Contingency and Necessary Beings

Beatrice leads Dante.

Kairosfocus continues to patiently lead me through the principles of right reason. Last time, I asked:

What are the tests we can use to determine whether a thing does not have a beginning or may not cease from being?

In other words, I want to know how to determine whether a thing is not contingent.

Kairosficus answers that it helps to understand contingency, first of all. He uses a terrific example:

The fire tetrahedron (an extension of the classic fire triangle) is a helpful case to study briefly:

For a fire to begin or to continue, we need (1) fuel, (2) heat, (3) an oxidiser [usually oxygen] and (4) an un-interfered-with heat-generating chain reaction mechanism. (For, Halon fire extinguishers work by breaking up the chain reaction.) Each of the four factors is necessary for, and the set of four are jointly sufficient to begin and sustain a fire. We thus see four contributory factors, each of which is necessary [knock it out and you block or kill the fire], and together they are sufficient for the fire.

From this example, we see that "the secret to understanding cause is to understand the issue of a necessary causal factor, the 'switch' that must be on for something to begin or continue to be." The necessary causal factor leads to the direct response to my question:

Once we see the significance of the necessary causal factor, we can now identify things that are not contingent: they have no necessary causal factors. So, we can go look for “switches” or for switch-prompted behaviour, i.e. the beginning/ending, or the possibility of ending, or of course obvious dependence on a feeding factor.

Kairosfocus continues on this line of looking for switches:

Any entity that is dependent for its ability to function on the particular co-ordinated physical arrangement of parts is contingent, as if the parts are moved around or separated such a composite entity will cease to be or will break down.

Auto parts shops have a surprisingly deep philosophical significance, never mind that chilling, long low whistle from under your car when the mechanic is looking at it.

By way of contrast, the truth asserted in the structured set of symbols: 2 + 3 = 5 always was, will always be, cannot be denied on pain of absurdity, etc. It cannot break down and does not need to be repaired.

It is a necessary being.

(We need not trouble ourselves for the moment on the 2400 year old debate on whether such may only be instantiated in physical entities. Suffice to say that such mathematical or more broadly propositional truths capture assertions about reality that may or may not be true, but if true can have very powerful implications. Thence, the “unreasonable” effectiveness of mathematics in science: If X then Y, holds, once X is found.)

Here is, I think, the answer to my question. The truth of something like a mathematical proposition--such as "two plus three equals five"--is not contingent. It is necessary. It seems here that if something is necessary it is not contingent; that is, something cannot be both necessary and contingent.

Interestingly, Kairosfocus calls the truth (as in, the truth of the equation above) a necessary being. I imagine, then, that a necessary being is more like a condition than like a life-form.

So, if I have this correct, then I think my world is a little bit rocked. But let me check facts, first. I therefore ask if Kairosfocus will help me confirm:

1. To test whether something is not contingent, look for the absence of "switches," which are necessary causal factors.
2. The truth of a statement such as "two plus three equals five" is necessary but is not itself contingent.
3. A necessary being is a necessary condition and not like a type of life-form.

Do I have this correct?