Paraconsistent Logic Applied To The Moral Logic

We can push the idea on deontic logic back to Aristotle. Aristotle observed the practical reason type of logical proof when he constructed the syllogism system. Aristotelian ought is not normative and is embedded in the nature of things. William Ockham presented the theoretically interesting question whether God can command men to hate Him. The idea on deontic logic did not change much until Scott. Scott's ethic is normative. Rosetues held that the rationality of a system of norms meant that fulfilling the norms did not yield any contradictories; and there were obligations which could be rationally fulfilled only in cases in which some norms had been already violated.Leibniz's and Bentham's.ideas on deontic logic are representive in modem times. Leibniz observed the similarity and interchange between deontic modality and traditional modality. Bentham presented a logic on will or imperative sentences in 1780.Ernst Mally was the first man who tried to construct deontic logic. But he failed. Finn logician Von Wright published the classical essay Deontic Logic in 1951, which marked that modern deontic logic came into being.Now there are many deontic logic formal systems, e.g. naive deontic logic systems OK. , OS5*,alethic deontic logic systems, e.g. MK, MS5*, etc. Although these systems have perfect completeness, they all contain deontic logic paradoxes.The root of Ross paradox is the much difference between the meaning and logical effect of combining the connective "V" with the deontic operator "0" or "P" and that of the combination of the counterparts of the three symbols above in natural language , as people know generally, "either", "should" and "permission". The two formulae embodying the paradox of commitment are the characteristic ones of the systems of monadic deontic logic. The paradox of commitment results from the fact that the normative systems explain absolutely such deontic conceptions as "should", "permission" and "prohibition". The semantic analysis of Chisholm's dilemma indicates that Chisholm's example itself is untenable in the sort of OSS* systems ,and such systems can't depict contrary-to-duty commands. This is because such kind of systems doesn't differentiate the levels of commands and accordingly there are no differences or order of preference among possible-worlds in its semantics. The Good Samaritan Paradox results from Anderson's reducing dentic logic to consistent alethic modal logic by the definition Op.After analyzing the Good Samaritan Paradox by semantics and the difference between the two concepts of necessity and ought we can conclude that Anderson's reduction definition Op is untenable no matter whether we define "S" as "penalty", "sanction" or as the realization of violating a prohibition . Op can only be elucidated by 0. The reason that results in the Jephta dilemma is that ethics conflict with each other sometimes .The dilemma reveals that obligation should be relative to some ethical norm.Various kinds of non-classical logic sprang up vigorously while classical logic came to a standstill relatively in the 1960's. After reflecting on many inconsistent propositions in the fields of logic, natural sciences and social sciences, people began challenging classical logic and believed that the law of contradiction is not valid universally .In the background da Costa founded paraconsistent logic.Professor Zhang Qing-yu gets paraconsistent modal proposition logic CnG' on the base ofCosta's paraconsistent proposition logic system Cn.We get paraconsistent alethic modal proposition logic CnMG' with completeness by adding a constant Q and axiomatic schemata OQ W Q(n> to C,G'. Then by definitionand we get paraconsistent alethic deontic logic CnDG'. CnDG' avoids the Good Samaritan Paradox, and can contain deontic dilemmas.However the formulae etc., about which we feel qualm, are still the theorems of CnMG'. This shows that it is only when we construct deonric logic systems on the base of paraconsistent relevance (entailment) logic that we can discard these doubtfu...