Carroll's Puzzle Exploration

Carroll's puzzle was put forward by the British logician Lewis Carroll at the end of the 19 th century.He believes that the use of MP rules can lead to infinite retrogression of reasoning.Because if you want to introduce the third proposition r from the two propositions p and q,then you must first add a premise p and q implicate r,which can be written as s,otherwise it is difficult to derive r from p and q.In the same way,you will need the premise t,that is,p,q and s contain r,and so on,so that there is infinity.This indicates that the MP rules does not guarantee the validity of reasoning,which in turn leads to doubts about the validity of deduction.In the face of puzzle,logicians have proposed many solutions.Rees and others proposed the stratification of premise and meta-premise from the perspective of premise and rules to avoid infinite retreat.Thomson et al.deny that the rule is a premise,trying to directly block the possibility of infinite retreat.Russell et al.propose different distinctions of inference rules and logical implications according to different reasoning and argumentation to explain the infinite retreat phenomenon.Boghossian acknowledges that the rule-circle is a necessary and acceptable form,and thus recognizes the infinite retreat of reasoning.Wieland believes that there is an obligation to reject the infinite retreat from the relationship between people's beliefs and reasoning.Peirce et al.emphasized that from the perspective of practical understanding,it is tested whether the reasoning results occur and ignores the infinite retreat of reasoning.From the perspective of dialectics,Feng Qi proposes that reasoning is a process of contradictory movement in which continuity and discontinuity are unified,and there is no problem of infinite retreat from the perspective of discontinuity.From the perspective of cognitive logic,Chen Xiao Hua proposes that the cognitive closed principle of weakening recognizes the infinite retreat of individuals in reasoning.On the basis of different interpretation schemes,this paper first analyzes Aristotle'sviews on the infinite retreat problem in the theory of proof theory,and then analyzes the difficulty from the key point of writing the rules.Then,from the perspective of intuitive simplicity,the advantages and disadvantages of different interpretation schemes are comprehensively compared,and the distinction between rules and premise is taken as the most reasonable and intuitive solution to the problem of blocking infinite retreat.Finally,from the perspective of the solution,I will respond to the problems of justification of deduction.