The ceteris paribus rule

Economics is a social science, and, unlike the physical sciences, cannot engage in controlled experimentation to demonstrate how variables are connected.

In the real world, economic variables  such as price and income, are constantly changing, and this creates a problem in demonstrating the relationship between variables. For example, a fall in price is likely to lead to a rise in consumer demand if we assume nothing else changes.

Of course, for independent reasons, income could also fall while demand does not rise.  The fall in price could have been counteracted by a fall in income. The ceteris paribus rule, that all other things remain the same, is used whenever attempting to demonstrate the link between economic variables. Without this assumption, positive economics is impossible.