Irrationality is no hindrance for something being true

you say "Bishop Berkeleys allegations are disputed and several modern mathematicians consider the formulation of Leibniz to be free of contradiction[1], but that really doesn't matter Even if a mathematical theory seems to produce true results, it obeys aristotelian logic. " your reference flys in the face of orthodox consensus on the issue as your reference points out "Robinson regards Berkeley's criticisms of the infinitesimal calculus as aptly demonstrating the inconsistency of reasoning" facts is Bunch agrees Berkeley was correct so does I. Gratten-Guinness Newton and Leibniz developed the calculus". Their ideas were attacked for being full of paradoxes." Newton"s formulation of calculus was self-contradictory ." B, Bunch , Mathematical Fallacies and Paradoxes Dover, 1982, p.192. "instead of having demonstrations justify results, results were used to justify demonstrations.I. Gratten-Guinness, From the Calculus to set theory 1630-1910, Duckworth, 1980, p.296. "Even if a mathematical theory seems to produce true results, it obeys aristotelian logic. " yes it does but the early formulation of calculus violates the law of non-contradiction "Newton"s formulation of calculus was self-contradictory yet it worked "one clear example is the dual nature of light ie both wave and particle" This is not a logical paradox, it is a result that contradicts intuition." wrong to say a thing is both a wave at the same time it is a particle violates Aristotelian logic law of excluded middle and it is a contradiction quote from wiki which agrees it is a paradox http://en.wikipedia.org... "Wave"particle duality postulates that all particles exhibit both wave and particle properties. A central concept of quantum mechanics, this duality addresses the inability of classical concepts like "particle" and "wave" to fully describe the behavior of quantum-scale objects. Standard interpretations of quantum mechanics explain this paradox as a fundamental property of the Universe," note it says "Standard interpretations of quantum mechanics explain this paradox as a fundamental property of the Universe" again "Wave"particle duality is an ongoing conundrum in modern physics. Most physicists accept wave-particle duality as the best explanation for a broad range of observed phenomena; however, it is not without controversy. Alternative views are also presented here. These views are not generally accepted by mainstream physics, but serve as a basis for valuable discussion within the community." note it says "Most physicists accept wave-particle duality " you say "There are two widespread meanings of the word paradox. One is the logical definition, that incompatible statements are true simultaneously" thus proving my point a thing is simultaneously a wave and particle- paradox irrationality again you say "The duality disappears in a rigorous mathematical formalism, where particles are replaced by wave packets or excitations of fields that is an alternative view http://en.wikipedia.org... "At least one scientist proposes that the duality can be replaced by a "wave-only" view. In his book Collective Electrodynamics: Quantum Foundations of Electromagnetism (2000), Carver Mead" but as the wiki entry above stated "Alternative views are also presented here. These views are not generally accepted by mainstream physics," but "Standard interpretations of quantum mechanics explain this paradox as a fundamental property of the Universe" you say "Your citations about quantum mechanics do not exactly specify which paradoxes" nevertheless there is a whole book written on the irrationality of GM "F. Selleri, Quantum Paradoxes and Physical Reality, Kluer Academic Publishers, 1990, and wick even states the orthodox view "Wick notes " I believe orthodox quantum theorists [slates] reason, ... The microscopic world exhibits paradoxes or contradictions and this fact is reflected in the best theory describing it." A. Wick, The Infamous Boundary, Birkhauser, Berlin, 1995, p.184" I have backed up my question with quote from books and scientists and mathematicians who point out the irrationality of mathematics and science con has given sources but it can also back up my claim- on mathematics con gives an alternative view in physics denying wave-particle duality-paradox but as shown this view is not accepted by the majority of physicists thus I have given evidence about irrationality in mathematics evidence from the orthodox view -con gives a reference which can back up my claim about calculus being irrational i gave evidence about irrationality in quantum mechanics -the orthodox view con gives an alternative view but as shown this alternative view is not accepted by most physicists so I win as con has not adequatfuted my claims