Is logic faith?

Originally posted by black beetle
Therefore, since you express no opinion for you have no rational way to confirm it, maybe now we could agree that it is wrong to state "I choose not to accept as true or established fact that of which I cannot become aware, either through my own perceptions, or through those recounted by others whom I can accept as rational and reliable sources"
😵

that doesn't follow at all. quite the reverse. it says the same thing. I choose not to accept or established fact what I cannot know -- and I do not express an opinion in most such cases.

In some cases, however, I may choose to express an opinion, knowing it is just that.

I don't need confirmation in order to express an opinion -- I prefer it, but it isn't necessary. Truth and opinion are somewhat different things, or are you unaware of that?

Religious faith, for example, is based entirely on opinion -- but a lot of people choose to embrace it anyway and merely opine that they can confirm the basis of their faith as fact. When two people cite, respectively, the Bible and the Koran for propositions that are directly contradictory -- Jesus was divine, Jesus was not divine, just a prophet -- what then?

Originally posted by twhitehead
On my monitor (a 21" CRT) the lines are curved in the third dimension. Kellys point is that in previous discussions we have claimed that a line that is straight in one dimension may be curved in others. He feels this violates the intended meaning of 'straight'.

I know what he says -- it is immaterial. Your example is flawed. What is the definition of "Straight Line"?

You may introduce whatever subjective content you choose with respect to the meaning of a word, but you risk not being understood and also being incorrect in the judgment of those who form the majority who comprise the consensus on the usage of the word at any given time.

Folks say you can't use words to mean whatever you like; I disagree. Yes, you can. But you may become increasingly isolated and unable to communicate properly if you do that and are sincere.

In your case, my opinion is you are merely saying this for effect, introducing immaterial content into a word you well know excludes this content in normal, contemporary usage.

Originally posted by KellyJay
You asked me about God? I may bave missed that, I'll go back and
attempt to see the context in which you did that.
Kelly

here it is again:

When you refer to God, what do you mean by the word "God."

There, I have used and mentioned the word in the same sentence. While answering the question, please also think about whether you know the difference.

Originally posted by black beetle
Therefore, since you express no opinion for you have no rational way to confirm it, maybe now we could agree that it is wrong to state "I choose not to accept as true or established fact that of which I cannot become aware, either through my own perceptions, or through those recounted by others whom I can accept as rational and reliable sources"
😵

A more direct way to reply to this:

we cannot agree -- I chose not to express an opinion chiefly because that opinion would be that you are more probably than not lying about where you are.

but since you are going to use what I said to distort even further the discussion, there it is.

you really ought to pay more attention to the specific words -- such as "choose"

Originally posted by Scriabin
that doesn't follow at all. quite the reverse. it says the same thing. I choose not to accept or established fact what I cannot know -- and I do not express an opinion in most such cases.

In some cases, however, I may choose to express an opinion, knowing it is just that.

I don't need confirmation in order to express an opinion -- I prefer it, but it ...[text shortened]... irectly contradictory -- Jesus was divine, Jesus was not divine, just a prophet -- what then?

I will make it clearer:

Since you express no opinion for you have no rational way to confirm it, you accept that you don't have the knowledge required in order to express an accurate opinion. This means that you accept your ignorance, and it is OK.

However, since you are ignorant, you cannot choose not to accept as true or established fact that of which you cannot become aware, either through your own perceptions, or through those recounted by others whom you can accept as rational and reliable sources. You cannot choose neither that it is true nor that it is false, because you are ignorant.

Methinks that since you are ignorant, you must just state that you do not know what is true and what is not true -and this is the reason why the Smiling Cat can be alive/ dead at the same time. This happens because a person that is aware of her/ his ignorance cannot be sure that her/ his choise is accurate, thus "right" or "wrong"; so her/ his sole decision is to state that s/he doesn't know.

On the other hand, an ignorant who is not aware of her/ his ignorance, is sure that her/ his opinion is anyway "true" and s/he never changes her/ his mind -trapped forever s/he remains. Therefore, regardless her/ his choise, s/he decides to choose her/ his personal truth. Methinks this attitude is wrong because this is a false decision.

