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.
**Signals of an opinion:** words like "best", "worst", "beautiful", "boring", "correct", "fair" - these are evaluations, not facts.
"Python is the best programming language" - that is an opinion. "Python is the most popular language according to the TIOBE index" - that is a fact (verifiable).
"A healthy diet is important for longevity" - is this a fact or an opinion?
Hidden opinions: how to spot them
The most dangerous opinions are those that look like facts. Let's learn to spot them.
**Verification algorithm:** 1. Are there evaluative words (good, bad, important)? 2. Can it be measured with a number or yes/no? 3. Would two people give the same answer? If any answer is "no" - the statement is an opinion.
Opinions are fine. The problem is when opinions are passed off as facts. The distinction is recognizable once the criteria are clear.
If something sounds confident - it's a fact
Confidence of delivery does not turn an opinion into a fact
A person can express a subjective opinion very confidently. Check the content, not the tone: can it be measured and verified?
How is the opinion "This is an expensive phone" turned into a fact?
Key Takeaways
- A proposition is a statement that is either true or false
- Questions, commands and exclamations are not propositions
- A fact can be verified; an opinion cannot
- Words like "notably", "everyone knows", "the best" are markers of hidden opinions
Next
Now we'll learn to build arguments from propositions - linking premises to conclusions
- Argument structure — next lesson
Вопросы для размышления
- Consider a recent argument - were there facts or only opinions?
- Which "facts" in the news are actually the journalist's opinions?
- Take a strongly held belief and restate it as a verifiable fact. What changes?