When arguing over whether an idea was scarce or not, Wenzel brought up this scenario: suppose you have a formula which only you know, and you write it down on a piece of paper and sell that piece of paper (the formula) on the condition that the formula doesn't get sold or otherwise divulged to any third party. The buyer then proceeds to violate that contract and sell the formula to someone else. Wenzel then says doesn't the fact that he is the only person privy to this formula and the only two places the formula occurs are on the sheet of paper and in his head mean that the formula is scarce? This is an important example that demonstrates the essential difference between a layman's conception of scarcity versus the economic conception of scarcity.
From a layman's perspective, it does indeed sound as if the formula is scarce; there are only two places in which it exists. This means that no one else has the information and is therefore incapable of acting on it. Since not everyone is in possession of this formula, it is scarce, in this view. Wenzel is right that the formula is scarce in the sense that no one else possesses the knowledge of the formula.
However, Wenzel ignores the insight that the formula is not rivalrous. Wenzel brings up that when person A sells the formula to B who illegally sells it to C, it now creates a 'rivalry' between A and C. But, he confuses the concept of rivalrousness with rivalry; his use of rivalry here means nothing more than competition. As Kinsella correctly pointed out that because of B's unlawful divulging of the secret formula, A and C are now competing against each other to attract consumers, but that this doesn't mean that the good is rivalrous. Rivalrousness means that a good cannot be simultaneously possessed (enjoyed) by 2 individuals at once. Clearly, we can see from the example, that the formula is capable of being possessed by both A and C as well as B all at the same time, and no one individual's use of the formula even minutely prevents the others from using the formula. C's use of the formula may affect A's ability to profit and derive monetary benefit from the formula, however, it does not prevent A from using (consuming) it.
I also think that if we're discussing intellectual property and regard homesteading as the legitimate means to acquiring property, it's useful to recognize that homesteading is a rule that depends on scarcity as a given to homesteading unowned resources. I'm sure we could say that someone might have 'homesteaded' the air by breathing it in and thus occupying it first, but we don't apply property rights to it because it fails to meet the qualifying criteria of being scarce which in turn depends on rivalrousness.
Property rights are only useful in a world where resources are not superabundant and there can be conflict over those resources; there cannot be conflict over breathable air (generally), nor can there be conflict over the use of an idea because they are not scarce. The conflict only comes into play when the idea is used to compete with someone else using the same idea; the conflict only occurs over the value attached to the idea viz the ability to profit from it. And Kinsella proved beyond a reasonable doubt in his book Against Intellectual Property we have no right to any "values" attached to an object since these values are subjective and depend on others for any values to be actualized. Just as we have no right to our reputation because a reputation is what others think of you, we have no right to any value in a piece of property, only in its physical integrity.
This concept is difficult to wrap one's brain around, particularly when we use terms interchangeably and vaguely, such as the way the terms scarce and rivalry were used during the debate. However, with clear thinking and clearly defined terms, the idea becomes much easier to grasp