Knowledge without Certainty

@Owen phil,

Owen phil wrote:

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.

Did you miss a bracket between "and" and "possibly", in the post to which I first replied?

1 Reply

@jgweed,

jgweed wrote:

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

True enough, but why does knowledge imply absolute certainty?

I do not believe that knowledge implies certainty (I mean "Cartesian certainty", and not merely the feeling of complete confidence that one is right. That is probably required for a sincere claim to knowledge, but claiming that one knows and its requirements is one thing. But knowing, and its requirements are an entirely different thing. One of the causes it is thought that knowledge requires certainty is just that people confuse the requirement for claiming to know with the requirement for knowing). However, I think that the main reason it is thought that knowledge implies certainty is the following argument: If I believe that I know that some proposition is true, then it might turn out that the proposition is not true, and in that case, my belief that I knew it was true would be false. I would not have known what I believed I knew. But, in that case, it is always possible that I may believe I know, and turn out to be wrong. So, I can never be in a position when I can legitimately claim to know anything at all. Not unless, that is, when I believe I know I cannot turn out to be wrong. And that means that when I believe I know, I cannot turn out to be wrong. And that, of course, entails that it be impossible that I turn out to be wrong, which is to say, that when I believe I know I must be certain, so that the proposition I believe I know cannot turn out to be false. That, I believe, is the main argument for the view that knowledge requires certainty: knowledge that can turn out to be wrong cannot be knowledge in the first place.

Note: I think this argument for knowledge implying certainty is wrong, but I am here expounding it, I am not espousing it. (And let me note, that I think there are other arguments besides the one I just gave, and the one I gave earlier about the confusion between the claim to know and knowing itself, that support the view that knowledge implies certainty. I am here alluding to an argument that commits a modal fallacy. But I don't want go into that argument now.

1 Reply

@thack45,

thack45 wrote:

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.

Being sure has little to do with the kind of certainty in issue. I am as sure as can be that Paris is the capital of France, but I am not infallibly certain that it is. For I might be mistaken that Paris is the capital of France. And what makes you think that math. is certain? I make mistakes in addition all the time.

1 Reply

@ughaibu,

No, there is no need for a bracket here.
p & <>(~p)

The conjunction is between the proposition p and the proposition <>(~p).

1 Reply

@Owen phil,

Owen phil wrote:

p & <>(~p), is not a contradiction.

Exactly. But I think that ACB is confusing modal possibility with epistemic possibility, and I know that p is true, but for all I know, p is false, is a contradiction.

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@ughaibu,

ughaibu wrote:

Owen phil wrote:
The operators apply to propositions not to other operators.
So, necessity and possibility aren't operators.

They are operators. They operate on propositions. They do not (in the present case) operate on operators. Wherever did you get the idea that they did?

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@kennethamy,

kennethamy wrote:

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.

Thanks for your replies. Can you please clarify the difference between:

1. I believe that p, but some future evidence disconfirming p may arise
and
2. I believe that p, but for all I know, p is false.

Is it just a question of the degree of doubt (i.e. the doubt is negligible in the first statement, but not in the second), or is there a more fundamental difference? Are there borderline cases between modal and epistemic possibility? For example, "it is possible that the United States will declare war on North Korea in the next five minutes" or "it is possible that a man will grow to be 10 feet tall within the next 10 years" or "it is possible that there is animal life on Mars"? Are those modal or epistemic possibilities?

1 Reply

@kennethamy,

kennethamy wrote:

I do not believe that knowledge implies certainty (I mean "Cartesian certainty", and not merely the feeling of complete confidence that one is right. That is probably required for a sincere claim to knowledge, but claiming that one knows and its requirements is one thing. But knowing, and its requirements are an entirely different thing.

I agree with this, for the reasons given in my OP.

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@Owen phil,

Owen phil wrote:

No, there is no need for a bracket here.
p & <>(~p)

The conjunction is between the proposition p and the proposition <>(~p).

Is this to say that there is some world in which both p and not-p?

2 Replies

@ughaibu,

Owen phil wrote:
No, there is no need for a bracket here.
p & <>(~p)
The conjunction is between the proposition p and the proposition <>(~p).

ughaibu: Is this to say that there is some world in which both p and not-p?

No.
There is no 'situation', such as (p & ~p), that is true.
There is no possible world in which (p & ~p) is true.
If a contradiction occurs, during a deduction, then we have made a logical error.

<>(~p) -> ~p, s not valid. It is equivalent to: p -> []p.

Logic 'abhors' contradictions...Bertrand Russell.

1 Reply

@Owen phil,

Owen phil wrote:

There is no possible world in which (p & ~p) is true.

So there is no world in which we can know P, if knowledge is JTB, and P be false. In other words, we can only know P in exactly those worlds in which P is true. If we know P, in what sense of possibility can P be possibly not true?

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@ACB,

I fail to see your deeper point with this.

Sometimes capitals can change names, just look at Stalingrad which became Leningrad, or x-Yoguaslavia which got seperated in to many states, with new capitals.

We all live by our plausible spheres, that which is outside it isn't plausible to us, some has big spheres and belive in much, some has small spheres and are skeptical.

