Cornell Univ math dept which none of them can even do correct logic, so, hopeless in doing correct math. All of which made worse in that these failing professors control Arxiv.org. The blind leading the blind.
See TRUE LOGIC corrections below::
Tenured and Tenure-Track Faculty Marcelo Aguiar Jason Manning Slawomir Solecki Dan M. Barbasch Karola Meszaros Philippe Sosoe Yuri Berest Justin Moore Birgit E. Speh Louis Billera Camil Muscalu Michael E. Stillman Xiaodong Cao Anil Nerode Robert S. Strichartz Robert Connelly Michael Nussbaum Steven Strogatz R. Keith Dennis Irena Peeva Edward Swartz Daniel Halpern-Leistner zzzzz Ravi Ramakrishna Nicolas Templier Timothy J. Healey Richard H. Rand Alex Townsend Tara Holm Timothy Riley Alexander Vladimirsky John H. Hubbard Laurent Saloff-Coste Marten Wegkamp Martin Kassabov Shankar Sen James E. West Allen Knutson Richard A. Shore Inna Zakharevich Lionel Levine Reyer Sjamaar David Zywina Emeritus and Retired Faculty Allen Back Allen Hatcher Alfred H. Schatz James H. Bramble David W. Henderson John Smillie Kenneth S. Brown J.T. Gene Hwang Moss E. Sweedler Stephen U. Chase Yulij Ilyashenko Daina Taimina Marshall M. Cohen Peter J. Kahn Robert E. Terrell Clifford J. Earle Harry Kesten Maria S. Terrell Roger H. Farrell G. Roger Livesay Karen Vogtmann Leonard Gross Michael D. Morley Beverly West John M. Guckenheimer
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.