Modus Tollens - Explanation

Explanation

The argument has two premises. The first premise is the conditional "if-then" statement, namely that P implies Q. The second premise is that Q is false. From these two premises, it can be logically concluded that P must be false.

Consider an example:

If the watch-dog detects an intruder, the dog will bark.
The dog did not bark
Therefore, no intruder was detected by the watch-dog.

Supposing that the premises are both true (the dog will bark if it detects an intruder, and does indeed not bark), it follows then that no intruder has been detected. This is a valid argument since it is not possible for the premises to be true and the conclusion false. (It is conceivable that there may have been an intruder that the dog did not detect, but that does not invalidate the argument; the first premise goes "if the watch-dog detects an intruder." The thing of importance is that the dog detects or doesn't detect an intruder, not if there is one.)

Another example:

If I am the axe murderer, then I used an axe.
I cannot use an axe.
Therefore, I am not the axe murderer.

Read more about this topic:  Modus Tollens

Famous quotes containing the word explanation:

    To develop an empiricist account of science is to depict it as involving a search for truth only about the empirical world, about what is actual and observable.... It must involve throughout a resolute rejection of the demand for an explanation of the regularities in the observable course of nature, by means of truths concerning a reality beyond what is actual and observable, as a demand which plays no role in the scientific enterprise.
    Bas Van Fraassen (b. 1941)

    How strange a scene is this in which we are such shifting figures, pictures, shadows. The mystery of our existence—I have no faith in any attempted explanation of it. It is all a dark, unfathomed profound.
    Rutherford Birchard Hayes (1822–1893)

    Natural selection, the blind, unconscious, automatic process which Darwin discovered, and which we now know is the explanation for the existence and apparently purposeful form of all life, has no purpose in mind. It has no mind and no mind’s eye. It does not plan for the future. It has no vision, no foresight, no sight at all. If it can be said to play the role of the watchmaker in nature, it is the blind watchmaker.
    Richard Dawkins (b. 1941)