Probabilistic thinking, statistical reasoning and the search for causes: Do we need a probabilistic revolution after we have thought data analysis?

My interest is in the relationship between probability and statistics (data analysis) with regard to teaching and learning. Ideas for teaching (exploratory) data analysis with no preparation in probability emphasize, among other things, finding relationships in sets of variables, identifying relevant variables, interpreting data with regard to sources of variation, possible explaining factors and causes. Probability is often introduced as an antithesis to deterministic situations. Some empirical research even blames children for looking for causes where there is "really" randomness. There is other research taking positions against stochastics.