I would try to test how well it jives with what I know about reality (or think I know), how well it fits with my experience of reality, how well it fits with relevant empirical investigations into reality, and how well does it fit in with how others have experienced reality. If the belief was part of a larger belief system, I would test for internal consistency. And finally, I may question a main assumption.

Those are all exercises of logic, and there is nothing informal about the logic involved. You're talking about avoiding contradictions, which is arguably the whole point of studying logic.

It depends on what the proposition is about. I would try to test how well it jives with what I know about reality (or think I know), how well it fits with my experience of reality, how well it fits with relevant empirical investigations into reality, and how well does it fit in with how others have experienced reality. If the belief was part of a larger belief system, I would test for internal consistency. And finally, I may question a main assumption.

For instance, if I came across an article advocating the quiver method as the best way of family planning, because it makes families happier and is in accord with God's will I would consider that to be foolish in a number of ways. Firstly, I would object that many people who use birth control are happy and fulfilled. (So it would not fit with my experience of reality). Secondly, I would check to see if there were any relevant studies on the subject matter (empirical investigations). Thirdly, I remember reading a couple articles about very large families and the children not having particularly good outcomes. (it doesn't fit well with others experience of reality. Fourthly, I would object that in their own belief system, God expects them to take part in providing for themselves by working and taking medicine when they are sick, so why would God not want them to take an active part in their reproductive planning. (Testing for internal consistency.) Then, finally, I would probably object that they do not have enough evidence to think that this is God's will for them or that God even exists.

One more example is the maxim to forgive those who wrong you. A Christian may tell me that it is a wise saying, because God told it to us and that it leads to a happier life. I reject that God had anything to do with the maxim, but I still think that the person who wrote it down was saying something wise, because in my own experience, I am happier when I forgive others than when I hold a grudge. From what I have read, this seems to be common in others' experiences as well. So, I would reason that forgiving wrongs is better (will make you happier) than holding grudges.

OK. With informal logic, how does one distinguish between wisdom and foolishness?

The mechanism by which properties come about is generally through re-organization. The new organization of the material determines many of its qualities. Those qualities may not be present in the material that was used prior to the re-organization, nor in anything that helped shape how it was organized, unless these factors share a similar organization. For example, with the computer, we see a reorganization of the material into something that can generate computer programs. The base material, in its previous organization, did not have this property. Nor do the humans organizing it, since the brain is not organized in the same way as a computer, although there are some general similarities. The property emerges through the organization of that which demonstrates it, not through the transmission of the property from something that already has it.

I am not using a formal logic like in mathematics - that is all I meant.

Actually what I am claiming is that your examples are simply analogous to my examples and do not show that the principle is anything other than universally true.

But let us assume that you are correct and your examples are not analogous to mine. What exactly are you claiming is the mechanism by which the different properties come about?

You chose an example where properties are passed following the principle suggested. So did the other commentator, Greg Johnson. However, it cannot be claimed to be a universal principle, unless it is universally true. If it is not universally true, it cannot be assumed to be true in a case where we cannot observe what is occurring. I have given examples where it is not true, showing it to not be universally true. I have no issue with saying it is true in some cases. I have issues with assuming it must be true and proves an intelligent God must exist for intelligent beings to exist. Even your example challenges the principle, because genetics do not possess the quality of intelligence. They possess instructions that cause biological structures to form that can give rise to intelligence. By this reasoning, the first cause may not possess intelligence, but rather a nature that allows for intelligence to arise.

Let us look at the color analogy. I think the closest comparison would be someone who has a recessive gene for some trait, but does not express it because they also a more dominant gene at the same loci. They marry and have a child, who does express that gene because their spouse also has a copy of the recessive gene. Would you in that situation say that the child was given something that their parents don't have because they don't also express that recessive gene?

If this is all you mean by giving properties that the original does not have, then okay, but such is different than what is being claimed by those who claim that one cannot give what one does not have.

On additional reflection, you may also be arguing for the idea that any organization within the universe requires intelligent design, which is also a different argument from the other two.

The issue is whether those processes give qualities that the original
did not have (or put another way, if something comes from nothing).

This is a different question. Something from nothing is different from giving qualities not originally possessed. For example, You can mix colors to create a color distinct from those used in mixing. Neither had the new color as a quality beforehand. Likewise, to go back to the computer example, neither a human nor the materials used nor the computer language have some of the qualities found in computer programs themselves. You are asking a distinct question, one that has to do with the First Cause argument of how things originally came into being, not the argument about whether a creator requires specific qualities in order to convey them. If you want to discuss the first cause argument, I will need to know this, since I have not been responding to that argument in this particular discussion.