Final answer:
To translate a statement into higher order logic, you need to use quantifiers and logical connectives. An example statement and its representation in higher order logic is provided. The book 'Introduction to Metamathematics' is recommended for further learning.
Step-by-step explanation:
To translate a statement into higher order logic, you need to represent the statement using quantifiers and logical connectives. The quantifiers used in higher order logic are the universal quantifier (∀) and the existential quantifier (∃). The logical connectives used include AND (∧), OR (∨), NOT (∼), IMPLIES (⇒), and IF AND ONLY IF (⇔).
For example, let's say we have the statement: 'Every even number is divisible by 2.' In higher order logic, this can be represented as: ∀x (even(x) ⇒ divisible(x, 2)), where 'even(x)' represents the predicate that x is even, and 'divisible(x, 2)' represents the predicate that x is divisible by 2.
If you want to learn more about higher order logic, I would recommend the book 'Introduction to Metamathematics' by Stephen Cole Kleene. It provides a comprehensive introduction to various topics in mathematical logic, including higher order logic.