I personally don’t feel the implication
If ZFC + PD is inconsistent then ZFC is inconsistent.
I have a couple of questions for you.
- I am under the impression that you are not committed to the consistency of ZFC + HUGE. Are you committed to the consistency of ZFC + LC roughly if and only if there is some good inner model theory for it? Are you also advocating a more general principle of this kind?
- Consider the statement: If ZFC is inconsistent then T is inconsistent. For how weak a T do you feel this? As an extreme, are you willing to take T down to EFA = exponential function arithmetic?
- As you can see from what I wrote about blurring pictures, my own view is one of relative clarity and therefore relative confidence. But you seem to have quite a different view, and I am wondering what you can say about your view (feelings, intuition)?