In this paper it is shown how a partial semantics for presuppositions can be given which is empirically more satisfactory than its predecessors, and how this semantics can be integrated with a technically sound, compositional grammar in the Montagovian fashion. Additionally, it is argued that the classical objection to partial accounts of presupposition projection, namely that they lack “flexibility,” is based on a misconception. Partial logics can give rise to flexible predictions without postulating any ad hoc ambiguities. Finally, it (...) is shown how the partial foundation can be combined with a dynamic system of common-ground maintenance to account for accommodation. (shrink)
Heim 1983 suggested that the analysis of presupposition projection requires that the classical notion of meanings as truth conditions be replaced with a dynamic notion of meanings as Context Change Potentials. But as several researchers (including Heim herself) later noted, the dynamic framework is insufficiently predictive: although it allows one to state that, say, the dynamic effect of F and G is to first update a Context Set C with F and then with G (i.e., C[F and G] = (...) C[F][G]), it fails to explain why there couldn’t be a ‘deviant’ conjunction and* which performed these operations in the opposite order (i.e., C[F and* G] = C[G][F]). We provide a formal introduction to a competing framework, the Transparency theory, which addresses this problem. Unlike dynamic semantics, our analysis is fully classical, i.e., bivalent and static. And it derives the projective behavior of connectives from their bivalent meaning and their syntax. We concentrate on the formal properties of a simple version of the theory, and we prove that (i) full equivalence with Heim’s results is guaranteed in the propositional case (Theorem 1), and that (ii) the equivalence can be extended to the quantificational case (for any generalized quantifiers), but only when certain conditions are met (Theorem 2). (shrink)
This paper criticizes the dominant approaches to presupposition projection and proposes an alternative. Both the update semantics of Heim and the discourse representation theory of van der Sandt have problems in explicating the presuppositions of disjunctions. Moreover, Heim's approach is committed to a conception of accommodation that founders on the problem of informative presuppositions, and van der Sandt's approach is committed to a conception of accommodation that generates over-interpretations of utterances. The present approach borrows Karttunen's idea that instead of (...) associating presuppositions with sentences, we should define the conditions that contexts must meet in order to satisfy-the-presuppositions-of a sentence. However, in place of Karttunen's conception of contexts in terms of common ground, the present theory substitutes a conception of contexts as objective entities that are independent of the attitudes of the interlocutors. Contexts, so conceived, may be defined as containing sets of relevant possibilities. This allows us to define the conditions under which a context satisfies-the-presuppositions-of a disjunction. (shrink)
The theorist who denies the objective reality of non-relational temporal properties, or ‘A-series’ determinations, must explain our experience of the passage of time. D.H. Mellor, a prominent denier of the objective reality of temporal passage, draws, in part, on Kant in offering a theory according to which the experience of temporal passage is the result of the projection of change in belief. But Mellor has missed some important points Kant has to make about time-awareness. It turns out that Kant's (...) theory of time-awareness also involves projection – but for him, the projection of temporal passage is necessary to any coherent experience at all, and for this reason events in the world cannot be represented except as exhibiting real tensed change. Consequently we cannot intelligibly suppose the world we know to be without the passage of time. This fact would permit a modest transcendental argument the conclusion of which is that we are entitled to describe the world in terms of temporal passage. (shrink)
Presupposition, vagueness, and oddness can lead to some sentences failing to have a clear truth value. The homogeneity property of plural predication with definite descriptions may also create truth-value gaps: The books are written in Dutch is true if all relevant books are in Dutch, false if none of them are, and neither true nor false if, say, half of the books are written in Dutch. We study the projection property of homogeneity by deploying methods of general interest to (...) identify truth-value gaps. Method A consists in collecting both truth judgments and, independently, falsity judgments. The second method, employed in experiment series B and C, is based on one-shot ternary judgments: completely true vs. completely false vs. neither. After a calibration of these methods, we use them to demonstrate that homogeneity projects out of negation, the scope of universal sentences and the scope of non-monotonic quantifiers such as exactly two, to some extent. We assess our results in light of different theoretical approaches to homogeneity—approaches based on presuppositions, scalar implicatures, and something like supervaluations, respectively. We identify free parameters in these theories and assess various variants of them based on our results. Our experimental paradigms may be of broader significance insofar as they can be applied to other phenomena which result in the failure of a sentence to have a definite truth value. (shrink)
