Intensionality: What are Intensional Transitives?: Jennifer Saul

This paper discusses the question of which verbs are intensional transitives. In particular, I ask which verbs Forbes should take to be intensional transitives. I argue that it is very difficult to arrive at a clear and plausible understanding of what an intensional transitive is— making it difficult to answer these questions. I end by briefly raising some questions about the usefulness of the category of intensional transitives.     

Opacity and the double life of singular propositions

In this paper I analyze David Kaplan?s essay “Opacity”. In “Opacity” Kaplan attempts to dismiss Quine?s concerns about quantification across intensional (modal and intentional) operators. I argue that Kaplan succeeds in showing that quantification across intensional operators is logically coherent and that quantified modal logic is strictly speaking not committed to essentialism. However, I also argue that this is not in and of itself sufficient to support Kaplan?s more ambitious attempt to move beyond purely logical results and provide unified, uncontroversial interpretations of both “believes” and “necessarily”. In the paper I raise several questions about the subject matter of logic and the role of semantics, with special focus on singular propositions.     

Our epistemic goal

David Lewis's modal realism claims that nothing can exist in more than one world or time, and that statements about how something would have been are to be analysed in terms of its counterpart. I first explain why the counterpart relation depends on de re modal statements in an intensional language, so that intuitive properties of similarity relations cannot be used to show that the counterpart relation is not an equivalence relation. I then look at test sentences in (the intensional) natural language, and show that none of them provide compelling evidence that a counterpart semantics is needed.     

Logical inference in English: A preliminary analysis

The perfect fit of syntactic derivability and logical consequence in first-order logic is one of the most celebrated facts of modern logic. In the present flurry of attention given to the semantics of natural language, surprisingly little effort has been focused on the problem of logical inference in natural language and the possibility of its completeness. Even the traditional theory of the syllogism does not give a thorough analysis of the restricted syntax it uses.My objective is to show how a theory of inference may be formulated for a fragment of English that includes a good deal more than the classical syllogism. The syntax and semantics are made as formal and as explicit as is customary for artificial formal languages. The fragment chosen is not maximal but is restricted severely in order to provide a clear overview of the method without the cluttering details that seem to be an inevitable part of any grammar covering a substantial fragment of a natural language. (Some readers may feel the details given here are too onerous.)I am especially concerned with quantifier words in both object and subject position, with negation, and with possession. I do not consider propositional attitudes or the modalities of possibility and necessity, although the model-theoretic semantics I use has a standard version to deal with such intensional contexts.An important point of methodology stressed in earlier publications (Suppes, 1976; Suppes & Macken, 1978; Suppes, 1979) is that the semantic representation of the English sentences in the fragment uses neither quantifiers nor variables, but only constants denoting given sets and relations, and operations on sets and relations.In the first section, I rapidly sketch the formal framework of generative syntax and model-theoretic semantics, with special attention to extended relation algebras. The second section states the grammar and semantics of the fragment of English considered. The next section is concerned with developing some of the rules of inference. The results given are quite incomplete. The final section raises problems of extension. Classical logic is a poor guide for dealing with inferences involving high-frequency function words such as of, to, a, in, for, with, as, on, at, and by. Indeed, the line between logical and nonlogical inference in English seems to be nonexistent or, if made, highly arbitrary in character-much more so than has been claimed by those critical of the traditional analyticsynthetic tradition.No theorems on soundness or completeness are considered because of the highly tentative and incomplete character of the rules of inference proposed. However, because of the variable-free semantics used, soundness is easy to establish for the rules given.The research reported here has been supported in part by National Science Foundation Grant No. SED77-09698.     

