not mathematical induction   Im not a logician but it seems to me there is another problem with the line of reasoning that hasnt been mentioned Even ignoring that the case for  horses fails this is not mathematical induction anyway   Compare with this If we had a proof P that all horses are white we could prove that one horse is white My horse is white Therefore the proof P is valid Therefore all horses are white   This is obviously flawed because my horse being white can occur even if not all horses are white Similarly we could argue that in the OPs  horse proof having all horses in a group of  horse be the same colour can occur for reasons other than all horses being the same colour as indeed it can   For this to be mathematical induction we would have an argument along the lines of   I have a proof P that shows for any size group of horses all of one colour a group of one more horse will also be all the same colour A group of one horse is a group of all one colour therefore all groups are the same colour   This is a correct form of argument but of course since we dont have a proof P it isnt true   Thus as well as the explanation due to special cases there is also an explanation due to a flawed form of argument that only resembles mathematical induction