Tag Archives: logic

What’s logical about English?

A common complaint about English – by those who are inclined to complain about English – is that it’s not logical enough. Whatever that means. Words aren’t premises and sentences aren’t syllogisms, after all.

If you inspect the targets of their opprobrium, you find soon enough that what they mean is that English isn’t tidy enough for them. It’s inconsistent. Lacking in symmetry. Their experience has led them to believe that for every up there should be a down, for every in an out; when they see an over, they think “therefore under,” and if there is no under, they are… underwhelmed.

They’ve condemned themselves to a lifetime of disappointment. English does not satisfy their need for an overarching tidiness. It is not a Zen garden; it is a forested mountain, every tree grown unplanned in its place and conditions, every rock where the ineluctable complexities of physics left it. It is not an edifice of modernist design with proportions based on the golden mean; it is a Winchester House of a language, a veritable Heathrow Airport of accretions (for those who have not been to Heathrow, let me just say I suspect that J.K. Rowling based Hogwarts on it). Like any natural language, English has been built up by habit, need, association, and analogy. It does have structure – in fact, it has some inflexible syntactic requirements. We have slots to fill, and fill them we do. We just sometimes grab whatever’s ready to hand to fill them.

Let’s consider a few examples. One case where a desire for logic has actually prevailed is “double negatives.” Anyone who has studied logic will tell you that in “not not” the second not undoes the first one. “There will not be cake” is disappointing; “There will not not be cake” is affirming. Thus, the reasoning goes, “I do have nothing” and “I don’t have nothing” are opposite. But anyone who has learned a Romance language ought to know ça ne vaut rien, no vale nada – that ain’t worth nothing.

Nothing, you see, is not not. It’s a noun, not an operator. And one thing languages like is agreement. Concord. Adjectives tend to take the same gender as the nouns they modify, for instance. In English, we use concord with tenses in some contexts: “Should we expect them tomorrow?” “They said they weren’t coming.” Notice how we use weren’t even though we’re talking about the future? We even let negative concord pass unremarked in some contexts: “They won’t be coming, I don’t think.” This doesn’t mean I don’t think they won’t be coming; it just retains the negative aspect.

But since it’s possible, with shifting emphasis, to make “There ain’t no one here” and “There ain’t no one here” mean opposite things, an argument can be made for disallowing negative concord for the sake of unambiguity. So the proscription stuck, defended by pleas for logic – although “if negative noun, then negative verb” is perfectly reasonable if that’s the rule in the language.

Syntax has its requirements – as linguists would say, there are principles and parameters that specify how it functions in a given language. Negative concord is one parameter we have managed to turn off. Others are not so easily disabled. It’s necessary to have an explicit subject (except in imperatives), for instance; I can’t write “Is necessary to have an explicit subject,” so I stuff in an it that has no meaning. It may not seem logical to have a pronoun with no referent, but consider that, from the view of our syntax, “if it has a sentence then it has a subject” is solid. Sometimes we grab and stuff on the fly – we may jam a word in the place where a word like it normally goes, even if in this case it’s a whole nother thing and what even were we thinking? This, too, comes from a simple if-then – just a little simpler than it might have been.

Another plea for logic comes when a word is pressed into service in a way that seems untidy. One I saw recently was an objection to using disconnect as a noun, as in “There is a real disconnect between the labourers and the management.” We don’t say “There is a connect between them,” we say connection, so it’s illogical not to say disconnection. Indeed, this is untidy, in the same way as it’s untidy that when my wife is at home I heat two servings of food and pour two glasses of wine, but when she’s not at home I heat one serving and open a beer (or go out for sushi). But our little untidinesses have reasons: my wife doesn’t drink much beer and doesn’t like sushi. And disconnect is an allusive use borrowed from electronics and telephony.

A line of communication is expected to remain connected, so there is no instance where we would say that it has experienced a connect. We grabbed a bit and stuck it where it fit, and in so doing made a metaphorical connection. There’s no need to construct a symmetrical positive use any more than there is a need for a 33-storey building to have 33 levels of basement. And there’s no need to disallow allusions just for the sake of tidiness – we don’t forbid lights on Christmas trees just because there are none on the house plants. If you want to make a connection, you make it; if you don’t, you don’t. That’s logical, no?

