What did Isaac Newton mean by this following quote of his? 
''It is inconceivable that inanimate brute matter should, without the mediation of something else which is not material, operate upon and affect other matter without mutual contact, as it must be, if gravitation in the sense of Epicurus, be essential and inherent in it. And this is one reason why I desired you would not ascribe innate gravity to me. That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it. Gravity must be caused by an agent acting constantly according to certain laws; but whether this agent be material or immaterial, I have left open to the consideration of my readers.  ''

Try to explain the quote to me in the simplest terms possible.
 A: Consider the image below which dipicts a "gravitational field" being produced by a massive object.  Other objects in turn respond to the "gravitational field" that is present in their local vicinity.  
That is, the moon in the image below isn't responding to the Earth directly through a mysterious action at a distance, but rather the moon is responding to the nearby gravitational field produced by the Earth. 
Newton is stating he belives that gravity must work locally through something like the gravitational field dipicted below, rather than being a true action at a distance.

A: You have to choose: either the gravitational field is a mathematical construct used only in calculations, or it is a physical object which exists in the space between the Earth and the Moon. If it is a physical object then that space is not a vacuum. It has some particles or waves in it, so it is not nothingness.
If it is just a mathematical description then we can postulate a true vacuum in that space, but in that case the force is acting at a distance with nothing to mediate it.
Trying to have it both ways is a contradiction and therefore wrong.
