“is” of Identity

Overview

The “is” of identity is a fundamental concept in logic and philosophy. It specifically refers to the usage of the verb “is” to denote that two expressions or terms refer to the exact same entity. This is distinct from the “is” of predication, which attributes a property to a subject.

Key Concepts

The core idea is sameness. When we say “The morning star is the evening star,” we are not attributing the property of being the evening star to the morning star. Instead, we are stating that both names refer to the same celestial body (Venus).

Deep Dive

Numerical identity is a relation that holds between an object and itself, and nothing else. The “is” of identity is the relational symbol for this concept. For example, in the statement “2 + 2 is 4,” the “is” signifies that the expression “2 + 2” and the numeral “4” denote the identical numerical value.

Applications

This concept is crucial in:

• Mathematics: Defining equality and equivalence.
• Logic: Formalizing identity statements and proofs.
• Linguistics: Analyzing sentence structure and meaning.
• Computer Science: Variable assignment and object references.

Challenges & Misconceptions

A common confusion arises with the “is” of predication. For instance, “Socrates is a philosopher.” Here, “is” attributes the property of being a philosopher to Socrates. The “is” of identity asserts that the subject is the predicate, not merely shares a characteristic.

FAQs

Q: How is the “is” of identity different from the “is” of predication?
A: The “is” of identity asserts that two terms refer to the same entity. The “is” of predication asserts that a subject possesses a certain property or belongs to a class.

Q: Can you give another example of the “is” of identity?
A: “The President of the United States is Joe Biden.” This statement asserts that the office and the person are numerically identical.