In this paper I will develop a lambda-term calculus, lambda-2Int, for a bi-intuitionistic logic and discuss its implications for the notions of sense and denotation of derivations in a bilateralist setting. Thus, I will use the Curry-Howard correspondence, which has been well-established between the simply typed lambda-calculus and natural deduction systems for intuitionistic logic, and apply it to a bilateralist proof system displaying two derivability relations, one for proving and one for refuting. The (...) basis will be the natural deduction system of Wansing's bi-intuitionistic logic 2Int, which I will turn into a term-annotated form. Therefore, we need a type theory that extends to a two-sorted typed lambda-calculus. I will present such a term-annotated proof system for 2Int and prove a Dualization Theorem relating proofs and refutations in this system. On the basis of these formal results I will argue that this gives us interesting insights into questions about sense and denotation as well as synonymy and identity of proofs from a bilateralist point of view. (shrink)

Vector models of language are based on the contextual aspects of language, the distributions of words and how they co-occur in text. Truth conditional models focus on the logical aspects of language, compositional properties of words and how they compose to form sentences. In the truth conditional approach, the denotation of a sentence determines its truth conditions, which can be taken to be a truth value, a set of possible worlds, a context change potential, or similar. In the vector models, (...) the degree of co-occurrence of words in context determines how similar the meanings of words are. In this paper, we put these two models together and develop a vector semantics for language based on the simply typed lambda calculus models of natural language. We provide two types of vector semantics: a static one that uses techniques familiar from the truth conditional tradition and a dynamic one based on a form of dynamic interpretation inspired by Heim’s context change potentials. We show how the dynamic model can be applied to entailment between a corpus and a sentence and provide examples. (shrink)

Vector models of language are based on the contextual aspects of words and how they co-occur in text. Truth conditional models focus on the logical aspects of language, the denotations of phrases, and their compositional properties. In the latter approach the denotation of a sentence determines its truth conditions and can be taken to be a truth value, a set of possible worlds, a context change potential, or similar. In this short paper, we develop a vector semantics for language based (...) on the simply typed lambda calculus. Our semantics uses techniques familiar from the truth conditional tradition and is based on a form of dynamic interpretation inspired by Heim's context updates. (shrink)

The paper develops Lambda Grammars, a form of categorial grammar that, unlike other categorial formalisms, is non-directional. Linguistic signs are represented as sequences of lambda terms and are combined with the help of linear combinators.

It is well known that the circumflex notation used by Russell and Whitehead to form complex function names in Principia Mathematica played a role in inspiring Alonzo Church's “lambda calculus” for functional logic developed in the 1920s and 1930s. Interestingly, earlier unpublished manuscripts written by Russell between 1903–1905—surely unknown to Church—contain a more extensive anticipation of the essential details of the lambda calculus. Russell also anticipated Schönfinkel's combinatory logic approach of treating multiargument functions as functions having (...) other functions as value. Russell’s work in this regard seems to have been largely inspired by Frege’s theory of functions and “value-ranges”. This system was discarded by Russell due to his abandonment of propositional functions as genuine entities as part of a new tack for solving Russell’s paradox. In this article, I explore the genesis and demise of Russell’s early anticipation of the lambda calculus. (shrink)

We extend Barbanera and Berardi's symmetric lambda calculus [2] to second-order classical propositional logic and prove its strong normalization.

As the 19th century drew to a close, logicians formalized an ideal notion of proof. They were driven by nothing other than an abiding interest in truth, and their proofs were as ethereal as the mind of God. Yet within decades these mathematical abstractions were realized by the hand of man, in the digital stored-program computer. How it came to be recognized that proofs and programs are the same thing is a story that spans a century, a chase with as (...) many twists and turns as a thriller. At the end of the story is a new principle for designing programming languages that will guide computers into the 21st century. -/- For my money, Gentzen’s natural deduction and Church’s lambda calculus are on a par with Einstein’s relativity and Dirac’s quantum physics for elegance and insight. And the maths are a lot simpler. I want to show you the essence of these ideas. I’ll need a few symbols, but not too many, and I’ll explain as I go along. -/- To simplify, I’ll present the story as we understand it now, with some asides to fill in the history. First, I’ll introduce Gentzen’s natural deduction, a formalism for proofs. Next, I’ll introduce Church’s lambda calculus, a formalism for programs. Then I’ll explain why proofs and programs are really the same thing, and how simplifying a proof corresponds to executing a program. Finally, I’ll conclude with a look at how these principles are being applied to design a new generation of programming languages, particularly mobile code for the Internet. (shrink)

This paper is the twin of (Duží and Jespersen, in submission), which provides a logical rule for transparent quantification into hyperprop- ositional contexts de dicto, as in: Mary believes that the Evening Star is a planet; therefore, there is a concept c such that Mary be- lieves that what c conceptualizes is a planet. Here we provide two logical rules for transparent quantification into hyperpropositional contexts de re. (As a by-product, we also offer rules for possible- world propositional contexts.) One (...) rule validates this inference: Mary believes of the Evening Star that it is a planet; therefore, there is an x such that Mary believes of x that it is a planet. The other rule validates this inference: the Evening Star is such that it is believed by Mary to be a planet; therefore, there is an x such that x is believed by Mary to be a planet. Issues unique to the de re variant include partiality and existential presupposition, sub- stitutivity of co-referential (as opposed to co-denoting or synony- mous) terms, anaphora, and active vs. passive voice. The validity of quantifying-in presupposes an extensional logic of hyperinten- sions preserving transparency and compositionality in hyperinten- sional contexts. This requires raising the bar for what qualifies as co-denotation or equivalence in extensional contexts. Our logic is Tichý’s Transparent Intensional Logic. The syntax of TIL is the typed lambda calculus; its highly expressive semantics is based on a procedural redefinition of, inter alia, functional abstraction and application. The two non-standard features we need are a hyper- intension (called Trivialization) that presents other hyperintensions and a four-place substitution function (called Sub) defined over hy- perintensions. (shrink)

