In a less technical essay written in this period, 'The Reform of Mathematical Notation', he explained that despite all the efforts of Frege and Russell and Hilbert
在这个时期，他写了一篇论文，题为《数学记法的改革》，其中说到，尽管有弗雷格、罗素和希尔伯特的努力，但
... mathematics has profited very little from researches in symbolic logic.
……数学从符号逻辑的研究中获益甚少。
The chief reason for this seems to be a lack of liaison between the logician and the mathematician-in-the-street.
主要的原因似乎就是，逻辑学家和数学家之间缺少一种默契。
Symbolic logic is a very alarming mouthful for most mathematicians, and the logicians are not very much interested in making it more palatable.
对于大部分数学家而言，符号逻辑是令人惧怕的，但对于逻辑学家而言，又没兴趣把它搞得让人舒服些。
His own effort to bridge the gap began with an attempt
艾伦自己进行了一项尝试，试图填平这条裂缝：
... to put the theory of types into a form in which it can be used by the mathematician-in-the-street without having to study symbolic logic, much less use it.
……要把类型理论转为一种形式，使数学家不必学习符号逻辑就能使用。
The statement of the type principle given below was suggested by lectures of Wittgenstein, but its shortcomings should not be laid at his door.
下面对类型原理的描述是由维特根斯坦在讲座中给出的，但其中的缺陷并不是由他造成的。
The type principle is effectively taken care of in ordinary language by the fact that there are nouns as well as adjectives.
自然语言中既有名词也有谓词，因此类型原理可以有效地用自然语言来描述。
We can make the statement 'All horses are four-legged', which can be verified by examination of every horse, at any rate if there are only a finite number of them.
我们可以给出这样的命题：所有的马都有四条腿。对于有限数量的马，我们可以通过逐个检查每匹马来证明。
If however we try to use words like 'thing' or 'thing whatever' trouble begins.
但如果我们引入"东西"或"任何东西"这样的词，就会带来麻烦。
Suppose we understand 'thing' to include everything whatever, books, cats, men, women, thoughts, functions of men with cats as values, numbers, matrices, classes of classes, procedures, propositions...
假设"东西"包括所有的事物，书、猫、男人、女人、想法、数字、矩阵、过程、命题……
Under these circumstances what can we make of the statement 'All things are not prime multiples of 6'.... What do we mean by it?
在这样的情况下，我们考虑这个命题：任何东西都不是6的质因式。这个命题是什么意思？我们能从中知道什么？
Under no circumstances is the number of things to be examined finite.
"东西"的数量是无限的，是无法通过检验来证明的。