according to which past similarities and differences take priority over future similarities and differences in determining the comparative similarity of alternative possible histories with respect to the present moment. R. H. Thomason and Anil Gupta have formalized Past Predominance in a semantics that combines selection functions with branching time; in this paper I show that Past Predominance can be formalized and axiomatized using ordinary (...) possible worlds semantics (without branching time). (shrink)

A part of Stalnaker (1968)’s influential theory of conditionals has been neglected, namely the role for an accessibility relation between worlds. I argue that the accessibility relation does not play the role intended for it in the theory as stated, and propose a minimal revision which solves the problem, and brings the theory in line with the formulation in Stalnaker & Thomason 1970.

In contemporary discussions of the Ramsey Test for conditionals, it is commonly held that (i) supposing the antecedent of a conditional is adopting a potential state of full belief, and (ii) Modus Ponens is a valid rule of inference. I argue on the basis of Thomason Conditionals (such as ' If Sally is deceiving, I do not believe it') and Moore's Paradox that both claims are wrong. I then develop a double-indexed Update Semantics for conditionals which (...) takes these two results into account while doing justice to the key intuitions underlying the Ramsey Test. The semantics is extended to cover some further phenomena, including the recent observation that epistemic modal operators give rise to something very like, but also very unlike, Moore's Paradox. (shrink)

T × W logic is a combination of tense and modal logic for worlds or histories with the same time order. It is the basis for logics of causation, agency and conditionals, and therefore an important tool for philosophical logic. Semantically it has been defined, among others, by R. H. Thomason. Using an operator expressing truth in all worlds, first discussed by C. M. Di Maio and A. Zanardo, an axiomatization is given and its completeness proved via D. (...) Gabbay’s irreflexivity lemma. Given this lemma the proof is more or less straight forward. At the end an alternative axiomatization is sketched in which Di Maio’s and Zanardo’s operator is replaced by a version of “actually”. (shrink)

T × W logic is a combination of tense and modal logic for worlds or histories with the same time order. It is the basis for logics of causation, agency and conditionals, and therefore an important tool for philosophical logic. Semantically it has been defined, among others, by R. H. Thomason. Using an operator expressing truth in all worlds, first discussed by C. M. Di Maio and A. Zanardo, an axiomatization is given and its completeness proved via D. (...) Gabbay’s irreflexivity lemma. Given this lemma the proof is more or less straight forward. At the end an alternative axiomatization is sketched in which Di Maio’s and Zanardo’s operator is replaced by a version of “actually”. (shrink)

Indeterminism, understood as a notion that an event may be continued in a few alternative ways, invokes the question what a region of chanciness looks like. We concern ourselves with its topological and spatiotemporal aspects, abstracting from the nature or mechanism of chancy processes. We first argue that the question arises in Montague-Lewis-Earman conceptualization of indeterminism as well as in the branching tradition of Prior, Thomason and Belnap. As the resources of the former school are not rich enough to (...) study topological issues, we investigate the question in the framework of branching space-times of Belnap (Synthese 92:385–434, 1992). We introduce a topology on a branching model as well as a topology on a history in a branching model. We define light-cones and assume four conditions that guarantee the light-cones so defined behave like light-cones of physical space-times. From among various topological separation properties that are relevant to our question, we investigate the Hausdorff property. We prove that each history in a branching model satisfies the Hausdorff property. As for the satisfaction of the Hausdorff property in the entire branching model, we prove that it is related to the phenomenon of passive indeterminism, which we describe in detail. (shrink)

We prove an existential analogue of the Goldblatt‐Thomason Theorem which characterizes modal definability of elementary classes of Kripke frames using closure under model theoretic constructions. The less known version of the Goldblatt‐Thomason Theorem gives general conditions, without the assumption of first‐order definability, but uses non‐standard constructions and algebraic semantics. We present a non‐algebraic proof of this result and we prove an analogous characterization for an alternative notion of modal definability, in which a class is defined by formulas which (...) are satisfiable under any valuation (the so‐called existential validity). Continuing previous work in which model theoretic characterization for this type of definability of elementary classes was proved, we give an analogous general result without the assumption of the first‐order definability. Furthermore, we outline relationships between sets of existentially valid formulas corresponding to several well‐known modal logics. (shrink)

