 Most paradoxes considered so far involve negation in an essential way, e.g. sentences saying of themselves that they are not true or knowable. The central role of negation will become even clearer when we formalise the paradoxes of self-reference in Section 2 below. Curry’s paradox is a similar paradox of self-reference that however does not directly involve negation. A semantic variant of Curry’s paradox comes from the following Curry sentence \(C\): “If this sentence is true then \(F\)”, where \(F\) can be any statement, for instance an obviously false one. Suppose the Curry sentence \(C\) is true. Then it expresses a true fact, that is, if \(C\) is true then \(F\). However, we already assumed \(C\) to be true, so we can infer \(F\), using Modus Ponens. We have now proved that if we assume \(C\) to be true, then \(F\) follows. This is exactly what the Curry sentence itself expresses. In other words, we have proved that the Curry sentence itself is true! But then we also have that \(F\) is true, and this is a paradox, since \(F\) can be any statement, including things that are obviously false (Smullyan (2006) let \(F\) be the sentence “Santa Claus exists”, thereby using Curry’s paradox to prove the existence of Santa Claus). In a classical logical setting where the implication  \(C \rightarrow F\) is equivalent to \(\neg C \vee F\), Curry’s paradox still implicitly involves negation, but Curry’s paradox is still independently interesting since it goes through with fewer assumptions about the underlying logic than the liar paradox. See the entry on  Curry’s paradox  for more details. 