Lesson 8.1 — Objects and Properties

A New Move

So far in this curriculum, we've worked with whole sentences. "It's raining." "I have a dog." Each one was a single TRUE-or-FALSE claim, and we glued claims together with AND, OR, NOT, IF.

Now we'll look INSIDE a claim. Most sentences are about something — a person, an animal, a thing — and they say something about it.

"Pedro is happy."

There are two parts:

• The object — who or what we're talking about. Here: Pedro.
• The property — what we're saying about it. Here: happy.

Together, object + property = a predicate. Predicates are claims about specific things.

How Logic Writes It

In logic notation, we write the property first, then the object in parentheses:

Happy(Pedro)

Read it as "Happy of Pedro" or just "Pedro is happy." It looks like math — and it kind of is. The property is like a function; the object is like the input. The output is TRUE or FALSE.

Build a Predicate

Pick an object. Pick a property. Watch the predicate form appear.

One Property, Many Objects

The same property can apply to many different objects:

• Happy(Pedro) — Pedro is happy.
• Happy(Maria) — Maria is happy.
• Happy(Spot) — Spot the dog is happy.

Each one is a separate claim. Each can be true or false on its own. Happy is the same property in all three — it just gets applied to different things.

One Object, Many Properties

The same object can have many properties:

• Happy(Pedro) — Pedro is happy.
• Tall(Pedro) — Pedro is tall.
• Smart(Pedro) — Pedro is smart.

Each one says something different about the same Pedro. You can stack them up the way English does: "Pedro is happy AND tall AND smart" is just three predicates joined by AND — old Module 1 territory, applied to predicates.

Why This Matters

Module 1 through Module 7 worked with whole-sentence claims. We couldn't talk about parts of sentences — we couldn't say "this claim is about Pedro" or "this claim uses the same property as that one." Now we can.

This unlocks the BIG moves: claims about every object, or some object. That's the next two lessons.

Tricky Bits

1. Properties are capitalized, objects start lowercase (usually). Conventions vary, but in logic it's helpful to keep them visually distinct: Tall(maria) or Tall(Maria). The property goes on the outside, the object on the inside of the parens.

2. "Is" disappears in the logic form. "Pedro is happy" becomes Happy(Pedro) — the "is" is implied by the predicate notation. English needs the word "is" as glue; logic doesn't.

3. Predicates can be more complex. "Pedro likes Maria" has TWO objects (Pedro and Maria) and a relation (likes) between them. Written as Likes(Pedro, Maria). We'll mostly stick with single-object predicates for now, but the notation extends.

Recap

• Object = who or what we're talking about.
• Property = what we're saying about it.
• Together they form a predicate: Property(Object).
• Each predicate is TRUE or FALSE in a given situation.
• Same property can apply to many objects. Same object can have many properties.