Brief Lessons in Logic, Part 2

It's been a while since the first lesson but here goes...

Now we said that the study of logic, or the study of argument, has to do with the branch of philosophy known as epistemology.

Now throughout some of the history of Western philosophy there has been a debate in the realm of epistemology between two schools of thought known as rationalism and empiricism. It was a debate about how we are to arrive at TRUTH.

Rationalists believed that truth could be discovered by means of reasoning and abstract reflection. Some even believed that we were born with some knowledge.

Empiricists believed that the only way to truth was through observational evidence, through sense experience.

Now, without going too much into it, both approaches are important, and most philosophers, scientists, etc. use both to arrive at conclusions...

The rationalist approach to truth could be called deduction.

The empiricist approach to truth could be called induction.

I'll start with induction...

Induction is an attempt to provide evidence for a conclusion but with no gurantee. Inductive arguments are evaluated on their relative strength - they're either good or bad, weak or strong, etc.

Here's an example of an inductive argument:

Premise 1: I just kicked this ball up and it came down.
Premise 2:Every other time I have kicked a ball up, it came down.
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Conclusion: If I kick this ball up right now, it will come down.

This inductive argument is fairly good or strong. Most people would have no trouble accepting it. It is based on observational evidence, and it provides a good basis to believe that if I kick a ball up it will come down.

But...

It is not guaranteed...

It is not likely, but what if the law of gravity failed to function right now, or what if the earth was destroyed while the ball is in the air, or what if God decided that he did not want the ball to come down...
These possibilities sound silly, and they are silly, especially in light of a strong or good argument like the one above, but the truth is that in an inductive argument, the truth of a conclusion cannot be guranteed...

Now, deduction is an attempt to guarantee the truth of a conclusion. Deductive arguments either work or they don't work. Deductive arguments are either valid or invalid,and sound or unsound.

Example:

Premise 1: If I am in Los Angeles, then I am in California.
Premise 2: I am in Los Angeles.
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Conclusion: I am in California.

This argument is valid.

Now the definition of a valid argument is quite possibly the most important definition in the study of logic or critical reasoning....

Don't ever forget this! Burn it into your head!

Here it is:

An argument is valid if and only if, it is impossible for it to have true premises, lead to a false conclusion.

Or you could think about it this way:

An argument is valid if the conclusion necessarily follows from the premises.

In other words, in a valid argument, given that the premises are true, then the conclusion must be true also. It necessarily follows. There's no way around it. In the above example, assuming it is true that If I am in Los Angeles, then I am in California. and assuming it is true that I am in Los Angeles, then the conlusion that I am in California , necessarily follows.

That is, it must be true that I am in California.

Again, this argument is valid because, assuming that the premises are true, the conclusion must be true.

We will visit the subject of validity again, as well as the issue of soundness.

But that's it for now.... post any questions... I'm not sure if I explained myself correctly... also, it takes a while to get this stuff, but once you do, it is very helpful...