This article focuses on the difficulty for a general theory of depiction of providing a notion of pictorial content that accommodates the full diversity of picture types. The article begins by introducing two basic models of pictorial content using paradigmatic positions that maximize the ability of the respective models to deal with pictorial diversity. Kulvicki's On Images is interpreted as a generalized projection-based model which proposes a scene-centred notion of pictorial content. By contrast, Lopes's aspect-recognition theory, in Understanding Pictures, (...) is taken to exemplify a recognition-based model of pictorial content. It is then considered how applicable these two notions of pictorial content are to a spectrum of different picture types, highlighting differences between mechanically produced and “freehand” pictures. It is shown that while the projection-based and recognition-based models are each required for some picture types, neither model can be applied over the whole spectrum of diverse picture types. This, it is argued, has the far-reaching consequence that neither the projection model nor the recognition model, nor any unitary combination of the two, can provide the basis for a theory of depiction applying to all pictures. (shrink)
I explain what exactly constrains presupposition projection in compound sentences and argue that the presuppositions that do not project are conditionalized, giving rise to inferable conditional presuppositions. I combine elements of and which, together with an additional, independently motivated assumption, make it possible to construct an analysis that makes correct predictions. The core of my proposal is as follows: When a speaker felicitously utters a compound sentence whose constituent clauses require presuppositions, the hearer will infer that the speaker presupposes (...) those propositions, unless the sentence contains some element that makes the hearer realize that, if the speaker actually presupposed them, she would be either uninformative or inconsistent in her beliefs. In these cases, the propositions that would have been presupposed, had the clauses been uttered in isolation, will not be presupposed, i.e. the clausal presuppositions will not project. (shrink)
Peter Kail’s comprehensive, thoughtful, and challenging book focuses on Hume’s use of projectionFthe appeal to mental phenomena to explain manifest features of the worldFin his treatments of external objects, causation, and morality. Almost all interpreters of Hume acknowledge a role for projection, but Kail is the first to unpack the metaphor, and to show the different ways in which projection works in different domains.
The title of my book, Projection and Realism in Hume's Philosophy, might mislead. One might protest, with some justification, that since neither "projection" nor "realism" is Hume's term and that both carry a severe threat of anachronism, discussing them in connection with Hume is misguided. Why might the readers of this journal wish to read such a work?Well, the first thing to note is that Hume's name has come to be associated with the metaphor of projection, understood (...) as having some kind of "non-realist" connotations, and, at the same time, he attracted readings that make him a "realist" of some sort or another in different areas.1 So, there seems to be some tension here.. (shrink)
The presupposition triggered by an expression E is generally satisfied by information that comes before rather than after E in the sentence or discourse. In Heim’s classic theory (1983), this left-right asymmetry is encoded in the lexical semantics of dynamic connectives and operators. But several recent analyses offer a more nuanced approach, in which presupposition satisfaction has two separate components: a general principle (which varies from theory to theory) specifies under what conditions a presupposition triggered by an expression E is (...) satisfied; and an ‘incremental’ component specifies that the principle must be checked on the basis of information that comes before E. Several researchers take this incremental component to be a processing bias, which can be overcome at some cost. If so, it should be possible, though costly, to satisfy presuppositions ‘symmetrically’, i.e. by taking into account linguistic material that comes both before and after the presupposition trigger. We test this claim with experimental means. Using inferential (and to some extent acceptability) tasks involving the anaphoric trigger aussi (‘too’) in French, we argue that symmetric readings are indeed possible (albeit degraded) in environments involving the connectives if, or, and unless. (shrink)
For a finite von Neumann algebra factor M, the projections form a modular ortholattice L(M). We show that the equational theory of L(M) coincides with that of some resp. all L(ℂ n × n ) and is decidable. In contrast, the uniform word problem for the variety generated by all L(ℂ n × n ) is shown to be undecidable.