This chapter focuses on four questions which help to understand the presupposition accommodation as Lewis defines it. The first is a question about how we recognize that an utterance involves a presupposition. The second question is about what it is to accommodate. The third question has to do with the role of scoreboard in accommodation. The fourth question has to do with Lewis's ceteris paribus condition. The chapter considers the characterization of accommodation due to Thomason, and argues that it (...) appropriately extends the range of phenomena taken to involve accommodation. It discusses a theory of the scoreboard building on Lewis's characterization which crucially reflects the interlocutors’ recognized goals and plans in language game, and argues that this type of scoreboard plays a natural role in facilitating and constraining accommodation. The author argues that some strong limits are a natural consequence of the nature of the game and its scoreboard. (shrink)

In The Revision Theory of Truth (MIT Press), Gupta and Belnap (1993) claim as an advantage of their approach to truth "its consequence that truth behaves like an ordinary classical concept under certain conditions—conditions that can roughly be characterized as those in which there is no vicious reference in the language." To clarify this remark, they define Thomason models, nonpathological models in which truth behaves like a classical concept, and investigate conditions under which a model is Thomason: they (...) argue that a model is Thomason when there is no vicious reference in it. We extend their investigation, considering notions of nonpathologicality and senses of "no vicious reference" generated both by revision theories of truth and by fixedpoint theories of truth. We show that some of the fixed-point theories have an advantage analogous to that which Gupta and Belnap claim for their approach, and that at least one revision theory does not. This calls into question the claim that the revision theories have a distinctive advantage in this regard. (shrink)

[IMPORTANT CORRECTION - See end of abstract.] In Syntactical Treatments of Modality, with Corollaries on Reflexion Principles and Finite Axiomatizability, Acta Philosophica Fennica 16 (1963), 153–167, Richard Montague shows that the use of a single syntactic predicate (with a context-independent semantic value) to represent modalities of alethic necessity and idealized knowledge leads to inconsistency. In A Note on Syntactical Treatments of Modality, Synthese 44 (1980), 391–395, Richmond Thomason obtains a similar impossibility result for idealized belief: under a syntactical treatment (...) of belief, the assumption that idealized belief is deductively closed, together with certain other plausible conditions on idealized belief, imply that an ideal believer with consistent beliefs cannot believe the truth of Robinson's Arithmetic. In this essay I assert an impossibility result similar to Thomason's but which does not assume that belief is deductively closed or ideal in any other way. There are technical mistakes in the formulations of Lemmas 1-4 and Theorem 2, however. Corrections can be found in the Erratum section of the author's website. (shrink)

The recent literature offers several models of the notion of matter of fact supposition1 revealed in the acceptance of the so-called indicative conditionals. Some of those models are qualitative [Collins 90], [Levi 96], [Stalnaker 84]. Other probabilistic models appeal either to infinitesimal probability or two place probability functions. Recent work has made possible to understand which is the exact qualitative counterpart of the latter probabilistic models. In this article we show that the qualitative notion of change that thus arises (...) is hypothetical revision, a notion previously axiomatized in [Arló-Costa 97] and [Arló-Costa & Thomason 96]. This notion is incompatible with AGM as well as with other standard methods of theory change. The way in which matter-of-fact supposition is modeled by hypothetical revision is illustrated via examples. The model is compared with other qualitative accounts of the notion of supposition encoded in two-place probability functions, with models of subjunctive supposition, as well as with some of the well know models of learning. Applications in knowledge representation and in the theory of games and decisions are summarized. (shrink)

There are numerous occasions on which we need to reason about a finite number of events. And we often need to consider only those events which are given or which we perceive. These give rise to the Criteria of Finiteness and Closedness. Allen's logic provides a way of reasoning about events. In this paper I examine Allen and Hayes' axiomatisation of this logic, and develop two other axiomatisations based on the work by Russell and Thomason. I shall show that (...) these three axiomatisations are weakly equivalent, and that only the last two meet the Criteria of Finiteness and Closedness (to different degrees). I shall then examine two ways of constructing instants of time in a finite and closed world, i.e. the Russell construction and the Thomason construction. I shall prove that these two constructions are equivalent under certain conditions. (shrink)