Ontology-free modal semantics

The problem with model-theoretic modal semantics is that it provides only the formal beginnings of an account of the semantics of modal languages. In the case of non-modal language, we bridge the gap between semantics and mere model theory, by claiming that a sentence is true just in case it is true in an intended model. Truth in a model is given by the model theory, and an intended model is a model which has as domain the actual objects of discourse, and which relates these objects in an appropriate manner. However, the same strategy applied to the modal case seems to require an intended modal model whose domain includes mere possibilia.Building on recent work by Christopher Menzel (Nous 1990), I give an account of model-theoretic semantics for modal languages which does not require mere possibilia or intensional entities of any kind. Menzel has offered a representational account of model-theoretic modal semantics that accords with actualist scruples, since it does not require possibilia. However, Menzel's view is in the company of other actualists who seek to eliminate possible worlds, but whose accounts tolerate other sorts of abstract, intensional entities, such as possible states of affairs. Menzel's account crucially depends on the existence of properties and relations in intension.I offer a purely extensional, representational account and prove that it does all the work that Menzel's account does. The result of this endeavor is an account of model-theoretic semantics for modal languages requiring nothing but pure sets and the actual objects of discourse. Since ontologically beyond what is prima facie presupposed by the model theory itself. Thus, the result is truly an ontology-free model-theoretic semantics for modal languages. That is to say, getting genuine modal semantics out of the model theory is ontologically cost-free. Since my extensional account is demonstrably no less adeguate, and yet is at the same time more ontologically frugal, it is certainly to be preferred.Special thanks to Brian Chellas, Charles Chihara, Harry Deutsch, Bernard Linsky, Kirk Ludwig, Christopher Menzel and Gila Sher for helpful discussion. My thanks also to an anonymous referee for this Journal for kind words and attention to detail. Portions of this paper were presented at the 1993 meeting of the Society for Exact Philosophy in Toronto, and at the 1994 conference of the Association for Symbolic Logic in Gainesville, Florida. Thanks to all who attended those sessions.     

Induction,focused sampling and the law of small numbers

Hilary Kornblith (1993) has recently offered a reliabilist defense of the use of the Law of Small Numbers in inductive inference. In this paper I argue that Kornblith's defense of this inferential rule fails for a number of reasons. First, I argue that the sort of inferences that Kornblith seeks to justify are not really inductive inferences based on small samples. Instead, they are knowledge-based deductive inferences. Second, I address Kornblith's attempt to find support in the work of Dorrit Billman and I try to show that close attention to the workings of her computational model reveals that it does not support Kornblith's argument. While the knowledge required to ground the inferences in question is perhaps inductively derived, Billman's work does not support the notion that small samples provide a reliable basis for our generalizing inferences.     

Incompatibility Semantics from Agreement

In this paper, I discuss the analysis of logic in the pragmatic approach recently proposed by Brandom. I consider different consequence relations, formalized by classical, intuitionistic and linear logic, and I will argue that the formal theory developed by Brandom, even if provides powerful foundational insights on the relationship between logic and discursive practices, cannot account for important reasoning patterns represented by non-monotonic or resource-sensitive inferences. Then, I will present an incompatibility semantics in the framework of linear logic which allow to refine Brandom’s concept of defeasible inference and to account for those non-monotonic and relevant inferences that are expressible in linear logic. Moreover, I will suggest an interpretation of discursive practices based on an abstract notion of agreement on what counts as a reason which is deeply connected with linear logic semantics.     

On Retaining Classical Truths and Classical Deducibility in Many-Valued and Fuzzy Logics

In this paper, I identify the source of the differences between classical logic and many-valued logics (including fuzzy logics) with respect to the set of valid formulas and the set of inferences sanctioned. In the course of doing so, we find the conditions that are individually necessary and jointly sufficient for any many-valued semantics (again including fuzzy logics) to validate exactly the classically valid formulas, while sanctioning exactly the same set of inferences as classical logic. This in turn shows, contrary to what has sometimes been claimed, that at least one class of infinite-valued semantics is axiomatizable.     

The Astounding Assumption of Infinite Life

The multimillennial philosophical discussion about life after death has received a recent boost in the prospect of immortality attained via technologies. In this newer version, humans generally are considered mortal but may develop means of making themselves immortal. If “immortal” means not mortal, thus existing for infinity, and if the proposed infinite‐existing entity is material, it must inhabit an infinite material universe. If the proposed entity is not material, there must be means by which it can shed its material substance and exist nonmaterially. The article examines arguments for how an infinite life would be possible given current physical understanding. The paper considers a Pascalian‐style wager weighing the likelihood of adjusting to existence wholly within a finite universe versus betting on there being some way to construe the universe(s) as a viable medium for infinite beings. Conclusion: the case for a finite being to exist infinitely has little viable support.     

A Response to Paul Griffiths’ Annihilationist Proposal

In his recent influential theological work, Paul Griffiths, the esteemed Buddhism scholar and Anglican convert to Catholicism, proposes, among other things, that annihilationism is a viable option for Christians, including Catholics, despite apparent magisterial prohibition. He argues, in effect, that every creature must be naturally mortal because bodily, including the angels. Therefore, de facto immortal creatures are not immortal by nature, but by a positive act of God in addition to the creative act. Accordingly, it makes no sense to assert the existence of an eternal hell. Rather, since sin is fundamentally corrosive, those who opt to continue down the rabbit's hole of sin literally become nothing. Hell, then, is a no‐place and a no‐time. Hence, as long as the damned continue to exist, they have the opportunity for eventual redemption as for eventual self‐annihilation. Griffiths attempts to defend this thesis in dialogue with Augustine, in particular, to the neglect of Aquinas, except to argue that Aquinas’ own arguments for the natural immortality of the human soul are incoherent. I will argue instead that spiritual being exists, that it is naturally immortal, that Aquinas demonstrates both, and that even an Augustinian such as Joseph Ratzinger recognizes Aquinas’ theological insights and builds on them.     

