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.