Property Modifiers and Intensional Essentialism

Abstract

In this paper, I deal with property modifiers defined as functions that associate a given root property P with a modified property [M P]. Property modifiers typically divide into four kinds, namely intersective, subsective, privative and modal. Here I do not deal with modal modifiers like alleged, which appear to be wellnigh logically lawless, because, for instance, an alleged assassin is or is not an assassin. The goal of this paper is to logically define the three remaining kinds of modifiers together with the rule of left subsectivity that I launch as the rule of pseudo-detachment to replace the modifier M in the premise by the property M* in the conclusion, and prove that the rule of pseudodetachment is valid for all kinds of modifiers. Furthermore, it is defined in a way that avoids paradoxes like a small elephant being smaller than a large mouse.

Refining Concepts by Machine Learning

“…For details and analysis of other kinds of modifiers, see[5] 10. Hypothesis is consistent with the training data, i.e.…”

“…Since the TIL logical system has been introduced in numerous papers and two books, see, for instance [2,3,4,5,7,8,17], here we just briefly summarise the main principles of a TIL fragment that we need for the purposes of this paper. TIL is a partial, typed hyperintensional lambda calculus with procedural as opposed to settheoretical denotational semantics.…”

“…For instance, the meaning of the sentence "He is smart" is the open construction wt [ 0 Smartwt he], he v , that cannot be evaluated until an individual is assigned to the free variable he as its valuation. 5 Hence, we don't treat this open construction as a concept. Since concepts should be at least in principle executable in any state of affairs, we explicate them as closed constructions.…”

“…No, it is just an explication. As a secondary result, it also decided that the modifier 'dwarf' is privative with respect to 'planet' (see [5]); a dwarf planet like Pluto is not a planet.…”

Search for Appropriate Textual Information Sources

“…2 Having formalised thousands of sentences in the form of TIL-constructions, we can now proceed in two closely interrelated ways. 3 First, we have integrated special rules rooted in the rich semantics of natural language into a standard proof calculus of Genzen's natural deduction or general resolution in order to derive logical consequences of the results of a prior search. 4 Second, by applying machine-learning methods adjusted to natural language processing in TIL, we explicate atomic concepts in order to 'understand' and manipulate them in the way human agents would do if only this task were not beyond their capacities.…”