In ‘Syntactical Treatments of Modality, with Corollaries on Reflexion Principles and Finite Axiomatizability’, Acta Philosophica Fennica16 (1963), 153–167, Richard Montague shows that the use of a single syntactic predicate (with a context-independent semantic value) to represent modalities of alethic necessity and idealized knowledge leads to inconsistency. In ‘A Note on Syntactical Treatments of Modality’, Synthese44 (1980), 391–395, Richmond Thomason obtains a similar impossibility result for idealized belief: under a syntactical treatment of belief, the assumption that idealized belief is deductively (...) closed, together with certain other plausible conditions on idealized belief, imply that an ideal believer with consistent beliefs cannot believe the truth of Robinson's Arithmetic. In this essay I show that an impossibility result similar to Thomason's can be obtained which does not assume that belief is deductively closed or ideal in any other way. (shrink)

T × W logic is a combination of tense and modal logic for worlds or histories with the same time order. It is the basis for logics of causation, agency and conditionals, and therefore an important tool for philosophical logic. Semantically it has been defined, among others, by R. H. Thomason. Using an operator expressing truth in all worlds, first discussed by C. M. Di Maio and A. Zanardo, an axiomatization is given and its completeness proved via D. (...) Gabbay’s irreflexivity lemma. Given this lemma the proof is more or less straight forward. At the end an alternative axiomatization is sketched in which Di Maio’s and Zanardo’s operator is replaced by a version of actually. (shrink)

We generalize two well-known model-theoretic characterization theorems from propositional modal logic to first-order modal logic. We first study FML-definable frames and give a version of the Goldblatt–Thomason theorem for this logic. The advantage of this result, compared with the original Goldblatt–Thomason theorem, is that it does not need the condition of ultrafilter reflection and uses only closure under bounded morphic images, generated subframes and disjoint unions. We then investigate Lindström type theorems for first-order modal logic. We show that (...) FML has the maximal expressive power among the logics extending FML which satisfy compactness, bisimulation invariance and the Tarski union property. (shrink)

So-called 'dynamic' semantic theories such as Kamp's discourse representation theory and Heim's file change semantics account for such phenomena as cross-sentential anaphora, donkey anaphora, and the novelty condition on indefinites, but compare unfavorably with Montague semantics in some important respects (clarity and simplicity of mathematical foundations, compositionality, handling of quantification and coordination). Preliminary efforts have been made by Muskens and by de Groote to revise and extend Montague semantics to cover dynamic phenomena. We present a new higher-order theory of discourse (...) semantics which improves on their accounts by incorporating a more articulated notion of context inspired by ideas due to David Lewis and to Craige Roberts. On our account, a context consists of a common ground of mutually accepted propositions together with a set of discourse referents preordered by relative salience. Employing a richer notion of contexts enables us to extend our coverage beyond pronominal anaphora to a wider range of presuppositional phenomena, such as the factivity of certain sentential-complement verbs, resolution of anaphora associated with arbitrarily complex definite descriptions, presupposition 'holes' such as negation, and the independence condition on the antecedents of conditionals. Formally, our theory is expressed within a higher-order logic with natural number type, separation-style subtyping, and dependent coproducts parameterized by the natural numbers. The system of semantic types builds on proposals due to Thomason and to Pollard in which the type of propositions (static meanings of sentential utterances) is taken as basic and worlds are constructed from propositions (rather than the other way around as in standard Montague semantics). (shrink)

