Sufficiency of J

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K is knowledge of P

P is true

S believes P

S is justified in believing P

F is a defeater from Gettier case

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J is only sufficient when all F have been dismissed by S, Dismissal can be performed by:

1) Investigation into J

2) Consideration of defeaters

3) Entailed dismissal

The subject s is not required to think about the defeater (2), they could investigate without considering F (1), or they could know something which entails F is dismissed.

In the COW example s is a dairy farmer who forms J observing a black and white blanket which he believes it’s a cow, and forms p as “there is a cow in the field,” where F is that unbeknownst to s, there is a cow in the field. In this case s has failed to recognize the sufficiency of evidence qua defeaters. As it is structured, p refers to general objects and therefor fails to dismiss the possibility of p referring to a different cow than the one observed.

In the CLOCK example s is a student where J is the time displayed on a University clocktower, p is “the time is 11:56am” and F is a broken clock stuck at 11:56. In this case s has not confirmed the reliability of the clock tower even though it is normally reliable. To defeat F the student would have had to confirm the clocks functionality within 12 hours of looking at the time. The student could’ve watched the clocktowers second or minute hand for 60s or less to confirm the clock was working, less time then the clock would remain visible while the student was walking. Without some form of defeater dismissal the most the student could’ve said was that “the clocktower said 11:56am.”

It’s possible that J is made too strong this way, however if the only difference between this model and the tripartite model is that K clearly fails in Gettier cases than I think it’s just strong enough. The fact that s is given greater responsibility is exactly what happens under ordinary conditions in lived epistemic conditions, people already take responsibility for dismissing defeaters.

For the model to fail there would have to be a Gettier case where someone has no way to dismiss F, or a case where someone has K and no way to dismiss F.

If I wake up in a dark room with no idea how long it’s been and only my watch displaying the time, do I know what time it is? No. JTB is correct as long as J is only sufficient when it dismisses defeaters.

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C1. Does theory iterate?

Defeaters are unknown, true conditions which reduce positive epistemic status.

Defeaters exclusively effect J.

Are there infinitely many defeaters for each p? Lets say W is a world where p appears true, and is true, and W* is any world which can be accessed through W but is Gettiered. The difference between W and any W* therefor is the addition of some condition F to W which reduces the positive epistemic status of p, in W*.

Are there infinite possible W? Yes.

Are there infinite non-trivially unique possible W for a specific p? No.

Are there infinite non-trivial unique possible W* for any specific W? No.

There are a finite number of unique ways for P to appear true. Because P must appear true in all W, there is a finite number of specific, unique W which can result in a single P. This also means there are a finite number of unique W* since in each W*, p must appear true. This means there are finite number of unique F. So in all cases the number of W* which must be dismissed is finite.

Therefor F is bound.

The number of possible F naturally decrease with iteration.

F therefor always heads to zero assuming conditions which allow p in the first place (external reality exists etc.)

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C2. Does this adjustment to the strength of J only effect K in Gettier case?

F must always be added to W, such that s remains unaware of F and/or the possibility of F and p appears/is true, these limits result in the number of possible F being highly bounded. As stated, F can only act to make a presumption by s true. If it’s possible for F to make a presumption by s true while s simultaneously remains unaware of the possibility of F, then s does not have sufficient justification to consider presumption as reasonable inference. The presumption is not sufficiently justified unless there is no F which has not been dismissed through consideration, investigation or some other means of dismissal. This inserts Gettier cases into definitions as the set of cases which examine or demonstrate the boundaries of K.

S must simply ensure through consideration, knowledge or investigation that no additional conditions could be added which would act as F.

F must always involve the collection of evidence (CoE), there is a minimum complexity threshold in CoE for F to even be possible. If CoE is trivially simple (observing object where K is “object exists”) then no F is possible under assumptions which allow CoE in the first place (the presumption reality exists, s can reliably observe it etc.). The complexity of CoE decides the number and type of observations necessary for sufficient J. In Gettier cases the complexity of CoE necessary to obtain K was greater than the actual CoE used by s, which is known because s used a Gettier presumption (a presumption which is formed in such a way that it allows Gettier case). F is only possible where CoE includes Gettier presumption. In the event CoE is complex enough that Gettier presumption becomes possible, s must either fail to presume, be justified in presuming or use a dismissal method.

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C3. Does s have to know they’re removing F, do they have to have awareness to dismiss F?

Consideration is intentionally removing presumption, so consideration involves awareness. Any other option can be done without awareness, Investigation is removing presumption through praxis regardless of awareness. Having previous knowledge also allows unaware dismissal since one doesn’t need to examine established knowledge for defeaters. Reasonable inference allows for unaware dismissal, because that would exclude elements of presumption which allow defeaters. Reasonable inference is possibly the stickiest, given it seems to allow room for Gettier presumption ( presumption which can be confirmed by happenstance) however, it definitionally wouldn’t be reasonable if it allowed Gettier presumption due to iterative application of defeater dismissal.

It also points out propositions where Gettier presumption comes from semantics of p. In COW and SHEEP cases the proposition “there’s a cow/sheep in the field,” aren’t entailed because proposition generalizes claim to refer to general objects “any sheep” or “any cow” rather than making claim about specific objects “sheep I saw” or “cow I saw.”

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Another possible way to state epistemic limit to J which removes defeaters:

P must be path independent.

If the method of obtaining K has an unknown and unaddressed defeasibility condition then P is not path independent as a different path to K could have resulted in different reduction in epistemic status and/or different K.

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Gettier cases show us the boundaries of Knowledge, the holes in the function where K is undefined, the limit of the asymptote, and since we define things in part by their boundaries, we should recognize and use Gettier cases as part of definition of knowledge.

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