From ErfWiki

Proposed Canon

Fate is one of the three axes of magic (along with Erf and Numbers) used to break a major class of magic into three different disciplines.^[1]

Attunement to Arkentools is governed by Fate magic.^[2]

Class\Axis	Magical Axis
	Fate
Hocus Pocus	Predictamancy
Spookism	Dollamancy
Stuffamancy	Changemancy
Eyemancy	Thinkamancy
Hippiemancy	Signamancy
Naughtymancy	Croakamancy
Stagemancy	Carnymancy
Clevermancy	Healomancy

Speculation

It should be noted that both Thinkamancy - associated with the Arkendish - and Croakamancy - associated with the Arkenpliers - lie in the axis of Fate. So far it is unclear what discipline of Magic powers the Arkenhammer (possibly Changemancy with its ability to occasionally turn walnuts to pigeons), but it would make perfect sense if that would be one of the Fate disciplines.

The Axis of Fate seems to focus on an active target's status. For instance, Croakamancy can return a character from dead to undead. Presumably, Healomancy restores hit points and removes other status effects. And Thinkamancy has been shown to alter loyalty scores. Predictamancy can determine a target's future state - alive, dead, carrying around a pair of Arkenpliers.