The main objective of this PhD Thesis is to present a method of obtaining strong normalization via natural ordinal, which is applicable to natural deduction systems and typed lambda calculus. The method includes (a) the definition of a numerical assignment that associates each derivation (or lambda term) to a natural number and (b) the proof that this assignment decreases with reductions of maximal formulas (or redex). Besides, because the numerical assignment used coincide with the length of (...) a specific sequence of reduction - the worst reduction sequence - it is the lowest upper bound on the length of reduction sequences. The main commitment of the introduced method is that it is constructive and elementary, produced only through analyzing structural and combinatorial properties of derivations and lambda terms, without appeal to any sophisticated mathematical tool. Together with the exposition of the method, it is presented a comparative study of some articles in the literature that also get strong normalization by means we can identify with the natural ordinal methods. Among them we highlight Howard[1968], which performs an ordinal analysis of Godel’s Dialectica interpretation for intuitionistic first order arithmetic. We reveal a fact about this article not noted by the author himself: a syntactic proof of strong normalization theorem for the system of typified lambda calculus λ⊃ is a consequence of its results. This would be the first strong normalization proof in the literature. (written in Portuguese). (shrink)

Combinatory logic (Curry and Feys 1958) is a “variable-free” alternative to the lambda calculus. The two have the same expressive power but build their expressions differently. “Variable-free” semantics is, more precisely, “free of variable binding”: it has no operation like abstraction that turns a free variable into a bound one; it uses combinators—operations on functions—instead. For the general linguistic motivation of this approach, see the works of Steedman, Szabolcsi, and Jacobson, among others. The standard view in linguistics is (...) that reflexive and personal pronouns are free variables that get bound by an antecedent through some coindexing mechanism. In variable free semantics the same task is performed by some combinator that identifies two arguments of the function it operates on (a duplicator). This combinator may be built into the lexical semantics of the pronoun, into that of the antecedent, or it may be a free-floating operation applicable to predicates or larger chunks of texts, i.e. a typeshifter. This note is concerned with the case of cross-sentential anaphora. It adopts Hepple’s and Jacobson’s interpretation of pronouns as identity maps and asks how this can be extended to the cross-sentential case, assuming the dynamic semantic view of anaphora. It first outlines the possibility of interpreting indefinites that antecede non-ccommanded pronouns as existential quantifiers enriched with a duplicator. Then it argues that it is preferable to use the duplicator as a type-shifter that applies “on the fly”. The proposal has consequences for two central ingredients of the classical dynamic semantic treatment: it does away with abstraction over assignments and with treating indefinites as inherently existentially quantified. However, cross-sentential anaphora remains a matter of binding, and the idea of propositions as context change potentials is retained. (shrink)

In this paper we discuss a new perspective on the syntax-semantics interface. Semantics, in this new set-up, is not ‘read off’ from Logical Forms as in mainstream approaches to generative grammar. Nor is it assigned to syntactic proofs using a Curry-Howard correspondence as in versions of the Lambek Calculus, or read off from f-structures using Linear Logic as in Lexical-Functional Grammar (LFG, Kaplan & Bresnan [9]). All such approaches are based on the idea that syntactic objects (trees, proofs, fstructures) (...) are somehow prior and that semantics must be parasitic on those syntactic objects. We challenge this idea and develop a grammar in which syntax and semantics are treated in a strictly parallel fashion. The grammar will have many ideas in common with the (converging) frameworks of categorial grammar and LFG, but its treatment of the syntax-semantics interface is radically different. Also, although the meaning component of the grammar is a version of Montague semantics and although there are obvious affinities between Montague’s conception of grammar and the work presented here, the grammar is not compositional, in the sense that composition of meaning need not follow surface structure. (shrink)

Along with offering an historically-oriented interpretive reconstruction of the syntax of PM ( rst ed.), I argue for a certain understanding of its use of propositional function abstracts formed by placing a circum ex on a variable. I argue that this notation is used in PM only when de nitions are stated schematically in the metalanguage, and in argument-position when higher-type variables are involved. My aim throughout is to explain how the usage of function abstracts as “terms” (loosely speaking) is (...) not inconsistent with a philosophy of types that does not think of propositional functions as mind- and language-independent objects, and adopts a nominalist/substitutional semantics instead. I contrast PM’s approach here both to function abstraction found in the typed λ-calculus, and also to Frege’s notation for functions of various levels that forgoes abstracts altogether, between which it is a kind of intermediary. (shrink)

This paper argues for the idea that in describing language we should follow Haskell Curry in distinguishing between the structure of an expression and its appearance or manifestation . It is explained how making this distinction obviates the need for directed types in type-theoretic grammars and a simple grammatical formalism is sketched in which representations at all levels are lambda terms. The lambda term representing the abstract structure of an expression is homomorphically translated to a lambda term (...) representing its manifestation, but also to a lambda term representing its semantics. (shrink)

Barbour shows that time does not exist in the physical world, and similar conclusions are reached by others such as Deutsch, Davies and Woodward. Every possible configuration of a physical environment simply exists in the universe. The system is objectively static. Observation, however, is an inherently transtemporal phenomenon, involving actual or effective change of the configuration, collapse. Since, in a static environment, all possible configurations exist, transtemporal reality is of the logical type of a movie. The frame of a (...) movie film is of one logical type, an element of a set of frames, the movie, itself of a second logical type. In a static no-collapse universe, the configurations are of the first logical type, transtemporal reality of the second. To run, the movie requires iteration, a third logical type. Phenomenal consciousness is subjectively experienced as of this third logical type with regard to physical configurations. Everett's formulation clearly describes the transtemporal reality of an observer, which follows the physical in the linear dynamics, but departs from it on observation, giving rise to the the appearance of collapse, and the alternation of dynamics defined in the standard von Neumann-Dirac formulation. Since there is no physical collapse, his formulation is disputed. Given an iterator of the third logical type, the appearance of collapse is simply evidence of iteration. Chalmers demonstrates that phenomenal consciousness is of this logical type, an emergent property of the unitary system as a whole. Given an iterative function of this nature, one contextual to the physical configurations, paradoxes of time are resolved. Subjectively, meaning from the perspective of the iterative process, time passes in an objectively static universe, and the appearance of collapse is effected. (shrink)

In this paper we define intensional models for the classical theory of types, thus arriving at an intensional type logic ITL. Intensional models generalize Henkin's general models and have a natural definition. As a class they do not validate the axiom of Extensionality. We give a cut-free sequent calculus for type theory and show completeness of this calculus with respect to the class of intensional models via a model existence theorem. After this we turn our attention to applications. (...) Firstly, it is argued that, since ITL is truly intensional, it can be used to model ascriptions of propositional attitude without predicting logical omniscience. In order to illustrate this a small fragment of English is defined and provided with an ITL semantics. Secondly, it is shown that ITL models contain certain objects that can be identified with possible worlds. Essential elements of modal logic become available within classical type theory once the axiom of Extensionality is given up. (shrink)

