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For the classical acquaintance theorist, that question, in turn, reduces to the question of how we can acquire knowledge through inference.
This claim plays a crucial role in her defense of the view that we can acquire knowledge of mathematical entities by perceiving sets.
The soul is not a supersensible object of whose faculties and powers we can acquire knowledge but an idea that makes our practice of ascribing experiences to ourselves intelligible.
This argument appears even more forceful for those who believe that the only reason that we can acquire knowledge of microscopic events and microscopic laws, is precisely the fact that microscopic events, in certain situations, have effects upon observable events.
In this way, by delineating the concepts that are a priori necessary for the cognition of objects, we can acquire knowledge of categories governing any possible object of cognition, and so acquire a sort of descriptive set of ontological categories, though these must be understood explicitly as categories of objects of possible cognition, not of the thing in itself.
This suggestion, alas, encounters the same difficulty as the externalist approach to testimony: it does not seem we can acquire knowledge from sources the reliability of which is utterly unknown to us.[52] According to skeptics, the limits of what you know are narrower than you would like to think.
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Then they can acquire knowledge of those parts simply by proving theorems from the given axioms.
But however it is understood, skepticism represents a challenge to the claim that human beings possess or can acquire knowledge.
Just as innovators commonly understand the fundamentals of a technology better than subsequent users, so users can acquire knowledge that would never have occurred to the innovators.
Another approach, developed by Resnik and Shapiro, is to claim that humans can acquire knowledge of mathematical structures by means of the faculty of pattern recognition.
A learning autonomous robot, one that can acquire knowledge through interaction with its environment and then adapt its behavior, greatly simplifies the designer's work.
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