Is there a definition for "context"?

Question

What is the/a definition for the term 'context'?

The term is used everywhere, and the dictionaries only give a description of it's meaning.
Definitions for other terms such as concept, perspective, etc, should be derivable from such a definition of 'context'.

To make my question clearer, this question about alternative logics contains the following phrase: "it is rational for anybody that if P is correct then P or Q is correct too": my contention is that this statement is entirely incorrect since the context in which P is correct or not, is not evident, and therefor nothing can be said about "P or Q". I would assume that somehow a context is included tacitly (for the rational bit at least), but for any such tacit context I would be able to propose a context in which P is incorrect or does not apply at all. I would think for any form logic the "context" in which it's statements applies should be well defined, and this brings me to my question: what is a "context"?

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Just a bit more on the P/Q-thing since answers seems to focus on that: if P is the statement "the sky is blue" and Q is "it is a starry night" then the 'wrongness' due to the lack of context is clear. The context must give a definition-space in which the relationship between P and Q exists (going into epistemology here).

Answer 1

The whole idea of logical validity is to divorce form from content; I think what the poster was highlighting is that in formal logic, context is irrelevant. If P, then P; this is true irregardless of context. Since that is true, then "If P, then P or Q" must also be logically true, because we already know P is true, thus it doesn't matter if Q is or not.

What you seem to be getting at, however, is the notion known as philosophical contextualism.

Contextualism describes a collection of views in philosophy which emphasize the context in which an action, utterance, or expression occurs, and argues that, in some important respect, the action, utterance, or expression can only be understood relative to that context. Contextualist views hold that philosophically controversial concepts, such as "meaning P," "knowing that P," "having a reason to A," and possibly even "being true" or "being right" only have meaning relative to a specified context. Some philosophers hold that context-dependence may lead to relativism; nevertheless, contextualist views are increasingly popular within philosophy.

Answer 2

I would suggest you take a look at Jacques Derrida's article "Signature Event Context", which delves into this issue. The key takeaway, for your purposes: there is no rigorous way to define (or limit) context.

As for your example case: when we write "If P if correct, then P or Q is correct", we are tacitly assuming that the context is the same on both sides of the comma. In other words, we are actually saying "If P is correct in a given context, then in that same context P or Q is correct." For example: let us assign "The sky is blue" to P, and "London is the capital of France" to Q. If P is true, then P or Q is true. Arguing that P is true during the day, but not true at night is completely irrelevant; the point is that if P is true at a given point in time (i.e., for a given context), then P or Q must necessarily be true at that same point in time.

Answer 3

I perceive 2 different questions which I think I can answer both.

1: The meaning of context

2: Why "if P is true then P or Q is true" is true

I will start with the second one: In boolean logic, the inclusive or operation (also called OR) evaluates to true if any one of its operands is true. When P is true in an OR operation, the other operands need not be evaluated because OR needs only one true statement. In "P OR Q", whether Q is true or false does not matter because P being true, OR evaluates to true. An alternative case where the value of Q would matter is the exclusive or (XOR), which says "either P or Q but not both". That is not the case, therefore "P OR Q" is true, whatever Q evaluates to (true or false). By the way: "true OR false" is true, just as "true OR true" is...

First question, the meaning of context: The word context has prefix "con", which means "bring together". The "text" is about the syntax, not the semantics. In language, a sentence is a context, consisting of individual words (or pieces of syntax) brought together. When you say "the meaning of something depends on its context", you mean that the semantics vary based on where the piece of logic is situated in the text brought together. In other words, it is situated inside a finite environment composed from its structure, evaluated in that environment, thus yielding a value.

I hope I was clear enough...

Answer 4

The way to define context is to use the foreground/backgeound distinction. If we define the text as the foreground object — the salient object or concept that is the focus of our perception (observation/discussion) — then context is those aspects of the background that affect our understanding of the text. If we are talking with someone they are the text because our attention is focused on them, but all sorts of extraneous factors — location, occupation, intention, mood, time-of-day, etc — influence the nature of the conversation and constitute the context.

'Context' literally means 'with the text', which points at its supplementary nature.

In the case of logic, please keep in mind that elements of context are often built into the structure. For instance, in the proposition:

if P is correct then P or Q is correct

... the first phrase — if P is correct — creates a context. Any case in which P is incorrect falls out of our view and ceases to influence our further discussion. Or put another way, since we have stipulated that P is correct, and there is no possible context in which P is both correct and incorrect, your contention is impossible. Part of the power of logic is that it creates contexts in which particular statements are universal: e.g. within the context 'P is correct', 'P or Q' is always correct. Logic fails when contexts get confused.