In Hegel ou Spinoza,1 Pierre Macherey challenges the influence of Hegel’s reading of Spinoza by stressing the degree to which Spinoza eludes the grasp of the Hegelian dialectical progression of the history of philosophy. He argues that Hegel provides a defensive misreading of Spinoza, and that he had to “misread him” in order to maintain his subjective idealism. The suggestion being that Spinoza’s philosophy represents, not a moment that can simply be sublated and subsumed within the dialectical progression of (...) the history of philosophy, but rather an alternative point of view for the development of a philosophy that overcomes Hegelian idealism. Gilles Deleuze also considers Spinoza’s philosophy to resist the totalising effects of the dialectic. Indeed, Deleuze demonstrates, by means of Spinoza, that a more complex philosophy antedates Hegel’s, which cannot be supplanted by it. Spinoza therefore becomes a significant figure in Deleuze’s project of tracing an alternative lineage in the history of philosophy, which, by distancing itself from Hegelian idealism, culminates in the construction of a philosophy of difference. It is Spinoza’s role in this project that will be demonstrated in this paper by differentiating Deleuze’s interpretation of the geometrical example of Spinoza’s Letter XII (on the problem of the infinite) in Expressionism in Philosophy, Spinoza,2 from that which Hegel presents in the Science of Logic.3. (shrink)

Textbook on Gödel’s incompleteness theorems and computability theory, based on the Open Logic Project. Covers recursive function theory, arithmetization of syntax, the first and second incompleteness theorem, models of arithmetic, second-order logic, and the lambda calculus.

I present and discuss three previously unpublished manuscripts written by Bertrand Russell in 1903, not included with similar manuscripts in Volume 4 of his Collected Papers. One is a one-page list of basic principles for his “functional theory” of May 1903, in which Russell partly anticipated the later Lambda Calculus. The next, catalogued under the title “Proof That No Function Takes All Values”, largely explores the status of Cantor’s proof that there is no greatest cardinal number in the (...) variation of the functional theory holding that only some but not all complexes can be analyzed into function and argument. The final manuscript, “Meaning and Denotation”, examines how his pre-1905 dis­tinction between meaning and denotation is to be understood with respect to functions and their arguments. In them, Russell seems to endorse an extensional view of functions not endorsed in other works prior to the 1920s. All three manuscripts illustrate the close connection between his work on the logical paradoxes and his work on the theory of meaning. (shrink)

This paper argues that the theory of structured propositions is not undermined by the Russell-Myhill paradox. I develop a theory of structured propositions in which the Russell-Myhill paradox doesn't arise: the theory does not involve ramification or compromises to the underlying logic, but rather rejects common assumptions, encoded in the notation of the $\lambda$-calculus, about what properties and relations can be built. I argue that the structuralist had independent reasons to reject these underlying assumptions. The theory is given (...) both a diagrammatic representation, and a logical representation in a novel language. In the latter half of the paper I turn to some technical questions concerning the treatment of quantification, and demonstrate various equivalences between the diagrammatic and logical representations, and a fragment of the $\lambda$-calculus. (shrink)

Although Kurt Gödel does not figure prominently in the history of computabilty theory, he exerted a significant influence on some of the founders of the field, both through his published work and through personal interaction. In particular, Gödel’s 1931 paper on incompleteness and the methods developed therein were important for the early development of recursive function theory and the lambda calculus at the hands of Church, Kleene, and Rosser. Church and his students studied Gödel 1931, and Gödel taught (...) a seminar at Princeton in 1934. Seen in the historical context, Gödel was an important catalyst for the emergence of computability theory in the mid 1930s. (shrink)

This paper presents a new system of logic, LF, that is intended to be used as the foundation of the formalization of science. That is, deductive validity according to LF is to be used as the criterion for assessing what follows from the verdicts, hypotheses, or conjectures of any science. In work currently in progress, we argue for the unique suitability of LF for the formalization of logic, mathematics, syntax, and semantics. The present document specifies the language and rules of (...) LF, lays out some notational conventions, and states some basic technical facts about the system. (shrink)

This paper considers two reasons that might support Russell’s choice of a ramified-type theory over a simple-type theory. The first reason is the existence of purported paradoxes that can be formulated in any simple-type language, including an argument that Russell considered in 1903. These arguments depend on certain converse-compositional principles. When we take account of Russell’s doctrine that a propositional function is not a constituent of its values, these principles turn out to be too implausible to make these arguments troubling. (...) The second reason is conditional on a substitutional interpretation of quantification over types other than that of individuals. This reason stands up to investigation: a simple-type language will not sustain such an interpretation, but a ramified-type language will. And there is evidence that Russell was tacitly inclined towards such an interpretation. A strong construal of that interpretation opens a way to make sense of Russell’s simultaneous repudiation of propositions and his willingness to quantify over them. But that way runs into trouble with Russell’s commitment to the finitude of human understanding. (shrink)

