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Branched Type Theory/Prior :: comes in when terms form a sentence of a single name - here we must distinguish whether quantified expressions of the same type occur - E.g. "__ has all the qualities of a great commander" - logical form: "For all f, if (for all x, if x is a great commander, then fx) then F__ "- PfPxCyxfx" - Easier e.g. "__ has one or the other property" - logical form: "For a f, f __" - "SFF" - order/Type: here you can say, even though the predicate of the same type, it also is of different order - Because this "f" an internal quantification of "f" s "- BTT: not only different types, but also different "orders" should be represented by different symbols.
Objects of thought Oxford 1971
Arthur N. Prior
Papers on Time and Tense 2nd Edition Oxford 2003