# Names within names

Usually when we have an expression, that itself can act as a name, contains an occurence of a 'name' the name that occurs also denotes as part of the containing expression.

For example 'the number 2' contains '2' and in this case '2' needs to denote to inform us which number is being discussed.

The expression '2*1' denotes the number 2, and '2' in this expression must denote the number as well so we understand which multiplication this is the value of.

In the case of 'Brian Cox' I could call him 'Brian' or in a formal setting 'Cox', however in the sentence: 'Brian Cox is an actor' neither the name 'Brian' or the name 'Cox' denote him, it is only the full expression 'Brian Cox' that denotes the man.

Is there a definition of 'name' that allows for this? Is a name an expression that can denote in the correct context?

In the majority of contexts without a 'full name' all most everywhere that expression that is a 'name' appears it will denote in a 'use' (not mention) context. Is this just a consequence of a traditional 'full name' or is there situations where a 'name' does not denote as part of a larger expression that does denote?

• Ok Karen. The use-mention distinction is strong with this one. Jan 13, 2023 at 13:30
• IMO the analysis of "Napoleon Bonaparte" into personal name+family name is not the same as "analyzing" 2 into 1+1... Jan 13, 2023 at 14:24
• @MauroALLEGRANZA I think the biggest difference is that in the case of '2' and '1+1' is that in the latter we are using the 'objects' named to refer to the object based on a fact related to the two objects being named, if we did not know how to add, we would not know that it is denoting 2. In the case of full names, could we treat the first and second name as not denoting? Jan 13, 2023 at 16:06
• @MauroALLEGRANZA Perhaps we need to change the definition of 'name'? Jan 13, 2023 at 16:24
• A name is a word that designates an object (abstract as "president" or concrete as "Nixon"). An object can have zero to multiple different names, which can be used in different contexts ("Jimmy, eat your dinner!", "Bon appétit, Mr. Carter"). Jan 13, 2023 at 19:38

This is not an issue that logicians typically care about because they begin their analysis of language in the post-parsing phase. The issue of how to parse language into meaningful tokens is a part of linguistics, not logic. In logic, they typically assume that the process of breaking down a sentence into phrases of individual meaning has been done and they ignore any issues that might be involved in doing so.

To untangle this issue, first we have to distinguish between a phrase type and a phrase occurrence. In the sentence "John only cares about John", the phrase type "John" has two occurrences. There is just one phrase type "John" in the whole world, but there are many phrase occurrences of "John". The simple term "phrase" is ambiguous as to whether it means a phrase type or a phrase occurrence and you have to figure out which is meant by context. The same is true of other grammatical terms like "name", "word", etc. Sometimes one is speaking of a name or word type and sometimes of a name or word occurrence. English is generally ambiguous about abstract objects in this way.

In logic, a "name" is a phrase occurrence that has no logical parts that have independent semantic function in that occurrence. It doesn't matter if the phrase occurrence has lexical parts so long as those parts have no semantic function in that occurrence, even if in other occurrences those parts do have semantic function. In fact, nothing about the construction of a phrase occurrence is relevant in logic if the phrase occurrence has no parts with independent semantics in that occurrence.

Note that in the above I was using "name" to refer to a phrase occurrence. The word can also be used to refer to a phrase type, and this might be called the lexical sense of the word. In this sense, a phrase type is a name if it is common for occurrences of the type to be used as a name. When you see "Brian Cox" in a sentence, "Brian" and "Cox", viewed as phrase occurrences (that is, just those specific instances in that specific context) are meaningless lexical tokens. Viewed as phrase types (that is, as English words) they are names, because each is a word that can be used as a name in other occurrences.

So, for example in the phrase

I met Brian Cox. Brian said...

There are two occurrences of the phrase type "Brian". The phrase type "Brian" doesn't refer to either occurrence; it refers only to the type. The phrase type "Brian" is a lexical name because it is used as a name in some contexts. Now, as to the occurrences in that example, the first occurrence is not a logical name because it is a meaningless part of a larger phrase. The second occurrence denotes Brian Cox and so that occurrence is a logical name. For the first occurrence, whether "Brian" is a name or not depends on whether you mean the phrase type "Brian" or the specific occurrence of "Brian" in that context.

• If I have a sentence like: 'I met Brian Cox. Brian said...', What would be the role of 'Brian'? It's a name in both senses but not acting as one in the first use? Jan 13, 2023 at 22:31
• @Confused, I think I already answered that question in my answer. Instead of me blindly trying again, it might be more fruitful for you to explain what you find unclear about my answer. Jan 13, 2023 at 22:41
• No problem, you distinguished that in the context of a sentence with 'Brian Cox' as the only denoting phrase that 'Brian' and 'Cox' are not 'names' in the logical sense this just begs the question what if I have a sentence where both 'Brian Cox' and 'Brian' or 'Cox' are used as a denoting phrase as well, what happens to them in that case? For example: If I say 'Brian Cox' and then use 'Brian' later on in the sentence? Jan 14, 2023 at 11:20
• @Confused, OK, I modified the answer in order to hopefully address your question. Normally the difference between type and occurrence is left implicit, but your confusion seems to revolve around that distinction. Jan 14, 2023 at 17:00
• Fair play on that respone, thank you Jan 14, 2023 at 22:04

It's simple math actually, in me humble opinion. There are a finite number of names; let's say a hypothetical world in which there are only 3 names; A, B, C.

Scenario 1 Only a first name allowed. Only 3 people can have distinct names; the fourth person will need to reuse a name e.g. A, B, C, then A or B or C ... so and so forth for the rest of the peeps.

Scenario 2 A last name allowed e.g. AB, AC, etc How many unique names are possible now? For simplicity's sake assume names like John John are allowed. There are 3 × 3 = 9 unique names possible. We can give more people distinct names.

Scenario 3 A first name, a middle name, and a last name allowed. 3 × 3 × 3 = 27 unique permutations/names possible. Less chances of getting people mixed up.

Relevant Factors

1. How many different first, middle, and last names are there?
2. How many people are there (population)?

Linguistically, the last name identifies the stock/family and the first name picks out the individual. Very similar/identical to the genus & differentia format for definitions.