We review the history of the philosophy of fondue since Aristotle so as to arrive at the formulation of the paradox of Swiss fondue. Either the wine and the cheese cease to exist (Buridan), but then the fondue is not really a mixture of wine and cheese. Or the wine and the cheese continue to exist. If they do, then either they continue to exist in different places (the chemists), but then a fondue can never be perfectly homogenous (it is a French fondue). Or the wine and the cheese continue to exist in the same place (the Stoïcs), but then wine and cheese have to be, oddly, penetrable and spatially expansible. Aristote attempted to solve this paradox by arguing that the cheese and wine continue to exist, but only potentially in the fondue. We sketch an alternative answer. The wine and the cheese continue to exist, but only non-spatially in the fondue. Wine and cheese, once mixed, become non-spatial constituents of the fondue, a bit like character traits are non-spatial constituents of persons. The wine and the cheese are in the fondue, but only the fondue is there in the fondue pot.