Intermediate Quantities: Logic, Linguistics, and Aristotelian Semantics
Intermediate quantifiers express logical quantities which fall between Aristotle's two quantities of categorical propositions - universal and particular. Few, many and most express the most commonly referred to intermediate quantifiers, but this book argues that an infinite number can be understood through a deeper examination of the logical nature of all intermediate quantifiers.
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The Grammar of Some English Quantifiers
Complexly Fractionated Quantifiers
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affirmative algebraic method Almost-all and/or any-rule apply argument forms Aristotelian Aristotle's square basic Carnes categorical propositions Chapter consider containing contradiction contradictory counter-example debt democrats are liberals denial distribution English entails enthymeme exactly example existential import existential quantifier extended Finch proposition follows fractional quantifiers G who loves grammatical higher-quantity i-quantity inference intermediate quantifiers intermediate syllogisms interpretation intuitions invalid least linguistic logically equivalent McCawley McCawley's means middle term minor premise Most-f natural language negative not-P notational pairs Peterson 1985a poets politicians are liars polysyllogism presupposition produce proof proportional propose proposition expressed quantification theory reason reference class relations replace represent result rule of quantity Section semantic sentence Similarly simply singers square of opposition statements structure sub-class subject term syllogistic forms syllogistic system synonymy theory TP diagram traditional rules traditional syllogism true universal quantifier valid forms valid syllogism valid traditional Venn Diagrams violated XYZ-N