Arguments & Logic

Separate the starting claims from the destination

A premise is a claim offered as a reason. A conclusion is the claim those reasons are meant to support. An explanation may tell you why an accepted event happened; an argument tries to establish something that is in question. Ordinary writing can mix these purposes, so first identify which claim is doing which job.

In deductive reasoning, validity concerns a necessary connection: if the premises were true, could the conclusion still be false? Validity alone does not make the premises true. A sound deductive argument also needs true premises. Checking the form and checking the evidence are therefore two separate tasks.

Worked example: a badge is not enough

Here is an invented game rule: every member of the repair crew carries a blue badge. Ada is a member of the repair crew. Therefore Ada carries a blue badge. Within these stated premises, the conclusion follows. Now reverse the reasoning: Ada carries a blue badge, so Ada must be a repair-crew member. That conclusion does not follow from the original rule.

To see why, invent a permitted counterexample: visiting pilots also carry blue badges. Ada could be a visiting pilot. The original statement about crew members remains true, but the reversed conclusion could be false. The rule never said that only repair-crew members have blue badges. One possible case is enough to show the inference is not guaranteed.

Strong evidence need not give a guarantee

Many useful real-world arguments are not deductive. If several carefully run trials favour a design, that can support trying it again without proving it will always succeed. Ask how the examples were selected, what alternatives remain and how wide the conclusion is. Turning “these three trials” into “everyone, forever” requires more than confidence.

Calling an inference invalid is not a judgement about the person making it. A conclusion might happen to be true even when the offered argument fails to establish it. Likewise, disagreeing with a conclusion is not enough to show that the reasoning is defective. Point to the precise connection you are testing.

Make a small argument map

Write each premise on its own line, then draw an arrow to the conclusion. Add any unstated assumption needed for that arrow to work. For the badge example, the missing assumption is that nobody outside the repair crew carries a blue badge. You can then ask whether that extra rule is justified, instead of hiding it inside the conclusion. A revised argument may become narrower and more useful.