Translate the following statement into FOL.“For every a, if a is a philosopher, then a is a scholar”

To translate the statement "For every a, if a is a philosopher, then a is a scholar" into First-Order Logic (FOL), we need to identify the predicates and quantify the statement properly.

Step 1: Define Predicates

1. Let $P(a)$ denote "a is a philosopher."
2. Let $S(a)$ denote "a is a scholar."

Step 2: Identify the Structure of the Statement

The statement is a universal quantification implying a condition:

• "For every a" indicates that we will use universal quantification.
• The "if...then..." structure corresponds to a conditional statement.

Step 3: Write in FOL

Now, putting it all together, we can express the statement in First-Order Logic as follows:

$\forall a (P(a) \rightarrow S(a))$

Explanation

This formula reads as: "For all individuals $a$, if $a$ is a philosopher ($P(a)$), then $a$ is also a scholar ($S(a)$)."

Final Answer

In First-Order Logic, the statement is expressed as:

$\forall a (P(a) \rightarrow S(a))$