Back to the phrase you addressed to vestesd: methinks that the agent that pushed you to decide what is true and what is false, is your ignorance and not your awareness; and of course its content is irrational although it seems to you logical due to the fact that your mind sees not the contradiction😵

Originally posted by Scriabin
A more direct way to reply to this:

we cannot agree -- I chose not to express an opinion chiefly because that opinion would be that you are more probably than not lying about where you are.

but since you are going to use what I said to distort even further the discussion, there it is.

you really ought to pay more attention to the specific words -- such as "choose"

I distort nothing; and we may agree that we disagree😵

Originally posted by black beetle
and this is the reason why the Smiling Cat can be alive/ dead at the same time.

I hope you are not talking about Schrodingers cat. His cat is far more complicated than that.

Originally posted by twhitehead
I hope you are not talking about Schrodingers cat. His cat is far more complicated than that.

This is the cat; I know that it is more complicated than that😵

Originally posted by twhitehead
I hope you are not talking about Schrodingers cat. His cat is far more complicated than that.

So I have to stand corrected as following:

"Methinks that since you are ignorant, you must just state that you do not know what is true and what is not true -the Smiling Cat could be alive or dead at the same time."

Excuse me for the inconvenience😵

Originally posted by Conrau K
[b]I don't see where your X & ~X fits in. Clearly all intermediate shades are ~Pure Blue and ~Pure red. Not one of them is both Red and ~Red or Blue and ~ Blue. I certainly don't see who one can assign some sort of fuzzy truth to them.

But there is no clear-cut 'pure' blue region. You can say that one region is definitely blue, one definitely red, an ...[text shortened]... ot-blue (and ~(X V ~X) implies X & ~X in formal logic). How does that not illustrate X & ~X?[/b]

(and ~(X V ~X) implies X & ~X in formal logic). How does that not illustrate X & ~X?

But in formal logic, it also seems that everything follows from a dialetheia:

X and ~X.
Therefore, P. (Where P is any proposition.)
(Because: X; so X or P; ~X; therefore P).

So, if we admit a dialetheia like X and ~X, then how do we avoid the commitment that indeed everything is true (trivialism)? It seems we would have to embrace some form of paraconsistency under which the inference from X and ~X to P fails to hold for at least some P. Do you have some ideas on this?

By the way, I am just looking for some discussion since this is one topic that interests me. I agree with all the points you have raised in this thread. (Except for your argument above, which confuses me: I am confused because earlier you stated that where it concerns properties that suffer from vagueness, X and ~X should have no truth value [fall in the truth-gap] or else be assigned some "fuzzy" truth value; whereas, here it seems now you are arguing that X and ~X is a dialetheia. Relatedly, this argument of yours invokes "formal logic", whereas earlier you invoked fuzzy logic.)

Originally posted by LemonJello
[b](and ~(X V ~X) implies X & ~X in formal logic). How does that not illustrate X & ~X?

But in formal logic, it also seems that everything follows from a dialetheia:

X and ~X.
Therefore, P. (Where P is any proposition.)
(Because: X; so X or P; ~X; therefore P).

So, if we admit a dialetheia like X and ~X, then how do we avoid the com ly, this argument of yours invokes "formal logic", whereas earlier you invoked fuzzy logic.)[/b]

So, if we admit a dialetheia like X and ~X, then how do we avoid the commitment that indeed everything is true (trivialism)? It seems we would have to embrace some form of paraconsistency under which the inference from X and ~X to P fails to hold for at least some P. Do you have some ideas on this?

I do not think that fuzzy logic necessarily admits dialetheia. In Lukasiewicz calculus, it is simply not possible to assert v(X) = 1 and v(~X) = 1, because v(~X) is defined as 1-v(x). So if X is true, then ~X must be false. Fuzzy logic only admits that the conjunction of X and ~X may have partial truth -- so X is simply not assertible on the grounds that X & ~X has some fuzzy truth-value. So the explosion simply stalls after the first premise.

