Non-Logical Conditionals: The Alogical Use of 'If...Then'

NORMAL LIFE EXAMPLES

Normal language is more vague than mathematical language, and so in normal language “if ... then ...” can signify some other things, as we mentioned above. So just because there’s an “if ... then ...” in a sentence, it doesn’t necessarily mean there’s a logical implication.

The difference between formal logical language and informal real-world language is something that we will come across repeatedly as it is a source of a great deal of confusion, both about logic and about the real world. The primary aim of normal language is communication, whereas the primary aim of logical language is to eliminate ambiguity. These are not mutually exclusive aims. When we communicate, we try to do it as unambiguously as possible. And when we are trying to eliminate ambiguity, we are usually doing it to try and communicate more clearly. But normal language communicates with the help of context, body language, intonation, human understanding and so on. Logical language does not have the benefit – or confusion – of any of those things. “If ... then ...” can only mean one thing in logical language, but in normal life it depends on the situation.

All of these varied uses of “if ... then ...” are not exactly logical but they’re not exactly illogical either: they don’t contradict logic, they just aren’t governed by it. The English language seems to lack a way of making this distinction, so we might say “non-logical” (although it’s a bit clumsy) or “alogical”, like apolitical, asexual or atheist. One of the points I will keep coming back to is that you can be alogical without being illogical, and indeed being alogical is unavoidable and sometimes beneficial or even crucial, whereas being illogical is undesirable.

So much for things that are not logical implications. What counts as logical?

“If you have white privilege then you have privilege.”

This is a logical implication, because it comes from the inherent definitions: white privilege is one specific form of privilege. More contentious is this:

“If you are white then you have white privilege.”

If we acknowledge that white privilege exists, then I do think this is logical. Perhaps in order to make it hold we need to be more specific about the context:

“If you are white in Europe or the US then you have white privilege.”

or perhaps more obviously.

“If you are white in a place that has white privilege then you have white privilege.”

You might think that the last deconstruction has become a bit pointless, and you have a point. The closer to a purely logical implication we get, the more obvious it should sound. This is the aim of finding the logic inside an argument: to make it more obvious.

However, although some people think this last statement is obvious, it is still contentious: some people claim that white privilege doesn’t apply to them, only to richer white people. They are using a different definition of “white privilege”. In Chapter 6 on relationships we will discuss the sense in which all white people have privilege, and the sense in which some white people are still lacking privilege for other reasons. The language itself is problematic as it is open to being used in so many different ways.

If we continue to use normal everyday language we are doomed to have problems being completely logical because the words we use are not completely logically defined, but we can get close enough that to call it anything other than logical would, in my opinion, be pedantry rather than precision. We’ll now try finding the logical implications inside a different contentious argument.