A neuron's signal, he realized, is a proposition, and neurons seemed to work like logic gates, taking in multiple inputs and producing a single output.
In this case"necessary" does not apply to a proposition but to a thing, and it means infinite, eternal, everlasting, self-caused, self existent.
但是最后一个命题就等价于p自己(而且这种等价性可以在系统内部证明),从而p就可以在系统内证明。
But this last statement is equivalent to p itself(and this equivalence can be proved in the system), so p can be proved in the system.
他发现神经元的信号就是一个命题,而神经元的工作类似于逻辑门,它接受多个输入然后产生单一的输出。
A neuron's signal, he realized, is a proposition, and neurons seemed to work like logic gates, taking in multiple inputs and producing a single output.
上面所引两段话的思想内容可以归结为一个命题:矛盾=背理,因而它在现实世界中是不可能出现的。
The thought-content of the two passages cited can be summed up in the statement that contradiction=absurdity, and therefore cannot occur in the real world.
一个命题肯定是正确的,只要父母们与孩子一起成长,尽管我们不是天才,但我们完全可以成为天才的父母。
A proposition is certainly correct, as long as parents and children grow together, although we are not genius, but we can become a genius parents.
Frege used these symbols in the Begriffsschrift in the unified form├─ for declaring that a proposition is(tautologically) true, not simply speaking about that.
由于一个命题是对它的否定的否定,因此,必定也存在着“一个对象能够既是红色的和绿色的”这样一个命题。
Since a proposition is the negation of its negation, there must also exist the proposition'An object can be red and green'.
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