In August 2009, after dozens of people reported seeing a mermaid leaping out of the water and doing aerial tricks, the Israeli coastal town of Kiryat Yam offered a $1 million award for proof of its existence.
Our analysis of the individual expected-benefit-maximizing strategies results in the characterization of the pure-strategy perfect Bayesian Nash equilibrium and proof of its existence for any setting.
First, it provides a proof for the existence of God by perfection, as the most intense limit case, given that simplicity is an attribute of perfection.
Nevertheless, this alleged proof for the existence of a true proposition does not reach its goal for a simple reason: The proof is in no way peculiar for truths in the sense of true propositions as Bolzano needs to have it.
Finally, Thomas Bayes wrote an essay discussing theological implications of de Moivre's results: his solution to a problem, namely that of determining the probability of an event by its relative frequency, was taken as a proof for the existence of God by Bayes.
As for the proof for the existence of minima naturalia itself, it begins by repeating that division is spoken of in two ways: physical division which brings about an actual division, severance or fragmentation of the magnitude and conceptual division which involves a mere mental division or positing that leaves the magnitude intact.
Fixed-point theory has attracted many mathematicians since it provides a simple proof for the existence and uniqueness of the solutions to various mathematical models (integral and partial differential equations, variational inequalities etc).
Given the fact that neither observation nor any other means of knowing (including revelation) gives a decisive proof for the existence or non-existence of a connection between a cause and its effect, we must suspend our judgment on this matter.
The skeptical empiricism of David Hume, the antinomies of Immanuel Kant, and the existential philosophy of Søren Kierkegaard convinced many later philosophers to abandon these attempts, regarding it impossible to construct any unassailable proof for the existence or non-existence of God.
According to the Sultan of Morocco, Mayo was "tangible proof for the existence of God".
