Being Critical

Logical errors are, I think, of greater practical importance than many people believe; they enable their perpetrators to hold the comfortable opinion on every subject in turn.

~Bertrand Russell

One of the more confusing concepts found in logic is deductive/inductive reasoning.

A good deductive argument is one whose premises being true would mean the conclusion must be true. For example:

Premise A: All birds can fly
Premise B: Penguins can't fly
Conclusion: Penguins are not birds.

The above argument is considered a valid deductive argument because if the premises were true, the conclusion must be true. But obviously the Premise A isn't true, penguins are considered birds. Nonetheless the deductive logic itself is still valid.

Here is a different example:

Premise A: Cats are mammals
Premise B: All mammals are warm blooded.
Conclusion: Cats are warm blooded.

The example above is a sound deductive argument because it is valid AND its premises ARE all true.

Now, an inductive argument supports rather than proves. In other words, if the premises of a strong inductive argument are true, the conclusion probably is true.

Example of a strong, inductive argument...

Premise A: There are 10 women in the room
Premise B: 9 of those women are brunette
Conclusion: Most likely all the women are brunette.

If Premise B had a lower sample number , the argument would become weaker. But what about this example?

Premise A: Most lights in the sky are UFOs.
Premise B: There are many lights in the sky.
Conclusion: The next light to be seen is probably a UFO.

Now, even though this is a strong inductive argument, premise A is not true. Thus, it is not considered a cogent inductive argument. I cogent inductive argument is a strong argument with the premises being true. So the Brunette Example previously would be considered a cogent inductive argument.