This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. I examine the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, undecidable propositions, (...) and abstraction principles in the philosophy of mathematics; to the modal and hyperintensional profiles of the logic of rational intuition; and to the types of intention, when the latter is interpreted as a hyperintensional mental state. Chapter 2 argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal cognitivism and modal expressivism. I also develop a novel topic-sensitive truthmaker semantics for dynamic epistemic logic, and develop a novel dynamic epistemic two-dimensional hyperintensional semantics. Chapter 3 provides an abstraction principle for epistemic (hyper-)intensions. Chapter 4 advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter 5 applies the fixed points of the modal μ-calculus in order to account for the iteration of epistemic states in a single agent, by contrast to availing of modal axiom 4 (i.e. the KK principle). The fixed point operators in the modal μ-calculus are rendered hyperintensional, which yields the first hyperintensional construal of the modal μ-calculus in the literature and the first application of the calculus to the iteration of epistemic states in a single agent instead of the common knowledge of a group of agents. Chapter 6 advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter 7 provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapters 2 and 4 are availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. -/- Chapters 8-12 provide cases demonstrating how the two-dimensional hyperintensions of hyperintensional, i.e. topic-sensitive epistemic two-dimensional truthmaker, semantics, solve the access problem in the epistemology of mathematics. Chapter 8 examines the interaction between my hyperintensional semantics and the axioms of epistemic set theory, large cardinal axioms, the Epistemic Church-Turing Thesis, the modal axioms governing the modal profile of Ω-logic, Orey sentences such as the Generalized Continuum Hypothesis, and absolute decidability. These results yield inter alia the first hyperintensional Epistemic Church-Turing Thesis and hyperintensional epistemic set theories in the literature. Chapter 9 examines the modal and hyperintensional commitments of abstractionism, in particular necessitism, and epistemic hyperintensionality, epistemic utility theory, and the epistemology of abstraction. I countenance a hyperintensional semantics for novel epistemic abstractionist modalities. I suggest, too, that observational type theory can be applied to first-order abstraction principles in order to make first-order abstraction principles recursively enumerable, i.e. Turing machine computable, and that the truth of the first-order abstraction principle for hyperintensions is grounded in its being possibly recursively enumerable and the machine being physically implementable. Chapter 10 examines the philosophical significance of hyperintensional Ω-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter 11 provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter 12 avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of hyperintensional epistemic two-dimensional semantics in order to account for the interaction between the interpretational and objective modalities and truthmakers thereof. This yields the first hyperintensional category theory in the literature. I invent a new mathematical trick in which first order structures are treated as categories, and Vopenka's principle can be satisfied because of the elementary embeddings between the categories and generate Vopenka cardinals while bypassing the category of Set in category theory. Chapter 13 examines modal responses to the alethic paradoxes. Chapter 14 examines, finally, the modal and hyperintensional semantics for the different types of intention and the relation of the latter to evidential decision theory. (shrink)

The Neutrosophic Precalculus and the Neutrosophic Calculus can be developed in many ways, depending on the types of indeterminacy one has and on the method used to deal with such indeterminacy. This article is innovative since the form of neutrosophic binomial factorial theorem was constructed in addition to its refrains. Two other important theorems were proven with their corollaries, and numerical examples as well. As a conjecture, we use ten (indeterminate) forms in neutrosophic calculus taking an important role (...) in limits. To serve article's aim, some important questions had been answered. (shrink)

Logicism is, roughly speaking, the doctrine that mathematics is fancy logic. So getting clear about the nature of logic is a necessary step in an assessment of logicism. Logic is the study of logical concepts, how they are expressed in languages, their semantic values, and the relationships between these things and the rest of our concepts, linguistic expressions, and their semantic values. A logical concept is what can be expressed by a logical constant in a language. So the question “What (...) is logic?” drives us to the question “What is a logical constant?” Though what follows contains some argument, limitations of space constrain me in large part to express my Credo on this topic with the broad brush of bold assertion and some promissory gestures. (shrink)

This paper is based on the comments I gave to Alfred Mele regarding his original Zygote Argument during my presentation at a small workshop on manipulation arguments in Budapest back in 2012. After those comments, Mele changed the conclusion of his original Zygote Argument and redefined 'incompatibilism' so that it would refer to the conclusion of his new Zygote Argument (Mele 2013+). Yet, over the last decade, Mele has made no comment in print about the changes he made nor the (...) invalidity objection that led to them. To my knowledge, Mele has only mentioned this 2015 paper once: in the context of defending his non-explanatory definition of 'incompatibilism' at the opening of Aspects of Agency (p. 6, n. 4), Mele draws his readers' attention to just *just this paper* as a place where they'll find the type of nonstandard/nontraditional definition of 'incompatibilism' that he rejects. If Mele had a general concern about unusual definitions of 'incompatibilism', he could have just as easily named almost any leading figure in free will for this purpose (since most reject the non-explanatory definition he now endorses). But for some reason, Mele thought an unemployed junior researcher should be singled out as an example. Moreover, if Mele were genuinely interested in helping his readers understand the ambiguity of terms like 'compatibilism' and 'incompatibilism' it is a mystery that he referenced a paper in which nothing of substance hung on the definitions given to these terms when he might have instead pointed them to my OTHER 2015 paper in which the MAIN AIM of the paper is to expose the difficulties facing anyone who wants to define the terms 'compatibilism' and 'incompatibilism' in a way that everyone will accept (including a critique of the definitions that Mele has adopted). By all appearances, Mele's aim was to give readers the false impression that my working definition of 'incompatibilism' played some role in my charge that his argument is invalid (which it doesn't, given that the term doesn't appear in either the premises or conclusion of that argument). In this paper, I simply use the invalidity of the simple 2-premise Zygote Argument to make a series of more philosophically significant points (e.g. regarding the dialectical structure of the free-will debate, the role of best-explanation reasoning, and to develop the first-ever "master manipulation argument"). Mele pays no attention to my answer to the "Now What?" question in this paper, even though that answer was the paper's main point. For those interested in a more recent discussion of how the logical and metaphilosophical observations made in this paper have helped to move the free-will debate forward, I suggest my contributions to the Wiley-Blackwell Companion to Free Will (Intro and Chapter 4, 2023) and my paper "Free Will, Self-Creation, and the Paradox of Moral Luck" (2019). (shrink)

A distinction is drawn among predicates, open sentences (or open formulas), and general terms, including general-term phrases. Attaching a copula, perhaps together with an article, to a general term yields a predicate. Predicates can also be obtained through lambda-abstraction on an open sentence. The issue of designation and semantic content for each type of general expression is investigated. It is argued that the designatum of a general term is a universal, e.g., a kind, whereas the designatum of a predicate (...) is a class (or its characteristic function) and the designatum of an open sentence is a truth-value. Predicates and open sentences are therefore typically non-rigid designators. It is argued further that certain general terms, including phrases, are invariably rigid designators, whereas certain others (general definite descriptions) are typically non-rigid. Suitable semantic contents for predicates, open sentences, and general terms are proposed. Consequences for the thesis of compositionality are drawn. (shrink)

This chapter offers an opinionated introduction to higher-order formal languages with an eye towards their applications in metaphysics. A simply relationally typed higher-order language is introduced in four stages: starting with first-order logic, adding first-order predicate abstraction, generalizing to higher-order predicate abstraction, and finally adding higher-order quantification. It is argued that both β-conversion and Universal Instantiation are valid on the intended interpretation of this language. Given these two principles, it is then shown how we can use pure higher-order (...) logic to ask, and begin to answer, metaphysical questions with non-trivial implications. In particular, while we must reject the popular idea that structural differences between sentences correspond to parallel distinctions in the logical structure of extra-linguistic reality, it may still be possible to give a purely logical characterization of objectual aboutness and related notions. (shrink)

