Truth and Validity
Created | Updated Jul 22, 2002
Undoubtably you've had an argument with someone at some point in your life- parents, spouse, law enforcement... Would you believe there is a method to this? Hopefully, this article will help you the next time you have an argument with your sister over whose turn it is at the computer.
Part One: Valid Arguments
In logic, an argument is comprised of a few statements. The first statements are called the premises, while the last statement is called a conclusion.
Here's an example of an argument:
If a bird can fly, then it has wings. A sparrow can fly. Therefore, a sparrow has wings.
As you can see, this argument has premises ("If the bird can fly, then it has wings. A sparrow can fly.") and a conclusion ("Therefore, a sparrow has wings"). In this argument, the conclusion follows the premise. As you can see, the premise forces the conclusion. This is called a valid argument. A valid argument is said to have a valid conclusion. A valid argument contains a universal truth: If the premises are all true, then the conclusion is true as well. In the example argument, both premises are true, so the conclusion must be true as well.
Valid Argument Form Number One: Modus Ponens
You can tell whether an argument is valid or not without even knowing if the premises (or its conclusion) is true. All you have to do is analyze the argument. As you will see, all logical arguments (sparring husbands and wives excepted) adhere to a strict formula. It’s all in the form. For example, the sparrow argument has the following argument:
Modus Ponens
If x, then y.
X
Therefore, y.
This argument form is called Modus Ponens, or, “Proposing Mode”. Any argument with this form is valid, regardless of what the statements are for x and y. The following argument is true, because it has a valid form:
If a Barghest yowls, then Lascadua sells out. A Barghest yowls. Therefore, Lascadua sells out.
This form makes certain the fact that if the first two statements are true, then the conclusion is also true as well. Remember, your premises must always be true for any argument to be valid.
Valid Argument Form Number Two: Modus Tollens
Observe:
If a car has the word FORD on it, then it is a Ford. This car does not have the word Ford on it. Therefore, it is not a Ford!
Is this valid? Absolutely. It is called Modus Tollens, or “removing mode” in Latin. It is more commonly called the Law of Indirect Reasoning.
Part Two: Invalid Arguments
Now, take a look at a different argument:
Some vertebrates are warm-blooded. Frogs are vertebrates. Therefore, frogs are warm-blooded.
This argument is invalid. Both of the premises are true, but the conclusion is false. In a valid argument, the conclusion is never false.
False Premises
If an argument contains false premises, then there is no guarantee that the conclusion will be true, even if the argument has a valid form. Read on:
If a kiwi is a fruit, then it can walk. A kiwi is a fruit. Therefore, a kiwi can walk.
As you can see, there is an obviously false conclusion, even though the argument form is valid. Remember the conclusion is true only if the premises are true.
Part Two: Invalid Arguments
Invalid arguments, sadly, seem to occur much more often than valid arguments, and as such you should be able to recognize them more easily.
Invalid Argument Form Number 1: Affirming the Consequent
If x, then y.
x.
Therefore, y.
This form of argument is often a common logical mistake. It seems to make sense, doesn’t it? It is invalid because the conclusion does not follow in order after the premises, even if it is a true statement. It is very easy to mix this form up with the Modus Ponens form. Here’s an example:
If I am happy, then I am with the one I love. I am happy. Therefore, I am with the one I love.
Obviously, this argument doesn’t work, because unless you have severe separation anxiety, you can be happy for other reasons as well.
Invalid Argument Form Number 2: Denying the Antecedent
If x, then y.
Not x.
Therefore, not y.
This is similar to Affirming the Consequent, except that it takes on a negative form. Look at this:
If children run, then pigs can wallow. Children cannot run. Therefore, pigs cannot wallow.
Even though both of the premises are true, the conclusion is false, because pigs might not be wallowing for any number of reasons.
Conclusion
Hopefully, you’ve learned something new about arguing, and the next time you get in an argument, put this to good use. Just don’t tell them that I told you how.
Part One: Valid Arguments
In logic, an argument is comprised of a few statements. The first statements are called the premises, while the last statement is called a conclusion.
Here's an example of an argument:
If a bird can fly, then it has wings. A sparrow can fly. Therefore, a sparrow has wings.
As you can see, this argument has premises ("If the bird can fly, then it has wings. A sparrow can fly.") and a conclusion ("Therefore, a sparrow has wings"). In this argument, the conclusion follows the premise. As you can see, the premise forces the conclusion. This is called a valid argument. A valid argument is said to have a valid conclusion. A valid argument contains a universal truth: If the premises are all true, then the conclusion is true as well. In the example argument, both premises are true, so the conclusion must be true as well.
Valid Argument Form Number One: Modus Ponens
You can tell whether an argument is valid or not without even knowing if the premises (or its conclusion) is true. All you have to do is analyze the argument. As you will see, all logical arguments (sparring husbands and wives excepted) adhere to a strict formula. It’s all in the form. For example, the sparrow argument has the following argument:
Modus Ponens
If x, then y.
X
Therefore, y.
This argument form is called Modus Ponens, or, “Proposing Mode”. Any argument with this form is valid, regardless of what the statements are for x and y. The following argument is true, because it has a valid form:
If a Barghest yowls, then Lascadua sells out. A Barghest yowls. Therefore, Lascadua sells out.
This form makes certain the fact that if the first two statements are true, then the conclusion is also true as well. Remember, your premises must always be true for any argument to be valid.
Valid Argument Form Number Two: Modus Tollens
Observe:
If a car has the word FORD on it, then it is a Ford. This car does not have the word Ford on it. Therefore, it is not a Ford!
Is this valid? Absolutely. It is called Modus Tollens, or “removing mode” in Latin. It is more commonly called the Law of Indirect Reasoning.
Part Two: Invalid Arguments
Now, take a look at a different argument:
Some vertebrates are warm-blooded. Frogs are vertebrates. Therefore, frogs are warm-blooded.
This argument is invalid. Both of the premises are true, but the conclusion is false. In a valid argument, the conclusion is never false.
False Premises
If an argument contains false premises, then there is no guarantee that the conclusion will be true, even if the argument has a valid form. Read on:
If a kiwi is a fruit, then it can walk. A kiwi is a fruit. Therefore, a kiwi can walk.
As you can see, there is an obviously false conclusion, even though the argument form is valid. Remember the conclusion is true only if the premises are true.
Part Two: Invalid Arguments
Invalid arguments, sadly, seem to occur much more often than valid arguments, and as such you should be able to recognize them more easily.
Invalid Argument Form Number 1: Affirming the Consequent
If x, then y.
x.
Therefore, y.
This form of argument is often a common logical mistake. It seems to make sense, doesn’t it? It is invalid because the conclusion does not follow in order after the premises, even if it is a true statement. It is very easy to mix this form up with the Modus Ponens form. Here’s an example:
If I am happy, then I am with the one I love. I am happy. Therefore, I am with the one I love.
Obviously, this argument doesn’t work, because unless you have severe separation anxiety, you can be happy for other reasons as well.
Invalid Argument Form Number 2: Denying the Antecedent
If x, then y.
Not x.
Therefore, not y.
This is similar to Affirming the Consequent, except that it takes on a negative form. Look at this:
If children run, then pigs can wallow. Children cannot run. Therefore, pigs cannot wallow.
Even though both of the premises are true, the conclusion is false, because pigs might not be wallowing for any number of reasons.
Conclusion
Hopefully, you’ve learned something new about arguing, and the next time you get in an argument, put this to good use. Just don’t tell them that I told you how.
