Problem's with Aquinas' Third Way

In Robert Arp (ed.), Revisiting Aquinas' Proofs for the Existence of God. Leiden, Netherlands: Brill. pp. 131-140 (2016)
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Abstract
The object of this paper is not arguments from contingency in general, but specifically Aquinas’s ‘Third Way’ as it appears in his Summa Theologica. I will raise three objections to this argument. First, the argument depends on the premise, that if everything were contingent, then there would have been a time during which nothing exists, but this is not self-evident and no argument is given for it here. Secondly, Aquinas tells us that a key premise in this argument, that an infinite order of things necessary through one another is impossible, has been proven just previously (in the ‘second way’) with respect to an infinite order of efficient causes. But this argument fallaciously equivocates between two different senses of the term ‘first’, and the fallacy does not disappear when applied to the ‘third way’. Thus, Aquinas not only fails, in this argument, to prove the existence of a thing necessary in itself, but fails to prove that anything is necessary at all. Lastly, this argument suffers from a puzzling ambiguity as to the meaning of the term ‘necessity’, and either way of interpreting the term consistently in the argument raises difficulties.
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