Implication (logic)

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Implication (also known as logical consequence,implies, or If ... then) is a logical operation. It is the relationship between statements that holds true when one logically "follows from" one or more others.

Implications take two arguments. It returns false if and only if the first term is true and the second term is false.

This may be problematic, because it means that from a false proposition, anything can follow.

Examples[change | change source]

The following shows a (valid) implication

  1. All humans are mortal (they die).
  2. Aristotle is human
  3. Therefore Aristotle is mortal

Now look at the implications I promise that if I am healthy, I will come to class. There are four possibilities:

  1. I am healthy, and I do come to class. I have kept my promise.
  2. I am healthy, and I do not come to class. I have not kept my promise.
  3. I am not healthy, and I do come to class. I have kept my promise.
  4. I am not healthy, and I do not come to class. I have kept my promise.

In the second scenario, the implication promised was false and the promise was broken.

Related pages[change | change source]