Knowledge without Certainty

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1. Knowledge is justified true belief.
2. We cannot be absolutely certain of any facts about the world.

Therefore, when I say "I know that Paris is the capital of France", I mean "I justifiably believe that Paris is the capital of France beyond reasonable doubt". In other words, "I justifiably believe it is so, but I could (theoretically) be wrong".

But I only know that Paris is the capital of France if it actually is. So if I say that I know it, I am asserting the following:

(a) Paris is the capital of France.
(b) I believe Paris is the capital of France, but I could be wrong.

Thus I am asserting:

(a) Paris is the capital of France.
(c) It may be false that Paris is the capital of France.

But (a) and (c) are contradictory. Necessarily, if Paris is the capital of France, it is true that it is the capital of France.

Therefore, if we assert that we know (rather than just "probably know") some empirical fact, we are implying a contradiction. We cannot meaningfully make a bald assertion that we know an empirical fact.

Let me be clear that if Paris is indeed the capital of France, then we do in fact know it. But, since there is theoretical doubt, it is contradictory to assert that we know it.

Any comments?

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"2. We cannot be absolutely certain of any facts about the world."

True enough, but why does knowledge imply absolute certainty?

I ask Correy, "What is the capital of France?"
He replies, "Why, Paris of course." He doesn't say "I believe Paris is the capital of France" unless he isn't sure or he is in a graduate philosophy seminar. In normal situations, theoretical doubt doesn't enter into it; "I believe so and so" is an expression of an actual uncertainty about a fact, not a theoretical caveat.

If Correy and I disagree about whether Paris is the capital of France, we can resolve the question because we know how to do so. We can consult maps, almanacs, ask Pierre who lives in Paris,etc..
"Ah,yes, you are right, Correy, Paris IS the capital of France." I don't add, at least in this case "but we could, of course, both be wrong."

1 Reply

@ACB,

If we are to restrict the idea of truth to mathmatics, then one can never be sure that Paris is the capitol of France. Likewise, one could never be sure that the capitol of France is not Asia.

1 Reply

@ACB,

ACB wrote:

1. Knowledge is justified true belief.
2. We cannot be absolutely certain of any facts about the world.

Therefore, when I say "I know that Paris is the capital of France", I mean "I justifiably believe that Paris is the capital of France beyond reasonable doubt". In other words, "I justifiably believe it is so, but I could (theoretically) be wrong".

But I only know that Paris is the capital of France if it actually is. So if I say that I know it, I am asserting the following:

(a) Paris is the capital of France.
(b) I believe Paris is the capital of France, but I could be wrong.

Thus I am asserting:

(a) Paris is the capital of France.
(c) It may be false that Paris is the capital of France.

But (a) and (c) are contradictory. Necessarily, if Paris is the capital of France, it is true that it is the capital of France.

Therefore, if we assert that we know (rather than just "probably know") some empirical fact, we are implying a contradiction. We cannot meaningfully make a bald assertion that we know an empirical fact.

Let me be clear that if Paris is indeed the capital of France, then we do in fact know it. But, since there is theoretical doubt, it is contradictory to assert that we know it.

Any comments?

0 Replies

This line of thought is always entertaining, but with all it's fruit, it is mostly nuts.

If you live on the 20th floor of a building, I guess you can't be 100% sure that your window is not in fact your apartment door. When we wander too far away from the practical and utilitarian, we soften our common sense. You're free to ponder at the window and debate if it could possibly be the front door, and I'd encourage you to try it. Meanwhile, I'll walk out of what I believe is the front door and take the elevator down.

Thinking thinking thinking is great, but doing doing doing is where real certainty is found.

Paris is the capitol of France because what "Paris" is and what a "capitol" is defined in such a way that the statement is not contradictory. Both the parameters of "Paris," and the definition of "capitol" have utility and are testable.

A
R
T

1 Reply

@ACB,

Certainty is the enemy of knowledge and it has ever been so, and while no amount of certainty makes knowledge useful, the smallest part of certainty make knowledge dangerous... In old Spain, the educated knew little more than the ignorant, and the saved knew little more than the damned, so while people were relatively equal in what they thought and believed, certainty justified lighting the sky with auto de fe's as knowledge would never do.... All virtue rests upon uncertainty and all vice strides with certainty...

