I used to think I knew what Peirce was talking about in this passage but it looks like it may be time to make a new examination of that.
- Guess 1. Strictly speaking he’s talking about his earlier system of “entitative graphs” which are logically dual to existential graphs as far as propositional calculus goes. That may not affect his point, except he did not extend the entitative graphs to cover the logic of relative terms, so he may be talking about the limitations of absolute versus relative terms.
- Guess 2. He may be alluding to the complex way he treated negation in his 1870 Logic of Relatives, which is very tricky but worth revisiting.
- Guess 3. He may be talking about the threshold between first intentional and second intentional relatives, which may or may not be the same thing as first order versus second order logic.
At any rate, I’ll be looking further into it …