| You should not treat a science with contempt simply because its subject matter is too messy or squishy to be codified using mathematics. Physics has long reigned as the queen of sciences because of the mathematical method; but the underlying assumption there is once again that the mathematical methods somehow make it "more true" than other sciences. After all, mathematics is transcendent, right?...
So which is more true? Theory or observation? I would say the latter, which is what cognitive science depends on: it is a realm of replicable empirical experiment, and therefore definitely science, definitely not alchemy. It therefore has authority, whether or not its results can be formulated in mathemtical terms.
To put it another way, if you don't assume that mathematics is the language of a transcendent truth, then those sciences that lord it over the 'soft' sciences by using mathematical precision (physics, chemistry) have no call to do so. What is decisive in doing real science is replicable experiment, not mathematical theory.
At some point, however, natural science does smack up against philosophy--for instance, in the 'observer problem' in quantum mechanics. Nothing is proven yet about the fundamental constitution of the universe; you can continue to believe in the transcendent Platonic realm if you really want to. Just as long as you realize that it's a belief not grounded in empirical fact.
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