Initially I used to believe that before Newton gave his Laws of Motion, people thought that Force was something that caused motion. It was Newton who first said that Force is something that causes acceleration and gave a mathematical equation for it.
But recently I came across this article which says that Newton had developed his Law of Gravitation by 1666 and published his Laws of Motion in 1686. How could Newton have given an equation for Gravitation when there was no mathematical definition of force existing at that time?
On further study I came to know that Hooke's Law was given by Hooke in 1676, again a date before Newton gave Laws of Motion. Doesn't that imply that before Newton gave his Laws of Motion, people had some mathematical intuition about Force? Or may be people meant something else by the term Force.