It's a provable fact of mathematical logic: All coherent systems of thought are incomplete, in that there are truths that lie outside, forever inaccessible, not provable within the system at hand. Therefore, we will never have the whole story until we are able to step outside our logical system--whatever system we have chosen--and seek our truth elsewhere. But where? Indian physicist Thandu Padmanabhan suggests an answer: in direct experience.
The only possible true adventure...lies outside perimeters of all systems of thought and this is what we shall seek. Begin with a beautiful fact: Nothing precludes the existence of experiences which cannot be communicated, verbalized, transmitted...within the honest-to-God system of Aristotelian logic! Nothing precludes the existence of concepts which cannot be communicated by any system of thought...[Realizing] this is probably the highest peak a logical intellect"can take you. And that is enough, in a way. Once the existence of the possibility is recognised, intellect self-destructs and something else--which, for the lack of a better name, I will call Direct Experience--takes over.