C-2 There is a courthouse in every town.
述詞以符號取代:
“Cx”: “x is a courthouse”;
“Tx”: “x is a town”;
“Ixy”: “x is in y”
| There is a courthouse in every town 每個城鎮都有一個法院 |
處理主詞部份 加入代名詞: | There is at least one thing such that it is a courthouse and it is in every town 至少有一事物,它是法院,且它座立於每個城鎮裡 |
代名詞轉變元: | There is at least one thing x such that x is a courthouse and x is in every town 至少有一事物x,x是法院,且x座立於每個城鎮裡 |
量詞符號化: | (∃x)(x is a courthouse and x is in every town) (∃x)(x是法院,且x座立於每個城鎮裡) |
處理受詞部份 加入代名詞: | (∃x)(x is a courthouse and each thing such that if it is a town then x is in it) (∃x)(x是法院,且無論事物為何,若它是城鎮,則x座落於它之內) |
代名詞轉變元: | (∃x)(x is a courthouse and each thing y such that if y is a town then x is in y) (∃x)(x是法院,且y為何事物,若y是城鎮,則x座落於y之內) |
量詞符號化: | (∃x)[x is a courthouse and (y)( if y is a town then x is in y)] (∃x)[x是法院,且(y)(若y是城鎮,則x座落於y之內)] |
述詞符號化: | (∃x)[Cx&(y)(Ty⊃Ixy)] |
D-2 There is a woman to whom everyone listens. Therefore, there is a woman who listens to herself.
中譯:有一個每個人都會服從於她的女人。
因此,有一個會服從於自己的女人
論域設置在「人」
述詞以符號取代:“Wx”:”x is a woman”; “Lxy”:”x listens to y”
先處理前提的部份
| There is a woman to whom everyone listens 有一個每個人都會服從於她的女人 |
處理主詞部份 加入代名詞: | There is at least a person such that she is a woman and everyone listens to her 至少有一人,她是女人且每個人都會服從於她 |
代名詞轉變元: | There is at least a person x such that x is a woman and everyone listens to x 至少有一人x,x是女人且每個人都會服從於x |
量詞符號化: | (∃x)(x is a woman and everyone listens to x) (∃x)(x是女人且每個人都會服從於x) |
處理受詞部份 加入代名詞: | (∃x)(x is a woman and each one such that he/she listens to x) (∃x)(x是女人且無論是誰,他/她會服從於x) |
代名詞轉變元: | (∃x)(x is a woman and each one y such that y listens to x) (∃x)(x是女人且無論y是誰,y服從於x) |
量詞符號化: | (∃x)[x is a woman and (y)(y listens to x)] (∃x)[x是女人且(y)(y服從於x)] |
述詞符號化: | (∃x)(Wx&(y)Lyx) |
| there is a woman who listens to herself 有一個會服從於自己的女人 |
處理主詞部份 加入代名詞: | There is at least a person such that she is a woman and she listens to herself 至少有一人,她是女人且她會服從於她自己 |
代名詞轉變元: | There is at least a person x such that x is a woman and x listens to x 至少有一人x,x是女人且x會服從於x |
量詞符號化: | (∃x)(x is a woman and x listens to x) (∃x)(x是女人且x會服從於x) |
述詞符號化: | (∃x)(Wx&Lxx) |
因此,論證述詞符號化後變成:(∃x)(Wx&(y)Lyx) / ∴