The differences between Goldman's Causal Theory of Knowledge and the Nyaya account of knowledge has no substantial difference as they relate to the Gettier problem and they fail to satisfactorily explain knowable events. After summarizing, the two positions there will be an explanation of how they are related along with examples and a rebuttal. After which a counter to the rebuttal with be given with an explanation of how that would fail to address the issue of giving a satifactory explanation of knowable events.
Causal Theory of Knowledge
Goldman lays out his arguments to prove that P knows x if x is, in the appropriate way, causally connected to P believing x.
Goldaman argues that in Gettier's Ford/Barcelona disjunction Gettier neglects to draw a causal connection between the fact that Smith happened to be correct and thus is not actually justified.
For P to believe x there needs to be a causal connection for P's believing x.
Goldman
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The following examples of the split beam test will do just that.
One observes photons acting as waves.
They act as waves in every known example.
They do in-fact act as waves.
One knows that photons act as waves.
When one measure photons and they act as particles.
All prior experience with every perceived object demonstrates that photons act as particles.
They do in-fact act as particles.
You know that they act as particles.
So, a&~a
Though additional premises could complete the syllogism making it coherent with the way things are believed to be, if one had only discovered a single knowable property they would have JTB+ and they would both have knowledge while attaining to an illusion.
If then what is expressed in the split beam test is true one now has grounds to know and has a truth-hitting experience that is false from Nyaya's 3rd requirement yet true at the same