How many hearts does River Song have?

Question

River Song is quoted by The Doctor as "Half Time Lord". She is also called daughter of the TARDIS despite the fact that she was actually born from human parents. Probably, it's a Wibbly-Wobbly stuff because the parents mated inside the TARDIS.

River Song can regenerate which shows a property of a Time Lord, but how many hearts does she have? One (number of human hearts) or two (number of Time Lord hearts) or average of both i.e. 1.5 (AFAIK, hearts can only exist in integers but it's Timey-Wimey stuff, so maybe it has partial quantum superposition or something similar)?

Answer 1

To the best of my knowledge no on-screen statement has been made conclusively either way, and Doctor Who 'canon' only exists inasmuch as sometimes it doesn't actively contradict itself. But we can extrapolate that the most likely scenario is:

River Song should have one heart.

She's a human, not a Gallifreyan, and that makes all the difference. Being a Time Lord shouldn't have any impact on gross biology like the quantity of one's organs, because "Time Lord" is not a race, nor a species. It just means you've been subjected to a suite of (poorly-defined) biotechnological enhancements invented by Gallifreyans--and almost always only used on Gallifreyans, so Time Lords have two hearts because Time Lords are almost exclusively Gallifreyan, not because being a Time Lord does that to you. (See the Doctor's daughter, who seems to probably be a Gallifreyan and not a Time Lord but had two hearts anyway.)

River Song is a human, born of human parents, who has "Time Lord DNA" upgrades/enhancement/modifications from TARDIS/Time Vortex technobabble [waves hand vigorously]. She's displayed Time Lord features like regeneration because of this (but there are many indications she didn't get the full suite of enhancements). There's no reason, however, that she should have two hearts: that seems to be a quirk of Gallifreyan anatomy and River Song is not Gallifreyan.

The idea of human Time Lords, by the way, is not new.

Answer 2

She has two and one. It's all a bit wibbly. Bear with me.

In her first incarnation, baby Melody appears to have one heart. At the start of A Good Man Goes to War she is described as being completely human;

VASTRA: As you were today, old friend. Point taken, I hope. Now, I have a question. A simple one. Is Melody human?

DOCTOR: Sorry, what? Of course she is. Completely human. What are you talking about?

DORIUM: They've been scanning her since she was born, and I think they found what they were looking for.

DOCTOR: Human DNA.

This is consistent with the fact that Galifreyans are born with one heart (as we see in the Prose novel "The Man in the Velvet Mask") and only develop the twinned heart after their first full regeneration:

The Doctor knew. His heart screamed inside his ribs, pounding furiously until it seemed it was going to burst. His hand formed a claw, squeezing at his chest, almost prepared to tear it open to ease the pain. He shrieked. The pain stopped, his heart with it. He fell. He struck the floor... One heart, he thought blissfully. One heart, soon to meet its twin.

In "Let's Kill Hitler", we briefly see a medical scan of the newly-regerated River Song in the hospital of the Sisters of the Infinite Schism. Although it's a 'blink-and-you'll-miss-it' moment, she does indeed appear to have two hearts...