Sirrah, your brother is legitimate.
Your father’s wife did after wedlock bear him,
And if she did play false, the fault was hers,
Which fault lies on the hazards of all husbands
That marry wives. Tell me, how if my brother,
Who, as you say, took pains to get this son,
Had of your father claimed this son for his?
(1.1.116–22) 

King John speaks these words to Robert Faulconbridge, explaining how his half-brother’s illegitimacy isn’t a legal barrier to his inheritance. Although their mother was wrong to engage in adultery, it matters little from a legal perspective that one of her sons is a bastard. She is the mother of both, and for all intents and purposes her husband claimed both children as his own. For these reasons, the Bastard has every right to inherit his foster father’s land. But though the legal precedents here seem relatively clear, it’s worth noting John’s reference to female infidelity as one of “the hazards of all husbands / That marry wives.” These words reflect a common patriarchal anxiety about female sexuality. This anxiety relates in part to the fear of cuckoldry. In this case, however, the king also emphasizes its relation to the ambiguity of all paternity—at least, in the world before modern genetics.

But thou from loving England art so far
That thou hast underwrought his lawful king,
Cut off the sequence of posterity,
Outfacèd infant state, and done a rape
Upon the maiden virtue of the crown.
. . .
That Geoffrey was thy elder brother born,
And this his son. England was Geoffrey’s right,
And this is Geoffrey’s in the name of God,
How comes it then that thou art called a king,
When living blood doth in these temples beat
Which owe the crown that thou o’ermasterest?
(2.1.94–98, 104–109)

The French King Philip addresses this speech to John, pointing out how the rules of succession in England clearly indicate that Arthur is the rightful king. When Richard the Lionhearted died without children, the throne should have gone to his next-oldest brother or his children. Legally, then, the next in line was Geoffrey and his son Arthur. But before he died, Richard skipped over Geoffrey by appointing John as king. This history explains why Philip says John has “cut off the sequence of posterity . . . / and done a rape / Upon the maiden virtue of the crown.” As if this legal argument weren’t enough to confirm Arthur’s claim, Philip goes on to discuss the physical resemblances between father and son. He seems eager to avoid any ambiguity surrounding Arthur’s paternity, thereby insisting that Arthur “is Geoffrey’s in the name of God.” In a play where legitimacy isn’t merely a legal matter, it makes sense that Philip would also insist on the boy’s biological validity.

A scepter snatched with an unruly hand
Must be as boisterously maintained as gained,
And he that stands upon a slippery place
Makes nice of no vile hold to stay him up.
That John may stand, then Arthur needs must fall.
So be it, for it cannot be but so.
(3.4.135–40)

In these lines addressed to the Dauphin Louis, Cardinal Pandolf predicts that John’s illegitimacy will cause him to act desperate in his attempt to maintain power. His key point is that John will feel compelled to kill Arthur, thereby eliminating his chief rival for the throne. However, in making this point, Pandolf is also preparing to introduce his idea that Louis should pursue the English throne for himself. Since Arthur is as good as dead, Louis can take over his claim, newly possible now that he has married Blanche and taken over English territories in France. The introduction of a third claim to the throne adds a complicating factor in the play’s broader dilemma around legitimate succession. As more claimants are empowered to assert themselves, the matter of succession increasingly emerges as a full-on crisis.