我们只说剑桥语法作者的观点。这个句子是在比较分句省略嵌入分句这一节的里的例句，嵌入分句作主语为单数，所以appears为单数形式，提示这里省略的主语是嵌入分句。如果我们去掉s，than后接appear。我们需要判断appear是复数谓语动词，还是不带to的不定式。这个句子的前面没有提供可以省略不定式的to的词项（如情态动词，rather than，other than或前面有to do不定式）。所以，我们可以判断这个句子如果than后接appear，appear应该就是复数谓语动词。也就是说，这个句子的than比较分句省略了主语，而保留了谓语动词。而作者在1112页讲述比较分句省略主语这个问题时，明确指出如下：

Restrictions on omission of subject

In clauses where the verb is retained, the subject can be omitted only when it is the counterpart to the comparative phrase or is understood as an embedded clause, as in (d) above:

[22] i More people came than [ were invited ].              [counterpart to comparative phrase]

ii He spent longer on it than [ seemed necessary].       [embedded clause]

即在比较分句保留谓语动词的情况下，只有在主语为比较对应项或主语被理解为是一个嵌入分句时，主语才可以省略。

好题老师提问的这个句子，than分句复数谓语动词对应的复数名词为主句的主语the difficulties. 而the difficulties既不是比较对应项，也不是嵌入分句，明显与作者提出的比较分句省略主语而保留谓语动词的“规则”是相悖的。所以，作者会认为本句用appear作谓语动词是不符合语法规范的。

我相信好题老师会从外刊找到一些类似结构用复数appear的句子。我认为这些句子在一定程度上可以认为是idiomatic，但不能认为是grammatical。即也许符合惯用，但不符合语法。

谢谢曹老师的参与。我和大家分享一下我的看法。

首先，我认为对于一些基本用法，无论哪本语法书都是相通的。但因为《剑桥语法》是用英语写的，可能使非母语读者出现理解的偏差。我谈一下我对这个问题的理解。

1. 该书这个句子The difficulties are even greater than appears at first sight. 作者把它归为嵌入分句一节，为什么？

因为主句主语difficulties是复数，但appears 却用了单数，因此它只能是嵌入分句，因为只能补全还原为than it appears at first sight that the difficulties are great. 但是如果appear 变复数，那么就不再是嵌入分句，补全还原为than the difficulties appear great at first sight. 这属于比较对应项difficulties为主语的省略。英语中than appear 用复数的用法是很普遍的。

国外出版物类似例句很多，我暂提供几个结构完全一样的： 1.The shifts required were much larger than appear at first sight. 2. It has more enemies than appear at first sight. 3. The rules are far less burdensome than appear at first sight. 4.The differences in level from the Forest Service projections are thus greater than appear at first sight.
    根据谷歌图书语料库统计，than appears 和than appear用法的出现频率统计，大约为2：1. 这个比率，如果认为than appear (复数）是不合乎语法的用法是根本站不住脚的。请看三个例句：

More instances have been brought to clear the one, or elucidate the other, than appear at first sight to have been necessary.

Brian Vickers, William Shakespeare: The Critical Heritage, 1995, p. 553

我们从书名可以判断，作者应该是研究莎士比亚的专家。肯定是educated speaker.

That Fisher's poetry is full of forms does not imply that there are more things in its heaven and earth than appear at first sight. 

Angela Leiton: On Form: Poetry, Aestheticism, and the Legacy of a Word, 2008年版 p.236

这本书是关于诗歌、唯美与文字遗产的，作者也肯定是受过良好教育的学者。

Second, there could be more differences than appear on the surface (such as lexical and syntactic inequality across languages, and the difficulty of translation).

Marion Grein, ‎Dialogue and Culture， 2007，p 253

这本书应该是关于语言和文化的。

图书预料库有很多类似例句，我们可以肯定用appear 也是正确的，只是句子结构发生了变化而已。

2. 我对《剑桥语法》这段话的理解：

Restrictions on omission of subject

In clauses where the verb is retained, the subject can be omitted only when it is the counterpart to the comparative phrase or is understood as an embedded clause, as in (d) above:

[22] i More people came than [ were invited ].              [counterpart to comparative phrase]

我翻译一下：主语省略的限制条件：在保留动词的从句中，只有当主语是比较从句的比较项或被理解为嵌入分句时主语可以省略。

注意作者的意思，作者提到两个前提，一个是主语为比较对应项，一个是当被理解为嵌入分句时。 我上面讲了，问题句因为主语是复数difficulties，appear 为单数，必须理解为嵌入分句it appears that. 但如果appear用复数就不能理解为嵌入分句了, 那属于比较对应项的省略。

He spent longer on it than [ seemed necessary].       [embedded clause]　作者把than seemed necessary 归为嵌入分句，也是因为这里只能理解为it seemed necessary that... 无法有别的变化，如果理解为than后省略he, 也不符合逻辑和表达习惯。

回到问题句：The difficulties are even greater than appears at first sight.  如果appear 改为复数，就是比较从句省略主语：than they (the difficulties) appear great at first sight. 如果appear是单数，即理解为嵌入分句。

以上是我的理解，欢迎大家指正和讨论！