Binary processes may be observed at various stages of intuitive and deliberative thought, which may in some cases plausibly be modelled as categories, but you’ll want to consider that on a case-by-case basis. Many of the relevant processes are binary simply because like formal logic, they involve toggle switches (true/false).
The simplifying processes alluded to in the question have been studied above all in the form of heuristics, i.e. mental strategies for judgement and decision-making that bypass a good deal of relevant computation in favour of simple cues that seem to (but may not) correlate well with success (Payne, Bettman, and Johnson 1993; Gigerenzer and Todd 1999; Czerlinski, Gigerenzer, and Goldstein 1999). A variety of models exist, most of which concern preferential decision-making, but categorization models also exist, and at any rate the two are closely intertwined. Most models involve binary processes in the selection process, particularly because judgement and decision-making involve matching objects against a criterion. Examples are the decision-making model Elimination by Aspects (Tversky 1972) and the categorization model Categorization by Elimination (Beretty, Todd, and Blythe 1997), which cycle through features in order of descending salience and/or effectiveness at narrowing down choice. Objects (options) that fail to meet the criterion under review are ruled out; it could thus be said that there is a binary matching principle at work even in cases where the cue (e.g. wine aroma) is not binary. Another popularly studied example is the recognition heuristic, which associates the known objects in a set with a higher criterion value than unknown objects in the same set: this strategy is modelled on a binary cue (match or no match, as opposed to a graded scale). The particular effectiveness of simple heuristics in situations with binary cues is discussed in Hogarth and Karelaia 2006.
It should be noted, however, that some of the most commonly mentioned studies of preferential decicion-making involve binary choice: which of the two? This binary feature is a research bias: binary choice is the minimal working example of preferential decision-making. Still, the recognition heuristic is of relevance to the question precisely because it does not provide a complete strategy for dealing with a variety of objects with different degrees of familiarity. It says simply that a first strategy can be to distinguish between completely unknown and not completely unknown, at which point the use of this heuristic is exhausted and the mind turns to other strategies. The real significance of this heuristic to the question therefore depends on its validity and documented application with non-binary sets and relative familiarity; the outcome of such tests would tell you a good deal about the real-world attestation of dichotomous thinking along these lines.
In the tradition of Payne and Gigerenzer, adaptiveness is a critical part of the heuristic process: environmental factors determine what reductive strategies we use. When simplifying reality through heuristic means, what features survive in our cognitive model of the world at the moment of judgement or decision-making will thus depend on why we are accessing these concepts in the first place. A binary set like day and night is more likely to occur to us when deciding whether to bring our bicycle lights when leaving the house, and less likely when scheduling a dentist appointment (though this too involves a binary set, available/unavailable).
The elimination models developed for decision-making have also been used to model memory access to semantic content. Rachel Giora has written a slew of articles advancing the idea that word senses that are salient in the mental lexicon are accessed first; other senses are activated if the first does not match the context (e.g. Giora 1999). The same matching paradigm could be extended across many aspects of syntax, for instance.
That should be a start, but it’s a topic of some scope. Keywords could combine members of the following sets:
- contrast, contrastive, binary, dual, dualistic, dichotomous, dichotomy
- heuristic, cognitive, salience, simplify, simplification, judgment, judgement, decision
@Nick Stauner's comment and @what's answer contain references to significant additional avenues to investigate.
Berretty, Patricia M., Peter M. Todd, and Philip W. Blythe. 1997 “Categorization by Elimination: A Fast and Frugal Approach to Categorization.” Proceedings of the Nineteenth Annual Conference of
the Cognitive Science Society. Eds M.G. Shafto and P. Langley. Mahwah, NJ: Lawrence Erlbaum Associates.
Czerlinski, Jean, Gerd Gigerenzer, and Daniel G. Goldstein. 1999. “How Good are Simple Heuristics?” Simple Heuristics That Make Us Smart. Eds. Gerd Gigerenzer and Peter M. Todd. Oxford: Oxford University Press. 97–118.
Gigerenzer, Gerd, and Peter M. Todd, eds. 1999. Simple Heuristics That Make Us Smart. Oxford: Oxford University Press.
Giora, Rachel. 1999. “On the Priority of Salient Meanings: Studies of Literal and Figurative Language.” Journal of Pragmatics 31: 99–129.
Hogarth, Robin M., and Natalia Karelaia. 2006. “ ‘Take-the-Best’ and Other Simple Strategies: Why and When They Work ‘Well’ With Binary Cues.” Theory and Decision 61: 205–49.
Payne, John W., James R. Bettman, and Eric J. Johnson. 1993. The Adaptive Decision Maker. Cambridge: Cambridge University press.
Tversky, Amos. 1972. “Elimination by Aspects: A Theory of Choice.” Psychological Review 79.4 (July): 281–99.