Problems with Existential Instantiation

[Terrell]

Why is it required to use a "fresh name/variable"? And because of that requirement, Existential instantiation always precedes universal instantiation. What I am thinking is, If we are picking elements at random from our universe of discourse then why can't universal instantiation pick that random element first before existential instantiation does? I would understand the rule that we cannot existentially instantiate more than one element(which will need more than one name/variable) because we can never be sure there is more than one, but the reason EI precedes UI in picking a random element eludes me.

 

[FactChecker]

Why is it required to use a "fresh name/variable"? And because of that requirement, Existential instantiation always precedes universal instantiation. What I am thinking is, If we are picking elements at random from our universe of discourse then why can't universal instantiation pick that random element first before existential instantiation does? I would understand the rule that we cannot existentially instantiate more than one element(which will need more than one name/variable) because we can never be sure there is more than one, but the reason EI precedes UI in picking a random element eludes me.

If you do universal instantiation first, how do you know that it did not pick an element, c, which does not satisfy the existential property? Also, it seems pointless to identify an element, c, for the universal property before an element which satisfies the existential property is identified.

 

[Terrell]

If you do universal instantiation first, how do you know that it did not pick an element, c, which does not satisfy the existential property? Also, it seems pointless to identify an element, c, for the universal property before an element which satisfies the existential property is identified.

If you do universal instantiation first, how do you know that it did not pick an element, c, which does not satisfy the existential property? Also, it seems pointless to identify an element, c, for the universal property before an element which satisfies the existential property is identified.

it all make sense now. was simply not used to reading symbolic logic. lol

 

[sysprog]

In non-presupposition-free logic the interpretation of the universal quantificational expression (∀x)[Px] as equivalent to the infinite conjunction (P1 Λ P2 Λ P3 ...) presupposes that every term designates, and the interpretation of the existential quantificational expression (∃x)[Px] as equivalent to the infinite disjunction (P1 V P2 V P3 ...) presupposes that something exists.