The principle of explosion is the law of classical logic and a few other systems (e.g., intuitionistic logic)
according to which "anything follows from a contradiction" - i.e., once
you have asserted a contradiction, you can infer any proposition, or
its converse. In symbolic terms, the principle of explosion can be
expressed in the following way (where "" symbolizes the relation of logical consequence):
This can be read as, "If one claims something is both true () and not true (), one can logically derive any conclusion (ψ)."
The principle of explosion is also known as ex falso quodlibet, ex falso sequitur quodlibet (EFSQ for short), ex contradictione (sequitur) quodlibet (ECQ for short), and ex falso/contradictione (sequitur) (Latin: "from falsehood/contradiction (follows) anything", literally "... what pleases").
The Latin phrase argumentum a fortiori literally means one of the following:
- "from the stronger"
- "even more so"
- "with even stronger reason"
It denotes a proof of a claim by means of an already proved strongerThere are two types of the a fortiori argument:
claim. For example, if it is forbidden to ride a bike with an extra
passenger, then it is also forbidden to ride a bike with two extra
passengers. Or, if one can lift a 100 lb object, then it follows that
one can lift a 50 lb object.
The a fortiori argument is most often used in order to reinforce a
claim, though sometimes also to incorrectly justify a claim taking it
as a premise (petitio principii).
3、Reductio ad absurdum
Reductio ad absurdum (Latin for "reduction to the absurd"), also known as an apagogical argument, reductio ad impossibile, or proof by contradiction, is a type of logical argumentIt makes use of the law of non-contradiction — a statement cannot be both true and false. In some cases it may also make use of the law of excluded middle — a statement must be either true or false. The phrase is traceable back to the Greek ἡ εἰς ἄτοπον ἀπαγωγή (hē eis átopon apagōgḗ), meaning "reduction to the absurd", often used by Aristotle.
where one assumes a claim for the sake of argument and derives an
absurd or ridiculous outcome, and then concludes that the original
claim must have been wrong as it led to an absurd result.
An ad hominem argument, also known as argumentum ad hominem (Latin: "argument to the man", "argument against the man") consists of replying to an argument or factual claim by attacking or appealing to a characteristic or belief of the person making the argument or claim, rather than by addressing the substance of the argument or producing evidence against the claim. The process of proving or disproving the claim is thereby subverted, and the argumentum ad hominem works to change the subject.