2) The Roots of Logic
The last essay took at the root and purpose of reason.
This one concentrates on a particular method within reason - logic.
Once again, we'll be looking at root and purpose.
Not because logic needs justifying - logic needs to be in place before we can justify things, but so that we can recognise why logic is appropiate so judge when and where to apply it.
For logic to be applicable, only one thing has to be in place - language.
Once we have language, i.e. we grasp and understand the concepts involved (and that's pretty much necessary for any kind of questioning or debate to even start) logic comes out of it. The most famous rule of logic is the law of non-contradiction.
The Law of Non-Contradiction: 'P & not P' cannot be true
And why it holds in a debate
Consider the following conversation:
"You're an idiot."
"No I'm not!"
"I know you're not, but you're still an idiot."
"I told you, I'm not an idiot."
"I don't disagree, you're not an idiot but you're still an idiot."
The speaker on the right is using the word 'not', but he might as well not be as it doesn't seem to mean anything to the speaker on the left. It becomes quite clear that ignoring the law of non-contradiction makes the word 'not' meaningless. Seeing as we are reasoning in a language where we use the word 'not' as we do, the law of non-contradiction comes naturally.
Whatever our picture of the world, it can only be a picture if we are using language correctly to describe it. If we are abusing our language when what are we actually saying?
So if our position contains a contradiction then that shows a problem with our picture, that it doesn't really make sense as it stands.
That is why the law of non-contradiction holds within a debate.
Alongside the law of non-contradiction there is another law.
The Law of the Excluded Middle: Either 'P' is true or 'not P' is true
This holds for the same reason as the law of non-contradiction.
It is another consequence of the meanings of the words 'or' and 'not'.
Using these two rules of logic we can build a method of logical inference.
A valid logical inference is when you prove that if some premises are true, then a conclusion is true.
Premise 1) Unicorns have horns
Premise 2) Sam is a unicorn
Conclusion: Sam has a horn
If you accept that premise 1 and premise 2 are true then the conclusion must also be true. This can be used to defend a statement against an opponent if it can be shown that it leads from premises that the opponent holds. By why is this. Why is a valid inference considered to be 'infallible'?
It's because that if an inference is valid, to accept the premises while denying the conclusion is to make a contradiction.
To deny that Sam has a horn while agreeing that Sam is a unicorn and that all unicorns have horns is to contradict yourself.
Methods of proof tend to work as follows:
1) Show that the premises contradict the denial of the conclusion.
2) By the Law of Non-Contradiction, if you hold these premises then the denial of the conclusion cannot be true.
3) By the Law of Excluded Middle, if the denial of the conclusion is false then the conclusion must be true.
4) So if you accept the premises then you must also accept the conclusion.
When and where is logic applicable?
Logic is best applied when the concepts in question are clearly defined.
Mathematics is the practice of logic.
Mathematical concepts are so well defined that mathematical problems can often be solved purely on logic, and when they can't, this too can be proved in advance using logic.
The language of Physics is very mathematical, and logic tends to be very applicable in science too. Once the concepts are defined it can be quite clear when there is a contradiction and problems can be spotted with relative ease.
Theories can be constructed from the ground up, starting from basic axioms as foundations.
Not all of our concepts are so crystal clear.
Our language has a whole range of concepts, ranging from mathematic ones that have very strict definitions to very loose ones that appear to elude strict definition altogether. Concept like 'love' tend to be so loose that an attempt to nail a strict definition will almost certainly be incorrect. 'Love' is a concept for poetry rather than logic, because rather than trying to nail strict rules, poetry lets the concept display it's true nature through loose examples.
This leads some people to prefer to avoid loose language in debate as it makes it much harder, maybe impossible, to get watertight conclusions. The thing is, are all questions worth asking supposed to have such definite answers? If we have a question that arises in the form of a loose language, would trying to re-phrase the question in a mathematical language lead us to a clear answer, or would it just change the question and lead the original question unanswered?
Like other methods, it seems that there is a time and place for strict logical method.
While some kind of logic will always applicable, it won't always give such definite answers, and it won't always be so obvious whether a contradiction is really a contradiction.
A circle is most certainly not a square, but whether love and hate are as incompatable isn't quite so obvious.