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When using a single letter as a noun for the first time, do we need to use an article before it? if so, what article should be used?

Example:

Suppose that [a/the] belief p is formed based on sufficient evidence.

If by naming it we somehow turn it into a proper name, we shouldn't use any article for it. If by naming it we make it definite, then we should use "the". Otherwise, we should use "a" for it. So which one is it?

  • Either "A person, Lewis, walked into the room" or "Lewis walked into the room", not "Person, Lewis, walked into the room". "Lewis" here is an alternative phrasing for "A person". "Person" is not a proper noun, therefore it needs an article. – AndyT Jul 20 '17 at 15:34
  • The fact that we are discussing a variable has nothing to do with it: Suppose that a box contains a cat or Suppose that the box contains a cat These are both correct in different contexts. – Jim Jul 20 '17 at 16:26
  • As an aside, I find the choice of the letter P here a little uncomfortable. It suggests that P is a proposition and not a belief. It may be that you really mean to refer not to the belief P but the belief that P. If P really is the belief itself, it may be more natural to use another letter, the obvious candidate is B. – Steve Lovell Jul 20 '17 at 16:27
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According to the APA style guide, variable names should be italicized, but otherwise incorporated into text as usual. In your example, p is definite so I would either use "the" or no article at all. I don't have an authoritative source on this, but referring to "a variable x", "the variable x", and "variable x" are all valid forms of discussing a variable in math lingo (context permitting).

We found that x increased where y > 1 (we found that the x increased is wrong here)

We found that the x values had a strong exponential correlation to y

https://owl.english.purdue.edu/owl/resource/560/22/

  • What do you think about @Andy 's comment above? – Sasan Jul 20 '17 at 15:48
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Part of the problem is that you've given us an example that isn't representative of dialog or narrative. It looks like a sample from a technical paper. The rules often change slightly when you move into the technical world. In that world, variables often omit the article.

(1) Suppose that the belief P is formed based on sufficient evidence.

and

(2) Suppose that a belief P is formed based on sufficient evidence.

and

(3) Suppose that belief P is formed based on sufficient evidence.

...are all basically synomymous. But, having written in both worlds, there are subtle differences. Example (1) suggests having previously introduced P, but you said this is the first occurance of the variable, so that's not it.

Example (2) suggests that the belief P represents has not been introduced.

Example (3) suggests that the belief P represents has been introduced.

So the real question here is whether or not you have previously introduced the belief represented by P.

  • It is said in the question that I am using "belief p" for the first time in the article. – Sasan Jul 20 '17 at 23:11
  • @Sasan: Specifically, "P" is used for the first time in the article. Thus, regarding my example (1) I said, "...but you said this is the first occurance of the variable...". Examples (2) and (3) are about whether or not the "belief" that "P" represents has been previously introduced. If what I said does not make sense, then how you're using the phrase "belief P" must be substantially clarified. Is "P" a variable refering to a belief, or is "belief P" a compound proper noun? – JBH Jul 20 '17 at 23:54
  • That is part of the question; Does naming it with a letter make a noun a proper noun? – Sasan Jul 21 '17 at 14:12
  • No, naming an object with a variable name does not make the compound variable a proper noun. As I say in my answer, the use of a variable invokes its own set of grammar rules. Given the conditions of your question, you would use either the sentence forms of examples (2) or (3) depending on whether or not the belief "P" represents has been previously defined. You don't mention whether or not that has happened in your question. – JBH Jul 21 '17 at 15:17
  • If belief p is not a proper name, how can I use "belief p" with no article? – Sasan Jul 21 '17 at 21:18
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This is interesting. In algebraic set/group theory, one might well have a defined class of sets named "p" where there are many distinct such sets but all have the required collection of parameters to be a class "p" set. In this instance, you would write "suppose that a set of type "p" ..." because we haven't identified a specific set.
If OTOH we have sets a through z but only one of each, then of course you'd write "... the set "p" ..."

  • ack; @JBH posted essentially the same thing before I could click "post" – Carl Witthoft Jul 20 '17 at 15:50
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    ;-) Great minds think alike! – JBH Jul 20 '17 at 15:56

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