# Random monotone function

In Razborov-Rudich's Natural Proofs paper, page 6, in the part they discuss that there are "strong lowerbounds proofs against monotone circuit models" and how they fit into the picture, there are the following sentences:

Here the issue is not constructivity - the properties used in these proofs are all feasible - but that there appears to be no good formal analogue of the largeness condition. In particular, no one has formulated a workable definition of a "random monotone function."

Isn't it easy to distinguish the outputs of a monotone function from a random string? Isn't the existence of strong lowerbounds telling us that there are no such things?

My question is:

What do they mean by a workable definition of a "random monotone function"?