In formal logic, an argument with a contradictory conclusion is not valid. In mathematical logic, an argument with a contradictory conclusion will be declared valid if the premises are themselves contradictory.
Can an argument with a contradictory conclusion be 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)*.
Can two contradictory things both be true?
In logic, the law of non-contradiction (LNC) (also known as the law of contradiction, principle of non-contradiction (PNC), or the principle of contradiction) states that contradictory propositions cannot both be true in the same sense at the same time, e. g. the two propositions “p is the case” and “p is not the case” …
Why is an argument with two contradictory premises always 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.
Can you have 2 conclusions in an argument?
A conclusion is a statement in an argument that indicates of what the arguer is trying to convince the reader/listener. What is the argument trying to prove? There can be only one conclusion in a single argument.
Is an argument with contradictory premises always valid?
But on a classical conception of validity, any argument with contradictory premises counts as valid, since it is impossible for all the premises of an argument with contradictory premises to be true, and so a fortiori impossible for the argument to have true premises and false conclusion.
Why can’t a valid argument have true premises and a false conclusion?
If a valid argument has a false conclusion, then at least one premise must be false. TRUE: A valid argument cannot have all true premises and a false conclusion. So if a valid argument does have a false conclusion, it cannot have all true premises. Thus at least one premise must be false.
Why are contradictions impossible?
Opposition between terms cannot be contradictory in nature, both because only statements (subject-predicate combinations) can be true or false (Categories 13b3–12) and because any two terms may simultaneously fail to apply to a given subject.
Are contradictions false?
It is a proposition that is unconditionally false (i.e., a self-contradictory proposition). This can be generalized to a collection of propositions, which is then said to “contain” a contradiction.
What is it called when two opposing things are true?
oxymoron. NOUN. A figure of speech in which apparently contradictory terms appear in conjunction (e.g. faith unfaithful kept him falsely true) I’ve heard this usually applied to an adjective-noun pair, such as in jumbo shrimp or military intelligence.
How many conclusions can be in a single argument?
An argument has only one conclusion because that is the accepted convention. As Bumble notes in a comment, multiple-conclusion logics exist. Wikipedia describes such logics as follows: A multiple-conclusion logic is one in which logical consequence is a relation, ⊢, between two sets of sentences (or propositions).
Can you have more than 2 premises?
The simplest arguments have only a single premise, but it’s common to have two or more. When arguments have multiple premises, there are two ways that those premises can logically support the conclusion: 1. Mutually.
What makes an argument valid?
An argument is valid if the premises and conclusion are related to each other in the right way so that if the premises were true, then the conclusion would have to be true as well.
What makes an argument valid or invalid?
Valid: an argument is valid if and only if it is necessary that if all of the premises are true, then the conclusion is true; if all the premises are true, then the conclusion must be true; it is impossible that all the premises are true and the conclusion is false. Invalid: an argument that is not valid.
How do you prove an argument is valid?
A formal proof that an argument is valid consists of a sequence of pro- positions such that the last proposition in the sequence is the conclusion of the argument, and every proposition in the sequence is either a premise of the argument or follows by logical deduction from propositions that precede it in the list.
How do you make an invalid argument valid?
Remember the key to judging deductive arguments to be valid or invalid is not whether the premises are true or false. Rather, the question is what are the premises saying and what are they not saying, and whether if they were true would the conclusion be true. If the answer is yes, then the argument is valid.
What is conclusion as valid or true?
Validity is a guarantee of a true conclusion when the premises are true but offers no guarantee when the premises are false. False premises can lead to either a true or a false conclusion even in a valid argument. In these examples, luck rather than logic led to the true conclusion.
What is an example of a valid argument?
A valid argument is an argument in which the conclusion must be true whenever the hypotheses are true. In the case of a valid argument we say the conclusion follows from the hypothesis. For example, consider the following argument: “If it is snowing, then it is cold. It is snowing.