Fire the entire Princeton Univ math dept-- unable to even teach Add in Logic is not OR but rather is AND
Now, what are the odds that if you do not know the correct Logic truth tables for the connectors-- And, Or, Equal+Negation, If-Then, what are the odds that your mathematics is valid?
Well, a slim chance, because the IF-THEN connector is vital to validity, and in New Logic, that means Reductio Ad Absurdum is not valid proof method. That means about 1/4 to 1/2 of all math is invalid.
So, I ask that the entire Princeton Math dept be fired until they have teachers there, that use a valid Logic
See TRUE LOGIC corrections below::
Princeton University Math dept
Michael Aizenman Professor
Zahra Aminzare Lecturer
Manjul Bhargava Professor
Nathaniel Bottman Postdoctoral Research Fellow
Nicolas Boumal Instructor
Jean Bourgain Visiting Lecturer with Rank of Professor Mathematics
William Browder Professor Emeritus
Tristan Buckmaster Assistant Professor
Francesc Castella Instructor
Sun-Yung Alice Chang Professor
Otis Chodosh Veblen Research Instructor
Maria Chudnovsky Professor
Peter Constantin Professor of Mathematics and Director of PACM
John Conway Professor Emeritus
Mihalis Dafermos Professor
Gabriele Di Cerbo Assistant Professor
Hansheng Diao Instructor
Theodore Drivas Postdoctoral Research Fellow
Zeev Dvir Associate Professor
Weinan E Professor
Tarek Elgindi Instructor
Tolga Etgü Visiting Fellow
Charles Fefferman Professor
Jonathan Fickenscher Associate Research Scholar
David Gabai Chair, Professor
Ziyang Gao Instructor
Javier Gómez-Serrano Assistant Professor, Director of Graduate Studies
Robert C. Gunning Professor
Jonathan Hanselman Assistant Professor
Helmut Hofer Visiting Lecturer with Rank of Professor Mathematics
Henry Horton Postdoctoral Research Associate zzzzzzz Yong Hou Lecturer Mathematics Tatiana Howard Lecturer
Wu-Chung Hsiang Professor Emeritus
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Mihaela Ignatova Instructor
Alexandru Ionescu Professor
Jennifer M. Johnson Senior Lecturer, Associate Departmental Representative
Nicholas Katz Professor
Casey Kelleher Postdoctoral Research Fellow
Daniel Ketover Instructor
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Simon Kochen Professor Emeritus
Joseph Kohn Professor Emeritus
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Elliott Lieb Professor Emeritus
Francesco Lin Veblen Research Instructor
Yueh-Ju Lin Instructor
Chun-Hung Liu Instructor
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Adam Marcus Assistant Professor
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Mark McConnell Senior Lecturer
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Evita Nestoridi Instructor
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Peter Ozsváth Professor, Director of Graduate Studies
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Correction of Logic errors by Archimedes Plutonium 3. Logic errors:: otherwise we cannot think clearly and think straight and true History of those pathetic errors::
by Archimedes Plutonium
The 4 connectors of Logic are:
1) Equal (equivalence) plus Not (negation) where the two are combined as one 2) And (conjunction) 3) Or (exclusive or) (disjunction) 4) Implication
EQUAL/NOT table: T = T = T T = not F = T F = not T = T F = F = T
Equality must start or begin logic because in the other connectors, we cannot say a result equals something if we do not have equality built already. Now to build equality, it is unary in that T=T and F =F. So we need another unary connector to make equality a binary. Negation is that other connector and when we combine the two we have the above table.
Equality combined with Negation allows us to proceed to build the other three logic connectors.
Now, unfortunately, Logic must start with equality allied with negation and in math what this connector as binary connector ends up being-- is multiplication for math. One would think that the first connector of Logic that must be covered is the connector that ends up being addition of math, not multiplication. But maybe we can find a philosophy-logic answer as to why Logic starts with equal/not and is multiplication rather than addition.
Here you we have one truth table equal/not whose endresult is 4 trues.
