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Then they can acquire knowledge of those parts simply by proving theorems from the given axioms.
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.
Platonists who accept both (1) and (2) deny that humans have some sort of information-gathering contact with abstract objects in the way proposed by Plato, Gödel, and Maddy; but these Platonists still think that humans can acquire knowledge of abstract objects.
This claim plays a crucial role in her defense of the view that we can acquire knowledge of mathematical entities by perceiving sets.
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.
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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.
Along with the other West African countries that bore the brunt of the epidemic, Liberia ranks near the bottom of the Human Development Index, a composite measure that assesses whether persons enjoy a long and healthy life, can acquire knowledge, and have an adequate standard of living (1 ).
Reinforcement learning algorithms that use deep neural networks are a promising approach for the development of machines that can acquire knowledge and solve problems without human input or supervision.
For the classical acquaintance theorist, that question, in turn, reduces to the question of how we can acquire knowledge through inference.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com