If A or B, then C. A,B are what?

April 5, 2007 11:31 AM

Vocabulary filter: if items 1,2,3,4 together bring about A, then 1,2,3,4 can be called the "prerequisites" of A. If any one or more of 1,2,3,4 bring about A, but not necessarily all, what name would I use for 1,2,3,4 ?

It's a boolean logic thing. "(1 AND 2 AND 3 AND 4) -> A" and I can say the elements of the set (1,2,3,4) are requirements, or preconditions, or necessities, or prerequisites, or... of A.

However, "(1 OR 2 OR 3 OR 4) -> A" and I'm stumped for a name for the elements of the set (1,2,3,4). The term "optional requirements" doesn't imply that at least one of 1,2,3,4 are required. The statement "A requires any one of 1,2,3,4" is valid, but that doesn't give me a succinct noun to use.

posted by Mozai to writing & language (24 comments total)

Causalities?
posted by zebra3 at 11:38 AM on April 5, 2007

If (1 AND 2 AND 3 AND 4) for A to be true, than 1 and 2 and 3 and 4 are all necessary.

If (1 OR 2 OR 3 OR 4) for A to be true, than 1 and 2 and 3 and 4 are all sufficient.

When you say "but not necessarily all" do you mean that (for example) if 1 then A and if 2 then A but if 1, 2, 3 and 4 then NOT A?
posted by Aloysius Bear at 11:38 AM on April 5, 2007 [1 favorite has favorites]

precursors?
posted by chrisamiller at 11:40 AM on April 5, 2007

right. i think these are called predicate variables, and the necessary/sufficient distinction is, as explained above, best understood through the and/or distinction.
posted by phaedon at 11:41 AM on April 5, 2007

"(1 AND 2 AND 3 AND 4) -> A" and I can say the elements of the set (1,2,3,4) are requirements, or preconditions, or necessities, or prerequisites, or... of A.

Uh...no you can't, at least not in English (and I don't remember this terminology from when I took logic). Just because 1, 2, 3 and 4 all imply A doesn't mean that they *alone* imply A.

If A->B, B is a consequence, that much is true.
posted by DU at 11:43 AM on April 5, 2007

yeah, well, i don't agree with you DU, but then i again, i slept through most of propositional logic.
posted by phaedon at 11:44 AM on April 5, 2007

In philosophy, at least, "necessary condition" and "sufficient condition" are the terms we use. Aloysius Bear nailed the definitions. They are a little jargon-y, but I don't know of a more common-sense word that'll be unambiguous.
posted by nebulawindphone at 11:44 AM on April 5, 2007 [1 favorite has favorites]

nebulawindphone: are you by any chance related to david velleman? not a big fan of kantians, but he rocks. *tip of the hat*
posted by phaedon at 11:48 AM on April 5, 2007

I don't mean to be ungrateful when I say I asked for a noun. "sufficient" is an excellent word, but it's an adjective.

I could say "sufficient conditions," but I will hold out for a more succinct name.
posted by Mozai at 11:48 AM on April 5, 2007

I do realise necessary and sufficient are adjectives. But "necessary condition" and "sufficient condition" are, by quite a wide margin I think, the most widely-understood terms.
posted by Aloysius Bear at 11:51 AM on April 5, 2007

Correctied: "all the elements of set (1,2,3,4) are a requirement of A." Satisfactory, DU?
posted by Mozai at 11:52 AM on April 5, 2007

You could use "[necessity|sufficer] for A" if you're set on noun forms, but necessary and sufficient conditions are the established ways of saying this.
posted by adamrice at 11:55 AM on April 5, 2007

OK, so you are looking for a term for the entire group of 1, 2, 3 and 4 when any one of that set is sufficient to bring about A. I guess I would just call it a "set of sufficient conditions", but that's not too clear. If you want a name that can be applied to each, I agree that each of them is definitely a "sufficient (but not necessary) condition" but that's hardly succinct.
posted by DU at 11:56 AM on April 5, 2007

I had also immediately thought of "necessary/sufficient conditions". Not sure you're going to be able to find a noun with the same meaning, but I wish you luck.
posted by vorfeed at 11:56 AM on April 5, 2007

so obviously, nobody's down with necessity and sufficiency.
posted by phaedon at 11:57 AM on April 5, 2007

Put me down as another vote for necessary/sufficient causes. No other terms are both concise and widely understood to signify the distinction you describe.

However, in the case of (1 OR 2 OR 3 OR 4) -> A, you can get away with saying that 1,2,3, and 4 are causes of A. If each independently produces the effect A, then it is a (sufficient) cause - but in common usage most people just drop "sufficient." The fact that there are other causes is a red herring.

(Traffic jam, flat tire, oversleeping, getting lost) --> being late for work. Each of these things is a cause of being late for work; thus the set is a list of causes. And as such, they can be distinguished from necessary conditions.

But seriously, necessity/sufficiency is the way to go here.
posted by googly at 12:12 PM on April 5, 2007

If it is a "writing and language" question--not math, formal logic, legal reasoning-- then simplify.

Each is "a cause."

The problem you're having seems to come from trying to aggregate them. Collectively, they are "causes", or, if you want to stress their independence, "some causes." Not interdependent, not joint, just..."causes." "Cause" incorporates the concepts of necessity and suffiency.

BTW, "causality" refers to the relationship between a cause and an effect. "Cause" refers to the thing itself.
posted by Phred182 at 12:12 PM on April 5, 2007

Well that's just spooky.
posted by googly at 12:15 PM on April 5, 2007

Cause/causes?

1, 2, 3, 4 are all causes of A. 1 is a cause of A, 2 is a cause of A, etc.
posted by anaelith at 12:19 PM on April 5, 2007

(Dammit, preview button, why must you mock me so?)
posted by anaelith at 12:19 PM on April 5, 2007

I think googly is brilliant.


Note to self: skip the last spelling check and just post.
posted by Phred182 at 12:34 PM on April 5, 2007

Off the top of my head, I would probably say "independently sufficient conditions" or "individually sufficient conditions", but I don't know any particular term that's standard for the situation you describe.

Reading the comments, I note that you particularly want something succinct. "Sufficient cause" and "cause" are both good options.
posted by coined at 1:56 PM on April 5, 2007

What about "alternative prerequisites"?
posted by Jabberwocky at 2:39 PM on April 5, 2007

"Causes".
posted by orthogonality at 3:51 PM on April 5, 2007