I came here to ask this and was immediately derailed by three threads.
However, there is a specific word for convincing your self what you have said is true- even though it may be a lie. Just one word and it is driving me around the twist.
In the book 1984 they use the word “doublethink” for sincerely believing your own lies.
Sorry- not the word I’m looking for. I came across it in a book such as “You are not so smart”
I don’t think “cognitive dissonance” is the term you are looking for, but it is a closely related concept.
I almost used Cognitive Dissonance in the original post (I deleted it) but after looking it up I didn’t think it really capture what I was looking for. Great minds…? 
It’s not self-deception, is it?
I would use self deluded rather than self deception. Also self deluding, self delusional and self delusion. Not sure about a hyphen. I’ve omitted it here but I am probably deluding myself.
TCMF-2L
George Costanza: “It’s not a lie if YOU believe it!”
Sorry, don’t know the word for it though. Cognitive dissonance is the closest thing I can think of.
Self delusion is the word.
Hmm… the OP didn’t specify that the speaker was definitely wrong, just that objective truth was not guaranteed- so none of the words that require the speaker to be wrong are appropriate either.
The word I would use would be ingenuous.
Similarly, you can be disingenuous whether or not it turns out that your words end up being objectively true.
To me ‘ingenuous’ means something like naive or innocent. I’ve never heard it used in this context before. I would just say ‘confident’ or ‘self-assured’ to avoid the presumption of falsehood.
Perhaps ‘self-reinforcing’ fits the OP better.
Or maybe you mean ‘rationalising’? Could you provide us with the context?
“convincing your self what you have said is true- even though it may be a lie. Just one word and it is driving me around the twist.”
I’m going to have to agree with “rationalize.”
Sincere
“He’s a legend in his own mind.”
Honest is another word.
Just because you’re not lying doesn’t mean you’re correct.
No, doublethink means the ability to hold two, mutually contradictory, ideas in your head simultaneously and accept the one that is most appropriate at the time.
confidence.
The word you are looking for is RELIGIOUS.