Week 6 - Truth, Validity, Deduction, Induction Flashcards
(32 cards)
What is a deductive argument?
It’s an argument where, if the premises are true, the conclusion must be true.
🧾 Example:
Premise 1: All humans are mortal.
Premise 2: Socrates is a human.
Conclusion: Socrates is mortal.
This conclusion is guaranteed if the premises are true.
What makes a deductive argument valid?
Its logical structure guarantees the conclusion follows from the premises.
🧾 Example:
All squares are rectangles.
This shape is a square.
∴ This shape is a rectangle.
Valid because the form ensures the conclusion follows
Can a valid deductive argument have false premises?
Yes. Validity is about structure, not truth.
🧾 Example:
All birds are mammals. (False)
A penguin is a bird.
∴ A penguin is a mammal.
Valid form, false premise = unsound.
What is a sound argument?
A deductive argument that is both valid and has all true premises.
🧾 Example:
All men are mortal.
Aristotle is a man.
∴ Aristotle is mortal.
Sound because it’s valid and all statements are true.
What does it mean to say deduction is “truth-preserving”?
If the premises are true, the conclusion is guaranteed to be true.
🧾 Example:
Math: If 2 + 2 = 4, and 4 + 1 = 5, then 2 + 2 + 1 = 5.
The truth “flows” from premise to conclusion
What is an inductive argument?
It generalizes from specific instances to draw a probable conclusion.
🧾 Example:
The sun has risen every day so far.
∴ The sun will rise tomorrow.
Plausible, but not certain.
Why is induction ampliative?
Because it adds new knowledge not found in the premises.
🧾 Example:
You see 100 white swans.
∴ You conclude all swans are white.
This generalization wasn’t in the original observations.
What makes an inductive argument strong?
A large, varied sample and no contrary evidence.
🧾 Example:
1,000 COVID-19 patients who took Drug X recovered in 3 days.
∴ Drug X likely helps recovery.
This is strong if the sample is reliable and representative.
Can inductive arguments lead to false conclusions?
Yes, even if all premises are true.
🧾 Example:
Every crow I’ve seen is black.
∴ All crows are black.
False if there’s even one white crow somewhere.
Why is inductive reasoning “non-monotonic”?
New evidence can change the conclusion.
🧾 Example:
You think all swans are white — until you see a black swan.
Your belief must now adjust.
What direction does deduction move in?
From general rules to specific conclusions.
🧾 Example:
All mammals breathe air.
A dolphin is a mammal.
∴ A dolphin breathes air.
What direction does induction move in?
From specific cases to a general conclusion.
🧾 Example:
Every dolphin I’ve seen breathes air.
∴ All dolphins breathe air.
Why is deduction considered more certain than induction?
Because its conclusions are logically necessary, not just probable.
Which reasoning type is used more in science: deduction or induction?
Induction — because science builds theories from observed data.
🧾 Example:
We observe that gravity causes apples to fall.
∴ We infer gravity is a general law.
Can inductive conclusions ever be certain?
No — they are always probabilistic.
What’s the difference between validity and soundness?
Validity = correct form; Soundness = valid + true premises.
Is this argument valid or sound?
All unicorns eat grass.
Charlie is a unicorn.
∴ Charlie eats grass.
Valid but not sound — unicorns don’t exist, so the premises are false.
Is this argument valid and sound?
All even numbers are divisible by 2.
8 is even.
∴ 8 is divisible by 2.
Yes — valid and all premises are true, so it’s sound.
What is Hume’s problem of induction?
The worry that we have no rational justification for believing the future will resemble the past.
Why can’t induction be justified by experience?
Because that would assume what we’re trying to prove — that experience predicts the future.
🧾 Example:
You’ve only seen white bread when toasting. That doesn’t guarantee every bread will toast the same.
Why can’t deduction justify induction?
Because induction isn’t logically certain — so deduction can’t guarantee its conclusions.
What kind of justification would Hume accept for induction?
None — he believed we use induction by habit, not logic.
How does Hume’s problem threaten science?
Science relies on generalizing from observations — but Hume showed this method isn’t logically justified.
Give a modern example of the problem of induction.
We believe the sun will rise tomorrow based on the past — but we can’t be logically certain it will.
