My apologies for not responding to this sooner. Since the comments on the page seem not to occur too frequently, I have not been keeping tabs on them.
I think that your issue (in terms of not knowing what we mean by falsehood or truth) is deep and interesting. One may consider Quine's paradox, which goes as follows:
"yields a falsehood when preceded by its quotation" yields a falsehood when preceded by its quotation.
We may take here falsehood as being (as you say) the opposite of a truth - informally or otherwise. Then we have context, we understand what "points at" what, and yet there is paradox.