Unlike art, philosophy does make truth claims.
Unlike science, philosophy’s truth claims are not judged by experiments. Instead, they are assessed on their overall persuasiveness (see my essay for more on that). On their ability to stick in the mind, to stimulate, to breed related claims.
Philosophies are mental constructs (I don’t like the word “memes”) that undergo evolution (there is inheritance, mutation, and selection) with the aim to best satisfy our minds’ craving to know how things really are. For a variety of reasons, science is unable to fully satisfy these cravings, so philosophy continues to exist.
But minds themselves evolve, so philosophy has to adapt to a quickly shifting landscape. It is therefor quite understandable that many philosophers borrow from science its approach to proving things, simply because science is so prominent nowadays. Sometimes, it helps their philosophies be more persuasive, but sometimes it backfires: a “rigorous” math-like proof applied to claims that are obviously unverifiable to begin with may sound off-putting — a travesty. Not everyone likes analytical philosophy, and I think this is one of the reasons why.