> Claiming you've not examined your own mental machinery is... concerning

The example was carefully chosen. I can introspect how I calculate 356*532. But I can't introspect how I calculate 14+17 or 1+3. I can deliberate the question 14+17 more carefully, switching from "system 1" to "system 2" thinking (yes, I'm aware that that's a flawed theory), but that's not how I'd normally solve it. Similarly I can describe to you how I can count six eggs in a row, I can't describe to you how I count three eggs in a row. Sure, I know I'm subitizing, but that's just putting a word on "I know how many are there without conscious effort". And without conscious effort I can't introspect it. I can switch to a process I can introspect, but that's not at all the same