The value of knowledge is in If... If we know this, then what conclusions may we reasonably draw from it... In our lives, knowledge is a castle of sugar cubes that needs shelter to be shelter, and in the end, it will pass with us... The knowledge we need is the knowledge certainty has always denied, and it is how to live in the moral world as moral people... Certainty always locates the center of happiness elsewhere, in more power, in God, in wealth... Knowledge is that understanding that points to our own lives and communities and behavior as holding the key to our happiness... Such knowledge is not glamourous enough for some, not abstract enough... Knowledge has all the value it needs without certainty...

0 Replies

@ACB,

ACB wrote:

1. Knowledge is justified true belief.
2. We cannot be absolutely certain of any facts about the world.

Therefore, when I say "I know that Paris is the capital of France", I mean "I justifiably believe that Paris is the capital of France beyond reasonable doubt". In other words, "I justifiably believe it is so, but I could (theoretically) be wrong".

But I only know that Paris is the capital of France if it actually is. So if I say that I know it, I am asserting the following:

(a) Paris is the capital of France.
(b) I believe Paris is the capital of France, but I could be wrong.

Thus I am asserting:

(a) Paris is the capital of France.
(c) It may be false that Paris is the capital of France.

But (a) and (c) are contradictory. Necessarily, if Paris is the capital of France, it is true that it is the capital of France.

Therefore, if we assert that we know (rather than just "probably know") some empirical fact, we are implying a contradiction. We cannot meaningfully make a bald assertion that we know an empirical fact.

Let me be clear that if Paris is indeed the capital of France, then we do in fact know it. But, since there is theoretical doubt, it is contradictory to assert that we know it.

Any comments?

But of course saying that you know that Paris is the capital, but then adding that you could be wrong, is giving with one hand, and taking with another. But what has that to do with whether it is true that you can know that Paris is the capital and nevertheless, you could be wrong? Nothing at all. As an example, consider this: If I say "It is raining, but I do not believe it" I would be talking nonsense. But it surely could be true that it is raining but I do not believe it is raining. So, my saying something may be nonsense, but the proposition, or the fact, may still be true. So, the mere fact that it would be nonsense to say that p does not mean that p is not true. For there may be conditions for saying p, which are extraneous to whether or not p is true.

Now, to get to the nub of your point. Can I know that p, and yet it could be that p is false? Let's distinguish this question sharply from a different question: Can I know that p, and p (actually) be false? The answer to this latter question is obviously-no. But how about the question, can I know that p, and it be possible that p is false? Well, of course. It is possible that Paris is not the capital of France since it is not self-contradictory that Paris is not the capital of France. That is, Paris is the capital of France is a contingent statement, and a contingent statement is (by definition) a statement whose negation is possible. Again, Paris is the capital of France, all right, but that does not mean that it would be impossible for future information to show that is (and was not) true. We can imagine the possibility of disconfirming evidence. But that, of course, in no way is any reason to think that such disconfirming evidence will occur, and thus, no reason to think that it is not true that Paris is the capital, and, thus, no reason to think that I do not know that Paris is the capital. So, the (mere) possibility that I am mistaken is, in no way, any reason to think that I am (in fact) mistaken. The difference is between possible error, and actual error. And they are not the same. Let me add this: another source of the confusion is that the term "possible" is ambiguous. It has a modal sense, and an epistemic sense. It is possible that p is false, means, in the modal sense either: a. the negation of p is not self-contradictory, or b. some future disconfirming evidence may arise. (I talked about these above). However, "possible" also has an epistemic sense. "It is possible that p" means (in this epistemic sense of "possible") something like, "for all I know, p is true". (For instance. "Is Joanne coming to the party?" "It is possible" = For all I know, Joanne is coming to the party. Now, if someone says, "I know that p, but it is possible that p is false" and if we understand him as using "possible" not in the modal sense of "possible", but in the epistemic sense of "possible", then we'll understand him as saying, that I know that p, but for all I know, p is false. And that certainly sounds wrong. But, we have to remember that when we say that I know that p is true, but it is possible that not-p, we are using "possible" in its modal sense, but not in its epistemic sense.

I hope the above (long-winded) answer, help to clarify what I think is going on here.

2 Replies

@failures art,

failures art wrote:

This line of thought is always entertaining, but with all it's fruit, it is mostly nuts.

