Yes. The problem is that one cannot consistently claim both (i) "I know A", "I know B", "I know C" etc, and (ii) "I do not know the conjunction of A+B+C etc". And since it would be unreasonable to deny (ii), the difficulty lies with (i).

Yes. The problem is that one cannot consistently claim both (i) "I know A", "I know B", "I know C" etc, and (ii) "I do not know the conjunction of A+B+C etc". And since it would be unreasonable to deny (ii), the difficulty lies with (i).

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Then I'm not wrong am I? I say it's not a contradiction, it's not a contradiction, and you agree that it's not a contradiction. That a contradiction can be reduced from it (as you say) may be important; in fact, it may be very important, but it has no bearing (so far as I can tell) on whether I'm right or wrong.

I do appreciate your post, however. I saw then (and continue to see now) that there is a problem when "may" is used, but I didn't know that the problem I saw ought to be characterized as something that implies a contradiction. Had I realized how to characterize it, I probably should have mentioned it when denying (and rightly so) that there is no contradiction.

What is the conjunction of A+B+C? What would the actual claim in (ii) be? "I don't know anything"? Who would claim, "I don't know anything", after claiming they know something?

No, the claim in (ii) would be "I don't know collectively everything that I claim to know individually" or "I don't know collectively everything that I confidently believe individually".

It is reasonable to claim to know collectively most of what one claims to know individually. If one has strong justification for believing a large number of things, it is likely that most of them are true, but that a few are not. One would have to be extraordinarily lucky to go through life without having any of one's confident beliefs proved wrong.

It is not unreasonable to deny (ii).

What is unreasonable is to deny the conjunction of (i) and (ii).

Fine. A contrary can be inferred from the statement, not a contradiction, so the statement is not a contradiction.

I do better at seeing contradictions (contradictory statements) when I'm comparing two statements, so I'll break the sentence apart. The sentence is, "I know that P, but for all I know, P may be false." I'll break it down into the following statements:

P1-1: I know that P.
P2-1: P may be false.

Knowledge implies truth, so P1-1 implies that P is true. Here it is written out:

P1-1: I know that P.
P1-2 (an implication of P1-1): P is true.
P2-1: P may be false

We cannot imply that P is true from P2-1, so we cannot conclude that P is true based on P2-1.

Moving on:
A statement doesn't exist in a vacuum, so I'll assume that the statements are being asserted. We would not assert P1-1 unless we believed we had a good reason to believe P is true, so it's inconsistent for someone to assert P1-1 (that has the implication that they have a good reason to believe P is true) and assert P2-1 (that has the implication that they have a good reason to believe P is false), but since when is that a contradiction?

To deny (ii) is to claim that none of your vast number of confident beliefs is wrong. (That is to say, it is logically possible for them to be wrong, but in fact none are.) But do you seriously believe this? Have you never experienced astonishment, arising from the falsification of something you were utterly convinced was true? And do you not expect to experience it again at some time?



I think you mean: "What is unreasonable is to claim the conjunction of (i) and (ii)". (Look at my wordings again.) And I would agree with that.

Then I'm not wrong am I? I say it's not a contradiction, it's not a contradiction, and you agree that it's not a contradiction. That a contradiction can be reduced from it (as you say) may be important; in fact, it may be very important, but it has no bearing (so far as I can tell) on whether I'm right or wrong.

I do appreciate your post, however. I saw then (and continue to see now) that there is a problem when "may" is used, but I didn't know that the problem I saw ought to be characterized as something that implies a contradiction. Had I realized how to characterize it, I probably should have mentioned it when denying (and rightly so) that there is no contradiction.

Yes. The problem is that one cannot consistently claim both (i) "I know A", "I know B", "I know C" etc, and (ii) "I do not know the conjunction of A+B+C etc". And since it would be unreasonable to deny (ii), the difficulty lies with (i).

Fine. A contrary can be inferred from the statement, not a contradiction, so the statement is not a contradiction.

I do better at seeing contradictions (contradictory statements) when I'm comparing two statements, so I'll break the sentence apart. The sentence is, "I know that P, but for all I know, P may be false." I'll break it down into the following statements:

P1-1: I know that P.
P2-1: P may be false.

Knowledge implies truth, so P1-1 implies that P is true. Here it is written out:

P1-1: I know that P.
P1-2 (an implication of P1-1): P is true.
P2-1: P may be false

We cannot imply that P is true from P2-1, so we cannot conclude that P is true based on P2-1.

Moving on:
A statement doesn't exist in a vacuum, so I'll assume that the statements are being asserted. We would not assert P1-1 unless we believed we had a good reason to believe P is true, so it's inconsistent for someone to assert P1-1 (that has the implication that they have a good reason to believe P is true) and assert P2-1 (that has the implication that they have a good reason to believe P is false), but since when is that a contradiction?

Yes, I understand what you pointed out. Thank you. And fine, I'll accept that. But, we still shouldn't call a statement that doesn't imply a contradiction a contradiction.

The complex statement, "I am in Florida, and I am not in Florida" is a contradictory statement, for the simple statements "I am in Florida" and "I am not in Florida" contradict one another.

The complex statement, "I am in Florida, and I am in South Carolina" is a contrary statement, for the simple statements "I am in Florida" and "I am in South Carolina" are contrary to each other.

The complex statement, "I know that P, but for all I know, P may be false" can be broken apart into simple statements just as I did in the previous two examples: "I know P" and "P may be false."

You said that what implies a contradiction is, itself, a contradiction, so let's see what "I know P" implies to see if it (along with "P may be false") implies a contradiction, for if it does, then the complex statement is, itself, a contradiction.

Knowledge implies truth, so "I know P" implies P is true, but the simple statement "P is true" (an implication of "I know P") and the simple statement, "P may be false" are not contradictory statements, so we have yet to derive the conclusion that the complex sentence is contradictory.

You, I, nor anyone else should say that we know P unless we have a good reason to think P is true, but be that as it may, it's still not the case that "P may be true" and "P may be false" are contradictory statements, so although the complex statement may not be contradictory, it is contrary-in other words, some implications of the simple sentences derived from the complex statement are contrary to one another.

I want pictures! SERIOUSLY!!!

PS: Georgia girls have the most adorable accents!

Funnin' aside, I'll review what I thought I knew about contraries. Thanks for your review of my post. I'll give it some thought.

A contradiction is deducible from "I know that P, but for all I know, P may be false", namely, "I know that P and I do not know that P.".

Exactly. It's not logically impossible; It's not a contradiction.

If I say to another that "I'm in Florida, and oh by the way, I'm also in South Carolina," a person that confuses "contrary" with "contradiction" might say that I have said something contradictory, but the sentence, "I am in Florida" and the sentence "I am in South Carolina" are not contradictory sentences, but the each sentence is contrary to the other.

Alright. But going with Ken's definition "I'm wholly in Florida, and oh by the way, I'm also wholly in South Carolina," is a contradiction. (Unless it is possible that they refer to the same object/space. I don't know.)