Thursday, April 28, 2005

Language and Logic

In my blog on Proper English, I noted that nonstandard varieties that express Standard English`he isn't going anywhere' with "he isn't going nowhere" differ in that Standard English uses the morpheme "any" to mark quantifiers that are in the scope of a negation whereas nonstandard varieties use the more iconic negative form "no." Phil objected on the grounds that "[he] isn't going nowhere' compels him to be on his way to somewhere'." Phil is judging this dialect by the truth-conditional standards of a formal logical system like the propositional calculus according to which the truth-table for "not" and "no," etc. has it that "not P" is false if "P" is true and therefore that "not not P" entails "P.

A fatal flaw with Phil's position is that I have never found anyone who does not understand a nonstandard form like "I ain't gonna go nowhere." Everyone who speaks Standard English knows that sentence means "I am not going to go anywhere." Ergo, saying "[he] isn't going nowhere' compels him to be on his way to somewhere'" is flatly wrong. That is not what what he said means and we all know that.

Phil's idea that we should hold dialects of English to the truth-conditional standards of formal logics is widely held I suspect. For some reason, though, when I was first taught logic and was given the "translations" of English sentences into the propositional calculus, I instinctively took the opposite position. What was being told to me didn't square with what I knew as a speaker of English. I don't recall having a specific problem with the truth table for "not" but I did have a problem with that for "if." (In fairness, logicians now almost invariably do not represent their translations as doing justice to English. Some were not so circumspect back in the day.)

So, one important respect in which English does not act like the propositional calculus is that it doesn't obey the law of double degation -- namely that two negatives make a positive. Another respect in which English proves to be different from the sort of logical calculi we learn in introductory logic courses involves universal quantifiers ("all," "every," "any," etc.) If your kid says, after you have turned down his/her request for permission to go to the mall, "But everyone will be there," he/she does not mean everyone in the world will be there or even that everyone in his/her school will be there but, rather, something like `everyone of any importance to him/her will be there.' As a result, we must conclude that English universal quantifiers like "every," unlike those of the predicate calculus, are typically restricted quantifiers -- usually restricted to aspects of the context.

The interesting thing about "any" is that it pops up as an indefinite pronoun in "if"-clauses ("If anyone comes to your party, I'll be surprised") and questions ("Is anyone going to the party") as well as in negative sentences in Standard English. Were there some deep connection between negative sentences, conditional clauses, and questions then we might fault the nonstandard dialect by its failing to appreciate this deep connection. The problem is that there isn't any such connection either syntactically or semantically.

As I noted earlier, it was the translation of "if" that threw me as a speaker of English. The analysis according to which "if P, then Q" is true in every circumstance except when "P" is true and "Q" is false as the truth-table of the earlier link makes clear, then we must accept as true that "if P, then Q" is true if "P" is false and "Q" is true and if both are false. There are forms that seem to support the former case, such as "If you're hungry, there's food in the fridge." These are what are calleed "biscuit" or "funny" conditionals and I shall doubless blog on about these at some point. However, the idea that all that is required to make a conditional true is a true consequent is, as a general rule, quite silly for there is something very wrong with "if I were a woman, the earth would be round" or "if Jello were Spam, then beef would be chicken."

Still another standard logical analysis that struck me as problematic was the very long standing veiw that "unless = "if..not" i. e., "I will leave if you don't leave" = "I will leave unless you leave." This is a spectacularly bad idea that only a logician and his/her mother could love.

In my dissertation, "Adverbial Subordinate Clauses in English," I studied a variety of adverbial clauses (e. g., "when"-clauses, "where"-clauses, "before"-clauses, etc.) as well as a variety of conditional clauses. Though written in 1971 it seems to be fairly frequently referred to in the literature today (as one can tell by googling my name and the dissertation title). Check out the title link is to a paper I found that must have been written by my buddy Bill Lycan which addresses my views of conditional clauses among other things.

To make a long story short, I gave an analysis of "unless," "if," "only if," and "even if" in a paper called "If and Unless" that is pretty hard to get ahold now that developed ideas in my doctoral dissertation, which were further developed by a long time friend and former OSU colleague, Bill Lycan, and me in writing a book which we ultimately chose not to publish largely because we didn't want the aggravation of trying simultaneously to please both linguists and philosophers. Fortuantely Bill redid the book for a purely philosophical audience some years later, publishing the result as Real Conditionals. It includes my basic syntactic and semantic views and our joint journal article on "funny conditionals."

