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01x05 - Modus Ponens And Modus Tollens
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Welcome to Fast Philosophy. This video is part of our Introduction To Logic series and explains what modus ponens and modus tollens are.
In our previous video on deduction, I explained that an argument is deductively valid when its conclusion is a logical consequence of its premises, whether or not the conclusion or premises are true. Modus ponens and modus tollens are the Latin names for two frequently-used deductively valid argument forms.
To understand modus ponens and modus tollens, you must first understand the logician's use of the words 'conditional' and 'negation'. A 'conditional' is a premise with the form 'if this, then that'; for example, 'if it is raining, then I will wear a coat out'. A 'negation' is a proposition of the form 'not something'; for example, if my proposition is 'it is raining', then the negation would be 'it is not raining'. Now we understand deduction, conditional and negation, we can understand modus ponens and modus tollens.
Modus ponens is a deductively valid argument form which uses the conditional. Let's illustrate this with a formal argument using the letters 'P' and 'Q' to represent different propositions. We can now understand modus pones to be any argument with the form:
P1 If P, then Q
P2 P
C Q
This works whatever you put in place of P and Q. And even if neither P nor Q is true, as long as the argument is in the modus ponens form, the argument will be deductively valid. For example:
P1 If it rains cats, then it will snow dogs
P2 It rains cats
C It will snow dogs
Now let's turn our attention to modus tollens, which is similar to modus ponens in that it is also a deductively valid argument form and uses the conditional. Modus tollens uses the negation as well. Let's illustrate with P and Q again:
P1 If P, then Q
P2 Not Q
C Not P
Again, the truth of P and Q do not matter -- it's the form that's important to deductive validity. So the argument is deductively valid in a modus tollens form, even if what we put in place of P and Q are false.
In our previous video on deduction, I explained that an argument is deductively valid when its conclusion is a logical consequence of its premises, whether or not the conclusion or premises are true. Modus ponens and modus tollens are the Latin names for two frequently-used deductively valid argument forms.
To understand modus ponens and modus tollens, you must first understand the logician's use of the words 'conditional' and 'negation'. A 'conditional' is a premise with the form 'if this, then that'; for example, 'if it is raining, then I will wear a coat out'. A 'negation' is a proposition of the form 'not something'; for example, if my proposition is 'it is raining', then the negation would be 'it is not raining'. Now we understand deduction, conditional and negation, we can understand modus ponens and modus tollens.
Modus ponens is a deductively valid argument form which uses the conditional. Let's illustrate this with a formal argument using the letters 'P' and 'Q' to represent different propositions. We can now understand modus pones to be any argument with the form:
P1 If P, then Q
P2 P
C Q
This works whatever you put in place of P and Q. And even if neither P nor Q is true, as long as the argument is in the modus ponens form, the argument will be deductively valid. For example:
P1 If it rains cats, then it will snow dogs
P2 It rains cats
C It will snow dogs
Now let's turn our attention to modus tollens, which is similar to modus ponens in that it is also a deductively valid argument form and uses the conditional. Modus tollens uses the negation as well. Let's illustrate with P and Q again:
P1 If P, then Q
P2 Not Q
C Not P
Again, the truth of P and Q do not matter -- it's the form that's important to deductive validity. So the argument is deductively valid in a modus tollens form, even if what we put in place of P and Q are false.
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