# Math Help - logic and proof

1. ## logic and proof

What is wrong with this argument? Let S(x,y) b " x is shorter than y". Given the premise $\left( {\exists x} \right)$ S(s,Max), it follows that S(Max,Max). Then by existential generalization it follows that $\left( {\exists x} \right)$S(x,x), so that someone is shorter than himself.

2. Originally Posted by TheRekz
What is wrong with this argument? Let S(x,y) b " x is shorter than y". Given the premise $\left( {\exists x} \right)$ S(s,Max), it follows that S(Max,Max). Then by existential generalization it follows that $\left( {\exists x} \right)$S(x,x), so that someone is shorter than himself.
It only follows that S(x, Max) if there is such a y such that x < y for all s. This value of y need not exist.

As an example, let the universe of discourse be the set $\{ 1 - n^{-1}| n \in \mathbb{Z}^+ \}$. No Max exists such that S(x, Max) for all x.

-Dan

3. I don't really get your explanation, could you try to explain it a bit more or maybe more examples. Sorry!

I don't get the example that you give me, but I understand that in order of S(x,y) to be valid, x has to be less than y and here x = y, so it can't happen right? Am I explaining it the right way? I also don't understand by the domain that you give me. Is that for all x and y?

Is this a type of fallacy?

4. Originally Posted by TheRekz
What is wrong with this argument? Let S(x,y) b " x is shorter than y". Given the premise $\left( {\exists x} \right)$ S(s,Max), it follows that S(Max,Max). Then by existential generalization it follows that $\left( {\exists x} \right)$S(x,x), so that someone is shorter than himself.
Please sort out your notation

RonL

5. Originally Posted by TheRekz
Is this a type of fallacy?
Yes the fallacy occurred in your first use of existential instantiation.
The basic rule for EI is: $\frac{{\left( {\exists x} \right)\phi (x)}}{{\phi (v)}}$ where v is an individual constant having no prior occurrence in the context.

6. so what type of fallacy is this? it it the affirming the conclusion?

7. Originally Posted by TheRekz
so what type of fallacy is this? it it the affirming the conclusion?
I have no idea what name your instructor/textbook would give to that fallacy. It is just a violation of the instantiation rules.