Changes

It is often held that from a contradiction anything can be inferred.  This can be demonstrated:

It is often held that from a contradiction anything can be inferred.  This can be demonstrated:

1. Take any contradiction, “A” and “Not A”, and take it to be true.

# Take any contradiction, “A” and “Not A”, and take it to be true.

2. Take anything that you want to prove, “P”

# Take anything that you want to prove, “P”

3. Now because “A and Not A” is true, “A” is true, by virtue of the simplification rule.

# Now because “A and Not A” is true, “A” is true, by virtue of the simplification rule.

4. “A or P” is true just so long as not both A and P are false.

# “A or P” is true just so long as not both A and P are false.

5. So, As “A” is true, “A or P” must be true.

# So, As “A” is true, “A or P” must be true.

6. If “A or P” is true, then one of “A” or “P” must be true.

# If “A or P” is true, then one of “A” or “P” must be true.

7. As “Not A” is true then “A” is false which means that the remaining term in “A or P” must be true.

# As “Not A” is true then “A” is false which means that the remaining term in “A or P” must be true.

8. “P”, absolutely anything you like, is true.

# “P”, absolutely anything you like, is true.

[[category:logic]]

[[category:logic]]