Language

Is "understanding" a proposition necessary, but not sufficient, for "believing" that same proposition? Further, where could one find arguments (discussion) for and/or against either position?

Comments

Let's assume the following:

(1) If you understand a proposition, then you also understand its negation.

(2) It is necessary, if you are to believe a proposition, to understand it.

(3) It's perfectly possible to believe a proposition and not believe its negation.

It follows from these that understanding a proposition is not sufficient for believing it. So there's an argument.

One might wonder why we should accept (1)-(3), of course.

I think most people would take (2) to be obvious enough. What's meant here by "understanding" is something like: being able to take mental attitudes towards. Belief is just such an attitude.

Regarding (1), this just seems to follow from your understanding what negation is. For detailed discussion, however, one might look at Frege's last essay "Negation".

Regarding (3), one would hope that it is true! Even if we sometimes believe contradictions, one would hope we didn't always have to do so!!

I confess I'm puzzled by Prof. Heck's reply. He defends the following three assumptions:

(1) If you understand a proposition, then you also understand its negation.
(2) It is necessary, if you are to believe a proposition, to understand it.
(3) It's perfectly possible to believe a proposition and not understand its negation.

I interpret those assumptions as follows:

(1*) Understanding P entails understanding not-P.
(2*) Believing P entails understanding P.
(3*) Believing P doesn't entail understanding not-P.

(1*)-(3*) imply a contradiction: Believing P does and doesn't entail understanding not-P. If so, then (1)-(3) imply everything (if I've interpreted them correctly). I also don't see how the falsity of (3) implies that we would always have to believe contradictions. If (3) is false, then believing P entails understanding not-P; I don't see how any unwelcome consequences follow from that.

PLEASE NOTE: (3) above was taken from Professor Heck's original posting, which he has since amended. [Alexander George on 6/6/2014.]

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