无法使用JSON.stringify将错误字符串化吗？

重现问题

尝试使用Web套接字传递错误消息时遇到问题。我可以复制自己遇到的问题JSON.stringify以迎合更广泛的受众：

// node v0.10.15
> var error = new Error('simple error message');
    undefined

> error
    [Error: simple error message]

> Object.getOwnPropertyNames(error);
    [ 'stack', 'arguments', 'type', 'message' ]

> JSON.stringify(error);
    '{}'

问题是我最终得到一个空对象。

我尝试过的

浏览器

我首先尝试离开node.js并在各种浏览器中运行它。Chrome版本28给出了相同的结果，有趣的是，Firefox至少尝试了一次，但忽略了以下信息：

>>> JSON.stringify(error); // Firebug, Firefox 23
{"fileName":"debug eval code","lineNumber":1,"stack":"@debug eval code:1\n"}

替代功能

I then looked at the Error.prototype. It shows that the prototype contains methods such as toString and toSource. Knowing that functions can't be stringified, I included a replacer function when calling JSON.stringify to remove all functions, but then realized that it too had some weird behavior:

var error = new Error('simple error message');
JSON.stringify(error, function(key, value) {
    console.log(key === ''); // true (?)
    console.log(value === error); // true (?)
});

It doesn't seem to loop over the object as it normally would, and therefore I can't check if the key is a function and ignore it.

The Question

Is there any way to stringify native Error messages with JSON.stringify? If not, why does this behavior occur?

Methods of getting around this

Stick with simple string-based error messages, or create personal error objects and don't rely on the native Error object.
Pull properties: JSON.stringify({ message: error.message, stack: error.stack })

Updates

@Ray Toal在评论中建议我看一下属性描述符。现在很清楚为什么它不起作用：

var error = new Error('simple error message');
var propertyNames = Object.getOwnPropertyNames(error);
var descriptor;
for (var property, i = 0, len = propertyNames.length; i < len; ++i) {
    property = propertyNames[i];
    descriptor = Object.getOwnPropertyDescriptor(error, property);
    console.log(property, descriptor);
}

输出：

stack { get: [Function],
  set: [Function],
  enumerable: false,
  configurable: true }
arguments { value: undefined,
  writable: true,
  enumerable: false,
  configurable: true }
type { value: undefined,
  writable: true,
  enumerable: false,
  configurable: true }
message { value: 'simple error message',
  writable: true,
  enumerable: false,
  configurable: true }

关键：enumerable: false。

接受的答案提供了解决此问题的方法。