Some people also like to laugh at how “illogical” English words are. “Why do our noses run and our feet smell? Why do we park in a driveway and drive in a parkway? Why do we say a bandage was wound around a wound? How come you can object to an object?” OK, now tell me why these are illogical.

Every one of them comes from a well-motivated historical development founded on consistent principles: metaphor, ergativity, historical sense developments and standard compounding rules, phonological shifts, stress-based differentiation of nouns from verbs. In every case there was an if-then judgement based on analogy. It just happened not to be exactly analogous to some other if-then judgements, and it produced results that seem inconsistent when juxtaposed. I think that’s fine – why not have funny things? But more than that, it’s not even illogical. In every case, we got to it from “if A → A´, then B → B´.” They just happened to be local judgements made in the context of a big, multifarious, inconsistent world.

But it would be illogical to treat a multifarious, inconsistent world as though it were elegant and pervasively consistent, wouldn’t it? It certainly wouldn’t be well adapted. It would be like laying down a strict grid street plan for a very hilly city (and San Francisco knows how well that worked out). It wouldn’t be as much fun, either. And it might do real harm.

This statement is false

Last weekend my brother and I were discussing the statement “This statement is false.” Today a colleague mentioned a similar statement, “The following statement is true. The previous statement is false.” Another colleague likened this kind of pure self-contradiction to the Cretan paradox, also known as the Epimenidean paradox: the statement “All Cretans are liars” said by a Cretan, which would seem to be a false if it’s true and true if it’s false.

But the difference between the Cretan paradox and pure self-contradiction is that the Cretan paradox has a real-world referent. It makes a statement about something external to the assertion. Pure self-contradiction has no real-world referent. It makes an assertion about nothing other than itself and thus has no truth value ascertainable.

As it happens, the source of the Cretan paradox is something Epimenides wrote in support of the immortality of Zeus:

They fashioned a tomb for thee, O holy and high one
The Cretans, always liars, evil beasts, idle bellies!
But thou art not dead: thou livest and abidest forever,
For in thee we live and move and have our being.

Epimenides was himself a Cretan. Thus we know through simple pragmatics that he must have been excluding himself without saying so. To treat it as a paradox is to be disingenuous. It’s fun sport, but in the end it just shows one of the things you can’t do in logical reasoning.

Statements such as the Cretan paradox are an illusion caused by conflation of one level of analysis with a higher level of analysis: an evaluation of the members of a set cannot itself be a member of the set evaluated; evaluation is a comparison of something against one or more criteria from an external perspective – what is being analysed is subsumed within its perspective. Once we acknowledge that the statement “All Cretans are liars” cannot be part of the set of statements evaluated (making it thus a simple problem in pragmatics rather than a trick of logic), we identify an unstated assumption that makes it function, without which we get a sort of Escher staircase illusion, something that can’t exist in the real world.

But with mutually evaluative statements such as the pure self-contradictions, each must be on an evaluative level above the other – each must subsume the other within its perspective. And at the same time each has no further reference; it has no claim to truth or falsehood as the set of all other statements by Cretans does (and as that set’s members individually do).

Analyzing an utterance or set of utterances is like weighing an object. In order to weigh an object, you have to lift it (or anyway support it) and you have to be resting on something that is not part of what you are weighing. In the Cretan paradox, we see that the statement that pretends to be part of the set of Cretan statements is actually weighing them and so cannot be part of them; it is evaluating them against their real-world references – that’s what it’s resting on. In the mutual contradiction case we’re looking at, each is weighing the other, and neither rests on anything else, because neither is being evaluated against anything external to itself. It’s like two dudes trying to lift each other simultaneously. In empty space.

Meaning in human communication, ultimately, is not a question first of all of logic; it is a question first of all of pragmatics. All communication is behaviour; when you utter something, you are doing something with the aim of producing a certain effect. The person hearing you will be conjecturing what effect you are trying to produce and responding accordingly. Logic helps serve this function, but pragmatics is the true basis. And the pragmatic value of things such as paradoxes is sport – mental play, fun. And a demonstration of the invalidity of certain kinds of reasoning.