Irrationality is no hindrance for something being true

Hello. I accept the challenge and look forward to debating this topic with you. I am Con and thus i will argue that the proposition "Irrationality is no hindrance for something being true" is wrong. Specifically, i interpret the proposition to mean that a proposition and its negation can both be true at the same time. My argument then will make the case that any proposition must be either true or false but not both true and false. This is generally taken as an axiom and thus cannot be proven, so I will make some quite informal statements to begin with then let Pro choose which level he wishes to debate on, either specific axamples or general motivations for accepting or refuting the axiom of noncontradiction.The examples given in the opening argument and in the text linked to are very vague and some of them seem to be based on misconceptions. Quantum mechanics, which I will assume refers to the standard model, is not known to be either consistent or inconsistent. It is however widely believed to be internally consistent. It is in certain conditions (where both GR and QFT effects are non-negligible simultaneously) inconsistent with general relativity, but their respective domains of validity have been restricted precisely because of the contradiction. That is the reason it is said that neither theory has the correct description of the phenomena where they contradict each other. Then, what if we where to ignore the contradiction? Well, we would have two different descriptions of a single underlying reality. When we measure the true values of whatever physical observable we choose to model, it would probably differ from both the calculated values.In general, the fact that a theory gives correct results in any finite number of cases does not excuse a contradiction, because if there is a contradiction there will be cases where the theory does not work to predict reality. It will be possible to make a lot of statements contradicting the observed reality that the theory was supposed to describe, if one finds and exploits a contradiction.The impossibility of contradiction is embedded in the very concepts of truth and falsehood. Although there are nonclassical logics that allow other truthvalues than these, the ones that are actually useful tend to have some form of law of noncontradiction.I find the statements on mathematics in Deans text to be examples of a widespread postmodernist misconception, probably related to Gödels incompleteness theorems. I will not go into more detail about that here unless my opponent wishes to do so. A collection of patient explanations of why postmodern relativist statements on the contradictions of science are gibberish is given in Alan Sokals and Jean Bricmonts book Fashionable nonsense which seems to be freely available here: http://emilkirkegaard.dk...There are also books on misuse of Gödel specifically since that is very widespread but i will leave that topic for now. I have assumed the existence of one underlying reality since communication between different subjective minds would be impossible otherwise. I believe that the core of the debate actually lies here.GR = General RelativityQFT = Quantum Field Theory / Standard Model