ve Leibniz essentially makes in the Monadology:Let a possible being mean a being whose existence is not self-contradictory, that may or may not be necessary. Let an impossible being mean a being that is self-contradictory. Let a necessary being mean a being whose opposite is a contradiction; that is a necessary being is one which cannot be conceived not to be, and one whose explanation is self-sufficient. Let a contingent being mean a being whose opposite is not a contradiction, that is a contingent being is one which can be conceived of as not existing, and one whose explanation is self-sufficient. If there are possible beings, they have a reason sufficient to explain them—either as a necessary being, that being self-sufficient or as a contingent being. (principle of sufficient reason). There cannot be an infinity of contingent beings (law against infinite regress with the definition of a contingent being). Either all beings are necessary, or there are both contingent and necessary beings (follows from the above premise). Therefore, if there are possible beings, there are necessary beings (follows from the above premise). If there were no possible beings, then all beings would be impossible; that is, they would be self-contradictory (by definition). Impossible beings do not exist. (law of noncontradiction and the definition of an impossible being). If impossible beings do not exist, neither does an argument claiming that nothing exists (follows from the above premise, and the assumption that there are no possible beings). This argument would not be an argument. (follows from the above premise). An argument that is not an argument is absurd (law of noncontradiction). Therefore, possible beings exist because they involve no contradiction (law of noncontradiction and the absurdity which follows from the above premise). Therefore, necessary beings exist (follows from the premise seven above this and the above premise). One should not...
