I kept getting pushed out of flow by words like "intuitionistically" and constructions like "derive absurdity" (as opposed to 'derive an absurd conclusion'). 'Intuitive' is a perfectly functional word, no need to make new ones up to sound formal.
I read it, but I still don't comprehend why anyone would stress the difference between<p>To prove ¬ϕ, assume ϕ and derive absurdity.<p>and<p>To prove ϕ, assume ¬ϕ and derive absurdity.<p>It just seems exactly the same, given that ¬¬ϕ = ϕ.<p>"Yes indeed, but the cancellation of double negation is precisely the reasoning principle we are trying to get."<p>You have to go to a very very deep level of maths if this is what you want to get.