Locke is what present-day aestheticians, critics, and historians call an intentionalist. He believes that when we interpret speech and writing, we aim—in large part and perhaps even for the most part—to recover the intentions, or intended meanings, of the speaker or writer. Berkeley and Hume shared Locke’s commitment to intentionalism, but it is a theme that recent philosophical interpreters of all three writers have left largely unexplored. In this paper I discuss the bearing of intentionalism on more familiar themes in (...) empiricist reflections on language, among them the signification of things (as opposed to ideas); the signifying role of whole propositions; and the possibility of reference to an “external” world. (shrink)
Simulationists have recently started to employ the term "empathy" when characterizing our most basic understanding of other minds. I agree that empathy is crucial, but I think it is being misconstrued by the simulationists. Using some ideas to be found in Scheler's classical discussion of empathy, I will argue for a different understanding of the notion. More specifically, I will argue that there are basic levels of interpersonal understanding - in particular the understanding of emotional expressions - that are not (...) explicable in terms of simulation-plus-projection routines. (shrink)
: In the 1980s, the analysis of presupposition projection contributed to a ‘dynamic turn’ in semantics: the classical notion of meanings as truth conditions was replaced with a dynamic notion of meanings as Context Change Potentials. We argue that this move was misguided, and we offer an alternative in which presupposition projection follows from the combination of a fully classical semantics and a new pragmatic principle, which we call Be Articulate. This principle requires that a meaning pp’ conceptualized (...) as involving a pre-condition p should be articulated as … … rather than as … pp’ …, unless the full conjunction is ruled out because the first or the second conjunct is semantically idle. In particular, … … is infelicitous - and hence … pp’ … is acceptable - if one can determine as soon as p and is uttered that no matter how the sentence ends these words could be eliminated without affecting its contextual meaning. An equivalence theorem guarantees that this condition suffices to derive Heim’s results in almost all cases. Extensions of the condition lead to several new predictions, in particular concerning some ‘symmetric readings’, as well as presupposition projection in quantified structures, which displays a complex interaction between the nature of the trigger and the monotonicity of the quantifier. (shrink)
Writers on presupposition, and on the ‘‘projection problem’’ of determining the presuppositions of compound sentences from their component clauses, traditionally assign presuppositions to each clause in isolation. I argue that many presuppositional elements are anaphoric to previous discourse or contextual elements. In compound sentences, these can be other clauses of the sentence. We thus need a theory of presuppositional anaphora, analogous to the corresponding pronominal theory.
The present paper presents an anaphoric account of presupposition. It is argued that presuppositional expressions should not be seen as referring expressions, nor is presupposition to be explicated in terms of some non-standard logic. The notion of presupposition should not be relegated to a pragmatic theory either. Instead presuppositional expressions are claimed to be anaphoric expressions which have internal structure and semantic content. In fact they only differ from pronouns and other semantically less loaded anaphors in that they have more (...) descriptive content. It is this fact which enables them to create an antecedent in case discourse does not provide one. If their capacity to accommodate is taken into account they can be treated by basically the same mechanism which handles the resolution of pronouns. The theory is elaborated in the framework of discourse representation theory. It is shown that pragmatic factors interfere in the resolution of presuppositional anaphors. The resulting account can neither be classified as wholly semantic nor wholly pragmatic. Section 1 presents a survey of standing problems in the theory of presupposition projection and discusses the major competing approaches. An argumentation for a purely anaphoric account of presupposition is given in section 2. Section 3 presents a coding of presuppositional expressions in an extension of discourse representation theory. The final section is devoted to a discussion of the constraints which govern the resolution of presuppositional anaphors. (shrink)
Karttunen observed that, if the complement of an attitude sentence presupposes p, then that sentence as a whole presupposes that the attitude–holder believes p. I attempt to derive some representative instances of this generalization from suitable assumptions about the lexical semantics of attitude predicates. The enterprise is carried out in a framework of context change semantics, which incorporates Stalnaker's suggestion that presupposition projection results from the stepwise fashion in which information is updated in response to complex utterances. The empirical (...) focus is on predicates of desire and on the contribution of counterfactual mood. (shrink)
