 Frege’s problems here stem from his requirement that the structure of thought conform perfectly with a notation for expressing the thought. The Logic “psychologistically” prioritizes the theory of thought over the theory of symbolization. If the authors had faced Frege’s objections, they could have insisted on inherent limitations in verbal expressions of thought. When one clearly and distinctly perceives that “5 is greater than 3” it is always affirmed. It is psychologically impossible to affirm “3 is greater than 5” unless the ideas are badly confused. If someone were to verbally assert “3 is greater than 5”, it would be a mystery what they were thinking unless it was a proposition about the words. Asserting a well-formed verbal expression corresponds to a well-formed thought only insofar as the thought is clear and distinct. Double negations are common in complex verbal propositions, but the Logic is not committed to these words signifying iterated “separations” that result in rejoinings. They can simply stand for affirmations. This means that when denial is described as “separating” ideas, that should be understood metaphorically. Denial in the Logic is perhaps better described as the recognition that the idea of the predicate is not among those included in the comprehension of the idea of the subject. And as usual, thoughts that are confused need to be sorted out before they can be precisely expressed. The same holds for triple negations and denials. (For a further discussion, see section 2.7.1 of the entry on  Frege.)