This post has a number of useful insights, but I'm not so sure about this:
Beginning with Plato and Kant (and company), as most universities do today, . . . teaches people to revere failed philosophical methods that are out of touch with 20th century breakthroughs in math and science.
As someone who is currently studying philosophy at the undergraduate level--and thus has first-hand knowledge of what it is like to start with Plato and Kant--I don't quite see where you're getting the claim that starting with ancient philosophers either (1) in fact teaches students to revere them/their methods, or (2) is at least meant to teach students to revere them/their methods. My own experience, what I've heard from fellow students, and the academic papers that we are actually assigned to read all run counter to your claim.
First, one of the primary, if not the main, purposes in starting with ancient philosophers is precisely to discuss how and where they went wrong. The professor does not just tell us whether a certain philosopher is right/wrong, but has the students critically evaluate that philosopher's claims both in papers and in discussions. Second, there are numerous academic articles written on their claims (just by virtue of the fact that they are ancient philosophers), which in turn means that those articles--and their arguments--combined with the students' own analyses provide a substantial foundation for 'critical thinking.' Third, regardless of the ancient philosophers' specific claims, the manner in which they argue for their conclusions and critically think themselves is tremendously helpful--both as a model to emulate and to not emulate--for students just starting to learn what constitutes a good argument. A charitable reading, which in particular recognizes the historical context, will show that many of the ancient philosophers do make good arguments, and value precision and rigor in so arguing; of course, many specific empirical claims are wrong, but insofar as those depend on context and not on poor argumentation they are irrelevant.
I do think that there is much wrong with philosophy, but that specific claim you made is a little shaky (and underspecified).
First, one of the primary, if not the main, purposes in starting with ancient philosophers is precisely to discuss how and where they went wrong
Isn't it history of philosophy, rather than philosophy? Learning why Aristotle's ideas on physics are wrong (e.g. "all bodies move toward their natural place") belong mostly in a History of Science course, not in a Physics course. Shouldn't it work the same for philosophy?
Part of the sequence: Rationality and Philosophy
Bertrand Russell
I've complained before that philosophy is a diseased discipline which spends far too much of its time debating definitions, ignoring relevant scientific results, and endlessly re-interpreting old dead guys who didn't know the slightest bit of 20th century science. Is that still the case?
You bet. There's some good philosophy out there, but much of it is bad enough to make CMU philosopher Clark Glymour suggest that on tight university budgets, philosophy departments could be defunded unless their work is useful to (cited by) scientists and engineers — just as his own work on causal Bayes nets is now widely used in artificial intelligence and other fields.
How did philosophy get this way? Russell's hypothesis is not too shabby. Check the syllabi of the undergraduate "intro to philosophy" classes at the world's top 5 U.S. philosophy departments — NYU, Rutgers, Princeton, Michigan Ann Arbor, and Harvard — and you'll find that they spend a lot of time with (1) old dead guys who were wrong about almost everything because they knew nothing of modern logic, probability theory, or science, and with (2) 20th century philosophers who were way too enamored with cogsci-ignorant armchair philosophy. (I say more about the reasons for philosophy's degenerate state here.)
As the CEO of a philosophy/math/compsci research institute, I think many philosophical problems are important. But the field of philosophy doesn't seem to be very good at answering them. What can we do?
Why, come up with better philosophical methods, of course!
Scientific methods have improved over time, and so can philosophical methods. Here is the first of my recommendations...
More Pearl and Kahneman, less Plato and Kant
Philosophical training should begin with the latest and greatest formal methods ("Pearl" for the probabilistic graphical models made famous in Pearl 1988), and the latest and greatest science ("Kahneman" for the science of human reasoning reviewed in Kahneman 2011). Beginning with Plato and Kant (and company), as most universities do today, both (1) filters for inexact thinkers, as Russell suggested, and (2) teaches people to have too much respect for failed philosophical methods that are out of touch with 20th century breakthroughs in math and science.
So, I recommend we teach young philosophy students:
(In other words: train philosophy students like they do at CMU, but even "more so.")
So, my own "intro to philosophy" mega-course might be guided by the following core readings:
(There are many prerequisites to these, of course. I think philosophy should be a Highly Advanced subject of study that requires lots of prior training in maths and the sciences, like string theory but hopefully more productive.)
Once students are equipped with some of the latest math and science, then let them tackle The Big Questions. I bet they'd get farther than those raised on Plato and Kant instead.
You might also let them read 20th century analytic philosophy at that point — hopefully their training will have inoculated them from picking up bad thinking habits.
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