Essence and Definition by Abstraction

We may define words. We may also define the things for which words stand. Definitions of words may be explicit or implicit, and may seek to report pre-existing synonymies, but they may instead be wholly or partly stipulative. Definition by abstraction seeks to define a term-forming operator by fixing the truth-conditions of identity-statements featuring terms formed by means of that operator. Such definitions are a species of implicit definition. They are typically at least partly stipulative. Definitions of things (real definitions) are typically conceived as statements about the essence of their definienda, and so not stipulative. There thus appears to be a clash between taking Hume's principle as an implicit, at least partly stipulative definition of the number operator and as a real definition of cardinal numbers. This chapter argues that this apparent tension can be resolved, and that resolving it shows how some modal knowledge can be a priori.

Implicit Definition of Flow Patterns in Street Canyons—Recirculation Zone—Using Exploratory Quantitative and Qualitative Methods

Air pollution is a major health hazard for the population that increasingly lives in cities. Street-scale Air Quality Models (AQMs) are a cheap and efficient way to study air pollution and possibly provide solutions. Having to include all the complex phenomena of wind flow between buildings, AQMs employ several parameterisations, one of which is the recirculation zone. Goal of this study is to derive an implicit or explicit definition for the recirculation zone from the flow in street canyons using computational fluid dynamics (CFD). Therefore, a CFD-Large Eddy Simulation model was employed to investigate street canyons with height to width ratio from 1 to 0.20 under perpendicular wind direction. The developed dataset was analyzed with traditional methods (vortex visualization criteria and pollutant dispersion fields), as well as clustering methods (machine learning). Combining the above analyses, it was possible to extract qualitative features that agree well with literature but most importantly to develop quantitative expressions that describe their topology. The extracted features’ topology depends strongly on the street canyon dimensions and not surprisingly is independent of the wind velocity. The developed expressions describe areas with common flow characteristics inside the canyon and thus they can be characterised as an implicit definition for the recirculation zone. Furthermore, the presented methodology can be further applied to cover more parameters such us oblique wind direction and heated-facades and more methods for data analysis.

Conceivability and Possibility

This article examines some philosophical questions about knowledge of modality, including how we determine whether a proposition is necessary or contingent and what procedures to use for recognizing possibility. It maintains that virtually anything is conceivable, and that conceivability is therefore incapable of providing a reliable test for possibility. Whether a conceivable state of affairs is genuinely possible depends on whether it is compatible with the class of necessary truths. But this means that we must have some independent way of recognizing necessity. The article explains that independent access to necessity in terms of the hypothesis that various modal truths constitute an implicit definition of necessity. To a large extent, our knowledge of necessity derives from our grasp of this definition. The article also criticizes Cartesian modal arguments for dualism, and raises an objection to the view that metaphysical necessity can be reductively explained in terms of subjunctive conditionals.