Master log, Stardate 20412.3
Tags: Intellectual; Overanalyzing
Once upon a time, I heard about these things called Gettier problems. At the time, I thought the concept was absolutely repulsive because to me it seemed obvious the whole thing was centered around fallacious reasoning. Yet somehow, these problems had managed to stand as a major problem for over 50 years! What a tragedy! How has the debate lasted so long without ever being resolved by the obvious!
In my ire, I managed to hash out an entire pseudo-paper on my thoughts on this. Of course, eventually I accepted that philosophy is not mathematics. Even if I had refined my arguments to meet the level of rationality and rigor I had intended, such arguments were still unlikely to convince anyone because there was always an alternative perspective they could take to sidestep my analysis entirely. And who's to say their new perspective isn't the correct one? Systematically refuting all possible alternative perspectives to leave only the valid one standing is generally an untenable problem.
I'm posting my pseudo-paper here in the hope that someone may find my work useful anyways (and also in the hope that it proves my new article posting system is working). Given the nature of how this was written, I encourage readers to take this with approximately the same level of seriousness they might for, say, Bobby Fischer's "A Bust to the King's Gambit."
Traditionally, knowledge has been defined as a justified true belief. This view was considered overturned with the landmark Gettier problems, which claim to produce cases in which a justified true belief is not sufficient to know something.
Originally, Gettier's claims were rejected because the counterexamples were based on false premises. However, other theories later became dominant when there were complications in the false premises response.
I argue that a variant of the false premises response was in fact sufficient after all, and that it produces far less complications than either the original false premises rejection or alternative theories.
The traditional justified, true belief (JTB) definition of knowledge is this:
A subject S knows that a proposition P is true if and only if:
- P is true, and
- S believes that P is true, and
- S is justified in believing that P is true
Gettier rejected this with two counterexamples. Gettier's claim is that these counterexamples produce justified, true, beliefs, but are not knowledge, and therefore JTB is an insufficient definition of knowledge.
Importantly, Gettier makes two additional claims which his analysis depends on:
For the purposes of this analysis, I will accept both of these claims as true.
Suppose that Smith and Jones have applied for a certain job. And suppose that Smith has strong evidence for the following conjunctive proposition: (d) Jones is the man who will get the job, and Jones has ten coins in his pocket.
Smith's evidence for (d) might be that the president of the company assured him that Jones would, in the end, be selected and that he, Smith, had counted the coins in Jones's pocket ten minutes ago. Proposition (d) entails: (e) The man who will get the job has ten coins in his pocket.
Let us suppose that Smith sees the entailment from (d) to (e), and accepts (e) on the grounds of (d), for which he has strong evidence. In this case, Smith is clearly justified in believing that (e) is true.
But imagine, further, that unknown to Smith, he himself, not Jones, will get the job. And, also, unknown to Smith, he himself has ten coins in his pocket. Proposition (e) is true, though proposition (d), from which Smith inferred (e), is false. In our example, then, all of the following are true: (i) (e) is true, (ii) Smith believes that (e) is true, and (iii) Smith is justified in believing that (e) is true. But it is equally clear that Smith does not know that (e) is true; for (e) is true in virtue of the number of coins in Smith's pocket, while Smith does not know how many coins are in his pocket, and bases his belief in (e) on a count of the coins in Jones's pocket, whom he falsely believes to be the man who will get the job.
The basic premise here is Smith deduces that the man who will get the job has ten coins in his pocket from the fact that Jones has ten coins in his pocket and the false premise that Jones will get the job. Gettier argues that if a belief is justified, then what is deduced from that belief is also justified, so therefore Smith is justified in believing the man who will get the job has ten coins in his pocket.
Suppose Gettier's claim of justification propagating through logical deduction is true. In deductive logic, an argument must be both valid and sound in order for it to be an acceptable argument.
A deductive argument is valid if it is impossible for the premises to be true while it's conclusion is false. An argument is sound if it is both valid and it's premises are true.
Smith's deduction is valid: If Jones really does have ten coins in his pocket and Jones really will get the job, then inevitably the man who will get the job must have ten coins in his pocket.
However, Smith's deduction is not sound: Jones will not get the job, so therefore not all premises are true.
The primary issue with this example, then, is Smith's deduction is not in fact a sound logical deduction, and therefore Gettier's second claim does not apply. If Gettier's second claim does not apply, then Smith is not justified in his belief that the man who will get the job has ten coins in his pocket. And if Smith is not justified in his belief that the man who will get the job has ten coins in his pocket, then there is no conflict between the concept of a JTB and the concept of what Smith knows.
This so-called "false premises" provision has been raised before in several variations. Some notable variants claim the definition of knowledge must be altered so that justified true beliefs that do not depend on false premises. These variants ultimately fell out of favor because they opened the question of how deeply one would have to prove the chain of premises before the argument became acceptable.
This problem is unnecessary however, because the definition of knowledge does not need to be modified to account for false premises. The JTB definition of knowledge needs no concept of premises because the definition of knowledge is not the definition of logical deduction. Logical deduction does require true premises in order to make a sound argument, but logical deduction is not the sole method through which a belief can be justified. Therefore, there is no issue of when to stop because at some point there will be justified, true beliefs that have been justified through means other than logical deduction.
Some have generalized Gettier problems such as the so-called "Sheep in the field" problem.
