Why Can True Premises Still Lead to a False Conclusion?

In the Prior Analytics, Aristotle systematically examined syllogisms: an argument depends not only on whether its statements are individually true, but on whether the conclusion necessarily follows from the premises. Modern logic calls this relationship deductive validity. An argument is valid when there is no possible case in which all its premises are true and its conclusion false.

Consider: “All pianos have keyboards; this instrument has a keyboard; therefore, it is a piano.” Both premises may be true, yet the conclusion can be false because the instrument might be an organ. The failure is not merely a shortage of facts. The reasoning wrongly reverses “pianos are keyboard instruments” into “keyboard instruments are pianos”.

Validity alone does not ensure a true conclusion about the world. An argument may have a valid form while resting on a false premise; modern terminology calls a deductive argument sound when it is valid and its premises are true. Inductive arguments normally offer probabilistic support rather than necessity, so they should not be assessed by mechanically applying the same standard.

My judgement is that arguments require two checks: whether the premises have evidence, and whether they genuinely support the conclusion. Checking facts alone can assemble unrelated truths into a false inference; checking form alone can reason impeccably from false information.

https://iep.utm.edu/val-snd/
https://plato.stanford.edu/entries/logical-consequence/