"We" in my writing generally refers to "all people". Since I do not believe anyone should do anything that is not his or her choice, my statement that we do think in threes is an assumption not an instruction. My reasons for coming to this are frankly the fruit of my relatively recent encounter with Peirce. Although I would describe my thinking over time as pragmaticist, I never thought about how we think until I was exposed to the triadic thinking of Peirce. Quite simply it seemed utterly obvious that it made a difference if you think in twos or in threes. If you think in twos you see one side or another. Binary. If you think in threes you have always a third possibility and triangles can be iterated infinitely.
Now at what point did I also come to think that we do think in threes? I have been at this for only a short time, perhaps three years. I inferred that this is the case from a look at history. It is those who have found a third way that have made progress. That is certainly one element on the contention. You could call it as Niebuhr did our capacity for transcendence.
As to logic - I believe that triadic thinking is conscious thinking and that everyone should think in threes, but that the number who consistently do is at present small and difficult to determine. I certainly do not think that everyone should be made to think thus.
I do not think, incidentally, that logic is about what we must do. I think logic is about what makes the most sense.
Triadic thinking is entirely an optional process and it involves, for me at least, thinking about more than three particular matters or terms. What makes the method triadic is that it encloses its stages in three related terms which I call the root triad - reality, ethics, aesthetics. To get through a conscious process using this triad, I would consider a sign and the word that expresses it and then an index of values of which there are four and then an action or expression which I relate to a linked term truth-beauty or beauty-truth. The whole process is a meditational or musement-like exercise grounded in the assumed efficacy of its elements to produce positive results.
Finally, it seems to me that what I am trying to do is not to specify what constitutes the optimal means of resolving philosophical questions or indeed any other question that depends on an extended articulation of categories. My effort is the modest one of seeking to provide to the ordinary person a viaticum on a journey to truth and beauty, to reiterate a phrase from Kenneth Burke. Is this pragmatic? I would not dare claim it since as I have indicated I am not seeking to abide by the pragmatic maxim's limitations. I am trying to arrive at a measurable means of proving out the power of memorial maxims to positively affect the course of history.