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RobbBB comments on Intuitions Aren't Shared That Way - Less Wrong
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The point is very well-made. But it's not a philosophy-specific one. Mathematicians with a preferred ontology or axiomatization, theoretical physicists with a preferred nonstandard model or QM interpretation, also have to face up to the fact that neither intuitiveness nor counter-intuitiveness is a credible guide to truth — even in cases where there is no positive argument contesting the intuition. Some account is needed for why we should expect intuitions in the case in question to pick out truths.
What else have we got (one)? We might accept QM's counterintuitive ideas about locality and causality on the basis of trust in empiricism. But where is the nonintutive basis for empiricism? Epistemology grounds out in intuitions as much as anything else. So when we accpet the counterintuitive content of QM, we are sacrificing one intuition to another.
What else have we got (two)? In mathematics, a theorem is considerred true if it is an axiom or derivable from an axiom. What third thing is there that would make an axiom true? It is not that intutitve axioms have some guarantee to fulfil some external criterion of truth (to correspond to affairs in Plato's Heaven perhaps) it is that there is no external criterion.
Epistemology and ethics, construed as systems or normative rules, must certainly hit rock bottom at some point -- in values, in concerns, in interests. But that's a foundational point, and I'm not sure we should retain the logic of criterionless foundational decisions once we're done with the founding.
I'm not sure 'assuming empiricism' is the foundation in question, though. Depending on what you mean by 'empiricism,' it might go at least a level or two deeper.
My point was that if you're going to criticize most philosophers for abusing intuitiveness, you should criticize most mathematicians for abusing it to an even greater degree. Mathematical realists, and mathematical platonists in particular -- a majority of mathematicians, as far as I'm aware -- are of the view that some mathematical structures we could build are right and others are just wrong, for one reason or another. What worries me isn't that the arguments for realism and platonism are weak; what worries me is that most mathematicians don't seem to even feel that they need to provide an argument to take this view seriously, as though the very act of noticing the intuition gave them reason to update in favor of realism.
I don't see what you're gettig at all. If there are ciiteria for being "foundational", how could they not be even more foundational? If there aren;t, how could foundations not be criterionless?
Then what would it be? Are you sayign empricisim has intutivie or apriori sub-foundations?
Personally, I wasn;t criticising phis. for abusing intutiveness.
I'm not saying there are criteria for making foundational decisions. (Though there may be causes. A cause differs from a criterion in that not all causes give me reasons to decide as I do.) I'm saying that we should be very wary about letting the arbitrariness of criterionless choices infect criterionful ones.
As I said, it depends on what you mean by 'empiricism.' So, what do you mean by it?
Do we have a choice? How to we protect any choice when it ultimately has an aribtrary foundation?
I don't see why: the problem seems to affect eveything.
"Empiricism is a theory of knowledge that asserts that knowledge comes only or primarily from sensory experience."
By choosing to treat non-foundational issues in a single unified way that is distinct from how we treat foundational issues, we keep our thought more ordered and localize whatever problems there might be to our axioms.
I see no need to assume such a doctrine. If it turned out to be false (say, if we were programmed from birth with many innate truths), we could still do science. It's also worth noting that the logically knowable truths are far greater in number than the empirically knowable ones.
That just says they are different. They have to be, because we can pin non-foundational issues to foundationail issues, but we can't pin foundational issues to foundational issues. However a difference is not the difference* -- the differnce tha would show that any arbitrariness of foundations affects what is founded on them
I suppose there could be a weak empiricism that just fills out the gaps in apriopri reasoning. However, it is doubtful that apriori reasoning can supply truth at all. See below.
So long as you are willing to accept valid derivations from arbitrary premises as actually true. One can derive all sorts of things from the cheesiness of the Moon..
Can you explain what makes you conclude this inequality? It isn't obvious to me.
Sure. p → p is a logical truth. p → (p → p) is also a logical truth. So too p → (p → (p → p)). You can iterate this procedure to build arbitrarily long assertions. Likewise for mathematical equations. I don't think that what we ordinarily mean by 'empirical facts' can be generated so easily. The empirical facts are a vanishingly small subset of the things we can know.
If that sort of thing is acceptable, can't I also generate new empirical truths by for example just concatenating existing truths together? Say "The moon orbits the Earth, and George Washington was the first President"? That seems to be very close to what you are doing. Worse, I can use counterfactuals in a similar fashion, so "If homeopathy works then the moon is made out of green cheese" becomes an empirical truth?
There's an argument here that these statements I'm using are mixes of empirical and logical truth, and if one buys into that then it seems like you are correct.
They're all just valid. You haven't got to sound yet.
OK, I see what you mean better now. For one single empirical fact (sound premise) on can generate an infinite number of sound logical sentences, which basically say the same thing in ever more complicated ways. If p is true, (p & T) is true as are (p & T &T..). Many people have the instict that these are trivial "cambridge" truths and don;t add up to konwing an extra countable infinity of facts every time you learn one empirical fact.
It would be intersting to think about how that pans out in terns of the JTB theory.
I think a semantic check is in order. Intuition can be defined as an immediate cognition of a thought that is not inferred by a previous cognition of the same thought. This definition allows for prior learning to impact intuition. Trained mathematicians will make intuitive inferences based on their training, these can be called breakthroughs when they are correct. It would be highly improbable for an untrained person to have the same intuition or accurate intuitive thoughts about advanced math.
Intuition can also be defined as untaught, non-inferential, pure knowledge. This would seem to invalidate the example above since the mathematician had a cognition that relied on inferences from prior teachings. Arriving at an agreement on which definition this thread is using will help clarify comments.
The former definition sounds more promising. "Untaught" and "pure" are scary qualifiers to ask philosophers to be committed to when they probe themselves (or others) with thought experiments. Philosophical intuitions might be less rigorous or systematic than mathematical ones, but it's not as though they come free of cultural trappings or environmental influences.