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This post is an answer to the question:
He was 'a third member' or he was 'the third member' Short answer:
A third member means simply: another member (an additional member) and I am referring to him as third because I have already mentioned two other members.
Example 2:
I have a Facebook account. I want to create ___ second Facebook account. Would I say a or the? Hint: I want to create another Facebook account.
Long Answer:
Ordinal numbers mark or designate the position or place (first, second, third, etc) of an item in a ordered series or sequence such as a list.
We can refer to an item's order as either definite (the plus ordinal number) or as indefinite (a plus ordinal number).
A definite reference to an item of a series (example: the third member) marks the member as being third in a determined, definite or known series or sequence. In this case, the third member will be equal to the cardinal number of that member in the series. I.e Example: the third chapter of a textbook or novel is Chapter #3 of that textbook or novel.
An indefinite reference to an item of a series (example: a third member) marks the member as being third in an undetermined, indefinite or unknown (to the listener) series. In this case, a third member does not have to refer to the cardinal number of that member on the list, although it can. Example: a third chapter of a textbook or novel is any chapter in that textbook or novel that is the third-one mentioned in a given context. This is basically equivalent to referring to any member of a series or sequence as another member except that its order of mention is also given.
Thus
>A third member [of the Committee of Public Safety] was the crippled lawyer Couthon
refers to Couthon as the third-mentioned member of an indeterminate or indefinite series. Saint-Just and Lazare Carnot have already been mentioned, and Couthon is now mentioned.
If the narrator wished to refer to Couthon as Member #3 on some determined, definite or known list, she would have referred to him as the third member. But since she refers to him as a third member it just means he is another member of an indeterminate, indefinite or unknown list. Since he is mentioned third in the present context, he is a third member.
In fact, probably 99% of the time you see the indefinite article with an ordinal number and an item name (such as a second season, a third member, a fourth suspect, a fifth person, etc.) you can think of the item as another member (an additional member) of the series, and a count is being kept of that item. But not its place on a determined or known list, but its place on an undetermined or unknown list.
A second season is another season of an indeterminate sequence or list of seasons and I am saying second because I have already mentioned one other season. A third member is another member of an indeterminate series of members and I am referring to it as third because I have already mentioned two other members. A fourth suspect is another suspect of an indeterminate series of suspects and I am saying fourth because three other suspects have already been mentioned. In other words, it just means another member along with the ordinal position it has been mentioned.
Note that, just as when referring to some other noun (example: seashell), the speaker can make a definite (the seashell) or indefinite reference (a seashell) to the same seashell, according to his pleasure or communicative purpose. So, the speaker can make a definite or indefinite reference to the same item of a series or sequence.
Let's take chapters of a book, since this may be easier to conceptualize. If a teacher says:
>Go home this weekend and read the first chapter, the second chapter and the third chapter of 'The Adventures of Tom Sawyer'
the teacher and the students both know that the teacher is referring to Chapter I, Chapter II and Chapter III of 'Tom Sawyer' (TS). How? Because the teacher used the plus the ordinal number. Thus the teacher referred to each chapter as being items or chapters in a definite or known series or sequence. Here that definite or known series is the sequence of chapters in the book. So, the first chapter of 'Tom Sawyer' is the same thing as Chapter I of 'TS', etc.
But if a teacher says
>Go home this weekend and read a first chapter, a second chapter and a third chapter of 'Tom Sawyer'
she is referring to the chapters as part of an indeterminate (undetermined, indefinite) series or sequence. Thus, the students can read any three chapters of 'Tom Sawyer'. And a first chapter can be any chapter of 'Tom Sawyer', and the same for a second chapter and a third chapter. In this case, the ordinal position does not have to correspond to the cardinal numbers of the chapters, although they can. So Betsy decides to read Chapter 17 as a first chapter, Chapter 4 as a second chapter (or: as another chapter and I am saying second because I have already mentioned one other chapter); and Chapter 33 as a third chapter of TS (or: as another chapter of TS and I am saying third because I have already mentioned two other chapters).
As soon as Betsy decides to read Chapters 17, 4 and 33, she has made her own sequence of chapters. And, now pay attention here: Betsy can refer to each item of her sequence as the item of a determinate sequence or as an item of an indeterminate sequence. It is up to her how she does it.
So, she can go back to school and refer to each chapter she read by a or the first, second or third chapter, as she desires. For instance, she can say
>The first chapter I read over the weekend was Chapter 17 of TS.
Here, the first chapter is a determinate reference to the first chapter on Betsy's list. So it must refer to Item #1 on Betsy's list. This is also the seventeenth chapter of TS.
But Betsy can also say:
>A first chapter that I read this weekend was Chapter 33 of TS.
What? I thought the first chapter that Betsy read was Chapter 17 of TS? Well, it was. But Betsy is not referring to the first chapter that she read, but a first chapter that she read, and that can refer to any of the three chapters that she read. And it does not have to correspond to the order she read them in.
Betsy is free to refer to the next chapter she read (<-why did I say 'the next chapter' here? If you can tell me that, then I have done my job of explaining this topic). Anyway, Betsy is free to refer to the second chapter she read as belonging to either a determinate series or to an indeterminate series. If she says
>the second chapter of TS that I read this weekend...
she must be is referring to Chapter 4 of TS, because the second chapter is a reference to a determinate series or sequence, and that list is the sequence of chapters that Betsy read. And the second chapter on that list is Chapter 4 of TS, which is also, of course, the fourth chapter of TS.
If she says
>A second chapter of TS that I read this weekend...
she can refer to any other, or "an other" item on her list that she has not yet mentioned. Note that another used to be spelled as two words: an other.
Confused? I hope not. Let's keep it simple. I have asked on doctor an opinion of what’s causing the pain in my shoulder, but I want to get ____ second opinion. Would a speaker say a or the? Hint, he wants another opinion.
Odds and Ends
Words such as another are considered to be among the ordinal modifiers in English, along with next, last, another, additional, other because like ordinal numbers, they refer to an item's place or position in a series or sequence such as numbered list.
Indeterminate means "Not fixed in extent, number, character or nature; left uncertain as to limits of extent, number, etc.; of uncertain size or character; indefinite, indistinct, uncertain"; "undetermined" (Oxford English Dictionary).
Determinate means "Definitely bound or limited, in time, space, extent, position, character, or nature; definite, fixed; clearly defined or individualized; distinct, as opposed to vague, undefined, or indefinite" (Oxford English Dictionary).
When applied to an item's position on a list, the third item refers to its cardinal equivalent. That is, the third item equals Item number three in a known series.
Does a list item have to exist to be referred to?
No, it does not have to exist.
For example: If Tom is writing a book and he has written the first 14 chapters (which you should know by now, can be referred to as Chapters 1-14) and he decides that the next chapter will be the last one...he can refer to this unwritten chapter as either the fifteenth chapter or as a fifteenth chapter. In this case, it will also be the last chapter that he writes and also a last chapter.
Can we really say A first item or a first chapter? Yes, we can do this, and we often do say it in the saying: There's a first time for everything. A first car, a first girl friend, a first kiss, a first job, a first paycheck... Likewise we can say There's a last time for everything (a last hurrah, a last tango, a last goodbye, a last farewell, a last breath).