Must and Can't (Deductions)

Sometimes we make guesses about situations based on evidence or facts. This is called a deduction. A deduction is a “smart guess” based on clues (evidence). Modals like must and can’t help us express how certain we are about these guesses.

1. What a deduction is

A deduction is a logical conclusion you make when you look at the evidence and decide what is likely or unlikely.

Examples

• “The lights are on. Someone must be home.” → Evidence: lights are on → deduction: someone is probably home
• “The kitchen is cold, and the stove is off. They can’t be cooking now.” → Evidence: kitchen cold + stove off → deduction: it’s impossible that they are cooking now

2. Using must for strong deductions

Use must when the evidence makes you feel very sure something is true (a strong logical conclusion).

Certainty	Modal	Example
very likely	must	"She must be at home."
possible	may / might / could	"She might be at home."
impossible	can’t	"She can’t be at home."

Form:

• Now (state/general): must + base form (must be / must know)
• Now (in progress): must be + -ing (must be sleeping / must be eating)
• Past: must have + past participle (must have forgotten / must have slept)
• Past (in progress): must have been + -ing (must have been sleeping)

Examples:

• “She must be tired. She worked all night.”
• “It’s so quiet in the house. Everybody must be sleeping.”
• “He must have been in the sun. He is sunburned.”
• “He must have been sleeping — he didn’t answer.”

3. Using can’t for strong negative deductions

Use can’t when the evidence makes you sure it’s impossible / not true.

Form:

• Now (state/general): can’t + base verb (can’t be / can’t live)
• Now (in progress): can’t be + -ing (can’t be snowing / can’t be working)
• Past: can’t have + past participle (can’t have finished / can’t have gone)
• Past (in progress): can’t have been + -ing (can’t have been sleeping)

Here, can’t means “it’s impossible (I’m sure)”.

Examples:

• “He can’t be at home. His car isn’t here.”
• “He can’t be working right now. He’s in the café with his children.”
• “She can’t have finished the project already. She started it yesterday.”
• “They can’t have been waiting long; they only arrived five minutes ago.”

Couldn’t have + past participle is also possible: "She couldn’t have finished it already." British English usually prefers can’t have for this meaning; American English also often uses must not have.

4. Asking questions about deductions

Deductive must and can’t usually make strong statements, so they are less common in neutral questions. To ask what another person thinks, use Do you think ...? or a possibility modal such as can or could:

• “Do you think Maya is at home?”
• “Can he really be at home?” (The speaker is surprised that this may be true.)
• “Could they have taken the wrong train?”

5. Key takeaway

• Must → strong logical certainty, very likely to be true
• Can’t → strong logical impossibility, very unlikely or impossible
• Deductions are based on evidence, not random guessing