1) "God is, or He is not"
2) A Game is being played... where heads or tails will turn up.
3) According to reason, you can defend either of the propositions.
4) You must wager. (It's not optional.)
5) Let us weigh the gain and the loss in wagering that God is. Let us estimate these two chances. If you gain, you gain all; if you lose, you lose nothing.
6) Wager, then, without hesitation that He is. (...) There is here an infinity of an infinitely happy life to gain, a chance of gain against a finite number of chances of loss, and what you stake is finite. And so our proposition is of infinite force, when there is the finite to stake in a game where there are equal risks of gain and of loss, and the infinite to gain.
Now Double negative elimination is a theorem of classical logic, but not of weaker logics such as intuitionistic logic and minimal logic. Because of their constructive flavor, a statement such as "It's not the case that it's not raining" is weaker than "It's raining." The latter requires a proof of rain, whereas the former merely requires a proof that rain would not be contradictory. (This distinction also arises in natural language in the form of litotes.) Double negation introduction is a theorem of both intuitionistic logic and minimal logic, as is \neg \neg \neg A \vdash \neg A .
But what does this mean: Ariadne abandoned by Theseus? It means that the combination of the negative will with the force of reaction, of the spirit of reaction with the reactive soul, is not nihilism’s last word. The moment arrives when the will to negation breaks its alliance with the forces of reaction, abandons them and even turns against them. Ariadne hangs herself, Ariadne wants to perish. Now this fundamental moment (“midnight”) heralds a double transmutation, as if completed nihilism gave way to its opposite: reactive forces, themselves denied, become active; negation is converted and becomes the thunderclap of a pure affirmation, the polemical and ludic mode of a will that affirms and enters into the service of an excess of life. Nihilism “defeated by itself.” Our aim is not to analyze this transmutation of nihilism, this double conversion, but simply to see how the myth of Ariadne expresses it. Abandoned by Theseus, Ariadne senses the approach of Dionysus. Dionysus the Bull is pure and multiple affirmation, the true affirmation, the affirmative will; he bears nothing, unburdens himself completely, makes everything that lives lighter. He is able to do what the higher man cannot: to laugh, play, and dance, in other words, to affirm. He is the Light One who does not recognize himself in man, especially not in the higher man or sublime hero, but only in the overman, in the overhero, in something other than man. It was necessary that Ariadne be abandoned by Theseus: “For this is the soul’s secret: only when the hero has abandoned her is she approached in a dream by the overhero.” Under the caress of Dionysus, the soul becomes active. She was so heavy with Theseus but becomes lighter with Dionysus, unburdened, delicate, elevated to the sky. She learns that what she formerly thought to be an activity was only an enterprise of revenge, mistrust, and surveillance (the thread), the reaction of the bad conscience and ressentiment; and more profoundly, what she believed to be an affirmation was only a travesty, a manifestation of heaviness, a way of believing oneself strong because one bears and assumes”- Deleuze, (Essays Critical and Clinical, p. 102)
“To pass from Theseus to Dionysus is, for Ariadne, a clinical matter, a question of health and healing. And for Dionysus as well. Dionysus needs Ariadne. Dionysus is pure affirmation; Ariadne is the Anima, affirmation divided in two, the “yes” that responds to “yes.” But, divided in two [dedoublee], affirmation returns to Dionysus as the affirmation that redoubles [redouble]. It is in this sense that the eternal return is the product of the union of Dionysus and Ariadne. As long as Dionysus is alone, he still fears the thought of the Eternal Return, because he is afraid that it brings back reactive forces, the enterprise of denying life, the little man (whether higher or sublime). But when Dionysian affirmation finds its full development in Ariadne, Dionysus in turn learns something new: that the thought of the Eternal Return is consoling, and at the same time, that the Eternal Return itself is selective. The Eternal Return does not occur without a transmutation. The Eternal Return, as the being of becoming, is the product of a double affirmation that only makes what affirms itself return, and only makes what is active become. Neither reactive forces nor the will to deny will return: they are eliminated by the transmutation, by the Eternal Return as selection. Ariadne has forgotten Theseus; he is no longer even a bad memory. Theseus will never come back. The Eternal Return is active and affirmative: it is the union of Dionysus and Ariadne”(Deleuze,"Essays Critical and Clinical", p. 105).