Question

What is wrong with this argument? Let \(S\left( {x,y} \right)\)be “\(x\)is shorter than \(y\).” Given the premise \(\exists sS\left( {s,Max} \right)\), it follows that \(S\left( {{\rm{Max}},{\rm{Max}}} \right)\)then by existential generalization it follows that \(\exists xS\left( {x,x} \right)\), so that someone is shorter than himself.

Short answer

The fact is unknown such as if Max is the person for which \(S\left( {s,Max} \right)\) is true.

Step-by-step solution

Definition of Argument    

Theargument is a collection of propositions that have premises and a conclusion.

To find incorrect fact in the given argument

Suppose \(S\left( {x,y} \right)\) “\(x\)is shorter than \(y\).”

The given premise is\(\exists sS\left( {s,Max} \right)\)and consider that \(\exists sS\left( {s,Max} \right)\)is true.

So, there exists a person \(y\) such that \(S\left( {y,Max} \right)\) is true.

The fact is unknown such as if the person \(y\)is Max.

Thus, it is not possible to conclude\(S\left( {Max,Max} \right)\).

Max cannot be shorter than himself as\(S\left( {Max,Max} \right)\)cannot be true.

Thus,\(\exists xS\left( {x,x} \right)\)is false.

Therefore, the fact is unknown such as if Max is the person for which \(S\left( {s,Max} \right)\) is true.