If you live on the 20th floor of a building, I guess you can't be 100% sure that your window is not in fact your apartment door. When we wander too far away from the practical and utilitarian, we soften our common sense. You're free to ponder at the window and debate if it could possibly be the front door, and I'd encourage you to try it. Meanwhile, I'll walk out of what I believe is the front door and take the elevator down.

Thinking thinking thinking is great, but doing doing doing is where real certainty is found.

Paris is the capitol of France because what "Paris" is and what a "capitol" is defined in such a way that the statement is not contradictory. Both the parameters of "Paris," and the definition of "capitol" have utility and are testable.

A
R
T

You seem to be confusing two different meanings of "certainty". You are talking about psychological or subjective certainty, which is generally what is commonly meant by "certainty" We sometimes use the term, "being sure" in the same way. All this comes to is having a high degree of confidence that what you believe is true. That you are right. So, in this subjective sense, both atheists and theists are certain. Clearly, this sense of "certainty" does not imply truth. And, as we know, a person can have high degree of confidence (be very sure) that his belief is true, and his belief turn out to be false. Clearly, although both the atheist and the theist may have subjective certainty, but one of them can be right. In any case, this subjective certainty is not what philosophers from Plato, to Descartes, to Russell, have been talking about when they claim that knowledge has to be certain. What Plato, and Descartes clearly had in mind was something quite different, namely objective certainty, or infallibility. In this sense of "certain" someone who is certain that some proposition, p, is true, is someone for whom it is impossible that he is wrong. He is infallible about p. In this objective sense, certainty implies truth (as contrasted with the other, subjective sense of "certainty"). A clear example of this is Descartes' famous Cogito. Descartes held that we could be infallibly certain that (for each of us) that we exist. That it would be impossible for us to believe that we exist and be mistaken. (For it would be impossible for me to believe I exist, and not exist). Now, it is this kind of certainty that philosophers are talking about when they discuss certainty and knowledge. Not the other subjective kind of certainty, or strong confidence. It is not merely that we are strongly confident that we exist. That is not the point. It is that it is impossible for us to be mistaken that we exist. And that is the point. And the issue is whether knowledge implies this kind of objective certainty. (Of course, when we think we know, we are confident that we are right. But that is quite irrelevant here. What is relevant is whether when we know, must we be right, and how to understand what that means).

I hope this clears matters up a little.

1 Reply

@kennethamy,

kennethamy wrote:

failures art wrote:

This line of thought is always entertaining, but with all it's fruit, it is mostly nuts.

If you live on the 20th floor of a building, I guess you can't be 100% sure that your window is not in fact your apartment door. When we wander too far away from the practical and utilitarian, we soften our common sense. You're free to ponder at the window and debate if it could possibly be the front door, and I'd encourage you to try it. Meanwhile, I'll walk out of what I believe is the front door and take the elevator down.

Thinking thinking thinking is great, but doing doing doing is where real certainty is found.

Paris is the capitol of France because what "Paris" is and what a "capitol" is defined in such a way that the statement is not contradictory. Both the parameters of "Paris," and the definition of "capitol" have utility and are testable.

A
R
T

You seem to be confusing two different meanings of "certainty". You are talking about psychological or subjective certainty, which is generally what is commonly meant by "certainty" We sometimes use the term, "being sure" in the same way. All this comes to is having a high degree of confidence that what you believe is true. That you are right. So, in this subjective sense, both atheists and theists are certain. Clearly, this sense of "certainty" does not imply truth. And, as we know, a person can have high degree of confidence (be very sure) that his belief is true, and his belief turn out to be false. Clearly, although both the atheist and the theist may have subjective certainty, but one of them can be right.

We are talking about atheism and theism, now? In that case, atheists say Paris is the capitol of France, and theists think that Berlin is the capitol of France.

Both are very "certain," but while one is demonstrating why they are certain, the other is waxing philosophical about how we can never be 100% sure.

This is a logical fallacy know as Loki's wager. You may have my head, but you may not have my neck. Now let us argue about where my neck ends.

kennethamy wrote:

In any case, this subjective certainty is not what philosophers from Plato, to Descartes, to Russell, have been talking about when they claim that knowledge has to be certain. What Plato, and Descartes clearly had in mind was something quite different, namely objective certainty, or infallibility.

In that case, why are we talking about Paris?

