Understanding Universal Generalization with Example

In this class, We discuss Understanding Universal Generalization with Examples.

The reader should have prior knowledge of existential instantiation. Click Here.

We take an example and understand universal generalization.

A(x) One can conclude (y)(A(y))

If someone says A(x) is true from this, can we conclude (y)(A(y))?

No, Not in all the condition

When can we conclude? We understand using an example.

The below example shows when we can conclude.

In the example, y is a free variable.

The free variable y is obtained by universal instantiation. So we can conclude.

The below example shows one situation when we can not conclude.

In this example, The variable y is a free variable obtained by the Existential quantifier. So, we can not conclude.

In the below example, we show the other situation when we can not conclude.

The variable y is the free variable given in the premise. So, we can not conclude.