Intension is the meaning or concept a term expresses in Formal Logic I. It is different from extension, which is the set of things the term applies to, and it matters when you analyze predicates and definitions.
Intension is the meaning a term carries in Formal Logic I, especially the property or concept a word or phrase expresses. If you see a predicate like "is red" or "is a mammal," the intension is the idea being picked out, not the list of things that fit it.
This is different from extension. Extension is the actual set of objects that fall under the term. For example, "evening star" and "morning star" have the same extension if they both refer to Venus, but they do not have the same intension because they present that object in different ways.
That difference matters because logic is not just about what exists in the world, it is also about how language is structured. Two expressions can point to the same thing while still carrying different informational content. Formal logic cares about that because arguments can change meaning even when reference stays the same.
In predicate logic, intension shows up most clearly in predicates. A predicate is the part of a statement that says something about a subject, such as a property or relation. The predicate "is tall" has an intension, the concept of tallness, and when you attach it to a subject, you make a claim about whether that subject has that property.
You can think of intension as the rule for applying a term, while extension is the collection of cases where the rule comes out true. That is why intension is useful when you translate ordinary language into symbolic form. It keeps you from treating different expressions as if they mean the same thing just because they point to the same object in a particular situation.
A common mistake is to confuse intension with a synonym or with a dictionary gloss. In logic, intension is about the conceptual content that gives a term its meaning in a statement. That is why intensional definitions focus on what something is, or what property makes it what it is, rather than just listing examples.
Intension matters in Formal Logic I because it helps you track meaning when you move from ordinary language into logical analysis. If you ignore intension, you can miss why two statements sound different even when they seem to refer to the same thing. That becomes a problem in predicate logic, where a small wording change can alter how a statement should be translated.
It also gives you a cleaner way to think about predicates. When a sentence says "Socrates is wise," the predicate "is wise" does more than name an object, it contributes a concept that can be tested against the subject. That is the kind of structure you need when you decide whether a statement is universal, particular, or relational.
Intension is useful anytime you compare terms that share a reference but differ in sense. It keeps you from flattening language into a simple list of objects. In class, this shows up when you analyze whether two expressions are interchangeable, whether a definition is too broad or too narrow, or whether a symbolic translation preserves the original claim.
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view galleryExtension
Extension is the set of things a term applies to, while intension is the meaning that makes the term apply in the first place. In Formal Logic I, this pair helps you separate reference from conceptual content. A term can keep the same extension in one context but still shift in intension if the way it is described changes.
Predicate
A predicate is the part of a statement that ascribes a property or relation to something. Intension lives inside the predicate because the predicate expresses the concept being attributed. When you translate a sentence into symbolic logic, you need to know what property the predicate actually conveys, not just what objects it names.
Subject
The subject is the thing a statement is about, and the predicate says something about it. Intension helps you see what is being claimed about the subject rather than treating the whole sentence as a vague label. That makes it easier to test whether the statement is meaningful, true, or properly translated.
Unary Predicate
A unary predicate applies to one subject and expresses a property like "is even" or "is red." Its intension is the property itself, which is why unary predicates are a clean place to practice separating meaning from extension. They are often the first step before moving to more complex relations.
A quiz question might give you two expressions that pick out the same thing and ask why they are not interchangeable in every sentence. You would answer by pointing to intension, then explain that the expressions differ in meaning even if they share an extension.
In a translation problem, you may need to identify the predicate and say what property or relation it expresses. That is where intension shows up most directly, because you are deciding what the sentence means before turning it into symbols.
If a problem asks whether a definition is intensional or extensional, look for whether it explains the concept or just lists members of the set. When you see a sentence about a subject and a property, focus on the concept being attributed, not only on the object named.
Intension and extension are the standard pair students mix up in logic. Intension is the meaning or concept behind a term, while extension is the set of things that term covers. If you remember "meaning vs. members," you will usually keep them straight in predicate logic and definition questions.
Intension is the meaning a term carries, not the list of things it names.
Extension is what falls under the term, while intension is the concept that makes the term work.
In predicate logic, predicates are the main place where intension shows up because they express properties or relations.
Two terms can have the same extension and still differ in intension, which is why wording matters in logic.
When you translate or analyze a statement, ask what property or relation the predicate is actually expressing.
Intension is the meaning or concept expressed by a term or predicate in Formal Logic I. It is the part of language that tells you what the term means, not just what it refers to. That is why it matters when you analyze definitions and translate ordinary statements into symbols.
Intension is the sense or concept behind a term, while extension is the set of objects that fit the term. "Morning star" and "evening star" can share an extension if both refer to Venus, but their intensions are different because they present the object in different ways.
It shows up in the predicate, since the predicate expresses a property or relation attributed to the subject. When you say something like "x is tall," the predicate carries the intension of tallness. That is what you need to identify before you can translate the sentence accurately.
Yes, and that is one of the main reasons the distinction matters. Two expressions can refer to the same object or set of objects while still meaning something different. Logic pays attention to that difference because it can change how a statement should be interpreted.