Question

Is it inferred that if it is not possible that \( p \) is not possible in \( K \), then it follows that \( p \) is possible in \( K \)?

Answer 1

Main Answer:

If it is not possible that
`\( p \)` is not possible in
`\( K \)`, then it follows that
`\( p \)` is possible in
`\( K \)`.

Step-by-step explanation:

This logical inference relies on the principle of double negation. Stating that it is not possible for
`\( p \)` to be not possible essentially asserts the affirmation of
`\( p \)'`s possibility. This stems from the logical equivalence between the denial of the negation of a proposition and the affirmation of the proposition itself. In other words, if one denies the impossibility of \
`( p \)` in \( K \), it logically entails the possibility of
`\( p \)` in
`\( K \)`. The application of this principle is fundamental in deductive reasoning, where the absence of a negative condition implies the presence of the positive condition.

Therefore, in the given scenario, the negation of the negation leads to the affirmation of \( p \)'s possibility in \( K \). This concise reasoning is grounded in classical logic and is a powerful tool in constructing valid arguments and drawing conclusions. Understanding the interplay of negations is crucial for clear and precise logical reasoning, ensuring that conclusions are accurately derived from given premises.