New Logic AND T & T = T T & F = T F & T = T F & F = F
AND is ADD in New Logic, and that makes a whole lot of common sense. AND feels like addition, the joining of parts. And the truth table for AND should be such that if given one true statement in a series of statements then the entire string of statements is true. So if I had P and Q and S and R, I need only one of those to be true to make the string true P & Q & S & R = True if just one statement is true.
The truth table of AND results in 3 trues and 1 false.
New Logic OR(exclusive) T or T = F T or F = T F or T = T F or F = F
OR is seen as a choice, a pick and choose. So if I had T or T, there is no choice and so it is False. If I had T or F there is a choice and so it is true. Again the same for F or T, but when I have F or F, there is no choice and so it is false. OR in mathematics, because we pick and discard what is not chosen, that OR is seen as subtraction.
OR is a truth table whose endresult is 2 trues, 2 falses.
New Logic IMPLIES (Material Conditional) IF/THEN MOVES INTO T -> T = T T -> F = F F -> T = U probability outcome F -> F = U probability outcome
A truth table that has a variable which is neither T or F, but U for unknown or a probability outcome. We need this U so that we can do math where 0 divided into something is not defined.
Now notice there are four truth tables where the endresult is 4 trues, 3 trues with 1 false, 2 trues with 2 falses and finally a truth table with a different variable other than T or F, with variable U. This is important in New Logic that the four primitive connectors, by primitive I mean they are independent of one another so that one cannot be derived by the other three. The four are axioms, independent. And the way you can spot that they are independent is that if you reverse their values so that 4 trues become 4 falses. For AND, reversal would be FFFT instead of TTTF. For OR, a reversal would be TFFT instead of FTTF.
To be independent and not derivable by the other three axioms you need a condition of this:
One Table be 4 of the same One Table be 3 of the same One Table be 2 of the same And to get division by 0 in mathematics, one table with a unknown variable.
So, how did Old Logic get it all so wrong so bad? I think the problem was that in the 1800s when Logic was being discovered, is that the best minds of the time were involved in physics, chemistry, biology and looked upon philosophy and logic as second rate and that second rate minds would propose Old Logic. This history would be from Boole 1854 The Laws of Thought, and Jevons textbook of Elementary Lessons on Logic, 1870. Boole started the Old Logic with the help of Jevons and fostered the wrong muddleheaded idea that OR was ADD, when it truly is AND.
Now the way people actually live, is an indicator of how well they thought and how well any of their ideas should be taken seriously. In the case of Boole, he went to class in a downpour rain, why without a raincoat? And reaching class, instead of changing into dry warm clothes, stood for hours in front of students, sopping wet and shivering. Of course he caught pneumonia, but instead of being sensible, common sense that even a fly would have, he insisted his wife give him cold showers and make the bed all wet and freezing. Of course, he would die from this. Now, does anyone today, think that a mind like that has anything to offer Logic or mathematics, is as crazy as what Boole was.
But once you have textbooks about Logic, it is difficult to correct a mistake because of the money making social network wants to make more money, not go around fixing mistakes. So this nightmarish mistakes of the truth tables was not seen by Frege, by Russell, by Whitehead, by Carnap, by Godel, and by 1908 the symbols and terminology of the Old Logic truth tables were so deeply rooted into Logic, that only a Logical minded person could ever rescue Logic.
by Archimedes Plutonium
3.1 The "and" truth table should be TTTF not what Boole thought TFFF. Only an utter gutter mind of logic would think that in a series of statements, that AND is true when all statements are true, but to the wise person-- he realizes that if just one statement is true, the entire series is true, where we toss aside all the irrelevant and false statements --(much what life itself is-- we pick out the true ones and ignore all the false ones). 3.2 The error of "if-then" truth table should be TFUU, not that of TFTT 3.3 The error of "not" and "equal", neither unary, but should be binary 3.4 The error that Reductio Ad Absurdum is a proof method, when it is merely probability-truth, not guaranteed 3.5 The error, the "or" connector is truth table FTTF, not that of TTTF