A vacuously valid argument is one that is valid just because the premises are unsatisfiable (= can not all be simultaneously true).
Can an argument be true and valid?
It is important to stress that the premises of an argument do not have actually to be true in order for the argument to be 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 is a vacuously true statement?
In mathematics and logic, a vacuous truth is a conditional or universal statement (a universal statement that can be converted to a conditional statement) that is true because the antecedent cannot be satisfied.
How do you know if an argument is valid or invalid?
Judge the reasoning and not the content (true or false statements). Think hypothetically. Ask, “IF the premises are true, are we locked into the conclusion?” If yes, then the argument is valid. If no, then the argument is invalid.
Can an inconsistent argument be valid?
Yes. An argument with inconsistent premises is valid, regardless of what the conclusion is. If an argument has inconsistent premises, then it is impossible for all the premises to be true at the same time; hence it is impossible for all the premises to be true while the conclusion is false.
Can an argument be true or false?
TRUE: A valid argument cannot possibly have all true premises and a false conclusion. If some argument really does have all true premises and a false conclusion, then it is obviously possible for such an argument to have true premises and a false conclusion. So the argument is invalid.
What is an example of valid?
The definition of valid is something effective, legally binding or able to withstand objection. An example of valid is a driver’s license that hasn’t expired. An example of valid is someone giving evidence that proves an argument.
Is vacuously true still true?
The phrase “vacuously true” is commonly applied to statements like ∀x∈X:P(x) because when X is the empty set, the statement is always true, regardless of what P represents.
What is the meaning of Vacuously?
1 : emptied of or lacking content. 2 : marked by lack of ideas or intelligence : stupid, inane a vacuous mind a vacuous movie. 3 : devoid of serious occupation : idle.
Can all conditional statements be true?
, is called the consequent. A conditional is considered true when the antecedent and consequent are both true or if the antecedent is false. When the antecedent is false, the truth value of the consequent does not matter; the conditional will always be true.
Can an unsound argument be valid?
Some unsound arguments are valid. They are unsound because they do not have all true premises.
Can an inductive argument be valid?
Inductive argument: involves the claim that the truth of its premises provides some grounds for its conclusion or makes the conclusion more probable; the terms valid and invalid cannot be applied.
Are valid arguments tautologies?
If the premises of a propositionally valid argument are tautologies, then its conclusion must be a tautology as well. If the premises of the argument are tautologies, then they are all true under every assignment of truth values to the sentence letters. A valid argument with true premises has a true conclusion.
Are all tautologies logical truths?
Note that every tautology is also a logical truth, and every logical truth is also a TW-necessity. But the converse is not true: some logical truths are not tautologies, and some TW-necessities are not logical truths.
Can you have a valid argument with contradictory premises?
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.
Is tautology always true?
A tautology is a formula which is “always true” — that is, it is true for every assignment of truth values to its simple components. You can think of a tautology as a rule of logic. The opposite of a tautology is a contradiction, a formula which is “always false”.
What is a tautology argument in philosophy?
A tautology is any argument where for any combination of truth values (true/false) assigned to the predicates within it, the logical flow of the argument is such that the conclusion will always turn out true.
What is wrong with tautology?
A Bad Reputation
A tautology is a proposition that is true in all possible circumstances – sometimes people say, “true by definition” or “self-evidently true”. The central idea is that it has no possibility of being false. Consider the sentence “All fish are fish”.