白马非马

韓非子是战国法家, 荀子的高徒, 秦始皇宰相李斯的同学。他说”白马非马”, 即白马不是马, 可以用集合論(Set Theory) 证明:

Let 马 = H = {w, b, r, y …}
w : 白马
b : 黑马
r :红马
y:黄马

Let 白马 = W = {w}

To prove:
H = W
We must prove:
(1)H ⊂ W and
(2)H ⊃ W

From definition we know:
(2) fulfilled because
w \in H \supset W
But, (1) not true since
H \nsubseteq W

\implies H \neq W

白马≠马
白马非马
[QED]

其他例子:
木魚非鱼

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