This section analyzed paradoxes related to planning and carrying out actions addressing seemingly impossible goals (i.e., the thinking, intending, exceeding oneself, and action paradoxes). The personality traits that may be involved in perceiving difficult challenges as realizable were introduced: namely, self-efficacy, locus of control, perceiving people and the world as changeable, need for achievement, and optimism. This laid the foundation for introducing the personality trait of “possibilitivity” (i.e., that people perceive insurmountable challenges on an undoable–doable continuum). The theory of this trait was followed by presenting the process of constructing and validating the PoDQ, concluding with the presentation of three diverse possibilitivity cases.