@thirstybear @mavnn @jay_peper my understanding of the term "formal" is that it would be devoid of semantics. In formal logics, is just about what you can derive from your axioms and derivation rules, not about the resulting statement corresponds to reality, or any other semantics. I always found it mind boggling that the terms "true" and "false" are, formally, entirely equivalent.
I think what you wanted to refer to is not a formal meaning of true, but a strict corresponding-to-reality meaning of true, in my understanding.
But I might be entirely off.
@[email protected] Ha! No, you're not completely off and it's a fair implication that I was being somewhat informal in my use of 'formal'. Yes, I had taken as one of my axioms was that the statement "Tom is at the party" would be true if and only if Tom is actually at the party. If I choose to define the semantics of 'true' to include whether Maria honestly (and with some arbitrary level of evidence) believed the statement at the time, then we get (I think) to @[email protected] 's position which I find completely reasonable especially in everyday conversation.
Personally I struggle more with @[email protected] 's assertion that 'formal' truth is based on information available. You could define truth as depending only on the information you have available, but if you apply that formally you get into a weird situation where you confidently state things as true (or false) when you know you have a high probability of not being correct - which could be logically consistent, but in the broader context could also frequently be called dishonest!