Do your beliefs imply a Necessary being exists?

[CliveStaples]

And as has been pointed out, you don't even get a result, cool or boring. All you get is a short comment informing you that you either accept the possibility of a Necessary Being, or that you don't, or a condescending "Never mind, these questions are hard and I don't blame you for not knowing how to answer them", followed by an open invitation to retake the survey. I've seen much more interesting surveys and tests linked on Facebook - at least you get to know what Star Wars character you'd make, how many kids you're having with which celebrity, or how you're going to die.

Uh, what? I got a logic proof:

Congratulations! Your answers (or a subset of them) appear to have an interesting implication: they imply that there is a Necessary Being.
Here's how:

I will first show that a Necessary Being is possible:
1. Suppose (for the sake of argument) that a Necessary Being is not possible.
2. It is possible for there to be something that has a cause. (by your report)
3. Therefore, it is possible for a contingent thing to have a cause. (by 1 & 2)
4. Therefore, it is possible for being contingent to have an instance that has a cause. (by definition of 'instance' & 3 [note 1])
5. It is possible for there to be a beginning of the existence of all contingent things. (by your report)
6. Therefore, it is possible for being contingent to begin to be exemplified. (by definition of 'begin to be exemplified' & 5)
7. Therefore, being contingent is such that (i) it is possible for it to begin to be exemplified and (ii) it is possible for it to have an instance that has a cause. (by 4 & 6)
8. For any property meeting (i) and (ii) above, it is possible for there to be something that causes that property to begin to be exemplified. (by your report)
9. Therefore, it is possible that something causes being contingent to begin to be exemplified. (by 7 & 8)
10. It is not possible for a contingent thing to exist prior to a beginning of all contingent things. (by definition of 'prior to': otherwise a contingent thing would exist while there are no contingent things, which is contradictory [note 2])
11. Therefore, it is not possible for a contingent thing to cause a beginning of all contingent things. (by definition of 'cause' & 10)
12. Therefore, it is not possible for a contingent thing to cause being contingent to begin to be exemplified. (by definition of 'begin to be exemplified' & 11)
13. Therefore, it is possible for there to be something that is not contingent that causes being contingent to begin to be exemplified. (by 9 & 12)
14. Therefore, it is possible for there to be a Necessary Being. (by definition of 'Necessary Being' & 13).
15. (14) contradicts (1).
16. Therefore, (1) is not true. (no true statement implies a contradiction)
17. Therefore, a Necessary Being is possible.
[note 1] You may translate 'property talk' into talk of instances of properties. For example, you may translate 'being contingent has instances' to 'there are contingent things'.
[note 2] To be clear, the 'all' in 'all contingent things' doesn't rigidly designate any particular contingent things: a beginning of all contingent things is an event in which there first begins to be some contingent things (where no contingent things previously existed).
I will now show that if a Necessary Being possibly exists, then one actually exists. To begin, recall (from your report) that if X and Y are each possible, then if X were actual, Y would still be possible (for any X and Y). In other words, a possible situation would be possible no matter what might happen to be actual. Therefore, whatever is possible is necessarily possible (by definition of 'necessarily such and such'). Call this principle 'the necessity of possibility' (which is also known as S5).

The deduction using the above principle is well known. Below is one way to spell it out.
Let '~' abbreviate 'it is not the case that'.
Let '◊' abbreviate 'it is possible that'.
Let '□' abbreviate 'it is necessary that' (or '~◊~').
Let 'N' abbreviate 'there is a Necessary Being'.
The deduction now proceeds as follows:
1. ◊ N.
2. So: ◊□ N. (by definition of 'N')
3. So: □◊□ N. (by the necessity of possibility)
4. So: ~◊~◊~◊~ N. (by substituting '~◊~' for '□')
5. So: ~◊□◊~ N. (by substituting '□' for the middle '~◊~')
6. So: ~◊◊~ N. (because □A implies A)
7. So: ~◊~ N. (because ◊◊A implies ◊A)
8. So: □ N. (by substituting '□' for '~◊~')

◊◊A implies ◊A:
1. ◊◊A.
2. So: ◊□◊A. (by the necessity of possibility)
3. So: ◊~◊~◊A. (by substituting '~◊~' for '□')
4. So: ◊~◊~◊~~A. (because A implies ~~A)
5. So: ◊~◊□~A. (by substituting '□' for '~◊~')
6. So: ~◊□~A. (because ◊~◊A implies ~◊A)
7. So: ~◊~◊~~A. (by substituting '~◊~' for '□')
8. So: ~◊~◊A. (because ~~A implies A)
9. So: □◊A. (by substituting '□' for '~◊~')
10. So: ◊A. (because □P implies P)

◊~◊A implies ~◊A:
1. If ◊A, then □◊A. (by the necessity of possibility)
2. So: if ~□◊A, then ~◊A. (by modus tollens)
3. So: if ~~◊~◊A, then ~◊A. (by substituting '~◊~' for '□')
4. So: if ◊~◊A, then ~◊A. (because ~~P implies P)

That doesn't seem like a 'short comment' to me.

My responses were:

1. (I can't say.) Is there a Necessary Being?

2. (I can't say.) Can anything be entirely inside of itself?

3. (It seems so.) Can there be a contingent thing that has no cause?

4. (It seems so.) Can a possible event be impossible to cause?

5. (It seems so.) Is it possible that there is anything that has a cause?

6. (It seems so.) Let P be any property that (i) can begin to be exemplified and (ii) can have instances that have a cause.

Is it thereby possible for there to be something that causes P to begin to be exemplified (by causing a first instance of it)?

For example, 'redness' is a property that began to be exemplified. And it can have instances that have a cause (because there can be red things that have been caused to exist). So, an event that causes the first red thing(s) would thereby cause 'redness' to begin to be exemplified.

7. (It seems so.) Is a beginning of the existence of all contingent things (such as in a Big Bang) possible?

8. (It seems so.) Suppose X and Y are each possible. If X were actual, would Y still be possible (for any X and Y)?

For example, assume unicorns and pegasusi are both possible. Then if unicorns became actual, would pegasusi remain possible?

Note: I am not asking if X and Y are jointly possible.
For example, a three-sided figure is still possible even if there happen to be no three-sided figures.