Existential Fallacy

A standard form categorical syllogism with two universalpremises has a particular conclusion. The idea is thatsome universal properties need not be instantiated. Itmay be true that 'all trespassers will be shot' even ifthere are no trespassers. It may be true that 'all brakelesstrains are dangerous' even though there are no brakelesstrains. That is the point of this fallacy.

(i) All mice are animals, and all animals are dangerous, so some mice are dangerous.
(ii) No honest people steal, and all honest people pay taxes, so some homest people pay taxes.

Assume that the premises are true, but that there are no instances of the category described. For example, in (i) above, assume there are no mice, and in (ii) above, assume there are no honest people. This shows that the conclusion is false.

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A standard form categorical syllogism with two universalpremises has a particular conclusion. The idea is thatsome universal properties need not be instantiated. Itmay be true that 'all trespassers will be shot' even ifthere are no trespassers. It may be true that 'all brakelesstrains are dangerous' even though there are no brakelesstrains. That is the point of this fallacy. （一个标准的三断论形式，有两个宽泛的前提和一个具体的结论。这些宽泛的前提不需要实例化《即不需要考虑其针对到某个具体对象时，该对象是否存在》。后面就不翻译了，都能看懂）

Examples:

(i) All mice are animals, and all animals are dangerous, so some mice are dangerous.
(ii) No honest people steal, and all honest people pay taxes, so some homest people pay taxes.

Proof:

Assume that the premises are true, but that there are no instances of the category described. For example, in (i) above, assume there are no mice, and in (ii) above, assume there are no honest people. This shows that the conclusion is false.

据个简单的例子：所有的恐龙都是动物，所有的动物都有危险性，所以现在有的恐龙有危险性；可事实是恐龙都不存在了。

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