A paradox about sets of properties is presented. The paradox, which invokes an impredicatively defined property, is formalized in a free third-order logic with lambda-abstraction, through a classically proof-theoretically valid deduction of a contradiction from a single premise to the effect that every property has a unit set. Something like a model is offered to establish that the premise is, although classically inconsistent, nevertheless consistent, so that the paradox discredits the logic employed. A resolution through the ramified theory of (...) types is considered. Finally, a general scheme that generates a family of analogous paradoxes and a generally applicable resolution are proposed. (shrink)

W. V. Quine famously defended two theses that have fallen rather dramatically out of fashion. The first is that intensions are “creatures of darkness” that ultimately have no place in respectable philosophical circles, owing primarily to their lack of rigorous identity conditions. However, although he was thoroughly familiar with Carnap’s foundational studies in what would become known as possible world semantics, it likely wouldn’t yet have been apparent to Quine that he was fighting a losing battle against intensions, due in (...) large measure to developments stemming from Carnap’s studies and culminating in the work of Kripke, Hintikka, and Bayart. These developments undermined Quine’s crusade against intensions on two fronts. First, in the context of possible world semantics, intensions could after all be given rigorous identity conditions by defining them (in the simplest case) as functions from worlds to appropriate extensions, a fact exploited to powerful and influential effect in logic and linguistics by the likes of Kaplan, Montague, Lewis, and Cresswell. Second, the rise of possible world semantics fueled a strong resurgence of metaphysics in contemporary analytic philosophy that saw properties and propositions widely, fruitfully, and unabashedly adopted as ontological primitives in their own right. This resurgence — happily, in my view — continues into the present day. -/- For a time, at any rate, Quine experienced somewhat better success with his second thesis: that higher-order logic is, at worst, confused and, at best, a quirky notational alternative to standard first-order logic. However, Quine notwithstanding, a great deal of recent work in formal metaphysics transpires in a higher-order logical framework in which properties and propositions fall into an infinite hierarchy of types of (at least) every finite order. Initially, the most philosophically compelling reason for embracing such a framework since Russell first proposed his simple theory of types was simply that it provides a relatively natural explanation of the paradoxes. However, since the seminal work of Prior there has been a growing trend to consider higher-order logic to be the most philosophically natural framework for metaphysical inquiry, many of the contributors to this volume being among the most important and influential advocates of this view. Indeed, this is now quite arguably the dominant view among formal metaphysicians. -/- In this paper, and against the current tide, I will argue in §1 that there are still good reasons to think that Quine’s second battle is not yet lost and that the correct framework for logic is first-order and type-free — properties and propositions, logically speaking, are just individuals among others in a single domain of quantification — and that it arises naturally out of our most basic logical and semantical intuitions. The data I will draw upon are not new and are well-known to contemporary higher-order metaphysicians. However, I will try to defend my thesis in what I believe is a novel way by suggesting that these basic intuitions ground a reasonable distinction between “pure” logic and non-logical theory, and that Russell-style semantic paradoxes of truth and exemplification arise only when we move beyond the purely logical and, hence, do not of themselves provide any strong objection to a type-free conception of properties and propositions. -/- Most of my arguments in §1 are largely independent of any specific account of the nature of properties and propositions beyond their type-freedom. However, I will in addition argue that there are good reasons to take propositions, at least, to be very fine-grained. My arguments are thus bolstered significantly if it can be shown that there are in fact well-defined examples of logics that are not only type-free but which comport with such a conception of propositions. It is the purpose of §2 to lay out a logic of this sort in some detail, drawing especially upon work by George Bealer and related work of my own. With the logic in place, it will be possible to generalize the line of argument noted above regarding Russell-style paradoxes and, in §3, apply it to two propositional paradoxes — the Prior-Kaplan paradox and the Russell-Myhill paradox — that are often taken to threaten the sort of account developed here. (shrink)

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

This essay unites current philosophical thinking on imagination with a burgeoning debate in the philosophy of memory over whether episodic remembering is simply a kind of imagining. So far, this debate has been hampered by a lack of clarity in the notion of imagining at issue. Several options are considered and constructive imagining is identified as the relevant kind. Next, a functionalist account of episodic remembering is defended as a means to establishing two key points: first, one need not (...) defend a factive view of remembering in order to hold that causal connections to past experiences are essential to how rememberings are typed; and, second, current theories that equate remembering with imagining are in fact consistent with a functionalist theory that includes causal connections in its account of what it is to remember. This suggests that remembering is not a kind of imagining and clarifies what it would take to establish the contrary. (shrink)

Are religious beliefs psychologically different from matter-of-fact beliefs? Many scholars say no: that religious people, in a matter-of-fact way, simply think their deities exist. Others say yes: that religious beliefs are more compartmentalized, less certain, and less responsive to evidence. Little research to date has explored whether lay people themselves recognize such a difference. We addressed this question in a series of sentence completion tasks, conducted in five settings that differed both in religious traditions and in language: the US, (...) Ghana, Thailand, China, and Vanuatu. Participants everywhere routinely used different verbs to describe religious versus matter-of-fact beliefs, and they did so even when the ascribed belief contents were held constant and only the surrounding context varied. These findings support the view that people from diverse cultures and language communities recognize a difference in attitude type between religious belief and everyday matter-of-fact belief. (shrink)

Among contemporary epistemologists and scholars of ancient philosophy, one often hears that transmitting propositional knowledge by testimony is usually easy and straightforward, but transmitting understanding and know-how by testimony is usually difficult or simply impossible. Further provocative conclusions are then sometimes drawn from these claims: for instance, that know-how and understanding are not types of propositional knowledge. In contrast, I argue that transmitting propositional knowledge is sometimes easy and sometimes hard, just as transmitting know how and understanding is sometimes (...) easy and sometimes hard. No general lessons can be drawn about the relationships among propositional knowledge, know how, and understanding by considering the case of testimony alone. (shrink)

