Newton's Rules of Reasoning minus his comments are as follows, where it should be realised that in the following quotation Newton meant by "experimental philosophy" what we call "natural science" and that a shorter version of "which admit neither intensifcation nor remission of degrees" is "which are invariant". Newton added these rules to the second edition of his Principia, in 1714. I prefix them with one important condition, and assume them, to start with, for my Natural Philosophy:

Provided we have no evidence to the contrary, to the best of our knowledge:

Rule I : We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances.
Rule II : Therefore to the same natural effects we must, as far as possible, assign the same reasons.
Rule III : The qualities of bodies, which admit neither intensification nor remission of degrees, and which are found to belong to all bodies within the reach of our experiments, are to be esteemed the universal qualities of all bodies whatsoever.
Rule IV : In experimental philosophy we are to look upon propositions inferred by general induction from phenomena as accurately or very nearly true, notwithstanding any contrary hypotheses that may be imagined, till such time as other phenomena occur, by which they may be either made more accurate, or liable to exception.

It is noteworthy and interesting that all four principles can be argued by probability theory at least if this is extended with some assumptions. See Rules of Probabilistic Reasoning.