4/6/2008.

Language, definitions, and ambiguity.

Nobody can define any reasonably complex concept such that the literal meanings of the words in the definition cover all and only the instances of that concept. It is impossible to construct an unamibiguous sentence of any importance in the English language. The purpose of language is to convey an idea, not to satisfy formal requirements.

I expect definitions to define, but I do not expect a definition to replace. Human language is *always* going to be ambiguous.

The best example is the many possible interpretations of a sentence as simple as "time flies like an arrow." They include:
    1) Time passes in a manner like the manner in which an arrow flies.
    2) A type of flies, time flies, are fond of an arrow.
    3) One should time flies in the same manner as one times an arrow.
    4) One should time flies in the same manner as an arrow times flies.

And so on. As I recall, there were at least 2 more. The point of any set of words is to convey to the listener the thoughts the speaker intends to convey.

I expect a definition to give someone who already has the concept the appropriate name for that concept and to assist someone who doesn't already have the concept in forming it.

Anything sufficient to point out the correct concept to someone who already has that concept is a definition.

It's possible for people to build false assumptions into a concept, to such an extent that the concept fails to have any referent, or at least, fails to have an unambiguous referent.

And that this is very easy and common to do, and that there is nothing wrong with doing it. In fact, both language and reason are typically massively ambiguous because it takes effort to remove ambiguity, so generally we are as ambiguous as we can get away with being.

It takes effort to remove ambiguity and generally we are either incapable or unwilling to bother. (Which is perfectly valid. We don't need to, so why should we? Literal correctness is not important.)

It's deceptive to talk about whether a "statement" is true or false. If the statement is just a sequence of words, the issue of its truth or falsity is whether it expresses a relationship between concepts that corresponds with reality. But the statement is a sequence of words, not concepts, and there is no "1 right way" to map words to concepts. Ordinarily, we mean the concepts as the person who uttered the sentence held them. But then if that person ceases to exist, so do those concepts. The statement now refers to concepts that no longer exist.

As an example, the statement 2 + 2 = 4 is true, in the sense that, to me, it expresses a relationship between concepts that I hold that accurately corresponds with reality.

It would matter if you told me that the a was randomly generated in a spreadsheet. It would matter if you didn't tell me that.

It would matter because then it would no longer be true in the ordinary sense, which is whether the concepts it corresponded to in the speaker or originator correspond with reality.

The ordinary sense is the most useful sense.

Generally, what we are concerned about is whether our own concepts and the relationships between them accurately map reality. The use of language to express concepts to others is at best secondary to our own ability to have maps of concepts that either correspond or do not correspond to reality.

Secondarily, we can express the relationships between our concepts with statements. But those mappings will always be imperfect. The statements always express an intentionality relative to the expected concept map in another person. If the other person doesn't have the expected concepts mapped the expected way, then the statement will fail to accurately convey the conceptual relationship intended.

I don't think it's meaningful to talk about whether the statement itself is true or false. You have to talk about whether some meaning of the statement is true or false. You can talk about the intended meaning if you like. You can talk about the particular meaning a particular person got out of it, if you like. You can talk about the meaning you would expect a person with a particular knowledge base to get out of it.

But I don't see how the statement itself can be true or false, absent some kind of "1 true meaning" for the statement, which I don't see how you can have. Perhaps one can construct such statements, but the vast majority of statements are not of this type.