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St. Thomas Aquinas argue that because God is an all-powerful being, we couldn’t not possible evaluate or conceive his nature; this is one objection against Anselm’s ontological argument for the existence of God, since God himself alone is the only being that is capable of knowing his own nature, only God would be able to use the argument. Aquinas ‘priori reason’ sufficed the possibility that a ‘priori reasoning,’ alone would be able to prove God’s existence. In terms, this is a contradiction since there is nothing that can be prove only by ‘priori reasoning ’. It was therefore unreasonable to claim that any idea of God reasonable implies his existence. — Thus, our conceptions of God we could only speculate either of his existing or not existing

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    What's your question? Jul 14, 2021 at 10:40

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You're right that Thomas Aquinas specifically rejected Anselm's version of ontological argument according to reference here:

Thomas Aquinas, while proposing five proofs of God's existence in his Summa Theologica, objected to Anselm's argument. He suggested that people cannot know the nature of God and, therefore, cannot conceive of God in the way Anselm proposed. The ontological argument would be meaningful only to someone who understands the essence of God completely. Aquinas reasoned that, as only God can completely know His essence, only He could use the argument.

However, Aquinas's own 5 proofs or called 5 ways were used to only demonstrate the existence of God in mostly a posteriori manner, should not be interpreted as any a priori proof, thus it seems on this issue Aquinas is consistent according to reference here:

Aquinas did not think the finite human mind could know what God is directly, therefore God's existence is not self-evident to us. So instead the proposition God exists must be "demonstrated" from God's effects, which are more known to us... However, Aquinas did not hold that what could be demonstrated philosophically (i.e. as general revelation) would necessarily provide any of the vital details revealed in Christ and through the Church (i.e. as special revelation), quite the reverse. For example, while he would allow that "in all creatures there is found the trace of the Trinity", yet "a trace shows that someone has passed by but not who it is."

And his five ways to demonstrate God's existence is also referenced as follows:

  1. the argument from "first mover";
  2. the argument from causation;
  3. the argument from contingency;
  4. the argument from degree;
  5. the argument from final cause or ends ("teleological argument").
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  • The first four argument, doesn’t necessary roll out the existence of a “sentient,” being in particular the monotheistic God of Christianity. It assume that something causes the first motion, by something not necessarily of God - and if everything has been put to motion by something else other than itself, then that something is also subject for the speculation of cause and effect. And if that something that causes everything to exists is exempt to those speculations, then why other things can’t exist on their own?
    – EquDox
    Jun 14, 2021 at 7:53
  • @EquDox you're certainly reasonable to have above critiques which many people naturally hold too. And Aquinas himself noticed such issue as referenced above "he would allow that "in all creatures there is found the trace of the Trinity", yet "a trace shows that someone has passed by but not who it is."". Thus he claimed his 5 ways are demo only, not proof, meaning it's not water tight. We can only say the principle of sufficient reason (PSR) holds universally in this contingent world, everything is interdependently arisen. And logic is more strict, PSR is not even a law in classic logic. Jun 14, 2021 at 22:53
  • What conclusion can be drawn, with the principle of sufficient reason (PSR)? It appears to me, that Aquinas’ 5 demo for the existence of God - can’t be airtight for resolving these objections it may hold for other circumstances, but none are bulletproof for criticism.
    – EquDox
    Jun 15, 2021 at 1:37
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    @EquDox PSR is most related to above 2nd and 3rd Aquinas's argument. PSR implies determinism only from God's eye, no human can prove it. In science, most specifically quantum physics, indeterminism is the belief that no event is certain and the entire outcome of anything is probabilistic. So even if you adopt indeterminism doesn't mean PSR must fail. Leibniz emphasized PSR exists (only God sees it all) but usually cannot be known by us human beings. Jun 15, 2021 at 2:10

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