The first way is the argument from motion [which requires a first Mover] … The second is from the nature of efficient cause [the chain of causation requires an uncaused Cause] … The third way is taken from possibility and necessity [roughly, ‘why there is something rather than nothing’ requires a necessary being] … The fourth way is taken from the gradation to be found in things [comparisons, e.g. ‘hotter’, relate to a perfect standard, ‘hottest’, so overall to God as the cause of perfection] … The fifth way is taken from the governance of the world [that things are evidently designed to an end, requiring a Designer]. (ST I, qu. 2, art. 3).
The first four are related to the Cosmological Argument, the fourth remotely to the Ontological Argument, the fifth to the Teleological Argument.
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"Quinque Viae." The Concise Oxford Dictionary of World Religions. . Retrieved January 22, 2018 from Encyclopedia.com: http://www.encyclopedia.com/religion/dictionaries-thesauruses-pictures-and-press-releases/quinque-viae
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