I think we need to be careful in that dogma is defined as a set of principles laid down by an authority. If an individual expresses their own truth that is not dogma. However, if that truth came from an authority, then we can call it dogmatic. But each individual has their own truth and it is up to each individual to work through that truth. That is separate from fact as your mathematics is pointing out.
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Agreed although when man is self governing he becomes his own authority and his own belief is dogma held as indisputably true.
This state may be preferable to external authority but both are a choice at an individual level.
I think your key word is 'indisputable'. If a self-governing individual is not willing to be confronted or explore his own beliefs, that is dogmatic much like a centralized authoritarian regime. But now you are into the area of faith. So how do you start to differentiate between dogma and faith?
Faith and Dogma synonyms although not perfect ones.
One of faiths definitions near enough to dogma.
It becomes hard to seperate the two if we use lower case f its a simple word that we can call a trusting hope e.g. I have faith that my relationship with wife will remain strong as we both work at supporting and encouraging each other even in hard times.
A capitalized F however has a totally different feel moving from trust to Truth.