# Validity stemming from contradictory premisses

## Can an argument with contradictory premises be valid?

Well, if the premises are contradictory, then they cannot all be true (that’s just what contradictory means) so they can’t all be true while the conclusion is false (the necessary condition for non-validity). So the argument cannot be non-valid, it must be valid. Thus an argument with contradictory premises is valid.

## Is an argument with contradictory conclusion valid?

Yes, an argument with contradictory premises is deductively valid. That’s because it’s impossible to have all its premises true and its conclusion false (since its premises can never all be true)*.

## Why is contradictory premises unreliable?

Because when the premises of an argument contradict each other, there can be no argument. If there is an irresistible force, there can be no immovable object. If there is an immovable object, there can be no irresistible force. Get it?’

## What is a contradictory proposition?

Propositions are contradictory when the truth of one implies the falsity of the other, and conversely. Here we see that the truth of a proposition of the form All S are P implies the falsity of the corresponding proposition of the form Some S are not P.

## Can you render an invalid argument valid by removing premises?

In classical logic no, but you can make a sound argument unsound by adding false premises. The difference between soundness and validity is usually ignored colloquially, but logical validity is neutral on the truth of the premises, it only cares whether inference would preserve that truth.

## Is an argument with contingent premises valid?

The definition applies to it because it is impossible for it to have true premises and a false conclusion (since it is impossible for it to have a false conclusion at all). All other sentences–that is, all those that are neither tautologies nor inconsistent–are called CONTINGENT.
Tautologies.

P ~P P & ~P
T F F
F T F

## Can a contradiction entail any statement?

The schema is (roughly) that whenever P entails a contradiction, P is false. That’s shorthand for saying that whenever a statement entails a contradiction, the statement can’t be true. In other words, Pick any “real life” statement you like that entails a contradiction.

## What is a method of coming up with a conclusion from an exchange of contradicting logical arguments?

Dialectic. The art or practice of arriving at the truth by the exchange of logical arguments. dialectics (used with a sing. verb) A method of argument or exposition that systematically weighs contradictory facts or ideas with a view to the resolution of their real or apparent contradictions.

## What is contrary and contradictory?

A contradictory statement is one that says two things that cannot both be true. An example: My sister is jealous of me because I’m an only child. Contradictory is related to the verb contradict, which means to say or do the opposite, and contrary, which means to take an opposite view.

A contradiction is something that is always false, regardless of it’s truth values.