The Linguistic Therapy of Evaluation: A Treatment Plan for Silvia

This paper describes the treatment of a depressed woman, Silvia (I. Caro, 2001), treated with the linguistic therapy of evaluation. The linguistic therapy of evaluation is a type of cognitive psychotherapy developed from the theory of general semantics. The theory and the treatment are based on the use of language and the role this plays in the development of emotional problems such as anxiety and depression. We briefly describe the main conceptual and assessment issues of the therapy and the procedure followed in the case of Silvia. The aim of the therapy is to change patients' evaluations, that is, to help them to develop an extensional orientation instead of an intensional orientation, which is assumed to be at the core of emotional problems. The paper ends with a brief review of the process and outcome research that has demonstrated the efficacy and the clinical process of the linguistic therapy of evaluation.     

It wasn’t up to Jones: unavoidable actions and intensional contexts in Frankfurt examples

In saying that it was up to someone whether or not she acted as she did, we are attributing a distinctive sort of power to her. Understanding such power attributions is of broad importance for contemporary discussions of free will. Yet the ‘is up to…whether’ locution and its cognates have largely escaped close examination. This article aims to elucidate one of its unnoticed features, namely that such power attributions introduce intensional contexts, something that is easily overlooked because the sentences that express these attributions admit of both intensional and extensional readings. I argue that this kind of power attribution should inform discussions of Frankfurt’s counterexample strategy, in that an alternative possibility should not be considered robust unless it’s up to the agent whether or not it’s realized. I argue, as well, that understanding robust alternatives in this way sheds light on the relationship between the Frankfurt literature and the Luck Objection to libertarianism.     

Modality,Quantification, and Many Vlach-Operators

Consider two standard quantified modal languages \(\textbf{\textsf{A}}\) and \(\textbf{\textsf{P}}\) whose vocabularies comprise the identity predicate and the existence predicate, each endowed with a standard S5 Kripke semantics where the models have a distinguished actual world, which differ only in that the quantifiers of \(\textbf{\textsf{A}}\) are actualist while those of \(\textbf{\textsf{P}}\) are possibilist. Is it possible to enrich these languages in the same manner, in a non-trivial way, so that the two resulting languages are equally expressive—i.e., so that for each sentence of one language there is a sentence of the other language such that given any model, the former sentence is true at the actual world of the model iff the latter is? Forbes (1989) shows that this can be done by adding to both languages a pair of sentential operators called Vlach-operators, and imposing a syntactic restriction on their occurrences in formulas. As Forbes himself recognizes, this restriction is somewhat artificial. The first result I establish in this paper is that one gets sameness of expressivity by introducing infinitely many distinct pairs of indexed Vlach-operators. I then study the effect of adding to our enriched modal languages a rigid actuality operator. Finally, I discuss another means of enriching both languages which makes them expressively equivalent, one that exploits devices introduced in Peacocke (1978). Forbes himself mentions that option but does not prove that the resulting languages are equally expressive. I do, and I also compare the Peacockian and the Vlachian methods. In due course, I introduce an alternative notion of expressivity and I compare the Peacockian and the Vlachian languages in terms of that other notion.     

The Myth of Reductive Extensionalism

Extensionalism, as I understand it here, is the view that physical reality consists exclusively of extensional entities. On this view, intensional entitities must either be eliminated in favor of an ontology of extensional entities, or be reduced to such an ontology, or otherwise be admitted as non-physical. In this paper I argue that extensionalism is a misguided philosophical doctrine. First, I argue that intensional phenomena are not confined to the realm of language and thought. Rather, the ontology of such phenomena is intimately entwined with the ontology of properties. After providing some evidence to the popularity of extensionalism in contemporary analytic philosophy, I investigate the motivating reasons behind it. Considering several explanations, I argue that the main motivating reason is rooted in the identification of matter with extension, an identification which is one of the hallmarks of the mechanistic conception of nature inherited from the founding fathers of our modern scientific outlook. I then argue that such a conception is not only at odds with a robust ontology of properties but is also at odds with our best contemporary physics. Rather than vindicating extensionalism contemporary science undermines the position, and the lesson to be drawn from this surprising fact is that extensionalism needs no longer be espoused as a regulative ideal of naturalistic philosophy. I conclude by showing that the ontological approach to intensional phenomena advocated throughout the paper also gains support from an examination of the historical context within which ‘intension’ was first introduced as a semantic notion.

