How one determines correlation with reality is a separate issue… . 'Truth' is a more primitive idea that underlies that…

I don’t think the issues are nearly so separate as you presume. If one is going to define truth as “correlation with reality”, then one must able to precisely define “correlation with reality” in order to render one’s concept of truth precise. If one fails to do so, then one leaves the concept of truth only vaguely defined. And under such a vague definition, one is not justified in deriving such a strong conclusion as, “If [‘true’] does not imply not false, then it seems to lose all meaning.”

To make that claim, one is in essence defining “true” with respect to its logical inverse “false”. But this definition is explicitly circular. Nothing can follow from it logically without placing it within a broader conceptual context. And placing it in that broader conceptual context, again, requires not merely saying “truth indicates correlation with reality,” it requires additionally defining in a conceptually rigorous fashion what “correlation with reality” actually means.

Either way, whether you want to take the rigid inverse relationship between true and false as axiomatic – or whether you take an identity relationship between “true” and “correlates to reality” as axiomatic instead – the use of the term “correlates to reality” without a physically-grounded definition establishing the nature of this correlation renders the statement something of a vapid claim.

If you want to accept that something can be both true and false at the same time, you have to have some concept of what those words mean.

Indeed. And likewise if you want to accept that some cannot be both true and false at the same time. But you have said nothing to establish why this “some concept” must be a formally precise concept. And it is only with respect to this formally precise concept of truth and falsity that such rigid claims as “T = ~F” make sense in any rigorous sort of fashion.

One of the major mechanisms through which our minds categorize the world is the establishment of dichotomous distinctions that serve to define two conceptual structures as polar opposites. But the broader reality to which those categorizations correlate more often consist of continuums that span the conceptual space between those poles…