Palaeorecords indicate that the average global temperature been relatively stable for the past ~10,000 years of the Holocene epoch, in contrast to cooling trends during previous interglacials and abrupt shifts during past Glacials. Hypotheses for this stability range from early anthropogenic emissions to orbital factors or the timing of carbon cycle feedbacks. An alternative suggestion grounded in dynamical systems theory is that Holocene stability reflects the Earth system residing near a climate “attractor”, with strong negative feedbacks acting to stabilise the climate’s state, and Glacial/Interglacial cycling representing either a limit cycle or tipping between Interglacial and Glacial basins of attraction. This in turn has led to the more recent hypothesis that human actions are eroding the resilience of the Earth system’s current state, and at some level could be sufficient to tip the whole Earth system towards a much warmer “Hothouse Earth” attractor. However, despite multiple hypotheses for Holocene stability, that the Earth system is close to the edge of a dynamical basin of attraction is often assumed rather than demonstrated. Here, I assess the basis for this hypothesis in the literature, finding that there is currently insufficient evidence to support this hypothesis over the alternatives of pseudo-stability from stable orbital forcing, lagged feedbacks, or more complex nonlinear dynamics. As such, more evidence is required to test these hypotheses, and in the meantime the presence of Holocene or Hothouse attractors should not be taken as a given. Given this, I outline some alternative frameworks for climate states and Earth system resilience that may be appropriate without strong attractors, centring adaptive capacity and stability through change.