In the book "An Introduction to Non-Classical Logic" by G. Priest, logics in which modus ponens fails are mentioned. I think that they can be relevant to the text "Generalized Modus Ponens and Inconsistency in Pairwise Comparisons". I also think that it might be helpful for readers to write something about such logics in a final version of this paricular article "Generalized Modus Ponens...". Anyway, I believe that it is not good too say nothing about the logics mentioned above. I hope that you agree with me. Do you?
Regards, Eliza Wajch
Article Generalized Modus Ponens and Inconsistency in Pairwise Compa...
I own Priest's book, and every once in a while I still go back to it (alas, I have not had the opportunity to use it to teach). There is also an edited volume The Law of Non-contradiction: New Philosophical Essays which you may be interested in if you haven't read it, as it contains papers challenging a far more central "rule" of logic. For philosophers, many logics are either held to be useless or to be considered attacks against reason, against philosophy, against all that is near and dear (of course, these are the same people that have spent some ~2,500 years arguing about whether the future tense entails fatalism).
Fuzzy logics, modal logics, and other non-classical logics have been successfully used in countless applications by researchers in diverse fields. It is very important to be familiar with such systems (IMHO).
I thank you for your answer very much. I need a non-classical logic of my kind in order to be closer to truth in science. Perhaps, this logic will be considered as classical in a not-too-distant future. I must deal with statements that are neither true nor false but they are of great importance. I want to be extremely honest if this is possible. This is simply my need and my choice - to be honest. Sometimes, it is unclear whether we use proper words to call objects. Kind regards, Eliza Wajch
Hi Eliza.
There are some types logics in which modus ponens fails. Such logics are called as logics with the restricted rules of a conclusions.
Paraconsistent First-Order Logic with infinite hierarchy levels of contradiction LP#
http://arxiv.org/abs/0805.1481
Relevant First-Order Logic LP# and Curry's Paradox resolution
http://arxiv.org/abs/0804.4818
DOI: 10.11648/j.pamj.s.2015040101.12
Paraconsistent second order arithmetic Z^#_2 based on the paraconsistent logic LP^# with infinite hierarchy levels of contradiction. Berry's and Richard's inconsistent numbers within Z^#_2
http://arxiv.org/abs/0906.3479
Foundation of Paralogical Nonstandard Analysis and Its Application to Some famous Problems of Trigonometrical and Orthogonal Series. Part I- II. 2004.
http://www.sciencedirect.com/preprintarchive
Thank you for your answers very much. They are helpful, especially the links to relevant papers are helpful.
The usual human logic the an example of the logics with the restricted rules of a conclusions. Obviously any standard predicate calculus is break down by the liar paradox and by the hairdresser paradox ,etc.
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