Reasonable Doubt on Non-Contingency

Continuing to work together with Kairosfocus to build a worldview.

Previously, I paused at the principle of cause and effect because of the way it was worded:

[d] if something has a beginning or may cease from being -- i.e. it is contingent -- it has a cause.

The wording implies we can systematically distinguish between contingent and non-contingent things. Later, as he explained the system for making the distinction, Kairosfocus introduced a mathematical equation as an illustration:

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.)

His point is the truth of the equation, the fact it is correct, is an example of a non-contingent thing. That is, the specific truth is itself a necessary being.

I was confused by this reasoning and shared my thinking about contingency and the mathematical equation:

The problem, as I have tried to work it out, is that the truth of 2 + 3 = 5 is contingent. Let me explain:

For the truth of 2 + 3 = 5 to begin or continue, we need (1) a material universe; (2) principles of rationality, such as the law of identity; and (3) a computer, that is, a being to arbitrate between the universe and rationality so as to determine the truth of expressions. There may be additional needs, but these three factors seem essential at the least.

We note also that the falsity of 2 + 3 = 4 depends on (1) to (3).

The truth or falsity of these expressions is an effect of the three factors of universe.

In my estimation, then, it is incorrect to say “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.” Specifically, the incorrect parts are “always was” and “will always be.” The expression 2 + 3 = 5 is true only as long as we have a material universe where things are identical only to themselves and interact with one another in regular ways. As long as we have, in other words, all three factors in play: materiality, regular constraints, and a translating/computing intelligence.

In response to this post, Kairosfocus commented:

To help you in brief, 2 + 3 = 5 does NOT depend on materiality, as sets can contain ANY entities. In fact, to address the Russell paradox, Zermelo-Fraenkel set theory joined to the von Neumann cumulative hierarchy -- yup THAT JvN from "Mars" again [there is a suspected nest of "Martians" in and around the old Austro-Hungarian empire's universities) -- builds in effect the set of natural numbers out of a chain of sets based on emptiness!

A simple look (let's duck the power sets issue) is to take the empty set O-slash. Take the set that contains this. Then put the two together to form a 3rd set. The fourth set collects the first three. Repeat ad infinitum. Ordinal numbers appear.

We have just created a successive collection that sets up the natural numbers, with cardinality at each step bound to that of the sets. These may be assigned labels, numerals 0, 1, 2, 3 . . .

Then, identify operations such as add and equal. The join operation add, on a set of cardinality 2 and one of cardinality 3 will yield one of cardinality 5.

At no stage have we depended on materiality, just logic. Though it is helpful to use our background as corporeal beings experiencing a physical world.

Numbers and operations on them APPLY to the physical world we experience, but do not depend on it to have validity, by extension, the same holds for logic.

I don't think this response resolves my issue. First, I had said--or meant--that the truth of 2 + 3 = 5 is contingent upon not only materiality but also principles of reason/intelligence and something to interpret the operation of the principles with respect to materiality. Another way of expressing my thinking is to ask:

Is it still true that 2 + 3 = 5 if (i) the universe is wholly uniform and immaterial, if (ii) there are no principles of reason that differentiate or manipulate information, and if (iii) there are no living or non-living entities in the universe that act or are acted upon by anything?

I don't see how the equation can have any meaning if a combination of at least two factors listed above is true. In a uniformly immaterial universe without principles of reason, how can 2 + 3 = 5 mean anything? There would be no 2, no 3, no 5, no operators, no vehicle or target for any action or conception, and no method governing difference between things (as there is no difference between things).

So, while I trust it's correct that the truth of 2 + 3 = 5 does not depend on materiality, as Kairosfocus says, my point is that the truth of the equation does depend on other factors. Indeed, the fact we need to conceive of numbers as sets demonstrates my point. If, contra factor (ii), there are principles of reason--such as conceptions of sets and operators--and if, contra factor (iii), there are entities such as ourselves that reconcile existence with (ii), then the equation can be true without reference to materiality. Yet, if either (ii) or (iii) holds along with (i), then the equation has no status whatsoever.

The proverbial jury remains out on non-contingency, as far as I can tell. It doesn't seem as though we have any way to verify whether something or some state exists with no contingencies whatsoever. If we have no way to verify, I'd like to use my version of the principle of cause and effect:

[d-1] A thing, A, has a beginning or may cease from being. A thing, A, therefore, has a cause.

This cause and effect principle flows seamlessly to the principle of sufficient reason:

[e] “Of everything that is, it can be found why it is.” (Principle of Sufficient Reason, per Schopenhauer.)

I think [d-1] and [e] work beautifully together, the first asserting the pervasive contingency of the universe and the second promising that everything in the universe can be traced to preceding factors.

Once we jettison non-contingency, we make quick progress. Everything falls together so nicely I wonder whether we should invoke another of Kairosfocus's principles:

[f] “to say that what is is, and what is not is not, is true.” (Aristotle, Basic Definition of Truth, i.e. “telling it like it is.”)

Perhaps contingency is and non-contingency is not: this may be the truth.

Now, non-contingency may very well be true, even if we cannot verify it. I do not deny the possibility that non-contingency exists. But I have no special judgment to make about non-contingency until I know how we systematically and independently verify it. In other words, the empty set may be a mental model of non-contingent reality, or it may be a mental model of human reasoning.

In this post, I've tried to isolate that part of the principle of cause and effect that seems to me unassailable. For the assailable part--that is, for non-contingency--I have explained why I see things like mathematical truths to be contingent, as these truths cannot exist or continue apart from a combination of factors. My explanation will falter or fail if it can be demonstrated that the truth of 2 + 3 = 5 does not in fact rely on any factor, that it is true regardless of a physical universe, principles of reason, and an interpreting entity that mediates the previous two items. I have argued that at least two factors must be present for the equation to have any meaning at all, let alone truth. Finally, by reducing the scope of the principle of cause and effect, I have sketched how it integrates flawlessly both with the principle of sufficient reason and the "telling it like it is" principle.

Clearly, the principle of cause and effect is a critical point of divergence. Things that are caused and create effects are commonplace and not a philosophical problem. Things that have no causes and no effects--well, I don't know that we spend time wisely dwelling too much on these, if they are at all. But things that have no causes yet create effects: these are the things that concern us. Our specific concern is how we prove that a thing is un-caused. Yet what seems unquestionable is that reasonable people can doubt the existence of un-caused things.