# Discrepancy between Classical Logic, Set Theory, Propositional Logic and Languages [closed]

In logic, "Or" strictly refers to logical disjuntion, while "And" strictly refers to logical conjuction.

But in common parlance, both can fill the role of Logical Disjunction

I understand that one should not use logic when talking to people because they may not understand you; but one needs to come clear and context does not always help. One should instead be redundant and repetitive.

When ambiquity arises (i.e. context does not help), how can you know what the person meant if you are unable to ask them to clarify it (e.g. it's written material, the person refuses to explain as they think logic is illogical and nonsense and that what they said was obvious, or any other reason)?

• You can't know, under those circumstances. That's the point of ambiguity. Language is not logic, and it does not always work. Neither does logic. We just have to do the best we can. Oct 12 '19 at 22:27
• @jlawler That is the whole point. Solving the problem that is ambiguity. Oct 12 '19 at 22:45
• It's not a problem so much as it is a feature. Ambiguity can't be "solved", or even avoided, any more than entropy or gravity can. One can solve individual problems involving ambiguity; but there is no general solution. Understanding requires interpretation and presupposition by both speaker and addressee, and there is no correlation between them, except in individual cases. Oct 13 '19 at 17:49
• "... but not concurrently both." as far as I can tell or means xor or and. of course that hinges on your definition of or. get it? Oct 17 '19 at 15:15
• @vectory Or does not mean And. en.wikipedia.org/wiki/Logical_conjunction en.wikipedia.org/wiki/Exclusive_or en.wikipedia.org/wiki/Logical_disjunction look at the Venn diagramms. My problem is that both Or and And can be used to mean Logical Disjunction. Each has a distinct function but both can fill the role of Logical Disjuntion. Oct 17 '19 at 15:26

There are two different answers, depending on the environment.

In certain contexts (logical formulae, programming languages, legal documents, Magic: the Gathering cards), avoiding ambiguity is very important. So in these contexts, there'll be some external rule that tells you how to interpret ambiguities. For example, in Magic: the Gathering rules text, "or" is an exclusive disjunction; an inclusive disjunction will be written "choose one or more". In C++ source code, "or" is an inclusive disjunction; an exclusive disjunction will be written "xor". This will be laid out in some sort of authoritative reference document that you can consult when needed, such as the C++ Standard.

In all other environments, context should make it clear. If context doesn't make it clear, you can request more context (e.g. asking a waiter in a restaurant whether you can choose both sides, or only one). This falls under a branch of linguistics called pragmatics, and pragmaticists have come up with various formalisms for how people determine these things (most famously Grice's maxims).

• Would man made clasifications; i.e from Authorities like some Academy, Society, University fail? Would adopting Logic in Languages fail? Oct 12 '19 at 22:48
• @GeorgeNtoulos There's no central authority that decides how language is used. (Some authorities try, but they're never all that successful.) 99% of the time, the way language is used is the product of thousands of years of evolution; in English, distinguishing between inclusive and exclusive disjunction was never evolutionarily advantageous enough to show up and/or stick around.
– Draconis
Oct 12 '19 at 22:55
• And that is where law comes into play. Law is forceful, violent and external. Someone else imposes the rules. I was asking if it would pose a problem if the Authorities simply decided that for official documents, media and education purposes the language is like this with the penalty of nulification(of the document) expelling the teacher, fines for the media. if one goes against the rule. Oct 13 '19 at 10:35
• @GeorgeNtoulos As I said in my answer, laws and contracts already have specialized rules for removing ambiguity. If people actually found the distinction necessary in everyday life, they'd use it.
– Draconis
Oct 13 '19 at 17:41
• @GeorgeNtoulos Your ideas of what English-speakers should find necessary don't seem to align with the 1.5 billion people who actually use the language. It's like saying that it's necessary for all fish to walk on land, getting confused when evolution hasn't gone that direction, and insisting on a massive engineering campaign to move all fish out of the water and onto land. If it were actually necessary, it would have happened through natural evolution. It hasn't.
– Draconis
Oct 13 '19 at 18:05