Question

8 A story for a better world All good people care about others. To care about someone means that you will make sacrifices for them. All sacrifices are painful. Worse still, people you care about will sooner or later hurt you. Painful and hurtful things make people sad. At the same time, good people are always happy, because they know that they have done the right thing. Good people can sleep at night very well. Happiness is not the same as the absence of sadness, nor is sadness the absence of happiness. Take the messy story above and write it down using tidy quantifiers.

1. Can you say, using the laws of logic, that if Angela is a good person then she will be happy, but that she will be sad as well?

2. If so, show the steps needed to arrive at that conclusion.

3. How would the answer to this question change if sadness was the same as absence of happiness?

Answer 1

Using quantifiers the moral of the story is:

Happiness =/=> ~Sadness

Sadness =/=> ~Happiness.

[The symbol =/=> means 'does not imply']

1) Angela is a good person => Angela is happy (since good people are always happy).

Also Angela will be sad because,

2) Angela is a good person => Angela cares about others (as good people care about others) => She will make sacrifices for them => These sacrifices will be painful for her => she will be sad (as painful things make people sad)

That is how we arrived at the conclusion that she will be sad as well.

3) If sadness => ~happiness, then that would mean contrapositively happiness => ~Sadness. Hence Answer to the previous question will change to "Angela is happy means that she can't be sad as well"