# Homework Help: Analyze the followin logical statements

1. Sep 18, 2008

### kehler

1. The problem statement, all variables and given/known data
Well this really isn't math. But I didn't know which other category it could fall under. And I figured math uses logic anyway... But do move it if it should be posted somewhere else.
The question is:
Analyse and discuss the logical statement shown below:
if someone has one cent, he is not rich
if someone is not rich, then giving him one cent will not make him rich
therefore, no matter how many times you give a person a cent will not make him rich

3. The attempt at a solution
I've never taken a course in logic before so I'm not too sure how to approach this. It seems obvious that the conclusion is false. Is it right to say that if the conclusion is false, one of the premises must be false? I'm thinking the first statement is true, although it is kinda relative to who the person's being compared to. If someone has one cent, and another person has no money at all, he will be in some sense 'rich'. But then again according to the dictionary, being rich is to possess great material wealth so he isn't exactly rich... The second statement I think is false. Well it seems more likely to be false that the first one and I don't think they can't both be true. But I really don't know how to argue that it's false :S. It would be easier if there were some kind of threshold where if one had more money than that, he could be considered rich..
Any opinions on this? I would really appreciate it if someone could tell me how to argue it logically.

2. Sep 18, 2008

### Defennder

Re: Logic

This is also known as the Sorites paradox. There are a lot of terms in the English language which are not defined rigorously in terms of numerical quantities such as "heap", "bald" and countless others. So the problem with this reasoning is that it assumes that you can define the term rich unambiguously in terms of the exact amount of wealth possessed by a person.

3. Sep 18, 2008

### kehler

Re: Logic

Oh I see. Thanks, i'll write that down. Does this mean that the statements are not logical then? Since one can't really assign a 'true' or 'false' to them...

4. Sep 18, 2008

### granpa

Re: Logic

the statements are false because giving someone one cent does make them slightly richer.

another example is fish evolving into amphibians. at what point did they cease to be fish? clearly being a fish isnt all or nothing. there are degrees of fishiness.

a better example might be heat. start at absolute zero and add one degree at a time. at what point does it become hot as it passes from cold to cool to lukewarm to warm to hot?

Last edited: Sep 18, 2008