Nearly all philosophers agree that only true things can be known. But does this principle reflect actual patterns of ordinary usage? Several examples in ordinary language seem to show that ‘know’ is literally used non-factively. By contrast, this paper reports five experiments utilizing explicit paraphrasing tasks, which suggest that non-factive uses are actually not literal. Instead, they are better explained by a phenomenon known as protagonist projection. It is argued that armchair philosophical orthodoxy regarding the truth requirement for knowledge (...) withstands current empirical scrutiny. (shrink)
Religion and the external world -- Projection, religion, and the external world -- The senses, reason and the imagination -- Realism, meaning and justification : the external world and religious belief -- Modality, projection and realism -- 'Our profound ignorance' : causal realism, and the failure to detect necessity -- Spreading the mind : projection, necessity and realism -- Into the labyrinth : persons, modality, and Hume's undoing -- Value, projection, and realism -- Gilding : (...) class='Hi'>projection, value and secondary qualities -- The gold : good, evil, belief and desire -- The golden : relational values, realism and a moral sense. (shrink)
This article provides a semantic analysis of Protagonist Projection, the phenomenon by which things are described from a point of view different from that of the speaker. Against what has been argued by some, the account vindicates the intuitive idea that Protagonist Projection does not give rise to counterexamples to factivity, and similar plausible principles. A pragmatics is sketched that explains the attitude attributions generated by Protagonist Projection. Further, the phenomenon is compared to Free Indirect Discourse, and (...) the proposed account is seen to preserve the relation between them. (shrink)
The widely accepted two-dimensional circumplex model of emotions posits that most instances of human emotional experience can be understood within the two general dimensions of valence and activation. Currently, this model is facing some criticism, because complex emotions in particular are hard to define within only these two general dimensions. The present theory-driven study introduces an innovative analytical approach working in a way other than the conventional, two-dimensional paradigm. The main goal was to map and project semantic emotion space in (...) terms of mutual positions of various emotion prototypical categories. Participants (N = 187; 54.5% females) judged 16 discrete emotions in terms of valence, intensity, controllability and utility. The results revealed that these four dimensional input measures were uncorrelated. This implies that valence, intensity, controllability and utility represented clearly different qualities of discrete emotions in the judgments of the participants. Based on this data, we constructed a 3D hypercube-projection and compared it with various two-dimensional projections. This contrasting enabled us to detect several sources of bias when working with the traditional, two-dimensional analytical approach. Contrasting two-dimensional and three-dimensional projections revealed that the 2D models provided biased insights about how emotions are conceptually related to one another along multiple dimensions. The results of the present study point out the reductionist nature of the two-dimensional paradigm in the psychological theory of emotions and challenge the widely accepted circumplex model. (shrink)
When people make sense of situations, illustrations, instructions and problems they do more than just think with their heads. They gesture, talk, point, annotate, make notes and so on. What extra do they get from interacting with their environment in this way? To study this fundamental problem, I looked at how people project structure onto geometric drawings, visual proofs, and games like tic tac toe. Two experiments were run to learn more about projection. Projection is a special capacity, (...) similar to perception, but less tied to what is in the environment. Projection, unlike pure imagery, requires external structure to anchor it, but it adds ‘mental’ structure to the external scene much like an augmented reality system adds structure to an outside scene. A person projects when they look at a chessboard and can see where a knight may be moved. Because of the cognitive costs of sustaining and extending projection, humans make some of their projections real. They create structure externally. They move the piece, they talk, point, notate, represent. Much of our interactivity during sense making and problem solving involves a cycle of projecting then creating structure. (shrink)
The goal of this paper is to offer a compositional semantics for subjunctive and indicative will conditionals, and to derive the projection properties of the types of conditionals we consider and in particular those of counterfactual conditionals. It is argued that subjunctive conditionals are "bare" conditional embedded under temporal and aspectural operators, which constrain the interpretation of the modal operators in the embedded conditional. Furthermore, it is argued that a theory of presupposition projection à la Heim together with (...) the present proposal about their logical form explains the projection facts. (shrink)
This paper discusses the metaphor of projection in relation to Hume’s treatment of causal necessity. I argue that the best understanding of projection shows it to be compatible with taking Hume to be a ‘sceptical realist’ about causal necessity, albeit an agnostic one.