Metaphysics and language: Quine, W. V. O. On the individuation of attributes. Körner, S. On some relations between logic and metaphysics. Marcus, R. B. Does the principle of substitutivity rest on a mistake? Van Fraassen, B. C. Platonism's pyrrhic victory. Martin, R. M. On some prepositional relations. Kearns, J. T. Sentences and propositions.--Basic and combinatorial logic: Orgass, R. J. Extended basic logic and ordinal numbers. Curry, H. B. Representation of Markov algorithms by combinators.--Implication and consistency: Anderson, A. R. Fitch on (...) consistency. Belnap, N. D., Jr. Grammatical propaedeutic. Thomason, R. H. Decidability in the logic of conditionals. Myhill, J. Levels of implication.--Deontic, epistemic, and erotetic logic: Bacon, J. Belief as relative knowledge. Wu, K. J. Believing and disbelieving. Kordig, C. R. Relativized deontic modalities. Harrah, D. A system for erotetic sentences. (shrink)

In this article, we will revisit a motivation to consider the advantages of a theory about structured contents over a semantics of possible worlds. We will argue that a structure represents the strategic organization of the content of “p” under conditions in which asserting it does not imply contradictory consequences. These are the winning conditions for the assertion of ‘p’. When ‘p’ is modally sensitive – it can change its winning parameters – knowledge of the structure thus represents the rational (...) point for assertions (about non-actualized realities) that are organized to maximize what can be deduced from ‘p’. In these cases, the known relevant structure is intensional. We will argue that actualist Possible World Semantics, seeking the conversion of intensional knowledge into a de re representation of possible states, pays the price of being blind to structural divergences; it can only poorly explain these structural divergences between non-actual states of information and correlate it with divergence between winning strategies of assertion. Our argument will begin exposing Frege’s legacy; resort to Dummett’s concept of ingredient sense as an alternative to Kripke’s grade two knowledge; and briefly go through a semantic strategy of Stalnaker and Thomason to represent modal statements. In addition to these authors, we will explore the contribution of Russell, Kaplan and Ecthemendy to our argument. (shrink)

Shame is a Jekyll-and-Hyde emotion--it can be morally valuable, but it also has a dark side. Thomason presents a philosophically rigorous and nuanced account of shame that accommodates its harmful and helpful aspects. Thomason argues that despite its obvious drawbacks and moral ambiguity, shame's place in our lives is essential.

Attitudes like shame and contempt seem to be at odds with basic tenets of Kantian moral theory. I argue on the contrary that both attitudes play a central role in Kantian morality. Shame and contempt are attitudes that protect our love of honour, or the esteem we have for ourselves as moral persons. The question arises: how are these attitudes compatible with Kant's claim that all persons deserve respect? I argue that the proper object of shame and contempt is not (...) the humanity within a person, but rather her self-conceit, or the false esteem that competes with love of honour. (shrink)

Kant’s non-voluntarist conception of political obligation has led some philosophers to argue that he would reject self-government rights for indigenous peoples. Some recent scholarship suggests, however, that Kant’s critique of colonialism provides an argument in favor of granting self-government rights. Here I argue for a stronger conclusion: Kantian political theory not only can but must include sovereignty for indigenous peoples. Normally these rights are considered redress for historic injustice. On a Kantian view, however, I argue that they are not remedial. (...) Sovereignty rights are a necessary part of establishing perpetual peace. By failing to acknowledge the sovereignty of native groups, states once guilty of imperialism leave open the in principle possibility for future violence, even though no current conflict exists. Only in recognizing self-government rights can states truly commit to the cosmopolitan ideal. (shrink)

This chapter begins with a discussion of Indian theories of inference. It identifies the unique features of Indian logic not found in Western logic. Indian theories of inference are primarily theories of adequate evidence, but they may also be viewed as systems of nonmonotonic reasoning, which is being used in modern computer simulation of actual human reasoning processes. The chapter then discusses Nyāya logic, Buddhist logic, Jaina logic, and Navya–Nyāya logic.

My chief aim has been to convey the thought that the application of model theoretic techniques to natural languages needn't force a distortion of intentional phenomena. I hope that at least I have succeeded in accomplishing this.

This article provides an overview of the subfield of Artificial Intelligence known as “Knowledge Representation and Reasoning.” This field uses the techniques of philosophical logic, but aims at providing a theoretical basis for the management of declarative information in automated reasoning systems. Three topics are singled out here for attention: planning and reasoning about actions, description logics, and nonmonotonic logics.