Routledge Dictionary of Language and Linguistics.pdf

Dictionary of language and linguistics 840can be carried over to the universal operator (cf. (b) below): Some people are late riserscorresponds to the expression Not all people are late risers(notation:). However, in contrast to the universal operator theexistential operator presupposes the existence of the designated objects in the real world( presupposition). (b) The universal operator (or universal quantifier), symbolized byor , and read as: ‘for all elements x in set S it is the case that…’. Everyday languageexample: All humans are mortal symbolized bywhere H=humans andM= mortal. The universal operator expresses a generalization and is in the truthfunctionalrelation of conjunction (cf. the mnemotechnically motivated symbolization:(small) for conjunction, (big) for the universal operator). The proposition All humansare mortal is, for a finite set S, equivalent to an enumeration of all elements, i.e. a and band c…are mortal. Through this parallel, the distributive reading of the universaloperator is confirmed: i.e. ‘for every single element it is the case that’ (in contrast to thecollective reading of all). (c) The iota operator symbolized by iota (ι), the ninth letter ofthe Greek alphabet, or by i, and read as ‘that element x for which it is the case that…’.The iota operator serves to identify a particular entity by means of a characteristic that istrue only of this entity ( definite description), e.g. to be the composer of ‘The MagicFlute’: ιx(Cx): ‘that element x of the set S that has the characteristic of being thecomposer of ‘The Magic Flute.’ (d) The lambda operator, symbolized by lambda (λ), theeleventh letter of the Greek alphabet, and read as ‘those xs for which it is the case that…’;e.g. λx(Lx): those people who are late risers. The lambda operator forms class names, i.e.complex one-place predicates, out of propositional functions (=open formulae).Referencesformal logic3 For the use of ‘operator’ in language acquisition theory, cf. pivot grammar.operator-operand relationcomplementation and modificationoppositionFundamental concept introduced by the Prague School especially for phonology: twosounds are in a relation of phonological opposition if they alone are capable ofdifferentiating two otherwise phonologically identical words with different meanings(e.g. /t/ and /d/ in tier vs deer, tank vs dank ( minimal pair). They are not necessarily