7.8 - Yuri Balashov PHIL 2500 Lecture Notes Multiple...

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Yuri Balashov, PHIL 2500 Lecture Notes Multiple Quantifiers John hates everyone: ( x) Hjx Æ Everyone hates everyone: ( y) ( x) Hyx Someone hates everyone: ( y) ( x) Hyx Peter respects someone: ( x) Rpx Æ Everybody respects someone: ( y) ( x) Ryx Someone respects someone: ( y) ( x) Ryx In ‘( y) ( x)’ and ‘( y) ( x)’ the order of quantifiers doesn’t matter: ( y) ( x) Hyx ( x) ( y) Hyx In ‘( y) ( x)’ and ‘( y) ( x)’ the order of quantifiers matters a lot : ( y) ( x) Ryx versus ( y) ( x) Ryx Paraphrase keys: ( x) ( y): For each x and for each y … ( x) ( y): There is an x and there is a y such that … ( x) ( y): For each x there is a y such that … ( x) ( y): There is an x such that for each y … E.g.: Someone hates everyone Æ There is a y such that for each x, y hates x Æ ( y) ( x) Hyx 1
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Yuri Balashov, PHIL 2500 Lecture Notes How does the choice of UD affect symbolization?
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