Justified True Belief

What is knowledge?  What does it mean to say you know something?   Since the time of Aristotle knowledge has been defined as (1) something true (2) something you believe, and (3) that belief is justified.  Edmund Gettier posed some problem that draw this definition into question.  We consider these in this post whether this definition of knowledge makes sense.

What is Knowledge?

It seems to me that there are clearly two kinds of things that we are referring to when using knowledge.

• Personal Knowledge – what a single person knows, and can say “I know X” about.
• Collective Knowledge – what a group, society, or culture has collected as knowledge.

Personal Knowledge

Consider these statements about some fact X:

• I think X
• I believe X
• I know X
• I am certain that X

Notice that all of these are active verbs. It involves an actual thinking agent to actively make these claims.  They represent different degrees of certainty about X.  In the first case X is implied to be quite uncertain but still more likely than not.   The second X is more likely, but not certain.   When you get to the level of knowing X, you are then certain that X is true, as certain as you can be, even though there is still the possibility that you are wrong.

In this case, knowing something is a state of being where you can make a claim that you know something, that you are certain enough about it that you would be embarrassed if this fact is found to be wrong.  What do you need to be that certain?  You need to have some justification for your belief in the fact.  You would have to have seen some evidence, either directly or having been told by a reliable source.  You probably need multiple occurrences of supporting evidence, and no evidence of contradicting evidence.

Collective Knowledge

The subject here is about epistemology, which is about what is known or knowable for the entire culture, maybe the world. This is the kind of thing we might say is “known to science.”   We know that quarks exist, and that it takes three of them to make a proton.

Science has a large collection of knowledge, written down in books and papers, carefully collected and vetted through a process of peer review and published in journals.  The entire collection of this can be called scientific knowledge.  It is far too vast for a single person to know in entirety.

The actual collection of scientific knowledge is a subset of all the papers written, because there is an acceptance cycle for the ideas in a paper after it gets published.  to be part of scientific knowledge, a published must be accepted by the scientific community in that field, and it must be referenced by other papers on the same topic.  Once it has been accepted by the community, and referenced by a suitable number of other papers, only then it can be considered to be “true”.

Why Two Types of Knowledge

I don’t think these two types of knowledge work the same way at all.  Some of the paradoxes proposed by Gettier come from confusing these two types of knowledge.  We will compare and contrast in a number of situations below.

First Gettier Problem

Smith and Jones have applied for a certain job. The president of the company assured Smith that Jones would be selected.  Smith has counted the coins in Jones’ pocket to be ten coins.  Smith is certainly justified in concluding he knows that the person who gets the job will have ten coins in his pocket.

However, it turns out that Smith also has ten coins in his pocket. And the president was wrong (or lying) so that Smith actually gets offered the job.  It is certainly still true that the person who gets the job will have ten coins in his pocket however he is wrong about the particulars, and the justification for this belief does not fit the actual outcome. Smith had a belief that was true and justified, but not knowledge.

Second Gettier Problem

Smith has a justified belief that “Jones owns a Ford” having seen him drive it many times and other evidence.  Smith is not sure of where Brown is at the moment, but concludes the fact: “Jones owns a Ford, or Brown is in Barcelona.”   In fact, Jones does not own a Ford, but by sheer coincidence, Brown really is in Barcelona. Again, Smith had a belief that was true and justified, but not knowledge.

Truth

Both of these are examples of personal knowledge.  Smith claims to know that Jones owns a Ford while quite clearly Jones, as it turns out, does not have this belief or knowledge.  We are not talking any kind of objective knowledge that is shared across a culture.  For this to be considered collective knowledge, the fact would need to be published, accepted, and referenced.  Smith is in a state of knowing something because he has a high confidence in his belief — even though that thing is wrong.  Consider these two parallel stories:

Smith is entering a theater without knowing who was supposed to perform, and as he does each person he passes comments on how great the performance Mick Jagger had just concluded.  Smith hears this ten times while working through the crowd to his seat.  Smith is now in a state of knowledge with respect to the fact “Mick Jagger just finished a performance.”

Consider the same theater but the only difference is that everyone he meets along the way lie to him.  Everyone still says how great the performance that Mick Jagger had just completed, but in reality Britney Spears had performed.  Smith is in a state of knowledge with respect to the fact “Mick Jagger just finished a performance.”  But in this case that fact is false.

In both of these cases Smith’s state is identical.  He believes the fact, and he has plenty of justification for this fact.  His brain is in exactly the same state. Because he is in the same state, if you ask him: “Do you know who just performed?”  he will in both cases respond with “Yes, I know that Mick Jagger just finished a performance.”  But in the second case, his belief is false, but he does not know it, and therefor can not be expected to act any differently.

Can we really say that in the first case he had “knowledge” while in the second case he did not?  His brain state is exactly the same!  As far as personal knowledge goes, the two stories are the same.

The difference is that the external world, outside of Smith, is different, but Smith has no access to that.  He can not know that he has been lied to.  As far as he is concerned, Mick Jagger really was on stage.

Truth of Collective Knowledge

To resolve whether Smith’s personal belief is knowledge or not, we have to access some collective knowledge about the theater.  When I use the phrase “But in reality Britney Spears had performed” I necessarily have to take a kind of omniscient view.  I can’t come to know this by just asking a random person in the audience, because if I asked Smith I would be wrong.

The assumption here is that I have to poll a lot of people, potentially everyone, and determine that most people agree that it was Britney Spears.  “Reality” is then some sort of agreement across the majority of people who could be expected to know, some sort of collective knowledge of the situation.