This paper compares current ways of modeling the inferential structure of practical reasoning arguments, and proposes a new approach in which it is regarded in a modular way. Practical reasoning is not simply seen as reasoning from a goal and a means to an action using the basic argumentation scheme. Instead, it is conceived as a complex structure of classificatory, evaluative, and practical inferences, which is formalized as a cluster of three types of distinct and interlocked argumentation schemes. Using (...) two real examples, we show how applying the three types of schemes to a cluster of practical argumentation allows an argument analyst to reconstruct the tacit premises presupposed and evaluate the argumentative reasoning steps involved. This approach will be shown to overcome the limitations of the existing models of practical reasoning arguments within the BDI and commitment theoretical frameworks, providing a useful tool for discourse analysis and other disciplines. In particular, applying this method brings to light the crucial role of classification in practical argumentation, showing how the ordering of values and preferences is only one of the possible areas of deep disagreement. (shrink)

This paper presents a dilemma which it has been alleged by Kim Frost must be faced by any defender of the notion of a two-way power and offers a solution to the dilemma which is distinct from Frost’s own. The dilemma is as follows: assuming that powers are to be individuated by what they are powers to do or undergo, then either there is a unified description of the manifestation-type which individuates the power, or there is not. If there is, (...) then two-way powers are revealed really to be one-way powers, after all. If there is not, then it is difficult to explain why the two-way power does not simply dissolve into a mere combination of two one-way powers. The paper offers an account of what a two-way power is that is distinct from the one Frost takes for granted, and argues that this different conception is the key to avoiding the dilemma. It is also argued that this alternative conception has several further advantages over its rival and also that it has no less of a claim than Frost’s notion to be prefigured in Aristotle’s original discussion. (shrink)

This paper argues that the proponents of epistemological scientism must take some stand on scientific methodology. The supporters of scientism cannot simply defer to the social organisation of science because the social processes themselves must meet some methodological criteria. Among such criteria is epistemic evaluability, which demands intersubjective access to reasons. We derive twelve theses outlining some implications of epistemic evaluability. Evaluability can support weak and broad variants of epistemological scientism, which state that sciences, broadly construed, are the best (...) sources of knowledge or some other epistemic goods. Since humanities and social sciences produce epistemically evaluable results, narrow types of scientism that take only natural sciences as sources of knowledge require additional argumentation in their support. Strong scientism, which takes sciences as the only source of knowledge, also needs to appeal to some further principles since evaluability is not an all-or-nothing affair. (shrink)

Sound is one of the types of waves that can be felt by the sense of hearing (ears). In physics, the definition of sound is something that is produced from objects that vibrate. Objects that produce sound are called sound sources. The sound source that vibrates will vibrate the molecules into the air around it. Sound is mechanical compression or longitudinal waves that propagate through the medium. This medium or intermediate agent can be liquid, solid, gas. So, sound waves can (...) propagate for example in water, coal, or air. Most sounds are a combination of various vibratory signals composed of harmonic waves, but pure sound can theoretically be explained by oscillating vibrational speed or frequency measured in Hertz (Hz) vibration units and amplitude or loudness of sound with measurements in decibels (dB). The effect sounds can have on us humans is simply astounding. While everyday life becomes stressful, overcrowded and increasingly hectic, we seek ways for inner peace and balance. The power of music, felt through overtone-rich sound therapy and sound massage, can be a solution. No matter how much scientific explanation is behind it, healing through music remains fascinating, even magical. This paper introduces a new field called cymatics and sound healing with their plausible impact to spirituality and consciousness research. (shrink)

Generic stereotypes are generically formulated generalizations that express a stereotype, like “Mexican immigrants are rapists” and “Muslims are terrorists.” Stereotypes like these are offensive and should not be asserted by anyone. Yet when someone does assert a sentence like this in a conversation, it is surprisingly difficult to successfully rebut it. The meaning of generic sentences is such that they can be true in several different ways. As a result, a speaker who is challenged after asserting a generic stereotype can (...) often simply dismiss the objection and maintain that the stereotype is true in a way that is compatible with the challenger’s objection. In this paper, a semantic theory for generics is presented that accounts for this type of defensive shifting in upholding generic stereotypes. This theory is then used to develop two strategies to object more efficiently. The first strategy is to immediately deny that either of the two possible ways in which a generic can be true obtains. The second strategy is to deny the satisfaction of an additional condition that is necessary for a generic sentence to be true. (shrink)

In virtue of what does a sign have meaning? This is the question raised by Wittgenstein's rule-following considerations. Semantic dispositionalism is a (type of) theory that purports to answer this question. The present paper argues that semantic dispositionalism faces a heretofore unnoticed problem, one that ultimately comes down to its reliance on unanalyzed notions of repeated types of signs. In the context of responding to the rule-following paradox—and offering a putative solution to it—this amounts to simply assuming a solution (...) to the problem in one domain and using it to solve the same problem in another. Given, moreover, the level at which the rule-following paradox undercuts dispositionalism—the level of the notion of a sign's repetition—the objections made to the view also rule out causal/informational theories of meaning as well as communitarian/assertion-theoretic ones as potential solutions to the rule-following paradox. (shrink)

Moral philosophers and psychologists often assume that people judge morally lucky and morally unlucky agents differently, an assumption that stands at the heart of the Puzzle of Moral Luck. We examine whether the asymmetry is found for reflective intuitions regarding wrongness, blame, permissibility, and punishment judg- ments, whether people’s concrete, case-based judgments align with their explicit, abstract principles regarding moral luck, and what psychological mechanisms might drive the effect. Our experiments produce three findings: First, in within-subjects experiments favorable to reflective (...) deliberation, the vast majority of people judge a lucky and an unlucky agent as equally blameworthy, and their actions as equally wrong and permissible. The philosophical Puzzle of Moral Luck, and the challenge to the very possibility of systematic ethics it is frequently taken to engender, thus simply do not arise. Second, punishment judgments are significantly more outcome- dependent than wrongness, blame, and permissibility judgments. While this constitutes evidence in favor of current Dual Process Theories of moral judgment, the latter need to be qualified: punishment and blame judgments do not seem to be driven by the same process, as is commonly argued in the literature. Third, in between-subjects experiments, outcome has an effect on all four types of moral judgments. This effect is mediated by negligence ascriptions and can ultimately be explained as due to differing probability ascriptions across cases. (shrink)

