Friday, November 24, 2017

Decisions and context, fallacy and hasty decisions

Mathematics does not lie, if the context is taken into account.


Modus putting ponens (or modus ponens, MP) is a valid argument form and an inference rule in propositional logic. In the MP it is part of a conditional (if P, then Q), the first or antecedent P is given or affirmed, and it is concluded that the consequent or Q is true. The statement is: "If P implies Q, and P is true, then Q is also true."

If P, then Q.  P. Therefore, Q. (Affirmation of the antecedent)

The invalid fallacy or reasoning:

If P, then Q. Q. Therefore, P. (Affirmation of the consequent)

Consider the following situation. Juan, on the way back home, passes an electrical appliance store that displays several models of flat-screen TVs. Thinking about the 2018 World Cup of Russia, he pauses for a moment to contemplate the spectacular images in a colorful model. The seller notices his interest, tells him that it costs $ 1,000 but if he buys at that moment the television only has to pay $. 750. So, Juan will save $ 250.

Question 1. If John buys the television, what would be the valid argument?

First: If I pay $ 750 for the TV, then I save.
I pay $ 750 per TV.
Then, I'm saving.

Second: If I pay $ 750 for the television, then I save,
I'm saving.
Then, I paid only $ 750 for the TV

Question 2. How much does Juan save? (Detail: Juan did not have or had the intention to buy the television, the passage through the store was fortuitous)