My critical comments on Part I of P. J. E. Kail's Projection and Realism in Hume's Philosophy are divided into two parts. First, I challenge the exegetical details of Kail's take on Hume's important distinction between natural and philosophical relations. I show that Kail misreads Hume in a subtle fashion. If I am right, then much of the machinery that Kail puts into place for his main argument does different work in Hume than Kail thinks. Second, I offer a (...) brief criticism of Kail's argument for reading Hume "as a realist about the external world". The two parts are tied together because it turns out that Kail and I disagree about how Hume thinks of philosophers' activity generally.One caveat:. (shrink)
It is widely held that quantum mechanics is the first scientific theory to present scientifically internal, fundamental difficulties for a realistic interpretation (in the philosophical sense). The standard (Copenhagen) interpretation of the quantum theory is often described as the inevitable instrumentalistic response. It is the purpose of the present article to argue that quantum theory doesnot present fundamental new problems to a realistic interpretation. The formalism of quantum theory has the same states—it will be argued—as the formalisms of older physical (...) theories and is capable of the same kinds of philosophical interpretation. This result is reached via an analysis of what it means to give a realistic interpretation to a theory. The main point of difference between quantum mechanics and other theories—as far as the possibilities of interpretation are concerned—is the special treatment given tomeasurement by the “projection postulate.” But it is possible to do without this postulate. Moreover, rejection of the projection postulate does not, in spite of what is often maintained in the literature, automatically lead to the many-worlds interpretation of quantum mechanics. A realistic interpretation is possible in which only the reality ofone (our) world is recognized. It is argued that the Copenhagen interpretation as expounded by Bohr is not in conflict with the here proposed realistic interpretation of quantum theory. (shrink)
I show that the quantum state ω can be interpreted as defining a probability measure on a subalgebra of the algebra of projection operators that is not fixed (as in classical statistical mechanics) but changes with ω and appropriate boundary conditions, hence with the dynamics of the theory. This subalgebra, while not embeddable into a Boolean algebra, will always admit two-valued homomorphisms, which correspond to the different possible ways in which a set of “determinate” quantities (selected by ω and (...) the boundary conditions) can have values. The probabilities defined by ω (via the Born rule) are probabilities over these two-valued homomorphisms or value assignments. So any universe of interacting systems, including those functioning as measuring instruments, can be modelled quantum mechanically without the projection postulate. (shrink)
The main question of this paper is how to understand the notion of a truth-maker. In section 1, I show that the identification of truth-making with necessitation cannot capture the pretheoretic understanding of notions such as ‘x makes something true’. In section 2, I examine Barry Smith’s reaction to this problem: he defines truth-making as the combination of necessitation and projection. I focus on the formal part of Smith’s account, which is shown to yield undesired results. However, in section (...) 3, I present an alternative account of projection, which fares better and can fruitfully be employed to circumvent the problems raised in section 1. Unfortunately, the account still has to face some troublemakers, as I show in the final section. I conclude, therefore, with a pessimistic view on the project of defining truth-making via necessitation and projection. (shrink)
This paper discusses some formal properties of trivalent approaches to presupposition projection, and in particular of the middle Kleene system of Peters (1977) and Krahmer (1998). After exploring the relationship between trivalent truth-functional accounts and dynamic accounts in the tradition of Heim (1983), I show how the middle Kleene trivalent account can be formulated in a way which shows that it meets the explanatory challenge of Schlenker (2006, 2008a,b), and provide some results relating to the application of the middle (...) Kleene approach to generalised quantifiers. (shrink)
The projection postulate, which prescribes “collapse of the state vector” upon measurement, is not an essential part of quantum mechanics. Rather it is only an optional discarding of certain branches of the state vector that are expected to be irrelevant for the purpose at hand. However, its use is hazardous, and there are examples of repeated measurements for which the conventional application of the projection postulate leads to incorrect results.
Conceptual projection from one mental space to another always involves projection to "middle" spaces-abstract "generic" middle spaces or richer "blended" middle spaces. Projection to a middle space is a general cognitive process, operating uniformly at different levels of abstraction and under superficially divergent contextual circumstances. Middle spaces are indispensable sites for central mental and linguistic work. The process of blending is in particular a fundamental and general cognitive process, running over many (conceivably all) cognitive phenomena, including categorization, (...) the making of hypotheses, inference, the origin and combining of grammatical constructions, analogy, metaphor, and narrative. Blending is not secondary to these phenomena but prerequisite, and its operation is not restricted to any one of these phenomena. We give evidence for blending from a wide range of data that includes everyday language, idioms, literary metaphor, non-verbal conceptualization of action, creative thought in mathematics, evolution of socio-cultural models, jokes, and advertising. Blending is in general invisible to consciousness and detectable only on analysis. Blended spaces are routinely necessary for constructing central meanings, inferences, and structures, and for motivating emotions. We show that the blending of highly schematic spaces yields the fusion of grammatical constructions and functional assemblies studied in Cognitive Grammar and Construction Grammar. Finally, recognizing the cognitive import of middle spaces allows us to propose a generalized four-space model of conceptual projection that subsumes a variety of previous models. We explore the consequences of this model for the theory of concept formation. Introduction 3 I. The four space model 4 II. The phenomenon of blended spaces 5 1. Dante's Inferno 5 2. Regatta 7 3. The riddle of the Buddhist monk 8 4. Getting ahead of oneself 9 5. Tuning in, and other actions 11 6. Complex numbers 12 III. Prototypes of blending and mistaken reductions 14 IV. Further evidence for conceptual projection into a blended space 17 1. President Bush on third base 18 2. President Nixon in France 19 3. Personification 21 V. Category extension 22 VI. Generic spaces 24 VII. Parameters and subschemes 25 VIII. Blending and grammar 30 IX. The concept of a concept 33 Notes 35 References 38. (shrink)
We carry out the Karttunen-Stalnaker pragmatic account of presupposition projection within a state-of-the art version of dynamic epistemic logic. It turns out that the basic projection facts can all be derived from a Gricean maxim ‘be informative’. This sheds light on a recent controversy on the appropriateness of dynamic semantics as a tool for analysing presupposition.