Perhaps 1=!1;
I mean... we can't be certain right?

kennethamy wrote:

In this sense of "certain" someone who is certain that some proposition, p, is true, is someone for whom it is impossible that he is wrong. He is infallible about p. In this objective sense, certainty implies truth (as contrasted with the other, subjective sense of "certainty"). A clear example of this is Descartes' famous Cogito. Descartes held that we could be infallibly certain that (for each of us) that we exist. That it would be impossible for us to believe that we exist and be mistaken. (For it would be impossible for me to believe I exist, and not exist). Now, it is this kind of certainty that philosophers are talking about when they discuss certainty and knowledge.

I was not aware that philosophers were in agreement about anything let alone what kind of certainty they liked to discuss.

kennethamy wrote:

Not the other subjective kind of certainty, or strong confidence. It is not merely that we are strongly confident that we exist. That is not the point. It is that it is impossible for us to be mistaken that we exist. And that is the point. And the issue is whether knowledge implies this kind of objective certainty. (Of course, when we think we know, we are confident that we are right. But that is quite irrelevant here. What is relevant is whether when we know, must we be right, and how to understand what that means).

So if a god doesn't think it's exists it doesn't. No gods exist, so therefore we must conclude that any gods that are out there don't think that they exist. Simple enough.

If we think we exist, then we must, but if we think something else exists...

kennethamy wrote:

I hope this clears matters up a little.

meh.

A
R
T

1 Reply

@failures art,

failures art wrote:

kennethamy wrote:

failures art wrote:

This line of thought is always entertaining, but with all it's fruit, it is mostly nuts.

If you live on the 20th floor of a building, I guess you can't be 100% sure that your window is not in fact your apartment door. When we wander too far away from the practical and utilitarian, we soften our common sense. You're free to ponder at the window and debate if it could possibly be the front door, and I'd encourage you to try it. Meanwhile, I'll walk out of what I believe is the front door and take the elevator down.

Thinking thinking thinking is great, but doing doing doing is where real certainty is found.

Paris is the capitol of France because what "Paris" is and what a "capitol" is defined in such a way that the statement is not contradictory. Both the parameters of "Paris," and the definition of "capitol" have utility and are testable.

A
R
T

You seem to be confusing two different meanings of "certainty". You are talking about psychological or subjective certainty, which is generally what is commonly meant by "certainty" We sometimes use the term, "being sure" in the same way. All this comes to is having a high degree of confidence that what you believe is true. That you are right. So, in this subjective sense, both atheists and theists are certain. Clearly, this sense of "certainty" does not imply truth. And, as we know, a person can have high degree of confidence (be very sure) that his belief is true, and his belief turn out to be false. Clearly, although both the atheist and the theist may have subjective certainty, but one of them can be right.

We are talking about atheism and theism, now? In that case, atheists say Paris is the capitol of France, and theists think that Berlin is the capitol of France.

Both are very "certain," but while one is demonstrating why they are certain, the other is waxing philosophical about how we can never be 100% sure.

This is a logical fallacy know as Loki's wager. You may have my head, but you may not have my neck. Now let us argue about where my neck ends.

kennethamy wrote:

In any case, this subjective certainty is not what philosophers from Plato, to Descartes, to Russell, have been talking about when they claim that knowledge has to be certain. What Plato, and Descartes clearly had in mind was something quite different, namely objective certainty, or infallibility.

In that case, why are we talking about Paris?

Perhaps 1=!1;
I mean... we can't be certain right?

kennethamy wrote:

In this sense of "certain" someone who is certain that some proposition, p, is true, is someone for whom it is impossible that he is wrong. He is infallible about p. In this objective sense, certainty implies truth (as contrasted with the other, subjective sense of "certainty"). A clear example of this is Descartes' famous Cogito. Descartes held that we could be infallibly certain that (for each of us) that we exist. That it would be impossible for us to believe that we exist and be mistaken. (For it would be impossible for me to believe I exist, and not exist). Now, it is this kind of certainty that philosophers are talking about when they discuss certainty and knowledge.

I was not aware that philosophers were in agreement about anything let alone what kind of certainty they liked to discuss.

kennethamy wrote:

Not the other subjective kind of certainty, or strong confidence. It is not merely that we are strongly confident that we exist. That is not the point. It is that it is impossible for us to be mistaken that we exist. And that is the point. And the issue is whether knowledge implies this kind of objective certainty. (Of course, when we think we know, we are confident that we are right. But that is quite irrelevant here. What is relevant is whether when we know, must we be right, and how to understand what that means).

