Is this 'neither' a determiner?

Let's consider the similar determiner "none of", that we would use with more than two items*:

However, this mirror will give us none of knowledge, truth or wisdom.

That seems pretty valid, no?

Let's also consider if the two qualities had been mentioned first, and use neither in its determiner sense:

We seek knowledge and truth. However, this mirror will give us neither prize.

Again, valid.

So, it seems by analogy that the first sentence is indeed using neither in its determiner sense. It's amusing that the meaning is that the mirror will give neither knowledge nor truth - the same meaning as the second sentence.

I would advise against the construction though, if only for the simple reason that it might lead some readers to ask questions like this. Therefore I'd favour the second sentence in its place.

*Opinions differ as to whether neither is allowed with more than two items, but that's not really relevant here.

Traditionally a determiner is needed before a common count noun to make a grammatical noun phrase, and you can have only one determiner. By this traditional definition neither (in neither...nor) will not fit, because you can have a well-formed noun phrase knowledge, which lacks a determiner (it is a mass noun), and you can have neither before another determiner, e.g., neither the dog...

Neither might instead be analyzed as part of a discontinuous coordinator, neither...nor, or as itself a coordinator which requires a negative complement nor. The neither...or version is not prescribed, but seems to mean the same thing, and the use of or rather than nor shouldn't affect the analysis.

However, when neither is not used as part of a coordinating constructions, it can be used as a determiner with quantifying function, e.g.,

Neither dog came.