Using Math To Tell A Lie

A more appropriate heading for this would be “How a logical truth can be a lexical lie”, but hey, gotta have that clickbaity title. But nevertheless, I will frame this article as if I am addressing the title.

Apparently, sociologists/psychologists classify lies with a three tier system; primary, secondary, and tertiary. According to an article on Psychology Today, children as young as 2-3 tell have developed the ability to tell lies. And children of age 7-8 have developed the skill to tell what is dubbed “tertiary lies”, which are lies that are “more consistent with known facts and follow-up statements”.

But how does telling a lie relate to mathematics? And exactly what tools can you use for such?

There exists a branch of logic, where logic is a branch of math, called propositional logic. Propositional logic is all about combining statements. A  statement is something you proclaim, that is either true or false.…

Mathematically speaking, what is a contradiction?

The world of predicate logic interests me, especially how it provides a foundation for understanding the logic behind many mathematical proofs. It is interesting to know how the negation, contrapositive and inverse are defined with respect to some implication $A \Rightarrow B$   ($A \wedge \neg B, \neg B \Rightarrow \neg A$  and  $B \Rightarrow A$ respectively). What got me thinking about predicate logic again was when I asked myself, “What is a contradiction?”

My big Collins Dictionary and Thesaurus defines ‘contradict’ as “to declare the opposite of (a statement) to be true” (verbatim). But, this leaves some room for debate as the meaning of the word “opposite” is not logically clear. Is the negation true? Is the inverse true? My reasoning says that a contradiction of the above implication is defined as $A \Rightarrow \neg B$. In a less formal way (and also less strongly), $A \not \Rightarrow B$.

Let me briefly pause here for the sake of those unfamiliar with the symbols I have already used. $\neg$ denotes ‘not’, $\Rightarrow$ denotes ‘implies’, $\wedge$ denotes ‘and’, and A and B are symbols which represent a statement, such as “dogs are black” or “black animals are dogs”.…