Imagine that someone is standing outside a field looking at something that looks like a sheep (although in fact, it is a dog disguised as a sheep). They believe there is a sheep in the field, and in fact, they are right because there is a sheep behind the hill in the middle of the field. Hence, they have a justified true belief that there is a sheep in the field. But is that belief knowledge?
This argument has a similar issue of a hidden unsound deduction. Let's call this person Bob. Bob observes (a) he sees something (b) this something looks like a sheep and (c) this something is standing in a field. From (a) and (b), Bob concludes that he sees a sheep. Critically, note this is a justified false belief, because the something is not in fact a sheep. Bob deduces that because he sees what he believes is a sheep, and (c) that something is standing in a field, therefore there is a sheep in the field. However, this deduction is unsound because it is based on the false premise that what Bob is seeing is a sheep. Therefore Bob's belief that there is a sheep in the field is not justified, because his justification for believing the dog is a sheep cannot propagate unless the logical deduction is sound.
Note that in fact, this problem is of exactly the same form as the original Gettier examples. The only difference is the erroneous deduction was obfuscated by the wording of the problem. Nevertheless, the deduction is both present and essential to the problem. If Bob had not gone on to deduce that the sheep is in the field but remained with his original statement that he believes he sees a sheep, the problem fails. In that case, the solution would simply be Bob has a justified false belief and the fact that there's another unseen sheep in the field never comes into play.
In previous variants, it has been claimed this type of explanation is insufficient. The argument goes that because the sheep was seen through sensory data rather than deduced logically, the justified false belief does not apply. It is argued it is unreasonable to reject sensory data as requiring logical justification, since sensory data is the primary means through which we observe the world. If that is insufficient, then virtually nothing can truly be justified.
My response is two-fold. Firstly, arguing sensory data is above considerations of uncertainty while also advocating arguments which depend on uncertainty in sensory data is a logically unsound position on this issue. Secondly, the conclusion that virtually nothing can truly be justified with uncertain sensory data is unsound, which I will demonstrate.
Imagine Larry has just taken some LSD. He looks around his room and notices there is a cat in front of him. He considers seeing a cat to be sufficient justification, so he thinks he is justified in believing there is a cat in front of him. In fact, there is a cat in front of him, so Larry has a justified, true belief that there is cat in front of him when in fact there is. By the JTB definition, Larry knows there is a cat in front of him.
Say the cat leaps away and a different cat leaps in front of him. By the same process, Larry concludes there is a different cat in front of him, and by the JTB definition he knows this cat is in front of him as well. Say that cat also leaps away and a different cat leaps in front of him. Say this process continues until 9 cats have been in front of Larry, all of which Larry saw, and all of which Larry knows were in front of him by the JTB definition.
Imagine now Larry sees the 10th cat leap in front of him. By the same process, Larry believes there is a cat in front of him and is justified by virtue of seeing it in front of him. This time, however, there is not a cat in front of him. This cat is merely a hallucination brought on by LSD. This time, then, Larry has a justified false belief, and so does not know there is cat in front of him by the JTB definition (although he believes there is a cat there).
What does one make of this case? Larry knows all 9 actual cats are present, but was deceived into believing there was a 10th cat as well. Therefore, only 9/10ths of what Larry concluded was actually true if sensory data was his only means of justification. If Larry suddenly stumbled across an oracle who could perfectly tell him which cats were real or not, it would not constitute a drastic reduction in his justified beliefs because 9 out of 10 of his justified beliefs were already true.
Thus, if there is an unreliable justification which can nevertheless distinguish truth from fiction a substantial majority of the time then the vast majority of beliefs justified from that will in fact be justified true beliefs. Therefore, it is incorrect to conclude that an imperfect justification method implies little or no beliefs can truly be justified.
Of course, these problems could always be formulated differently, in which case they will merely get refuted differently.
Author's note: This was going to be a counter-argument to some other arguments I read about Gettier problems, but I never got far enough into writing the proper paper to use it.
Some argue that this constitutes strengthening the definition of justification, and therefore is not equivalent to the original JTB formation. I argue that regardless of how you interpret what was "sufficient" justification originally, arbitrary justification was never a valid interpretation.
Imagine Alice stumbles across a claim. Alice believes the claim to be true, but knows objectively the claim is equally likely to be either true or false. So Alice flips a fair coin, saying that if the coin is heads it will affirm the claim is true, and if the coin if tails it will affirm the claim is false. The coin comes up heads, so Alice decides she is justified in believing the claim is true.
Say the claim happens to be true. Does Alice have a justified, true, belief? The claim is known to be true, and the problem asserts Alice believes in the claim, so the question simplifies to "Is Alice's true belief justified?"
Alice's justification for her belief is she flipped a fair coin and it came up heads. If the coin had come up tails, Alice would have rejected the claim as false. Therefore, her justification process was equally likely to justify the claim as to refute it. However, the claim was already equally likely to be true or false even before Alice performed her justification. Effectively, her justification added nothing that Alice didn't have before she attempted to justify her belief. Let's call this a "null justification."
Is a null justification an acceptable justification for a justified true belief? For any belief, a null justification can be constructed in order to satisfy the justification condition. If this is acceptable, then the justification clause can be eliminated entirely, and the JTB definition reduces to simply a true belief.
Therefore, regardless of how you define justification, it must be at least strong enough to exclude null justifications, since that is logically equivalent to having no justification at all. This is implicit in the definition of a JTB, since otherwise the definition would be reduced to simply saying a true belief is acceptable. Thus, disallowing null justifications is not a strengthening of the original JTB definition, regardless of how justification is defined.
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