The illative sense is an epistemological concept coined by John Henry Newman (1801–1890) in his Grammar of Assent.
And, although supernatural reasons might be given from theology, as a philosopher[1][2] he also looked into ordinary life experiences: when and why do we start or stop believing a person?
[7] There must be, therefore, in the mind a power that collects, accumulates, and connects probabilities to a higher degree of certainty.
For Newman it is the automatic data-collecting and -processing capacity in the sub-conscious mind, by which we get to know better or deeper both the content and certainty of the first principles of our knowledge, and of many natural and supernatural (religious) concepts and notional and/or real assents thereof.
Of course, it applied to his own gradual conversion from Anglicanism to Catholicism: "For myself, it was not logic, then, that carried me on; as well might one say that the quicksilver in the barometer changes the weather.