# 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.

Logical Inference
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.
For example:

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.

### Quote: For logic to be

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For logic to be applicable, only one thing has to be in place - language.

Hmmm.... depends on what you mean by language. In theory, a person who lived in complete isolation his entire life could use logic, and never develop language. Chimps and dolphins use logic to a limited degree. I haven't seen Todangst in a while, and he's the PhD guy, but if I remember correctly, abstraction is pretty much all you need for logic.

I suppose language is symbolic representation of logic, but the logic can happen without being externally represented.

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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.

I see what's happening now. You're still using this only for dispute resolution. This is why I don't like to use "reason" this way. Even for dispute resolution, language is not strictly necessary, but some form of communication is.

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The most famous rule of logic is the law of non-contradiction.

I don't care about most famous, but shouldn't we address the law of identity first? I realize that non-contradiction is part of identity, but without addressing the existence of self, we are presuming part of the law.

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the law of non-contradiction comes naturally.

Specifically, the law of non-contradiction becomes axiomatically necessary from the law of identity. If I exist, it is impossible that I do not exist, for if I did not exist, I could not recognize my own existence. Once we become aware of "other," we realize that every "other" is also a "self." Each self is also bound by the law of noncontradiction.

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Premise 1) Unicorns have horns
Premise 2) Sam is a unicorn
Conclusion: Sam has a horn

You realize that Sam might have ten horns, right? Specificity is really important.

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Logic is best applied when the concepts in question are clearly defined.

Logic can only be applied when the concepts are clearly defined. The conclusion is as equally unknown as the undefined terms.

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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.

I'm a bit distressed by this paragraph. It's not that it isn't true, it's that you seem to be pidgeon-holing logic into the realm of the educated. Everyone uses logic every day. The only difference is that scientists and mathematicians know how to label what they're doing, and they sometimes used more advanced logic.

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'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.

I have severe problems with this. You seem to be setting us up for the premise "Some things are beyond logic." That's baloney. Some things are very difficult to define when you start getting fifty people together in a committee. Nevertheless, for the purpose of a logical proof, I can define love in any way I see fit, and if the definition remains consistent throughout my proof, and my syllogism is valid, my conclusion will be valid within the context of my definition.

Having multiple definitions is not equivalent to being undefinable.

Love, as a cultural concept, is nebulous because:

A) It has multiple definitions.

B) Most people use the definitions interchangeably.

C) Most people have never stopped to define each definition, and are themselves unclear about which definition they are using at any given moment.

I'm sorry, but I simply can't agree that the "true" nature of some things is indefinable. Think about it. The moment you label something as indefinable, you have given it a property -- a definition. Any boundary is a definition. The word "indefinable" is not properly defined. Like supernatural, anything that is indefinable is, by definition, nonexistent. When we say indefinable in normal conversation, we mean, "extremely difficult to define" or "beyond my capacity to define."

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This leads some people to prefer to avoid loose language in debate as it makes it much harder, maybe impossible, to get watertight conclusions.

In the strictest sense, loose language must be avoided in debate. In an colloquial argument, we can do whatever we want. If we want to call it a real debate, we must avoid loose language.

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The thing is, are all questions worth asking supposed to have such definite answers?

Which questions are worth asking? Who decides that? Supposed to have answers? What does that mean?

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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.

Um.... if we want a scientific, logical answer, we must either refine the definitions or abandon the question.

The time and place for strict logical method is if you want a valid, reliable answer. If you want vague answers, you're free to avoid strict logic. I strongly object to the leap you've made here. Essentially, it appears that your argument is "Vague language exists. Therefore, logic doesn't always work." That's true, but it's a deceptive thing to say.

Logic, when used properly, always works. Vague language is not an alternative to logic. It is a fault in a logical argument. It's fine for day to day interactions in most cases, because we can infer what people mean, and misunderstandings are not the end of the world. We accept "loose" logic for matters that do not require strict logic. This does not in any way lead to the conclusion that logic is not always applicable when we want to reach a valid, true conclusion.

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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.

The fault in this statement is that it equates "We don't use logic" with "We can't use logic." You're also equating formal logic with informal logic, and you haven't bothered to even introduce us to the two concepts. You're implying that day to day informal logic is on equal footing with formal logic, depending on the question. That's true in a colloquial, but not a scientific sense. If I need to cook for six people, I can go too the store and eyeball the carrots to see how many I need. If you sent twenty people to the store with the same task, you'd probably get twenty meals for six people, all within the acceptable portion size. This is informal use of logic, and it's fine because we haven't asked for anything more specific. However, formal logic is absolutely necessary if we want to discover the objective answer to a question with either certainty, or a scientifically reliable degree of probabalistic certainty.

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A circle is most certainly not a square, but whether love and hate are as incompatable isn't quite so obvious.

Again, you are implying that because definitions are difficult, they are impossible. This simply does not follow. I see where you're going with this, I think, but you've not built a strong case. Love and hate, though colloquially vague, could be described scientifically. Their scientific meaning will be narrow, and will not encompass the wide range of feelings that we mean when we speak colloquially of love, but that's because "Love" is a conglomerate of feelings.

Honestly, your approach so far seems to be, "Some things are really hard to define, so it's ok if we don't use logic on them."

In day to day existence, I'm ok with that. In the end, I'll be happy to concede that the pseudo-logical ambiguity that many people use to believe in and live by a religious code is useful in day to day life. I'll also concede that there are people whose lunch hour is made brighter by reading the horoscope and getting excited when it matches something in their life.

But, you still have not addressed the incompatibility of informal logic with formal logic for the purposes of describing objective reality.

I feel like we're right back where we left off a couple of months ago. I've never denied that some people get a pragmatic benefit from being religious, or that some people are happy believing in a god. I have no problem admitting that the placebo effect of religion is real, and that it is valid to conclude that some effects of religion are beneficial. No problems, no disagreements.

But, there is no god, and it is formally illogical to believe in one. Illogic = irrational.

Atheism isn't a lot like religion at all. Unless by "religion" you mean "not religion". --Ciarin