I think that the converse of philosophy is not to loathe/hate/be apathetic of philosophy. If we assume that the etymology of the word philosophy is "love of wisdom," then its converse would be "hatefulness towards wisdom" or "loathing wisdom." In other words, it's the wisdom that is "not loved," rather than philosophy that is "not loved."
With that in mind, at first I would have suggested ked- as an ancient Greek word for hate based on its etymological relation to the English word "hate" (with a meaning of care, trouble, sorrow), as seen in the following sources:
-hate (v.) Old English hatian "regard with extreme ill-will, have a passionate aversion to, treat as an enemy," from Proto-Germanic *haton (cognates: Old Saxon haton, Old Norse hata, German hassen, Gothic hatan "to hate"), from PIE root *kad- "sorrow, hatred" (cognates: Avestan sadra- "grief, sorrow, calamity," Greek kedos "care, trouble, sorrow," Welsh cas "pain, anger"). (Source)
The etymology of the english term hate is initially traced back to the greek term kedos. The –os is a greek linguistic device that is added to many of the root words in that language. The root of kedos is thus ked. (Source)
Thus, I would expect a word like:
It's pronounceable, but I've never heard it used. Ever. And, as pointed out in the comments, despite the etymological relationship, kedos is not a true translation of hate.
But there is hope yet. The opposite of phil- is generally recognized as phob- (even though in my mind, phob- is more commonly used to indicate fear). (Source) So that would give us:
This appears to be a recent construction, but appears to be the intended meaning. (Source)
The fear of abstract knowledge or philosophical thinking; anti-philosophy.
Another direction is to use the prefix miso-, which is listed as an opposite of philo- using this non-authoritative source. But it does appear to have the desired meaning, based on its meaning of hatred as listed here.
Forming compound words having the sense of "hatred of", "dislike of", "contempt for". (Source)
This yields the word:
A hatred of wisdom or knowledge. (Source)
Interestingly, checking out the ngram (here), misosophy is used extremely rarely, but phobosophy not even listed at all.
As an aside, I have read that the classical opposite of philosophy is sophistry, defined as:
- Plausible but fallacious argumentation.
- A plausible but misleading or fallacious argument. (Source)
But this does NOT appear to be the word that the is being asked for.