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Mitchell_Porter comments on Train Philosophers with Pearl and Kahneman, not Plato and Kant - Less Wrong
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Aristotle is a more straightforward example. If you made an effort to understand Aristotle's four types of causes and ten categories of being - if you critically tried out that worldview for a while, tried to understand your own knowledge and experience in those terms, identified where it works and where it doesn't, the logic of the part that works and the problem with the part that doesn't - it would undoubtedly be instructive. Aristotle is such a systematic thinker, you might even fall in love with his system and become a neo-Aristotelian, bringing it up to date and evangelizing its relevance for today's world.
This seems to be more indicative that if one thinks hard enough about any world view it will seem to be useful and make sense. This is essentially as much of an argument to take Aristotle seriously as C. S. Lewis's claim that "I believe in Christianity as I believe that the sun has risen: not only because I see it, but because by it I see everything else." is an argument to take Christianity seriously.
This doesn't answer the question or even the type of question as phrased by Viliam. The claim isn't that you can use a systematic approach to make your own thoughts ordered in some fashion, but how to make the claims pay rent.
Beating moistened clay against cold iron has a similar effect. On what basis do you claim Aristotle's memeload is preferable, beyond it's ability to make impressions?
Aristotle's categories and causes are all very familiar concepts, so familiar that people don't reflect on them. These "memes" are already there, they're just not organised and criticised. It's like physics. You can go through life without ever sorting out your ideas about force, energy, momentum... or you can take a few steps on the road which leads, if you continue along it, to arcana like the mass of the Higgs boson. Similarly, you can go through life without wondering what it means to "have a property" or to "be a cause", or, you can take up metaphysics. Aristotle is to metaphysics what Newton is to physics, one of the early landmark thinkers whose subsequent imprint is ubiquitous.