Collective knowledge is in general more true than personal knowledge and that is because it has to be based on some sort of consensus.  That eliminates the simplest forms of deception.  It is much much harder to lie successfully to a large group of people.  Yet is it not perfect.  Obviously, for thousands of years the collective wisdom was that the Sun went around the Earth until relatively recently we found it to be the opposite.  Collective knowledge is not perfect, and it is not always better than what particular individuals know, but in general collective knowledge is truer than personal knowledge.

Personal and Collective Knowledge Agreement

I would say in both cases that Smith knows that Jagger was there in every way that anyone can mean knowing something.  In both cases he is completely convinced.  There is no way he could know that he is wrong.   It is a fact that people will say “I know X” only to later have to “change their mind.”

There is no way for anyone to be sure that anything they know is not false.  In some cases it might take a considerable conspiracy, but it remains that any fact that you know might be false.

For personal knowledge, it appears that belief and justification is all that is needed in order to be in a state of “knowing” which is indistinguishable from any other state of knowing.  People don’t believe things they know to be false.  If they don’t know that it is false, and they have sufficient justification for believing it, then you can say Smith has personal knowledge because his belief is justified to the extent that his confidence is up to the “knowing” level.

It is all Temporal

There have be periods of time that you don’t know something, and other periods of time that you do know something. Over time this might flip back and forth over the same thing as you get more and more evidence.

For example, Smith might know that the king is in Washington supported by plenty of evidence of the fact.  On Wednesday, the king is secretly transported to Mara Lago, and then on Thursday returned to Washington.  Only a few people knew about the trip.

Smith had knowledge on Monday. He knows “the king is in Washington.” And he has this knowledge on Thursday as well.

On Wednesday, he has the exact same brain state, but it is not at that time true.  There is something monstrously unappealing to say that Smith has knowledge on Monday, does not have knowledge on Wednesday, and has knowledge again on Thursday.

Smith could never know if what he believes in knowledge, and nobody around him could ever know it either.

Knowing whether Smith’s knowledge is true or not once again requires an omniscient view of where the king really is at the moment.  That is collective knowledge, not personal knowledge.  When we set up these stories, we do so from an omniscient viewpoint, and we can simply say how things are, but in real life it is not that simple.  You have to someone do a poll of all the people who are around the king, weighting responses from closer people more heavily, and then come to some sort of agreement that the trip actually happened.

We can’t just ask Jones.  Say that Jones has been told that the king will take a trip to Elbonia on Tuesday.  Smith and Jones would disagree on Tuesday and Wednesday.  Even though both of them have justified belief.

Knowledge is basically never eternal. The truth of knowledge is temporal and dependent upon things very far away from the personal knowledge.

Personal Knowledge Might not be True

A person can never know whether personal knowledge is true or not.  And nobody around them can know that either.  We can compare two people’s personal knowledge.

Or we can try to compare to some sort of collective knowledge, maybe something written in a newspaper, but that is not perfect either.

Gettier’s Problems Discussed

Smith has a personal knowledge that “the person who gets the job will have ten coins in his pocket.”  He has been lied to, and so this knowledge is not true, but he is convinced of the true of it, and he has good reasons for believing this.

Then it becomes known that Smith gets hired.  This might affect his belief, making him no longer believe that “the person who gets the job will have ten coins in his pocket” even though it is still true at an omniscient level.  He may then later count the coins in his own pocket, and reenter a state of knowing that “the person who got the job had ten coins in his pocket.”

I think it is wrong to say that Smith did not have knowledge before.  He had wrong knowledge.   The problem with JTB is that personal knowledge can be wrong.  Therefor, we can’t say that personal knowledge is always true, and truth is simply not a requirement for something to be considered personal knowledge.

Collective knowledge can’t be guaranteed to be true either, although it is almost always better (more often true) than personal knowledge.

In the case of Jones owning the Ford, I would say that Smith has a knowledge that Jones owns the Ford, even though that knowledge is wrong.   Similarly the combined statement “Jones owns a Ford, or Brown is in Barcelona” is knowledge for Smith only because of the car ownership part.  That fact that this statement turns out “in reality” to be true for the opposite reasons has no bearing on whether Smith considers it knowledge or not.

If Smith was told that Jones does not own the Ford, then he might step back — lower the confidence — of the belief in the combined statement.  This effects his state after being told, but does not alter the state before being told.   We can still say that before being told, Smith knows that Jones owns a Ford, and this was knowledge at that time.

Conclusions

I believe the problem with JTB definition of knowledge is that we can never know (without being omniscient and even then only if we are eternal as well) whether a particular belief is true or not.

When a person says “I know X” is means simply that the belief is justified by supporting evidence that the person is relatively certain of the fact.   No matter how certain they are, there is always the possibility that it is wrong.

In all of the cases of Gettier’s problems, the apparent contradictions comes when we compare some sort of omniscient or collective knowledge, with the specifics of Smith’s personal knowledge.

Nobody is omniscient, and so there is no way to be 100% sure that any given knowledge is true or not.  To base our definition of knowledge on whether it is true or not is a hopeless situation where every new fact discovered can flip beliefs previously considered to be knowledge to not being knowledge, and vice versa.  You would be continually rewriting the books.

Collective knowledge however uses consensus to raise the likelihood of being true.  In fact, collective knowledge might be our best approximation at the truth, however it is far from perfect.

Personal knowledge is just a well justified and confident belief.   Nothing more.