The incompatible food triad is a problem (“philosophical puzzle” seems too strong) that has interested philosophers and other nerds for decades. The puzzle probably originates with Wilfrid Sellars.
The problem is: Are there three foods such that all three do not go together but every pair of them does go together?
I first encountered the puzzle on George Hart’a great webpage, which includes a bunch of clever and funny proposed solutions. It has also been written up in the Guardian. My purpose here is to propose a new solution to the problem.
The ingredients I believe satisfy the incompatible triad are:
Each pair of these ingredients is a known dish:
The linked recipes admittedly contain some other ingredients such as spices. But spices are not essentia. Only the paired ingredients constitute the being of the dishes.
Clearly (1)&(2)&(3) is not a known food. And it certainly does not sound very good to me. Hence these ingredients form an incompatible triad – any two of them together are delicious but a mixture of all three is just not right.
It is interesting to note that lye is used only in the preparation of Lutefisk, olives, and in a certain pretzel-making process. By itself lye is caustic; its ingestion is harmful and in some cases fatal. A strong interpretation of the problem might disqualify lye from inclusion. Is it even a food? But I would argue that this is too strict: olives must be cured and Cod must be killed to become food. So if lye becomes food in virtue of its combination with other ingredients, it is still to be counted as potential food from the outset.
One might object that combination destroys ingredients, such that lye ceases to be just when the mixture comes to be. So lye is neither potentially nor actually food but potentially something that gives rise to food. This goes back to a problem discussed by Aristotle, of whether an ingredient that continues to exist can be said to be mixed at all (Sharvy developed this formally in 1983[pdf]). But if the ingredient is destroyed in the act of mixture, then the olives and fish would cease to be olives and fish and would become Bacalhau à Gomes de Sá. Hence like lye, olives could not be food but just that which gives rise to food. But I say that olives are food; so lye must also be a food.
Of course some would say that certain combinations in this triad are not really edible, or at least should not be eaten. Perhaps some things really are just a matter of taste.