T.A.Gardner says:
"Those are the rules. But they are useless without data and information to run the equations, just like in mathematics."
Here I was trying to clarify that logic does not require data or information. Mathematics does not require it either.
Both logic and mathematics are defined by their axioms. They exist without any data. They exist without any information. Both are more than just an equation.
Let's take a well known equation used in science: F=mA. This relates force, mass, and acceleration. No data is required for this equation to exist. It DOES, however, exist as the result of a theory of science, transcribed into mathematics to give it the power of prediction.
This single equation is the more important in all of science, since it focused for the first time on trying to discover what forces there are, what mass really is, and the concept of accleratino (which is a derivative of a derivative of position as it changes over time (speed), and how THAT changes over time (acceleration).
Whether is a planet, a moon, or an apple, the equation holds true. Any theory of science only remains so until it is falsified. This relation has never been falsified yet.
Now, to the topic of data:
Data is the result of an observation. All observations are subject to the problems of phenomenology, and are therefore not a proof of any kind.
This ALSO means that it is not possible to prove any theory of science True. Science is an open functional system, where proofs are not possible. Science consists only of falsifiable theories. Nothing else.
Proofs are only possible in closed functional system such as mathematics or logic. They are closed because they are defined (including their operating limitations) by axioms. You cannot go outside and change these axioms. They are the rules of the game. Change any single rule, and you are playing a different game.
Thus, F=mA requires no data. It requires no observation. It simply exists. You can certainly apply data and observations while you use it, but the equation itself does not require data or observation to exist.
The theory of science was created through observations and data and insight by Newton, but the equation that results does not require it. Once created, the theory no longer requires data, observation, nor even Newton.