The claim we make, if I may simplify a bit, is that "I will promote you to full professor if you can get your next book published" means something like `I will promote you to full professor in any (relevant and reasonably expectable) circumstance in which you can get your next book published.' That is, conditional sentences require for their analysis a restricted universal quantifier ranging over relevant and expectable circumstances. Note that should the professor of this example publish his book but at the same time get caught having sexual relations with an underage coed, he would likely be fired and reported to the police. He would certainly not be promoted. However, I will not have rendered my conditional promise false. The antecedent was true and the consequent false, which, as we have seen, makes conditionals of the propositional calculus false, but my conditional was not false since the restricted quantifier came into play in a critical way. Circumspect behavior by the professor was clearly relevant to my conditional and his having sexual relations with an underage student was clearly unexpected.

These three examples -- perfectly reasonable double negation in nonstandard English (and French), the fact that English universal quantifiers are typically restricted, and the fact that the logical analysis of "if" falls flat on its face -- ought to establish that English isn't a logical language which is intended to facilitate valid deductions but is rather a langauge intended to facilitate human communication.

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Blogger Marc André Bélanger said...

One of the problem of positing formal logic standards to language is that words like "not" are not as precisely defined, in real life, as in logic.

French here is interesting. One could say, in French, either « Il ne va nulle part. » or « il va nulle part. » Both «ne» and «nulle» are understood as negatives. But, in fact, they are not really like the logicians "not". The usual French negative, «pas» actually has an interesting history. It use to be that the difference was between « Il n'avance » ("He isn't going forward") and « Il n'avance pas » ("He isn't going forward at all"), where «pas» was the word for "step"; the second sentence meant something like "He's not taking even one step". With time, «pas» became the "dominant" negative; and now we have « Il n'avance pas » (more formal) and « Il avance pas » (more familiar).

With two "negatives" there's always one which is not a negative per se, but a sort of augmentative.

12:11 PM

Anonymous Anonymous said...

On another note, if you analyze statements with OR in terms of formal logic, you can answer them with yes or no, which is usually never expected or useful.

E.g., "Would you like tea or coffee?"
"Are you going now or later?"

The logician may answer "yes" for either, if one statement at least is true. That's obviously not what the questioner wants.

3:06 PM

Blogger The Language Guy said...

Masecorc Andre, I don't know French well enough to comment on the view that the "extra" negatives in French are augmentives. They are not really augmentatives in nonstandard varieties of English but are also not true negatives.

And, Pekka, you are quite right about this. This sort of thing is covered in my blog on "The Meaning of Meaning" where I distinguish conventional meaning from contextual significiance. It is the latter that is relevant to speakers, not the former. So, if your mother/wife/girl friend says, "Would you mind taking out the trash?" and you say, "Yes," you are in a world of trouble.

7:34 AM

Anonymous Anonymous said...

I am honored to be a prop for such erudition!

12:05 PM

Anonymous Anonymous said...

Of course I couldn't keep my mind on the content; I got distracted by the form.

Your post begins with an adverbial clause that isn't possible for me: "My blog on Proper English, ..." in the same position where we would expect adverbials like "Last week, ..." or "According to Antonin Scalia, ...".

Is this actually a possible adverbial for you? I need an "In" at the front.

9:03 AM

Blogger The Language Guy said...

Wow, what a blunder! Somehow an initial "In" got deleted during editing. I have fixed the problem. Thanks for pointing this out.

What really caught my eye was your use of "adverbial clause." My dissertation was titled, "Adverbial Clauses in English."

Again, thanks.

9:12 AM

Blogger Wayne Leman said...

Does the concept of "fuzzy logic" from 25 or so years ago help any?

3:43 PM

Blogger The Language Guy said...

I will confess that I have no personal expertise in the application of fuzzy logic to accounts of meaning in natural langauge. A quick googling of "fuzzy logic" suggests that it is alive and well today in some fields. I ran across the claim that modern autofocus cameras use fuzzy logic in determineing focus.

It is arguably useful in accounting for vagueness. The adjective "old" for instance, has a hidden parameter "for an x," where x is a reference class." So, John at 85 could be "old" and a dog at 15 could be said to be "old," but John's grandson at 15 would not be said to be "old." So we have "old for a dog" and "old for a human," as well as many other things.

However, even within a given reference class, there is some indeterminacy for "old." Petr Hajek has a nice bit on "Fuzzy Logic" in the The Stanford Encyclopedia of Philosophy which discusses the predicate "old," saying that a claim like "John is old (for a human)" could be absolutely false (is 15) or absolutely true (is 95) or true to this or that degree. So, if John is 59, then the claim that he is old might be 85% true.

8:05 AM

Blogger Thomas said...

I'm no expert, but I have read about a so-called grammar gene, where language within a community, no matter how "non-standard," is instinctively put into a grammatical order by offspring and therefore, over time, make sense to that community because it's grammatically correct to them and through usage becomes a standard way of communicating.

10:37 AM


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