God is both omnipotent and not omnipotent.

Judges 1:19 is a straightforward grammatical/referential issue, not a theological one: the subject of 'could not drive out' is Judah (the tribe), not the LORD — the verse's own grammar reads, 'the LORD was with Judah and he [Judah] took possession of the hill country, but he [Judah] could not drive out the inhabitants of the plain, because they had chariots of iron.' This reading is confirmed by the book's larger theology: Judges systematically attributes Israel's incomplete conquest to Israel's own disobedience/lack of faith, not to divine incapacity (compare the parallel in Josh 17:16-18, where Joshua explicitly tells the tribe of Joseph that iron chariots are surmountable with faith and effort). This is a basic exegetical point about pronoun antecedents, resolved by ordinary grammatical-historical reading. The 'stone' paradox is a different matter — it is a genuine logical puzzle, but its solution has been settled since Aquinas (*ST* I q.25): omnipotence means the power to do whatever is intrinsically, logically possible to do; a task described in inherently self-contradictory terms ('a stone that an omnipotent being cannot lift') does not describe a coherent task at all — it is structurally identical to asking whether God can make a square circle. The inability to 'do' a logical contradiction is not a limitation of power but a recognition that the phrase picks out nothing describable, i.e., a category error (treating 'power' as applying to a linguistically well-formed but metaphysically incoherent pseudo-task). Likewise 'can God sin' or 'can God cease to exist' are not limitations but expressions of God's necessary moral and metaphysical perfection.

Classical theism's careful definition of omnipotence as maximal power consistent with logical coherence and God's own necessarily good nature (Anselm's 'a being than which none greater can be conceived' cannot coherently be conceived as capable of self-contradiction or moral evil, since such 'capacities' would be defects, not perfections) is the philosophically rigorous standard; the naive univocal notion of 'power' the paradox trades on is not what any serious theological tradition has ever meant by omnipotence.