We define a notion of projective meaning which encompasses both classical presuppositions and phenomena which are usually regarded as non-presuppositional but which also display projection behavior—Horn’s assertorically inert entailments, conventional implicatures (both Grice’s and Potts’) and some conversational implicatures. We argue that the central feature of all projective meanings is that they are not-at-issue, defined as a relation to the question under discussion. Other properties differentiate various sub-classes of projective meanings, one of them the class of presuppositions according to (...) Stalnaker. This principled taxonomy predicts differences in behavior unexpected on other models among the various conventional triggers and conversational implicatures, while holding promise for a general, explanatory account of projection which applies to all the types of meanings considered. (shrink)
Goodpaster's principle of moral projection is intended to support a program of corporate moral improvement based on an analogy between persons and corporations. In this paper I try to show that the analogy breaks down at a crucial point — namely at the search for amotive for moral improvement. Further, the analogy may foster a tendency to suppose that corporations, like persons, have intrinsic value. I conclude that the analogy does more harm than good for the following reasons: (a) (...) it distracts from the crucial question, which is, how can we motivate people to shape the institutions in which they work into morally better ones? and (b) it may reinforce a morally dangerous tendency to serve corporations for their own sakes. (shrink)
Understanding the pattern by which complex sentences inherit the presuppositions of their parts (presupposition projection) has been a major topic in formal pragmatics since the 1970s. Heim’s classic paper “On the Projection Problem for Presuppositions” (1983) proposed a replacement of truth-conditional semantics with a dynamic semantics that treats meanings as instructions to update the common ground. Heim’s system predicts the basic pattern of presupposition projection quite accurately. The classic objection to this program (including other versions of dynamic (...) semantics) is that the treatment of binary connectives is stipulative, and other, equally natural treatments fail to make the right predictions about presupposition projection. I give a variation on Heim’s system that is designed to escape this objection. I show that the most liberal possible version of this variant is equivalent to a strong-Kleene system in terms of its definedness conditions. (shrink)
Modal interpretations of quantum mechanics admit two kinds of state: physical states, which specify the values of observables on a system, and theoretical states, which specify a probability distribution over possible physical states. They appear to use this distinction to deny the projection postulate, claiming that collapse corresponds only to a change from discussing the theoretical state to discussing the physical state. I argue that modal interpretations should adopt a projection postulate at the level of the theoretical state. (...) However, other features of modal interpretations might render the projection postulate immune from the usual objections. (shrink)
The phenomenon we now know as projection was first observed by Frege in his brief remarks about presupposition in “Sense and Reference.” Frege observes there that the assertion that Kepler died in misery gives rise to the implication that the name Kepler has a referent; but that so too does the assertion that Kepler did not die in misery. Here we have the source of the observation that if p is a presupposition of S, then p is implied by (...) (utterances of) S and by (utterances of) the negation of S. Since Frege, it has been observed that those implications which are shared by a sentence S and by its negation are also typically shared by a variety of other entailment-canceling embeddings of S: in questions, in the antecedents of conditionals, and under epistemic possibility modals. This observation has entered the canon in the form of the “family of sentences” test (Chierchia and McConnell-Ginet 2000). This test is 1 standardly used to demonstrate that some particular element of content projects. An application of the test is demonstrated below. (shrink)
The class \ of t rue p airing a lgebras is defined to be the class of relation algebras expanded with concrete set theoretical projection functions. The main results of the present paper is that neither the equational theory of \ nor the first order theory of \ are decidable. Moreover, we show that the set of all equations valid in \ is exactly on the \ level. We consider the class \ of the relation algebra reducts of \ (...) ’s, as well. We prove that the equational theory of \ is much simpler, namely, it is recursively enumerable. We also give motivation for our results and some connections to related work. (shrink)