# Problems with Existential Instantiation

• I
• Terrell
In summary: However, in presupposition-free logic there is no such presupposition, and so the interpretation of the universal quantificational expression (∀x)[Px] as equivalent to the finite conjunction (P1 Λ P2 Λ P3 ...) and the interpretation of the existential quantificational expression (∃x)[Px] as equivalent to the finite disjunction (P1 ∨ P2 ∨ P3 ...) are equivalent.
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.

Terrell said:
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
FactChecker said:
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.
FactChecker said:
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

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.

## 1. What is Existential Instantiation?

Existential instantiation is a logical rule that allows us to conclude the existence of an object based on a statement that asserts its existence.

## 2. What are some common problems with Existential Instantiation?

One problem with existential instantiation is that it may lead to incorrect conclusions when used with statements that contain negations or universal quantifiers.

## 3. How do we avoid these problems with Existential Instantiation?

To avoid these problems, we can use other logical rules such as universal instantiation or existential generalization, which allow us to make more accurate conclusions.

## 4. Can you give an example of a problem with Existential Instantiation?

One example is the statement "Some birds can fly." Using existential instantiation, we can conclude that there exists a bird that can fly. However, if we add a negation to the statement, such as "Some birds cannot fly," we cannot make the same conclusion.

## 5. How is Existential Instantiation used in scientific research?

In scientific research, Existential Instantiation is used in deductive reasoning to make conclusions based on observations or data. It allows scientists to infer the existence of certain phenomena or objects based on evidence and previous knowledge.

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