Complex simplex numerals

It is commonly assumed that basic cardinal numerals such as English three are simplex expressions whose primary function is to quantify over entities denoted by the modified NP (e.g., Kennedy 2015; Rothstein 2017; Ionin & Matushansky 2018). In this paper, we explore cross-linguistic marking patterns suggesting that cardinals in fact lexicalize complex syntactic and semantic structures derived from the primitive notion of the number scale. The evidence we will investigate comes from various morphological shapes of cardinal numerals when used to count objects and when used for abstract arithmetical counting.

Simplicity and the form of grammars

The goal of theory construction is explanation: for language, theory for particular languages (grammar) and for the faculty of language FoL (the innate endowment for language acquisition). A primitive notion of simplicity of grammars is number of symbols, but this is too crude. An improved measure distinguishes grammars that capture genuine properties of language from those that do not. The theory of FoL must meet the empirical conditions of learnability (under extreme poverty of stimulus), and evolvability (given the limited but not insignificant evidence available). Recent work provides promising insights into how these twin conditions may be satisfied.

Levels of Ontology and Natural Language

Two levels of ontology are commonly distinguished in metaphysics: the ontology of ordinary objects, or more generally ordinary ontology, and the ontology of what there really or fundamentally is. This chapter argues that natural language reflects not only the ordinary ontology but also a language-driven ontology, which is involved in the mass-count distinction and part-structure-sensitive semantic selection (as well as perhaps the light ontology of pleonastic entities in the sense of Schiffer). The language-driven ontology does not constitute another level of representation, but is taken to be a (selective) ontology of the real, given a plenitudinous or maximalist conception of reality. The language-driven ontology aligns closely with the functional part of grammar and a commitment to it is mandatory with the use of language. This gives rise to a novel view according to which part of ontology should be considered part of universal grammar on a broadened understanding. The chapter recasts the author’s older theory of situated part structures without situations, in purely ontological terms, making use of a primitive notion of unity.

A bilateral Hilbert-style investigation of 2-intuitionistic logic

We develop a bilateral Hilbert-style calculus for 2-intuitionistic logic of Heinrich Wansing. This calculus is defined over signed formulas of two types: formulas signed with plus correspond to assertions, while formulas signed with minus correspond to rejections. In this way, the provided system is a Hilbert-style calculus, which does take rejection seriously by considering it a primitive notion on par with assertion. We show that this presentation is not trivial and provide two equivalent axiomatizations obtained by extending intuitionistic and dual intuitionistic logics, respectively. Finally, we show that 2-intuitionistic logic is in some sense definitionally equivalent to a variant of Nelson’s logic with constructible falsity.

Is incompatibilism compatible with Fregeanism?

This paper considers whether incompatibilism, the view that negation is to be explained in terms of a primitive notion of incompatibility, and Fregeanism, the view that arithmetical truths are analytic according to Frege’s definition of that term in §3 of Foundations of Arithmetic, can both be upheld simultaneously. Both views are attractive on their own right, in particular for a certain empiricist mind-set. They promise to account for two philosophical puzzling phenomena: the problem of negative truth and the problem of epistemic access to numbers. For an incompatibilist, proofs of numerical non-identities must appeal to primitive incompatibilities. I argue that no analytic primitive incompatibilities are forthcoming. Hence incompatibilists cannot be Fregeans.

John Cook Wilson

John Cook Wilson (b. 1849–d. 1915) was Wykeham Professor of Logic at the University of Oxford. He made a number of contributions in various areas of philosophy, including important work on knowledge, metaphysics, perception, logic, probability, and the interpretation of Plato and Aristotle. His most distinctive doctrines concerned knowledge. He held, first, that knowledge (or its exercises, in cases of what he called “apprehension”) is a primitive notion distinct from, and excluding, other mental states like belief or opinion. And he held, second, that what is known must obtain independently of its being known. The combination of those two doctrines formed the basis of what has come to be known as Oxford Realism, a family of views about knowledge and reality that builds on Cook Wilson’s articulation and defense of the two doctrines. Although Cook Wilson’s own work is no longer widely read, it has exerted an important influence on later work in epistemology via works in the broad Oxford Realist tradition, including works such as Prichard 1950 (cited under Knowledge) and Austin 1962, Hinton 1973, Snowdon 1980–1981 (cited under Legacy), McDowell 1982, Travis 1989, and Williamson 2000 (all cited under Legacy).

Crime as Prime

This paper develops an account of core criminal terms like ‘murder’ that parallels Williamson’s account of knowledge. It is argued that while murder requires that the murderer killed, and that they did so with a certain state of mind, murder cannot be regarded as the conjunction of these two elements (the action, the actus reus, and the associated mental element, the mens rea). Rather, murder should be seen as a primitive notion, which entails each of them. This explains some of the problems around criminal attempt. Attempted murder cannot be seen simply as involving the state of mind of murder minus success; rather, it has to be seen as a self-standing offence, that of attempting to commit the murder.

A Passage Theory of Time

This paper proposes a theory of time that takes the notion of passage as its basic primitive. Any notion of passage that is worthy of that name should make for real change across time. It is argued that real change across time in turn requires the obtaining of incompatible facts. The proposed theory will therefore be a form of fragmentalism, which makes room for the obtaining of incompatible facts by taking the world to exhibit a type of fragmented structure. The preferred form of fragmentalism and the primitive notion of passage are elucidated in some detail. It is argued that the resulting picture resolves the problem of change and meets the puzzling yet necessary conditions for the reality of passage

The Axiomatic Approach to Truth

This chapter sketches the motivations for treating truth as a primitive notion and developing axiomatic theories of truth. Then the main axiomatic systems of typed and type-free truth are surveyed.

Vague Objects

In this chapter the theory of propositional vagueness is generalized to vagueness at other types. Once propositional vagueness is supplemented with a primitive notion of objectual vagueness, it can be seen that property vagueness, adverbial vagueness, operator vagueness, and so on, may all be defined. The chapter examines some widely discussed accounts of objectual vagueness that understand objectual vagueness as standing in vague identity or mereological relations. A more general test for objectual vagueness is proposed, according to which an object is vague if it converts any precise property to a vague proposition.