Remote conclusions of the Faith

[Birdmanman]

It seems that, in almost every body of belief, there may be remote conclusions
implied by two or more of the beliefs together that have not been fully worked out.
For example, if say that: I believe that God is one in substance, and I believe that God is that which created the universe, and I believe that the universe is good,
then it seems that, even if I do not explicitly say it, I further accept, by an almost trivial deduction, that “that which created something good is one in substance.”

But there are many, many beliefs included in the dogmas of our Faith, and it would seem that many of these beliefs may interact or relate with one another in such a way, like the example above, that there are necessary conclusions that can be drawn from them which are not themselves explicitly stated, necessary conclusions that are so remote or would take so long or so much study to draw out that we could not, ourselves, draw them out in their entirety unless we are intelligent theologians or had a lot of time.

My question, then, is, do you think that there is a way, through reason, to be certain that one part of the Dogmas of the Faith do not have any of these ‘remote conclusions’ that are self-contradictory, or contradictory to other parts of the Dogmas of the Faith?

That is, is there a way to show that if you begin with a set of non-contradictory propositions, none of the conclusions of a part of the set of non-contradictory propositions will ever contradict the conclusions of another part of the set of non-contradictory propositions?

For example, we have a set of propositions p, q, r, s, t, u, and v. The propositions on their surface, from just looking at them initially, are not contradictory to or inconsistent with any other proposition or group of propositions in this set. We then discover that from p, q, and r, we can deduce that ‘w’ is true, and from t, u, and v we can deduce that ‘x’ is true. Is it necessarily so that ‘w’ and ‘x’ are also not contradictory to one another? [that is, that ‘x’ is not really ‘~w’, and vice versa?].

I thank anyone who might help for their assistance and patience.

 

[spiderweb]

I’m not very strong in Philosophy, but since no one else has tackled this question, I will give my thoughts.

I think you’re first deduction is wrong because it’s not necessarily true: “that which created something good is one in substance.” For example: A human artist is one in substance. A human artist creates paintings. The painting is good. Therefor That which created something good is one in substance.

An artist could create an abstract painting. A monkey could create an abstract painting. Both paintings are good, but the human artist and the monkey are not one in substance.

God is truth and He does not contradict. You’ve heard the question; “Can God create a four sided triangle?” This is a contradiction of what a triangle is.

So if you have multiple truths that lead to conclusion A, and other multiple truths that lead to conclusion B where A and B seem to contradict each other, than either the reasoning used to come to either conclusion is incorrect or the understanding of either conclusion is faulty, or some combination.

I hope that helps somewhat and maybe someone else will jump in here and explain it better.

 

[Bob_Crowley]

My Boolean Algebra is very rusty, and I always had trouble factorising it compared to ordinary Algebra, but it seems to me that using the statement that all the propositions are non-contradictory implies that they cannot be contradictory no matter how far you take the complications.

If p.q = 1, and q.r = 1, then p.q.r = 1. You can extend this to the whole range of propositions, and the result will always be 1 by my understanding, no matter what combination you might come up with.

So provided the original propositions are always correct, then I don’t see how they can contradict each other, no matter how far you push the combinatorial factors.

 

[inocente]

Imagine translating all the propositions into a symbolic logic so as to be able to treat them as axioms. You could then form every possible theorem from them, which is a big job for which you would need a computer.

I’m not sure, but at this point I think you’d run up against Gödel’s incompleteness theorems. You’d find either that you can’t prove the propositions are constant or that they are incomplete, not because there’s anything wrong but because that’s just necessarily how logic works in non-trival systems.

A bestseller which makes it easier to understand why this is so is:
Gödel, Escher, Bach: An Eternal Golden Braid, Hofstadter 1999