Proof and evidence are usually distinguished like this: Proof definitively decides on the truth, whereas evidence is a weak or strong indicator of truth which is not definitive.
To make a clearer distinction between proof and evidence, consider the following concepts in statistical hypothesis testing: Null hypothesis represents the “normal” or “natural” expectations about some event (e.g. that it happens randomly according to a known probability distribution). Alternative hypothesis represents what might be the case, in case the null hypothesis is invalid. It’s crucial to note that the null hypothesis is known but the alternative hypothesis is unknown. Type I error is a failure to accept a valid null hypothesis, whereas type II error is a failure to reject an invalid null hypothesis.
Let us now redefine proof and evidence in these terms: A proof is what corrects a failure to accept a null hypothesis (type I error) . In this way, proof leads to the acceptance and assertion of a known null hypothesis as the final decision about the truth. On the other hand, an evidence is what corrects a failure to reject a null hypothesis (type II error). In this way, evidence leads to the rejection of a known null hypothesis. This rejection provides only an indirect indication about the truth, because the alternative hypothesis, which is supposed to be accepted and assumed, is unknown.
Now we can distinguish proof and evidence sexually. In Encore, Lacan says that the only known form of enjoyment is phallic enjoyment, and that the other (feminine) enjoyment remains unknown and enigmatic. We can paraphrase Lacan in terms of the null hypothesis and the alternative hypothesis: “Were there another hypothesis than the null hypothesis, it shouldn’t be / could never fail to be that one.”
The known null hypothesis of “natural normality” is based on phallic enjoyment, and that’s why proof is masculine. The alternative hypothesis remains to be an enigma, and that’s why evidence is feminine. Finally, we must distinguish masculine and feminine ways of truth.
Notice that a “failure to accept” is a single layer of denial, whereas a “failure to reject” is a denial of denial, a double denial . Thus, a type I error (failure to accept) is a localized error that remains linked to a valid index of truth (null hypothesis, phallic enjoyment) as its simple denial. In the masculine way of truth, this is the function of the particular exception, which serves as the Master-Signifier (authorization). By contrast, a type II error (failure to reject) is an errant error that is not linked to any index of truth. It nonetheless summons speculations about the possibility of a valid alternative hypothesis, which remains to be an enigmatic question that “shouldn’t be / could never fail to be” in Lacan’s words. This errant error is equivalent to the spectral presence of the objet petit a (embodiment); it is the feminine way of truth.
Işık Barış Fidaner is a computer scientist with a PhD. Admin of Yersiz Şeyler (Placeless Things) blog, Admin/Editor/Curator of Žižekian Analysis, and one of the admins of “Žižek and the Slovenian School” group on Facebook. Twitter: @BarisFidaner
 Of course, it’s really impossible to prove a hypothesis. But this is a general problem with the notion of “proof”. It’s related to the fact that masculinity is an imposture.
 A denial of denial is certainly not a negation of negation. About this, see “Refusing and Defusing The Moral Bomb”.