Logical Reasoning · 3.2.4
Strength and cogency of inductive arguments
Students learn to judge how well the premises of an inductive argument (based on examples or observations) support its general conclusion, calling it strong or weak. When an argument is strong and all its premises are actually true, students identify it as cogent, a trustworthy inductive argument.
The official learning standard (3.2.4)
“Determine and justify the strength of an inductive argument and hence determine whether the strong argument is cogent.”
What it means
Students learn to judge how well the premises of an inductive argument (based on examples or observations) support its general conclusion, calling it strong or weak. When an argument is strong and all its premises are actually true, students identify it as cogent, a trustworthy inductive argument.
How it is examined
This appears in Paper 1 as objective items asking students to judge whether a given inductive argument is strong or weak, or whether a strong argument is cogent. In Paper 2 it may appear as short structured questions requiring students to justify their judgement with reasoning based on the given premises.
Worked example
Consider the inductive argument: 'The sun rose in the east on 1st January, 2nd January, 3rd January, ..., and every day this year. Therefore, the sun will rise in the east tomorrow.'
Determine the strength of this argument and state whether it is cogent.
- Identify the premises: the sun rose in the east on every observed day (a very large number of consistent observations).
- Since the premises give many consistent, relevant observations supporting the conclusion, the argument is strong (the conclusion is very likely true if premises are true).
- Check whether the premises are actually true: it is a known true fact that the sun has risen in the east every observed day.
- Since the argument is strong and its premises are true, the argument is cogent.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
What's the difference between a strong inductive argument and a valid deductive argument?
A valid deductive argument makes the conclusion certainly true whenever the premises are true. A strong inductive argument only makes the conclusion very probable, not certain, because it generalises from limited observations or examples rather than proving it logically.
Can a weak inductive argument still be cogent?
No. Cogency requires the argument to be strong first, its premises must strongly support the conclusion, and then also requires all premises to be true.
A weak argument, even with true premises, can never be cogent because the support for the conclusion is insufficient.
How many examples are needed to make an inductive argument strong?
There's no fixed number in the syllabus; strength depends on how relevant, consistent and representative the examples are, not just quantity. More consistent, relevant observations generally increase strength, but a single contradicting case can still weaken an otherwise strong argument.