Sometimes, a group of people can produce a morally bad outcome despite each person’s individual act making no difference to whether the outcome is produced. Since each person’s act makes no difference, it seems the effects of the act cannot provide a reason not to perform it. This is problematic, because if each person acts in accordance with their reasons, each will presumably perform the act—and thus, the bad outcome will be brought about. I suggest that the key to solving (...) this problem is to make it true of each person that their act would in fact make a difference to the relevant outcome. Fortunately, I contend, this can be accomplished by each person simply forming a particular type of attitude. I argue that each person has an obligation to form the relevant attitude in collective action cases, on pain of being immoral or irrational. (shrink)

[ES] En recientes décadas se ha observado un renovado interés por algunos de los temas clásicos de la ontología, desde áreas de conocimiento externas a la filosofía, sin embargo, este renacimiento ontológico ha «estimulado» una multiplicidad y diversidad de teorías y concepciones «ontológicas» que ha dado como consecuencia una proliferación de «ontologías» y de interminables batallas para determinar qué tipo de «entidades» estudian sus respectivos «dominios», que a su vez se consideran autónomos e independientes entre sí, inclusive de la propia (...) ontología. En este sentido, el propósito de este trabajo es caracterizar y representar de manera adecuada estas «ontologías», dentro del marco general del debate acerca de la naturaleza de la ontología. Es así que, en la primera sección haré un diagnostico de la ontología contemporánea; en la segunda proporcionaré algunas definiciones y caracterizaciones de las principales concepciones, en especial de las denominadas «ontologías aplicadas»; y en la tercera analizaré sí estas concepciones pueden ser consideradas diversos tipos de ontología o simplemente son diversos niveles de ontología. El marco de la discusión no se centrará en confrontar todas estas nociones, sino en describirlas y analizarlas para ofrecer un enfoque sobre el estado actual de la ontología y sus problemas. [EN] In recent decades there has been a renewed interest in some of the classic themes of ontology, from areas of knowledge external to philosophy; however, this ontological revival has «stimulated» a multiplicity and diversity of «ontological» theories and concepts that has resulted in a proliferation of «ontologies» and endless battles to determine what kind of «entities» study their respective «domains», which in turn are considered autonomous and independent, even of ontology itself. In this sense, the purpose of this work is to adequately characterize and represent these «ontologies», within the general framework of the debate about the nature of ontology. Thus, in the first section I will make a diagnosis of contemporary ontology; in the second I will provide some definitions and characterizations of the main concepts, especially the so-called «applied ontologies»; and in the third I will analyze whether these concepts can be considered different types of ontology or simply are different levels of ontology. The framework of the discussion will not center on confronting all these notions, but to describe and analyze them to provide a focus on the current state of ontology and its problems. (shrink)

If each of the subtypes of autism is defined simply as constituted by a set of symptoms, then the criteria for its observation are straightforward, although, of course, some of those symptoms themselves might be hard to observe definitively. Compare with telling whether or not someone is bleeding: while it might be hard to tell if someone is bleeding internally, we know what it takes to find out, and when we have the right access and instruments we can settle (...) the issue. But matters are not so simple for the autism subtypes. For one thing, how do we settle which symptoms to group together under one heading? One key difference between “autism disorder” and “Asperger’s disorder” is that the former exhibit language delays (sometimes extreme), whereas the latter do not. But is that a sign of genuinely distinct conditions or is that an artifact of the distinct groups of subjects that Leo Kanner and Hans Asperger worked with? And in general, although there are certainly types of behavior that are taken to be indicative of autism, none by itself is taken by diagnosticians to be either necessary or sufficient for a definitive diagnosis for any of the autism subtypes. What is the diagnostician to do? This is not merely an academic issue, as many parents can attest. Are we in a situation, then, that each practitioner has his or her own “pet” signs that are the “real keys” to the diagnosis? That would suggest that the term “autistic” might meet the fate of the outdated term “neurotic,” which turned out to be a pseudo-scientific term for an inexact clumping together of unrelated phenomena. The assumption amongst specialists seems to be that we will reach the point with "autism" that we have with "water": there will be a root essence to autism whose presence or absence settles a diagnosis. If that is to be the case, however, we have to settle the level of application of the concept. Does the term apply to people who exhibit particular behaviors? Or is it possible to exhibit “autistic” behaviors without actually being autistic, because autism is instead a particular feature of the mind (as, for example, in Baron-Cohen’s “impaired theory of mind module” theory, discussed below) which usually but not necessarily has behavioral effects? Or is autism located instead in the brain, perhaps in damage to key areas, which in turn would typically have an effect on modules of the mind? Or perhaps autism is located in genetics or biology, so that some people with damage to the brain caused by accidents so that they exhibit autistic symptoms would not actually be autistic. Conversely, supposing one had an “autistic brain” but showed none of (or not a sufficient number of) the symptoms, would one not be autistic? The assumption is that the genotypes and phenotypes will line up neatly, but if they do not, what happens to the concept “autistic?” (There is an analogy in the philosophy of sex and gender: androgen insensitive individuals tend to self-identify as female and have outward female traits, but have XY chromosomes—should we go with chromosomes or self-identity in assigning sex category?) Finally, the implications for these complications for diagnosis and categorization, with the attendant social and medical implications is discussed. The typical assumption of the medical profession is that autism cannot be “cured.” That assumes that autism is not simply the symptoms. However, at the same time, the tests used to diagnose ASDs work simply from the symptoms (for example, Baron-Cohen’s Sally/Anne test, which ASD children of a certain age almost all fail, but which practically no ASD adult fails). This implies an inherent confusion over the status of the concept. I conclude that attempts to make sense of some true or accurate summary of what it is to be autistic (such as one would find in the DSM) are almost certainly misguided and will vanish into history along with “neurotic.” But as with racial terms, which are similarly shifting and perverse, the term has already passed into the public sphere and will have a lasting and dangerous influence beyond its short scientific shelf-life. (shrink)

Creepiness and the emotion of the creeps have been overlooked in the moral philosophy and moral psychology literatures. We argue that the creeps is a morally significant emotion in its own right, and not simply a type of fear, disgust, or anger (though it shares features with those emotions). Reflecting on cases, we defend a novel account of the creeps as felt in response to creepy people. According to our moral insensitivity account, the creeps is fitting just when its (...) object is agential activity that is insensitive to basic moral considerations. When, only when, and insofar as someone is disposed to such insensitivity, they are a creep. Such insensitivity, especially in extreme forms, raises doubts about creeps’ moral agency. We distinguish multiple types of insensitivity, respond to concerns that feeling the creeps is itself objectionable, and conclude with a discussion of epistemic issues relating to the creeps. (shrink)

