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. This also why we know that mathematical logic is junk, and not any logic at all.
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)*.
Why is an argument with contradictory premises 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.
Does a contradiction make an argument invalid?
In the corresponding truth table there is a row where the hypothesis are all true and the conclusion false, therefore the argument is invalid. But there is also a row where the conditions are true and the conclusion is true. This is not, then, a contradiction, but it is invalid.
What is a contradiction in formal logic?
In traditional logic, a contradiction occurs when a proposition conflicts either with itself or established fact. It is often used as a tool to detect disingenuous beliefs and bias.
Does every valid argument have a true conclusion?
All valid arguments have all true premises and true conclusions. All sound arguments are valid arguments. If an argument is valid, then it must have at least one true premise.
Are all fallacies invalid?
@Curious Yes informal fallacies may be valid, but formal fallacies would be invalid, that is, the form is what is invalid about the argument.
Can a contradiction exist?
Dialetheism (from Greek δι- di- ‘twice’ and ἀλήθεια alḗtheia ‘truth’) is the view that there are statements that are both true and false. More precisely, it is the belief that there can be a true statement whose negation is also true. Such statements are called “true contradictions”, dialetheia, or nondualisms.
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.
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” …
How do you prove a contradiction?
To prove something by contradiction, we assume that what we want to prove is not true, and then show that the consequences of this are not possible. That is, the consequences contradict either what we have just assumed, or something we already know to be true (or, indeed, both) – we call this a contradiction.
Can two contradictory statements be false?
Contraries may both be false but cannot both be true. Contradictories are such that one of them is true if and only if the other is false.
What is the meaning of contradictory statement?
asserting the contrary or opposite; contradicting; inconsistent; logically opposite: contradictory statements. tending or inclined to contradict. noun, plural con·tra·dic·to·ries. Logic. a proposition so related to a second that it is impossible for both to be true or both to be false.
Is a statement or situation that seems contradictory but is actually true?
A paradox is a statement that may seem contradictory but can be true (or at least make sense).
What is an example of a contradiction?
A contradiction is a situation or ideas in opposition to one another. Declaring publicly that you are an environmentalist but never remembering to take out the recycling is an example of a contradiction. A “contradiction in terms” is a common phrase used to describe a statement that contains opposing ideas.
What’s the difference between contrary and contradictory?
Contradictories cannot at the same time be true nor at the same time false. Two statements are contrary to one another if they are both universals but differ in quality. Contraries cannot at the same time both be true, but can, at the same time, be false.
What is contradictory opposition of 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.
What are the different types of contradiction?
Therefore A ^ Ā is a logical contradiction and a dialectical contradiction as well. The two types of contradictions are actually the two manifestations of the same contradiction in different contexts.