Logic
Propositions
Цели урока
- Understand what a proposition is in logic
- Distinguish between propositions and non-propositions
- Tell facts from opinions
- Recognize hidden opinions disguised as facts
"Everyone knows that..." - do they really?
- Evaluating news: fact or interpretation?
- Online debates: separating emotions from arguments
- Decision-making: is it based on data or feelings?
- Negotiations: what can be proven vs what can only be asserted
What is a proposition
A **proposition** is a statement that can be evaluated as true or false. It is the basic building block of logic.
**Rule:** A proposition must be either true or false - there is no third option. If it cannot be determined - it is not a proposition.
"x > 5" is not a proposition because the answer depends on x. But "5 > 3" is a proposition (and it is true).
Which of these sentences is a proposition?
Truth values: only two options
In classical logic a proposition can only be **true (T)** or **false (F)**. There is no "maybe", "probably", or "partially".
**Important:** "We don't know" ≠ "cannot be determined". The proposition "Life exists on Mars" has a definite truth value - we simply don't know it yet.
This is known as the **law of excluded middle**: every proposition is either true or false. Tertium non datur - there is no third option.
"In 100 years, humans will be living on the Moon" - is this a proposition?
Facts vs Opinions: the subjectivity trap
A **fact** can be verified objectively. An **opinion** is a subjective evaluation. Opinions often masquerade as facts.