By Massimiliano Carrara, Alexandra Arapinis, Friederike Moltmann
Unity and Plurality provides novel methods of wondering plurality whereas casting new gentle at the interconnections one of the logical, philosophical, and linguistic points of plurals. the quantity brings jointly new paintings at the good judgment and ontology of plurality and at the semantics of plurals in ordinary language. Plural reference, the view that yes plurals resembling 'the scholars' seek advice from a number of entities right now (the person students), is an procedure favoured via logicians and philosophers, who take sentences with plurals ('the scholars gathered') to not be dedicated to entities past participants, entities resembling sessions, sums, or units. against this, linguistic semantics has been ruled via a singularist method of plurals, taking the semantic price of a distinct plural akin to 'the scholars' to be a mereological sum or set. in addition, semantics has been ruled by way of a specific ontological view of plurality, that of extensional mereology. This quantity goals to construct a bridge among the 2 traditions and to teach the fruitfulness of nonstandard mereological methods. A staff of major specialists investigates new views that come up from plural common sense and non-standard mereology and discover novel functions to normal language phenomena.
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Additional resources for Unity and Plurality: Logic, Philosophy, and Linguistics
My argument above for the plausibility of the law made extensive use of modal terminology. For instance, I claimed that any plurality can form a set, and that any concept can be used to define a corresponding extension. I believe progress can be made by taking this modal terminology seriously. Let’s therefore introduce the modal operators and ◊. ” I will elaborate on this interpretation in the next section. As formulated above, the criteria of existence assert an outright collapse of pluralities and concepts to, respectively, sets and extensions.
Since ≤ is reflexive and transitive, the modal logic S4 will be sound with respect of our intended system of possible worlds. 2. Since the domains of our worlds always increase along the accessibility relation ≤, there will be no need for any free logic or existence predicate once quantification is introduced. 2. This system will be our background modal logic in what follows. All the modal assumptions that are used in the formal arguments described below are available in this system. 6 Two sorts of generality Two different kinds of generalization are available in the modal framework with which we are concerned.
What does it mean that the largeness of Simmias overcomes the shortness of Socrates? How can largeness be compared to shortness? I suggest that Plato sees opposites on the model of the hot and the cold—they are comparable because they can compromise each other: when one adds hot and cold water together one gets lukewarm water. This means that the difference between the opposites is reduced to a difference of value and strength, rather than a difference of quality. Generalizing, the difference between opposites is a difference of the quantity in a qualitative common scale between them, which allows for opposites to be compared and to overpower one another.