We know that every infinite can be made well-ordered with an unknown order. Also we can expand the induction principle on any infinite set in the sense that it can made well ordered. Now partially ordered set may not be a well ordered set with respect to the partial order. Let a partially ordered set $(X, \leq)$ with respect to this particular order $'\leq'$ and suppose that this partial order $'\leq '$ does not make the set $X$ well-ordered.
My question is-
Can we expand "induction principle" to the partially order set $(X,\leq)$ keeping in mind that $(X,\leq)$ is not well ordered?
I have great confusion here.