..but I still fail to see your deeper point with headline and post.

1 Reply

@ughaibu,

If p is analytic, then ...
If p is known, shown to be true, then ~p is a contradiction.
If (p is known to be the case) then ~p cannot be shown to be true.
[]p -> ~(<>~p)

(|-p) -> ~(<>(~p)). If p is shown to be logically true, then ~p is logically false.

For synthetic, contingent, propositions: If p is known to be true, eg. It is raining is confirmed by scientific methods, then ~p cannot be shown to be the case by scientific methods.

Perhaps there is a sense of physical necessity which has application here, but I am not clear about the meaning of physical necessity, are you?

1 Reply

@ACB,

ACB wrote:

kennethamy wrote:
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.

Thanks for your replies. Can you please clarify the difference between:

1. I believe that p, but some future evidence disconfirming p may arise
and
2. I believe that p, but for all I know, p is false.

Is it just a question of the degree of doubt (i.e. the doubt is negligible in the first statement, but not in the second), or is there a more fundamental difference? Are there borderline cases between modal and epistemic possibility? For example, "it is possible that the United States will declare war on North Korea in the next five minutes" or "it is possible that a man will grow to be 10 feet tall within the next 10 years" or "it is possible that there is animal life on Mars"? Are those modal or epistemic possibilities?

I don't really understand the purport of your question (and that does not mean I don't understand your question).

1. is true
2. is contradictory. For it is inconsistent to say that I know that p, and also that for all I know, p is false.

I don't see how doubt has anything to do with it.

But it is not inconsistent for me to assert I believe that p, and for all I know there will be disconfirming evidence in the future. I think that the difference between modal and epistemic possibility is a difference in kind, not in degree. It is logically possible that the US will declare war etc. and since it is highly unlikely (given all I know) that the US will declare war, it is false that for all I know the US will declare war.

Perhaps a better example would be this: In the Middle Ages mathematicians were still trying to square the circle. So far as they were concerned, for all they knew, it was possible to square the circle. But, nevertheless, it was logically (modally) impossible to square the circle. Another case (from Kripke). For all I know (it is epistemically possible) I might have had other parents than I do have. But (at least according to Kripke) it is "metaphysically impossible" (modally impossible) for me to have had parent other than the ones I had.

2 Replies

@HexHammer,

My OP was about the logic of saying "I know p" while claiming that p is not certain. It was not primarily about the possibility that capital cities can change. I was assuming, for the purpose of this argument, that I have no reason to believe that Paris has ceased to be the capital of France since I last heard about it. I am therefore certain for all practical purposes that it is still the capital, but I do not have "Cartesian" certainty about it.

By the way, Stalingrad became Volgograd. Leningrad was (and is again) St Petersburg.

1 Reply

@ughaibu,

ughaibu wrote:

Owen phil wrote:

No, there is no need for a bracket here.
p & <>(~p)

The conjunction is between the proposition p and the proposition <>(~p).

Is this to say that there is some world in which both p and not-p?

No. It is only to say that p is a contingent proposition, since although it is true, it is not logically impossible for it to be false. You are confusing: (1) It is impossible that, both p and not-p, with 2. It is impossible that p and possible not-p. (1) is true, but (2) is false. The same old modal fallacy, once again.

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@ACB,

ACB wrote:

By the way, Stalingrad is now Volgograd. Leningrad was (and is again) St Petersburg.

OoooOOoops! Ty for update. Mr. Green

Thanks for clarification.

Most programs up till 2000, was programmed in strictly logically manners, and would freeze up because they would make endless calculation to find a logically answer.
Now they'r programmed to end with a certain amount of time, and either come up with an answer or no answer.

For humans interacting with eachoter, it would be tiresome to have a normal conversation based upon absolute certainty, we do not demand to know the atomic weight of veggies we buy at the supermarket, it would be illogical. We do not demand to accurately know the distance to anything in nanometers.

Only when it actually serves an importaint purpose, accurate things comes to play, such as GPS navigation, fine optics ..etc.

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@ughaibu,

ughaibu wrote:

Owen phil wrote:
There is no possible world in which (p & ~p) is true.
So there is no world in which we can know P, if knowledge is JTB, and P be false. In other words, we can only know P in exactly those worlds in which P is true. If we know P, in what sense of possibility can P be possibly not true?

In the same old modal sense of possibility, obviously. Necessarily, if p is true, then p is true. But, it is not the case that if p is true, then p is necessarily true. The modal fallacy rears its ugly head once again. You really ought to be straight on this by now.

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@kennethamy,

I am still digesting your reply, but please note the following:

kennethamy wrote:

1. is true
2. is contradictory. For it is inconsistent to say that I know that p, and also that for all I know, p is false.

You have misread (2). I said "I believe that p...."

1 Reply

@ughaibu,

ughaibu wrote:

Owen phil wrote:
The operators apply to propositions not to other operators.
So, necessity and possibility aren't operators.

How would it follow from the proposition that necessity and possibility operate on propositions, and not on other operators, that they are not operators? For heaven's sake!

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Knowledge without Certainty

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