So if a god doesn't think it's exists it doesn't. No gods exist, so therefore we must conclude that any gods that are out there don't think that they exist. Simple enough.

If we think we exist, then we must, but if we think something else exists...

kennethamy wrote:

I hope this clears matters up a little.

meh.

A
R
T

My serious answer to you did not deserve your unserious replies. I thought you were genuinely interested in the issue. I was mistaken. I will not make that mistake again.

1 Reply

@kennethamy,

It was quite a serious reply. Are you the arbiter of what is to be considered and not considered in discussion here? If you are, how can you be certain?

My point, however I choose to convey it, is that philosophical musings about how we know things are certainly fascinating, but more often than not they are used as mental gymnastics to avoid what we do not want to know.

E.g. - Theists are terrified by the certainty of no god existing, so they are comforted that there is a dialog they can engage in which nobody can be "certain" of anything. It's a false stalemate.

A
R
T

0 Replies

@ACB,

ACB "(a) Paris is the capital of France.
(c) It may be false that Paris is the capital of France.
But (a) and (c) are contradictory. Necessarily, if Paris is the capital of France, it is true that it is the capital of France."

It is false to say that (a) and (b) are contradictory.

p & <>(~p), is not a contradiction.
If it were then we must say p -> []p.
Paris is the calpital of France, implies Necessarily (Paris is the calpital of France) ...is clearly false.

[](p -> (p is true)), because (p is true) =df p.
[](p -> p) is tautologous.

2 Replies

@Owen phil,

Owen phil wrote:

& <>

Assuming that this indicates "and if and only if", then for any proposition, eg, "I'm replying to your post", you're contending that "I'm replying to your post and if and only if I'm not replying to you post" isn't a contradiction. Before deciding whether or not it's a contradiction, can you explain what it means, please.

1 Reply

@ughaibu,

p & <>(~p), means (p is true) and It is possible that (p is false).
<-> is iff, <> is 'it is possible that'.

I apologise for assuming these symbols were agreed upon.

ACB said ..
(a) Paris is the capital of France.
(c) It may be false that Paris is the capital of France.
But (a) and (c) are contradictory.

I read this remark as: (a) Paris is the capital of France (b) It is possible that Paris is the capital of France is false.

If p = (a) Paris is the capital of France, and, <>(~p) is (c) It may be false that Paris is the capital of France, then p & <>(~p) is not contradictory as ACB claimed.

1 Reply

@Owen phil,

Owen phil wrote:

p & <>(~p), means (p is true) and It is possible that (p is false).

Okay, I see. Some proposition is both true and possibly untrue. Are you applying an operator to another operator? If not, could you present a clearer formalisation, please.

1 Reply

@ughaibu,

In keyboard talk ....

[]p means, p is necessarily true ..logically true.
~([]p) means, (p is necessary) is false.
[](~p) means, (~p) is necessary.
~([]~p) means, (~p) is necessary, is false.

<>p means, p is possibly true ..logically possible.
~(<>p) means, (p is possible) is false.
<>(~p) means, (~p) is possible.
~(<>~p) means, (~p) is possible, is false.

Note that: []p <-> ~<>(~p) and <>p <-> ~[](~p).

1 Reply

@Owen phil,

Owen phil wrote:

[]p means, p is necessarily true ..logically true.
~([]p) means, (p is necessary) is false.
~([]~p) means, (~p) is necessary, is false.

<>p means, p is possibly true ..logically possible.
~(<>p) means, (p is possible) is false.
~(<>~p) means, (~p) is possible, is false.

Note that: []p <-> ~<>(~p) and <>p <-> ~[](~p).

To repeat, are you applying an operator to an operator? If not, then I think that you're committed to a hierarchy.

1 Reply

@ughaibu,

The operators apply to propositions not to other operators.

I don't understand what you mean by a 'heirarchy'.

1 Reply

@Owen phil,

Owen phil wrote:

The operators apply to propositions not to other operators.

So, necessity and possibility aren't operators.

3 Replies

@ughaibu,

No. (~, <>, []) are operations on propositions
For example, in p <-> ~(~p), each not applies to a proposition. (~~) is nonsense.

p -> [](<>p) is another example that is tautologous.
The necessity operator does not apply to the possible operator, rather,
the necessity operator applies to the proposition that (p is possible). ([]<>) is also nonsense.

1 Reply

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