We often use language for no other reason than simply to express our willingness to be sociable.
【翻译】我们经常使用语言仅仅是为了表达我们想要交际的意愿。

1.  other than：表示“从...中排除”，意为“除此之外”。仔细体会其含义：

Everyone other than John can help her. （唯独约翰不能帮她）

Nobody other than John can help her. （只有约翰能帮她）

2.  表示“比较意义”的 than，很少单独使用，一般前面都有比较级。除此之外，than 有时可以跟表示“排除”意义的词语连用，这时前面无需使用比较级。也就是说，没有比较级的时候，多用于different, else, other, no other, none other, otherwise, anywhere，rather than，would rather...than 等之后，表示“排除”意义。例如：

I have a different car than this one.

除了这辆车外，我还有一辆不同的车。

She has no other friend than Jane.

除了简以外，她没有别的朋友。

It was none other than the professor.

不是别人，正是教授本人。

The student is otherwise than his teacher thought.

那个学生并不是老师想像的那种人。

You won't find such freedom anywhere than in our country.

这种自由除我们国家以外其他地方找不到。

You are buying direct, rather than through an agent.  

你这是直接购买，而不是通过代理人。

Kids would rather play than study 

孩子们宁愿玩也不愿学习。

3.  之所以接不定式，是因为它是 reason 的定语。不要认为 than 是介词。现在把no other than 去掉：

We often use language for the reason to express our willingness to be sociable.

reason 后接不定式是常见现象。不定式作定语，表示“动状关系”。等于：

We often use language for the reason for which to express our willingness to be sociable.

We often use language for the reason (why/that/for which) we express our willingness to be sociable.

4. reason to do sth. 的 更多例句：

I have no reason to quarrel with him.
我没有跟他口角的理由。
《汉英大词典》
We have every reason to believe that the news is true.
我们有充分的理由相信这消息是可靠的。
《汉英大词典》
I still have no reason to doubt his word.
我还是没有理由怀疑他的话。
《柯林斯高阶英汉双解学习词典》
I don't have any particular reason to distrust them.
我没有任何特别的理由怀疑他们。
《柯林斯高阶英汉双解学习词典》
I had no reason to doubt him.
我没有理由不相信他。
《牛津词典》
There is no compelling reason to believe him.
没有令人信服的理由让人相信他。
《牛津词典》