Williams and the Desirability of Body‐Bound Immortality Revisited

Bernard Williams argues that human mortality is a good thing because living forever would necessarily be intolerably boring. His argument is often attacked for unfoundedly proposing asymmetrical requirements on the desirability of living for mortal and immortal lives. My first aim in this paper is to advance a new interpretation of Williams' argument that avoids these objections, drawing in part on some of his other writings to contextualize it. My second aim is to show how even the best version of his argument only supports a somewhat weaker thesis: it may be possible for some people with certain special psychological features to enjoy an immortal life, but no one has good reason to bet on being such a person.     

An approach to intensional logic

A system of tensed intensional logic excluding iterations of intensions is introduced. Instead of using the type symbols (for ‘sense’), extensional and intensional functor types are distinguished. A peculiarity of the semantics is the general acceptance of value-gaps (including truth-value-gaps): the possible semantic values (extensions) of extensional functors are partial functions. Some advantages of the system (relatively to R. Montague's intensional logic) are briefly indicated. Also, applications for modelling natural languages are illustrated by examples.     

Rational Inference: The Lowest Bounds

A surge of empirical research demonstrating flexible cognition in animals and young infants has raised interest in the possibility of rational decision‐making in the absence of language. A venerable position, which I here call “Classical Inferentialism”, holds that nonlinguistic agents are incapable of rational inferences. Against this position, I defend a model of nonlinguistic inferences that shows how they could be practically rational. This model vindicates the Lockean idea that we can intuitively grasp rational connections between thoughts by developing the Davidsonian idea that practical inferences are at bottom categorization judgments. From this perspective, we can see how similarity‐based categorization processes widely studied in human and animal psychology might count as practically rational. The solution involves a novel hybrid of internalism and externalism: intuitive inferences are psychologically rational (in the explanatory sense) given the intensional sensitivity of the similarity assessment to the internal structure of the agent's reasons for acting, but epistemically rational (in the justificatory sense) given an ecological fit between the features matched by that assessment and the structure of the agent's environment. The essay concludes by exploring empirical results that show how nonlinguistic agents can be sensitive to these similarity assessments in a way that grants them control over their opaque judgments.     

FOIL Axiomatized

In an earlier paper, [5], I gave semantics and tableau rules for a simple firstorder intensional logic called FOIL, in which both objects and intensions are explicitly present and can be quantified over. Intensions, being non-rigid, are represented in FOIL as (partial) functions from states to objects. Scoping machinery, predicate abstraction, is present to disambiguate sentences like that asserting the necessary identity of the morning and the evening star, which is true in one sense and not true in another.In this paper I address the problem of axiomatizing FOIL. I begin with an interesting sublogic with predicate abstraction and equality but no quantifiers. In [2] this sublogic was shown to be undecidable if the underlying modal logic was at least K4, though it is decidable in other cases. The axiomatization given is shown to be complete for standard logics without a symmetry condition. The general situation is not known. After this an axiomatization for the full FOIL is given, which is straightforward after one makes a change in the point of view.This paper is a version of the invited talk given by the author at the conference Trends in Logic III, dedicated to the memory of A. MOSTOWSKI, H. RASIOWA and C. RAUSZER, and held in Warsaw and Ruciane-Nida from 23rd to 25th September 2005.     

Does Science Influence the Logic we Ought to Use: A Reflection on the Quantum Logic Controversy

In this article I argue that there is a sense in which logic is empirical, and hence open to influence from science. One of the roles of logic is the modelling and extending of natural language reasoning. It does so by providing a formal system which succeeds in modelling the structure of a paradigmatic set of our natural language inferences and which then permits us to extend this structure to novel cases with relative ease. In choosing the best system of those that succeed in this, we seek certain virtues of such structures such as simplicity and naturalness (which will be explained). Science can influence logic by bringing us, as in the case of quantum mechanics, to make natural language inferences about new kinds of systems and thereby extend the set of paradigmatic cases that our formal logic ought to model as simply and naturally as possible. This can alter which structures ought to be used to provide semantics for such models. I show why such a revolution could have led us to reject one logic for another through explaining why complex claims about quantum mechanical systems failed to lead us to reject classical logic for quantum logic.