不管有沒有受過哲學訓練，人類對於哪些命題是可知的，和哪些命題是不可知的都有一定的共識。對於那些可被知道的命題，霍桑稱為「一般命題」（NP）；對於那些人類直覺認為不可知的命題，霍桑則稱其為「樂透命題」（LP）。這兩類的命題雖然看似彼此無關，但事實上不然，因為前者的為真往往蘊含後者的不為真。霍桑透過人們對於這兩類命題的知識直覺和封閉原則，以樂透悖論重述懷疑論者的主張，帶出懷疑論者對於人類知識的挑戰。
樂透悖論引出的最大挑戰就在於，當知識主體運用手上的知識，藉由封閉原則推論出她知道LP時，她無法接受這樣的結論，因此回過頭主張一開始自己不知道NP，並且因此而否定在其他不涉及LP的情境下（亦即，樂透悖論沒有出現的其他情境。），她能夠知道該NP。知識理論家面對樂透悖論的挑戰，回應的方法可分為兩種，一種是主張出現在知識歸屬語句的「知道」的語意會隨著脈絡不同而有所改變，另一種則主張「知道」的語意不會隨著脈絡的不同而有所改變。前者的理論是脈絡論，而後者指的則是知識不變論和霍桑自己所提議的敏感的溫和不變論。霍桑主張在這三個知識理論中，雖然每個理論都各有優缺點，但綜合來說，敏感的溫和不變論能在違背最少的知識 相關直覺下，合理的說明樂透悖論。

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