Philosophy: TestAS practice testlets

Logic studies what makes reasoning correct. An argument consists of premises, statements offered as reasons, and a conclusion that is supposed to follow from them. An argument is valid if the conclusion must be true whenever all the premises are true; in other words, it is impossible for the premises to be true and the conclusion false. Validity concerns the form of the argument, not the actual truth of its statements. An argument is sound if it is valid and all its premises are in fact true. Only a sound argument guarantees a true conclusion.

Some argument forms are always valid. In modus ponens, from "If P, then Q" and "P", it follows that "Q". In modus tollens, from "If P, then Q" and "not Q", it follows that "not P". Two similar-looking forms are invalid. Affirming the consequent concludes "P" from "If P, then Q" and "Q": if it rains, the street is wet; the street is wet; but it may have been cleaned, so it need not have rained. Denying the antecedent concludes "not Q" from "If P, then Q" and "not P".

Deductive arguments aim at validity. Inductive arguments, which generalise from observed cases or predict the future from the past, can at best make their conclusions probable. That every swan observed in Europe was white made it likely, but not certain, that all swans are white; black swans were later found in Australia.

Informal fallacies are errors of reasoning that depend on content rather than form. An ad hominem attack rejects a claim by attacking the person who makes it rather than the claim itself. A straw man misrepresents an opponent's position in a weaker form and then refutes that version. A false dilemma presents two options as the only possibilities when others exist. A slippery slope argument claims, without sufficient reason, that a first step will inevitably lead to a chain of extreme consequences. An appeal to authority is fallacious when the authority has no expertise on the question. Circular reasoning assumes what it sets out to prove.

Recognising these patterns does not settle a debate, but it helps to separate strong reasons from rhetorical tricks, both in the arguments of others and in one's own.

A thought experiment introduced by Philippa Foot in 1967 and developed by Judith Jarvis Thomson has become one of the best-known cases in moral philosophy. A runaway trolley is heading towards five workers on the track, who will be killed if nothing is done. You stand next to a lever. If you pull it, the trolley will be diverted onto a side track, where it will kill one worker. Most people say that pulling the lever is permissible, perhaps even required.

In a second version, there is no side track. You stand on a footbridge above the track next to a large stranger. The only way to stop the trolley is to push him off the bridge; his body would stop the trolley, and he would die, but the five would be saved. The numbers are the same, five lives against one, yet most people say that pushing the man is wrong. The puzzle is to explain the difference.

A simple consequentialist view cannot explain it, because in both cases the outcome is one death instead of five. A consequentialist may accept that both actions are right and treat the intuition against pushing as a mistake, perhaps a product of our aversion to physical violence. Others look for a principle that separates the cases.

One candidate is the doctrine of double effect, which goes back to Thomas Aquinas. It distinguishes between harm that is intended, either as an end or as a means, and harm that is merely foreseen as a side effect. According to the doctrine, an action with a bad effect may be permissible if the action itself is not wrong, the bad effect is not intended, the bad effect is not the means to the good effect, and there is a proportionately serious reason for accepting it. In the lever case, the death of the one worker is a foreseen side effect: if he could somehow escape, the plan would work just as well. In the footbridge case, the death of the stranger is the means: his body is used to stop the trolley.

The doctrine has been applied in medicine, for instance to the use of pain-relieving drugs that may shorten a dying patient's life, and in the ethics of war, where it separates targeting civilians from accepting civilian casualties in attacking a military target. Critics argue that the distinction between intending and foreseeing is unclear, and that it may allow people to describe their intentions conveniently. Kantians offer a related explanation: pushing the stranger treats him merely as a means, while diverting the trolley does not.