I think that, however, were we to admit dialetheia, the disjunctive syllogism would no longer be valid. So, X or P, ~X, P is no longer valid. A counter-example would be v(X) =1, v(~X) =1 (which were the initial premises) and v(P) =0.

Except for your argument above, which confuses me: I am confused because earlier you stated that where it concerns properties that suffer from vagueness, X and ~X should have no truth value [fall in the truth-gap] or else be assigned some "fuzzy" truth value; whereas, here it seems now you are arguing that X and ~X is a dialetheia. Relatedly, this argument of yours invokes "formal logic", whereas earlier you invoked fuzzy logic

Well, as I see it, if we accept a truth-value gap, then X and ~X obtains trivially. If X can be assigned no value, then ~(X or ~X) is true, and, according to formal logic, then X and ~X is also true. I think that I only mentioned this in my last post as an aside, simply to illustrate that fuzzy logic is not the only way in which bivalence fails. Personally, I prefer fuzzy logic because I think it reflects our natural usage. When a girlfriend "I am sort of fat, sort of not" she is probably asserting (or intending to assert) that she is sort of in-between, that her 'fatness' is something vague.

Originally posted by Conrau K
Good. I only disagree with the statement that X & ~X is always incoherent. I can see many instances in natural language where such contradictory statements have currency, especially when we deal with vague properties (like fatness, blueness, tallness).

But in those examples it is the X which is not clearly defined, not the logical operation. In your case, there are elements for which you can't even say if it belongs to your set X.

Originally posted by Palynka
But in those examples it is the X which is not clearly defined, not the logical operation. In your case, there are elements for which you can't even say if it belongs to your set X.

Precisely. X is not defined; it is some vague proposition. So there are instances when X may seem partly true and ~X seem partly true, and their conjunction not seem incoherent.

Originally posted by LemonJello
[b](and ~(X V ~X) implies X & ~X in formal logic). How does that not illustrate X & ~X?

But in formal logic, it also seems that everything follows from a dialetheia:

X and ~X.
Therefore, P. (Where P is any proposition.)
(Because: X; so X or P; ~X; therefore P).

So, if we admit a dialetheia like X and ~X, then how do we avoid the com ly, this argument of yours invokes "formal logic", whereas earlier you invoked fuzzy logic.)[/b]

Now that I give it a bit more thought, I think that dialetheia is actually quite sound. In formal logic, one of the most recognisable shortcomings is that the inference from X and ~X to P is trivially true -- everything follows from false premises. So I can argue "The earth is round and the earth is flat; therefore, I own a pair of sunglasses" and this is perfectly valid (assuming that I do no mean another thing by 'round' and 'flat'😉 yet intuitively invalid. It is valid because no counter-example can be conceivably constructed. Since contradictions are always false, there can never be a counter-example in which X and ~X is true and P false. But no one seriously believes that since because of this contradiction, I therefore own a pair of sunglasses. The conclusion seems totally irrelevant from the premises. But if, however, we admit a dialetheia (perhaps in some paraconsistent modal world) that the earth is both round and flat, then the conclusion is no longer trivially entailed.

So I do not really understand your accusation that diatheleia commits us to trivialism. In fact, it seems to be the solution for trivialism. The disjunctive syllogism (X or P; ~X; therefore P) simply does not follow if we allow that X and ~X obtain in some situations. Since the truth of ~X no longer implies the falsity of X (because they can both be true), so the disjunction of X and P is still true whether ~X is false or true or whether P is false or true. P does not follow trivially from such a dialetheia.

Originally posted by Conrau K
Precisely. X is not defined; it is some vague proposition. So there are instances when X may seem partly true and ~X seem partly true, and their conjunction not seem incoherent.

If you don't even know what X is, how can you say it's true, partly true or untrue? Moreover, what does ~X mean if you can't define X?

There is no conjunction until you define the sets.