The term "philistine" applies to culture in general, which is not quite "intellectuality", as this latter substantive "intersects" with it.
(SOED) culture […] 6. A particular form, stage, or type of intellectual development or civilization in a society.
(OED) philistine adj. […] 2. Uneducated, unenlightened; indifferent or hostile to culture; aesthetically unsophisticated. (user LPH's bold and italic)
There is a specific term to name believers in the negativeness of intellectualism. (Wikipedia)
anti-intellectualism Hofstadter described anti-intellectualism as “resentment of the life of the mind, and those who are considered to represent it; and a disposition to constantly minimize the value of that life.
There is one problem with this term: you can't quite call those thinkers anti-intellectuals, would they so much as little refute intellectuality in a rational manner; strictly speaking, anti-intellectuals are intellectuals and the term is inherently a paradox: you do not criticize what you do not know.
Let's look now at the term "aintellectual", a term of recent origin that would come to mind naturally, but that few dictionaries include.
(Urban dictionary) absence or complete lack of intelligence
♦ The only word we could come up with to express the extent of the stupidity my niece's stepmother.
"j is so ridiculously dumb, she is aintellectual!"
It seems that there is only a gradation of disinterest in intellectual matters, and in the extreme this comes down merely to complete dumbness. Apparently there is no single word counterpart of "philistine", not even an in-between, possibly because one of the important aspects of the essence of being man is intellect; is hardly a human being a human being without intellect, if that is conceivable.