I've already asked this question on Physics.SE, but it got no response; its not a conventional physics question, but really on how to interpret physical equations and physics.
Newtons law of gravity for two particles is proportional to the product of their masses divided by the square of their displacement.
Supposing that the particles are point particles then gravitional attraction will bring them closer together, and in fact infinitesimally closer together. Now in Newtons time there was no theory, as far as I am aware of inter-atomic forces that would have kept these two particles apart, so the gravitional attraction is asymptotically infinite. This is nonsensical, and either one can say that point particles cannot arbitrarily approach one another, or that particles can never be point particles and must have extension - this in fact includes the previous solution, as the notional point positions of the centre of mass of a particles with extension cannot obviously approach one another.
In Classical Mechanics, in retrospect this could have counted as evidence of either particles cannot be point masses; or of some then unknown repulsive force that acts at very small distances - are there any other alternatives? Why would physicists ignore then such a simple observation? What does this tell us about the process of theory-formation in Physics?