Problems with definitions


In this very short essay I will argue that certain words cannot be defined by other words, and that certain words cannot be defined by bodylanguage. And if these two methods are the only methods for defining words, then words that cannot be defined by both methods cannot be defined at all. Then I argue that they are somehow defined anyway.

Good definitions

There are a couple of principles which we employ for making good definitions. I’ll give an example of this:

Simplicity principle. The definition ought to be as simple as possible.

But there is at least one strong principle, that all definitions must abide to be useful. It’s similar to the idea that circular logic is useless:

Non-circularity principle. The word we are defining cannot be used to explain what it means.

It doesn’t matter if it’s directly or indirectly used in its own definition. By ‘indirectly’ I mean a word is defined by using a synonym of itself and that synonym is defined by using the word we’re trying to define.

E.g., Suppose that ‘hard’ is defined as ‘tough’ and ‘tough’ is defined as ‘hard’, then we have indirectly defined ‘hard’ in a circle.

Definition of ‘definition’

How would one go about defining ‘definition’? There seems to be only one way of defining something directly using words is “I define ‘X’ as ‘Y’”. One might object that there is another way, for instance “When I use ‘X’ I mean ‘Y’”. But this is simply a synonymous expression, and in that sense it’s the same way. When prompted for a definition of what ‘mean’ means in that context, how would one define ‘mean’ without using the word ‘definition’ or the word ‘mean’? I suppose that there could be other ways, but I also suspect that these are synonymous expressions and not real alternatives. There is no way to define something without using the meaning ‘this means that’, however one would use words to give that meaning.

Definition of ‘thing’

All languages contain at least a word for the basic unit of the language. The basic unit is presumably defined as ‘whatever one can talk about’, but this begs the question as we shall see.

I think that the English word for the basic unit is ‘thing’ or perhaps ‘object’. Evidence of this is in the language: something, everything, nothing.

We can try to get around the limitation of language by using pronouns like: that. So, we could hypothetically attempt to define thing as this ‘That which is existent’. But the word ‘that’ is not meaningful on its own. It refers to the basic unit, which is ‘thing’, so when we say ‘That which is existent’ we mean ‘something which is existent’. So our definition is ‘A thing is something that is existent’ This is circular.

Defining indirectly by using words

We can also define words indirectly by using words. The method goes like this: Keep giving examples and how that the other persons “gets it”. I don’t see any way to use this to define the above two examples.

General problems with defining

I know that there are at least two methods of defining something: 1) with other words, and 2) with body language. The latter is typically done by pointing at the object when saying the word. We use this method when learning babies the names of things.

Given that these are the only two methods of defining something one can construct this argument:

W := A particular word.

1. If W is defined, then it is either defined with other words or it is defined by using body language. (premise)

2. W is not defined with other words. (premise)

3. W is not defined by using body language. (premise)

4. W is not defined. (1, 2, 3 note that I skipped a conjunction step)

As we have seen, some words are not possible to define by using language. I will now argue that abstract things are not definable by using body language. First, let us examine what body language can define.

Body language

The easiest definable thing by using body language is a noun. The method is basically this: Say the word for the thing and “point” at it. Pointed is to be understood broadly, so that showing a thing to a person is also a form of pointing. This method works and we use it a lot in practice.

It is also imaginable that numbers in the lower end can be defined by using body language. Suppose I keep saying “two” and then keep pointing at objects that there are two of. I think that people will in general “get it” and infer that I’m not talking about the objects in particular but the amount of objects. I think that all the other natural numbers can be defined by using the lower numbers. It may be necessary to alternate between objects that there are two of and objects that there are some other number of. This is because that the person might otherwise infer that we’re defining a word for everything. Which gets us to the next part.

I showed earlier that it is troublesome to define “thing”, by using other words. However, I imagine that it is fairly easy to define by using body language. The idea is to just keep pointing at something and say “thing”.

My skepticism lies with defining very abstract things with body language. One example is ‘definition’. That seems not possible to define by using body language. I imagine that the “logical connectors” would be hard to define also (e.g.: ‘and’, ‘or’, ‘if/then’, etc.) or the quantifiers (‘all’, ‘some’, ‘none’).

Further thoughts

It seems that words that cannot be defined by other words or body language, cannot be defined at all. But yet, we observe that people do know the meaning of these words. We, therefore, seem to have hit a problem. One theory is that some meanings are defined by evolution; defined in the genes.