meaning of a difficult sentence

I came across a sentence, which I am utterly incapable of understanding. I can , at the first place , not understand meaning of verb " dispatch " here . Why has the writer used this verb with 'as'? Has the writer used " had a brisk way of dispatching " as an idiom ? My reason for this is that we have an idiom " have a way of doing sth ".

Whether the world is made of matter, spirit or green cheese is not a question over which Marx lost much sleep. He was disdainful of such large metaphysical abstractions, and had a brisk way of dispatching them as idly speculative. As one of the most formidable minds of modernity, Marx was notably allergic to fancy ideas.

The text is from a book by Terry Egelton

Solution 1:

Whether the world is made of matter, spirit or green cheese is not a question over which Marx lost much sleep.

The assertion being that as Marx did not lose much sleep, the above question bothered him very little if at all...

He was disdainful of such large metaphysical abstractions...

[Metaphysical : Based on abstract reasoning.- OLD]

He had no respect for thinking about these abstract and for the most part unanswerable type questions.

and had a brisk way of dispatching them as idly speculative.

[Dispatch : 1. Send off to a destination or for a purpose. - OLD]

Dispatching is being used figuratively here, he would send the questions away as not being worth entertaining, as such questions were lazy and with no definitive answers (idle speculation).

As one of the most formidable minds of modernity, Marx was notably allergic to fancy ideas.

The last part of the passage conveys an opinion of the author that most modern great minds do not like (are allergic to) such fancy ideas (of the abstract, metaphysical nature) previously suggested.

Solution 2:

Standard idiom: having a [particular] way of doing something

The use of "dispatch ... as" is unusual; I would suggest the writer has "borrowed" it from the synonymous and more usual construction "dismiss ... as".