Malte Schlenker
LMU Munich
Eliot Watkins (2026) advanced a paradox for Kratzer semantics of deontic modals and all similar semantics according to which ‘ought’ is upwards monotonic:
Consider:
GAME: I have to press the right button of a machine to win 10€. Playing the game costs 1€. There are 100 buttons. I do not know which button is the right button. Plausibly, I ought to push the right button, and win the 10€. Since pushing the right button entails pushing a button this entails that I ought to push a button via upwards monotonicity.
But I ought not push a button, since I should expect to lose money pushing a button.
I argue that we can defuse GAME, and thus defend Kratzer semantics, by showing that ‘ought’-statements relevant for GAME are embedded in the context of implicit quantifiers that impose additional restrictions on the monotonicity of their combined contexts.
First, I distinguish two ways of understanding I ought to push a button. The first reads the statement as responding to whether there are any ways of pushing the button that one ought to do, while the second reads the statement as responding to whether one should push the button in all the ways relevant to the discussion.
Reading 1: there is at least one way of pressing the button that I ought to do.
Since even if Kratzer semantics is true both the existential quantifier and the ‘ought’ modal create contexts that are upwards monotonic. But embedding one upwards monotonic context in another generates an embedded context that is also upwards monotonic. The reading would be consistent with Kratzer semantics and come out true in GAME. Since it would come out true, it can’t be the sense relevant for our intuition that we ought not press the button.
Reading 2: for all contextually relevant ways of pressing the button φ, I ought to φ.
Here, we embed the upwards monotonic context of the ought modal in a non-upwards monotonic context of a universal quantifier. But merging these contexts does not generate an upwards monotonic context! Thus, if this is the salient reading of the sentence in GAME, then the reading relevant for the intuition is false while also being consistent with Kratzer semantics.
Second, I argue that Reading 2 is most natural because we ask a deliberative question in GAME for which only the second answer is informative: While I can’t infer from the truth of Reading 1 that I ought to push the button in any particular way, I can do so from Reading 2. Thus, only the latter guides my actions well, which is what we are after in deliberative contexts.
Bibliography
Watkins, Eliot. “How to be reasonable about the meaning of ‘ought’,” in Philosophical Studies Vol. 183 (Mar. 2026), pp. 1381-1409.
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SOPhiA 2026 