Despite his awareness that organisms are well suited to the habitats they are typically found in, Aristotle nowhere tries to explain this. It is unlikely that he thinks this “fit” (as I call it) between organisms and their habitats is simply a lucky coincidence, given how vehemently he rejects that as an explanation of the fit between organisms’ various body parts. But it is quite puzzling that Aristotle never explicitly addresses this, since it is a question that seemed so (...) pressing to later philosophers and biologists such as Darwin. In this paper I offer a solution to that puzzle. As I argue, the type of habitat an organism lives in is partly constitutive of its essence or nature. The reason Aristotle does not ask, for instance, why marsh-dweller birds live in marshes, is that it is simply constitutive of their nature that they do so. Given that habitat is built into a kind’s essence, the answer to such a question is obvious and the question would have seemed to him trivial. By attending to the details of his biological treatises, I show that Aristotle’s conception of a living being’s essence is much more nuanced than one can glean from his discussions in the Physics and Metaphysics alone. (shrink)

A frequent caveat in online dating profiles – “No fats, femmes, or Asians” – caused an LGBT activist to complain about the bias against Asians in the American gay community, which he called “racial looksism”. In response, he was asked that, if he himself would not date a fat person, why he should find others not dating Asians so upsetting. This response embodies a popular attitude that personal preferences or tastes are simply personal matters – they are not subject (...) to moral evaluation. In this paper, I argue, against this popular attitude, that a personal preference like racial looksism is indeed wrong. A preference like racial looksism is wrong because it is an overgeneralization that disrespects individuality by treating people as exchangeable tokens of one type, and such disrespect denies its objects appreciation that their dignity entitles them to. As it turns out, there is on my account a relevant moral difference between racial looksism and simple looksism. (shrink)

The aim of the paper is to develop general criteria of argumentative validity and adequacy for probabilistic arguments on the basis of the epistemological approach to argumentation. In this approach, as in most other approaches to argumentation, proabilistic arguments have been neglected somewhat. Nonetheless, criteria for several special types of probabilistic arguments have been developed, in particular by Richard Feldman and Christoph Lumer. In the first part (sects. 2-5) the epistemological basis of probabilistic arguments is discussed. With regard to the (...) philosophical interpretation of probabilities a new subjectivist, epistemic interpretation is proposed, which identifies probabilities with tendencies of evidence (sect. 2). After drawing the conclusions of this interpretation with respect to the syntactic features of the probability concept, e.g. one variable referring to the data base (sect. 3), the justification of basic probabilities (priors) by judgements of relative frequency (sect. 4) and the justification of derivative probabilities by means of the probability calculus are explained (sect. 5). The core of the paper is the definition of '(argumentatively) valid derivative probabilistic arguments', which provides exact conditions for epistemically good probabilistic arguments, together with conditions for the adequate use of such arguments for the aim of rationally convincing an addressee (sect. 6). Finally, some measures for improving the applicability of probabilistic reasoning are proposed (sect. 7). (shrink)

There is a libertarian argument for live donor organ markets, according to which live donor organ markets would be permitted if we simply refrained from imposing any substantive and controversial moral assumptions on people who reasonably disagree about morality and justice. I argue that, to the contrary, this endorsement of live donor organ markets depends upon the libertarians’ adoption of a substantive and deeply controversial conception of strong, extensive property rights. This is shown by the fact that these rights (...) would prevent states intervening in cases of preventable and intuitively impermissible wronging of others that can arise when free individuals engage in voluntary offers and exchanges. I outline two forms of such wronging: discrimination and disrespectful demands. I argue that although these types of acts are morally impermissible, the policy question of whether and how they should be regulated by states is non-trivial. I then argue that there is good reason to think that organ markets would rely on disrespectful demands. This may help explain the widespread moral repugnance people feel toward organ trading. It also provides a prima facie, though not decisive, case for states to prohibit such markets. (shrink)

In this ground-breaking article submitted for publication in mid-1986, Lucinda Vandervort creates a radically new and comprehensive theory of sexual consent as the unequivocal affirmative communication of voluntary agreement. She argues that consent is a social act of communication with normative effects. To consent is to waive a personal legal right to bodily integrity and relieve another person of a correlative legal duty. If the criminal law is to protect the individual’s right of sexual self-determination and physical autonomy, rather than (...) simply to regulate the type and degree of force that may be used to obtain compliance from a victim, the point of reference must be the individual complainant, as a person who makes choices, not social norms or objective tests based on the ordinary person. To determine whether consent is voluntary, attention must be directed to the presence or absence of factors that had a coercive impact on the individual complainant, a specific person with a collection of social, cultural, and psychological experiences, needs, fears, values, and priorities. Individuals have the right to exercise self-determination in accordance with their own values and perceptions, not those of a mythical victim. Accordingly, Vandervort argues that the prosecution may show either refusal, the absence of affirmative voluntary agreement (including passivity or the absence of consent due to unconsciousness), or circumstances that invalidate any apparent consent. Any of these prove the absence of consent for the purposes of establishing the actus reus of sexual assault. -/- The definition of consent as the affirmative communication of voluntary agreement is also shown to have a variety of implications for the interpretation and application of the law of sexual assault and the handling of evidentiary issues at trial in sexual assault cases. Key among these is the pivotal significance of the legal definition of consent as a tool to bar availability of the defence of “mistaken belief in consent.” Vandervort argues that in many cases the defence of “mistaken belief in consent” is based on ignorance of the law of consent, mistake about the legal definition of consent, or a failure to appreciate the legal significance of facts that are well-known, and not on a mistaken belief in an erroneous set of facts. The broad proposition asserted here is that a statutory criminal law is enforceable only if all defences based directly or indirectly on belief in the validity of extra-legal norms that authorize infringement of rights protected by the criminal law are barred. This proposition and the characterization of some mistakes about consent as legal, not factual, are also shown to be useful to exclude rape-myths and stereotypical assumptions---the stuff of which “social” definitions of consent have long been constructed---from the decision-making process at trial. -/- . (shrink)