philosophize vs cogitate

philosophize and cogitate both are verbs.

Word	Noun	Adjective	Verb	Adverb
philosophize	No	No	Yes	No
cogitate	No	No	Yes	No

As verbs, cogitate is a hypernym of philosophize; that is, cogitate is a word with a broader meaning than philosophize:

philosophize: reason philosophically
cogitate: use or exercise the mind or one's power of reason in order to make inferences, decisions, or arrive at a solution or judgments

Other hypernyms of philosophize include cerebrate, think.

philosophize (verb)	cogitate (verb)
reason philosophically	use or exercise the mind or one's power of reason in order to make inferences, decisions, or arrive at a solution or judgments
	consider carefully and deeply; reflect upon; turn over in one's mind