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Author Topic: The Principle of Contingent Causation: The Impossibility of Infinite Regress.  (Read 28 times)

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Nishant Xavier

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The Augustino-Thomistic Argument from Contingency and Necessity provides Basic Foundational Evidence for the Existence of Almighty God.

Let's define Contingency and Necessity. You, me, our parents, then theirs, the Planet Earth, etc all exist contingently, i.e. are contingent beings.

By Contingent Beings is meant a being whose existence or the existence of which is contingent, i.e. dependent on the existence of another.

Thus, you and me are dependent for our existence on the existence of our parents, all life on Planet Earth is contingent upon Earth etc.

Now, the argument may be formulated both logically and mathematically:

1. Now, every Contingent Being, by definition, is Contingent, i.e. Dependent on a Prior Being's Existence.

if we wrote it mathematically, for every Contingent Being, CB, CB(n) is dependent on CB(n-1); CB(n-1) on CB(n-2) etc.

2. But it is impossible for this series of contingent causation to go on until infinity.

Again, mathematically, this is obvious. If CB(n) is dependent on CB(n-1), and so on (and negative beings are impossible; we are speaking of real beings here. The nth Being in existence, the 2nd being etc; so also, there is no "zeroth" being; n must be a natural number here), then that can proceed back until at most Being 2, B2=CB2, contingent upon B1. [B1 cannot be contingent upon anything, since no B0, as we come to down].

3. Therefore, not every Being in existence is a contingent being.

4. Specifically, the First Being in Existence exists Non-Contingently.

We already showed this above when we saw B2 is contingent upon B1, but B1 is not contingent upon any prior being, being the First Being in existence. [The only alternative to the existence of an actual first being is an infinite series of contingent beings, but that is impossible because an infinite series never ends; and if there were an actual infinite of real beings, we would never have gotten to the present moment; again, an infinite series cannot be formed by successive addition, because no matter how beings you add to each other, whether it is 1 or 1 trillion, n will always be finite. Therefore, granted that we got here, granted that we are 1 in a series of contingent beings, the number of beings in existence is finite.]

Therefore B1, the First Being, is a Non-Contingent Being, a Necessary Being, One Whose Existence is not contingent/dependent on a Prior Being.

Let's Debate.
God Bless.

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Nishant Xavier

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"The Thomistic Argument from Contingency: Mathematical Proof of God's Existence
Saint Thomas Aquinas gave a wonderful proof of God's Existence that is generally referred as the Argument from Contingency. It is the purpose of this article to propose this proof anew in a Mathematical Form for the edification of Christians and the destruction of Atheism.

1 Mathematical Formulation of the Contingency Principle
2 Further Elaboration/Explanation of the formulation
3 Corollary from the Mathematical Formulation of the Contingency Argument
4 References

Mathematical Formulation of the Contingency Principle
St. Thomas' argument from contingency may be formulated like this: if each contingently existing being considers himself Bn, then, because he exists contingently, he depends for his existence on a prior being B(n-1). Now, B(n-1) likewise, if it is contingent, depends on B(n-2). Nevertheless, this series cannot go on until Infinity. At a certain time, we will arrive at a B1, the First Being in existence, and since there is no "zeroth" Being or B0, B1 exists Necessarily, i.e. is not a contingent being. This was Aquinas' Third Way, under Question 2, Article 3 in the Summa Theologica[1]

Further Elaboration/Explanation of the formulation
Let's use the operator ~= to symbolize "is contingent/dependent on".

B(n) is Contingent, i.e. B(n)~=B(n-1)

But B(n-1), if it is contingent, is dependent on B(n-2), i.e. B(n-1)~=B(n-2)

Now, it is very clear this series cannot go on indefinitely.

At a certain time, we will come to B1, the First Being in Existence. It must now be observed that there is no such thing as a "0th" Being in Existence. It therefore follows clearly, logically, and mathematically that B1 is not a contingent being.

we now define the operator !~= to symbolize "is NOT contingent/dependent on".

Therefore, since there is no B0, then B1 !~= "B0", i.e. in words, B1 is a Necessarily Existent Being, not Contingent but Necessary.

Corollary from the Mathematical Formulation of the Contingency Argument
Now beings that begin and cease to exist, like human beings, clearly are contingent and not necessary. We showed above that B1 is not contingent being.

Contingent beings are thus temporal beings, because there is a certain moment in time when we began to exist and when we will cease to exist. But what we proved above about the Necessarily Existent Being shows He is a Being of a different order. He is an Eternally Existent Being, one who has always existed even before the beginning of time. How do we know this? Because B1 is Necessarily Existent, as we showed above.

Now, if contingent being are temporal beings, and the First Being/First Cause is non-contingent, He is thus Non-Temporal, i.e. Eternal.

We therefore arrive, by a series of few logical and mathematical steps, at an Eternal First Being who created our temporal Universe."