Is logic faith?

Originally posted by Conrau K
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 p or true or whether P is false or true. P does not follow trivially from such a dialetheia.

So I do not really understand your accusation that diatheleia commits us to trivialism. In fact, it seems to be the solution for trivialism.

Not at all. You seem to be thinking here that trivialism is the problem when things follow from a false proposition, but that is explicitly wrong. Trivialism is basically the thesis that every proposition is true. If it were the case that something followed from a FALSE proposition, then it would also be the case that trivialism, obviously, is false. The reason why dialetheism could lead to trivialism (and many prima facie think it does) is because it affirms the idea that contradictions can be true. (Obviously, if under normal convention contradictions are always simply false, then there is absolutely no threat of trivialism).

But at any rate, I do think you are right that there is something wrong with the disjunctive syllogism when we are dealing with a dialetheia. I think you are quite right in your analysis there.

EDIT: Also, the website has good discussion: http://plato.stanford.edu/entries/dialetheism/

ConrauK, I guess I would also add this as further clarification. Yes, in normal convention the inference from X and ~X to P is taken as valid, but nobody would take it as sound because contradictions are always false. Now, the problem with admitting a dialetheia, so some claim, is that now it is sound because you start with a contradiction that is nevertheless true. Of course, this charge is predicated on the idea that the disjunctive syllogism still holds.

At any rate, that dialetheism entails trivialism certainly holds under explosion, so it seems that the dialetheist must embrace some form of paraconsistency (at least under the definitions of 'explosive' and 'paraconsistent' given in the above link).

Originally posted by LemonJello
Sorry I haven't responded sooner -- I was on vacation.

[b]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.

Then this is the part I was failing to understand before. Also "according to formal logi ture the currency of natural usage, even when it comes to the vague properties.[/b]

Doesn't make any sense to me how you get to employ formal logic here and yet not there. Also, I fail to see how you go from X's being in the truth-value gap to ~(X or ~X) being true. If X is in the truth-value gap, then why would something like ~(X or ~X) not also be in the truth-value gap?

~(X or ~X) is the definition of a truth-value gap. In a truth-value gap, X can be neither affirmed nor denied; it is neither true nor false. Hence, ~(X or ~X). And under classical rules, the inference from ~(X or ~X) to X & ~X is valid. Obviously there is something suspect about that. The two mean the opposite: the first says that X is neither true nor false; the other says that it is both true and false. I admit that there is something dodgy about the above inference but then again, I am not the one championing formal classical logic.

Basically, I think I understand what you are saying, but I am not at all convinced we need fuzzy logic in order to capture the currency of natural usage, even when it comes to the vague properties.

Does this mean that you, like Palynka, believe that there is an exact numerical definition which divides blue from not-blue or for any vague property and its negation?

Originally posted by LemonJello
[b]So I do not really understand your accusation that diatheleia commits us to trivialism. In fact, it seems to be the solution for trivialism.

Not at all. You seem to be thinking here that trivialism is the problem when things follow from a false proposition, but that is explicitly wrong. Trivialism is basically the thesis that every proposition ...[text shortened]...

EDIT: Also, the website has good discussion: http://plato.stanford.edu/entries/dialetheism/[/b]

Trivialism is basically the thesis that every proposition is true. If it were the case that something followed from a FALSE proposition, then it would also be the case that trivialism, obviously, is false. The reason why dialetheism could lead to trivialism (and many prima facie think it does) is because it affirms the idea that contradictions can be true.

I think you are travelling too quickly for me! Does trivialism follow whether or not we accept the inference from X & ~X to P?