Download Parts of a Whole: Distributivity as a Bridge between Aspect by Lucas Champollion PDF

By Lucas Champollion

This publication makes use of mathematical versions of language to provide an explanation for why there are particular gaps in language: issues that we'd anticipate as a way to say yet cannot. for example, why will we say I ran for 5 minutes yet now not *I ran to the shop for 5 minutes? Why is five kilos of books appropriate, yet *five kilos of booklet not appropriate? What prevents us from asserting *sixty levels of water to precise the temperature of the water in a swimming pool while sixty inches of water can show its intensity? And why do we now not say *all the ants in my kitchen are numerous? the restrictions on those structures contain strategies which are as a rule studied individually: element, plural and mass reference, size, and distributivity. during this e-book, Lucas Champollion presents a unified point of view on those domain names, connects them officially in the framework of algebraic semantics and mereology, and makes use of this connection to move insights throughout unrelated our bodies of literature and formulate a unmarried constraint that explains all the judgments above.

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Extra info for Parts of a Whole: Distributivity as a Bridge between Aspect and Measurement

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For example, Caesar’s assassination occurred on March 15, 44 bc, in the Roman senate. 4). The distinction between events and individuals is more difficult to draw. A popular assumption is that this distinction follows the lines of the 3D/4D controversy (Markosian 2014). Non-instantaneous events have temporal parts (they are 4D objects or perdurants), but all the proper parts of an individual are present at each point in time (they are 3D objects or endurants), or at least throughout the individual’s lifetime.

Despite this, each of them has been criticized at times. Moltmann (1997, 1998) emphasizes that transitivity does not match the natural language use of the part of construction. A similar point can of course be made for reflexivity. For example, (5a) and (5b) are odd, but they should be true if part of obeyed transitivity and reflexivity, respectively. (5) a. This knob is part of this door, this door is part of the doors in my house, so this knob is part of the doors in my house. b. John is part of himself.

C. ⇒ John and Bill are boys. Algebraic closure (17) extends a predicate P so that whenever it applies to a set of things individually, it also applies to their sum. 2) and is indicated by the star operator. (17) Definition: Algebraic closure (Link 1983) The algebraic closure ∗ P of a set P is defined as {x | ∃P ⊆ P[x = P ]}. ) According to this definition, x ∈ ∗ P means that x consists of one or more parts such that P holds of each of these parts. That is, either P holds of x or else there is a way to divide x into parts such that P holds of each of them.

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