[gerard.casey]

A student wrote to me:

“First, in your second video, on categorical propositions, you state that “Some propositions come to us without quantifiers and we have to use our understanding of the language in context to determine what is being said.” The example you provide is “Women can’t drive.” Looking critically at these three words, I think that the implied meaning, by default so to speak, is that all women can’t drive. While I do understand the importance of context, I believe that without a quantifier such as “some”, “most”, “in general”, etc., such a proposition does in fact mean “all”. I may hope that the listener understands that I don’t in fact mean “all”, but those three words do technically communicate “all”. Would you disagree? You go on to state that “The rule of thumb here is that unless the proposition is obviously singular or obviously universal, it should be taken as particular.” I don’t understand how that assertion can be made. As I see it, the rule of thumb is that unless a quantifier is given, it should be taken as universal.”

I replied: “I would say that the expression “Women can’t drive” is, as it stands, ambiguous. If you are speaking to someone face to face you can ask them to clarify what he’s said. “Did you mean ‘all’ or ‘some’?” Where the communication is not face to face, one has a problem. The reason for taking the particular interpretation as a default lies in the argumentative context and what I call ‘the principle of charity’. Let me explain. If someone asserts a universal proposition, all it takes to undermine it is a single counterexample. If my proposition is taken to be the chauvinist and sexist “No women can’t drive” then it can be refuted simply by finding just one woman capable of driving. Now, when you’re engaged in argument with someone, you don’t want to attack a ‘straw man’, that is, the weakest version of the argument your interlocutor is putting forward. The principle of charity then requires you to interpret ambigious propositions as the easier-to-defend particular rather than the more-difficult-to-defend universal. I agree with you, however, that often people intend in such locutions to assert a universal propositions and if that is clear from the context, then that is how one must take it.”

The student continued: “I suppose I’m particularly sensitive to this because I’m an English teacher. I teach English as a foreign language here in XXX. I warn my students that if they don’t mean to communicate “all”, they need to add some quantifier. A common assertion from my students is “Americans like guns.” Again, without a quantifier, I see this as an assertion that all Americans like guns.”

I replied: “I would think that the context in which such an assertion is made warrants your interpreting it as a universal statement .”

The student continued: “Second, in the same video, you state that “‘Men are sometimes honest’ will be internally translated into the particular proposition ‘Some men are honest.'” You continue to say that “in doing so we lose a little of the sense of the original proposition, but we retain the essential semantic content.” I simply don’t think that is the case. I see these two propositions as entirely different. “Men are sometimes honest” communicates that all men are honest at times and dishonest at times. Perhaps they are honest 30% of the time and dishonest 70% of the time, for example. The second proposition, “Some men are honest” communicates that some men are always honest and some men are always dishonest. For example, 30% of men are always honest and 70% of men are always dishonest. Two completely different propositions, no?”

I responded: “A little later in the lectures, I discuss a concept introduced by H. P. Grice called “conversational implication”. A particular affirmative proposition such as “Some men are honest” is perfectly consistent with “Some men are not honest” [see the upcoming discussion of sub-contraries in the square of opposition]. If I were to come into a classroom after a test and say “Some students have done particularly well”, most students would, conversationally take this to imply “Some students have not done particularly well”. But implication [understood logically] is one thing; conversational implication, which is perfectly understandable, is another. The aim of translation in logic – from our natural language to our logical symbols – is to enable us to deal with logical implications securely. Once in our symbols, our logic is unambiguous; translation, however, is always an art rather than a science.”

Professor Gerard Casey
School of Philosophy
University College Dublin
Dublin 4, Ireland
353 1 716 8201

[deansopko]

Professor Casey,

First, thanks so much for the quick reply. I really appreciate it.

I absolutely love your “principle of charity.” It’s a great way to state this idea. And in an argument with another native-English speaker, I totally agree. If face-to-face, I would likely clarify whether or not the person were asserting a universal proposition. However, when the opportunity for clarification is not available, I understand what you’re saying about not wanting to attack the weakest version of the argument. I by no means want to create a straw man and then attack that. That’s a cop out, as I see it.

Concerning my second question, though…

I’m in agreement when you say that “Some men are honest” is logically consistent with “Some men are not honest.” However, neither of these sentences is at all consistent with “Men are sometimes honest.” In the first two examples, the quantifier “some” modifies the noun “men”. In “Men are sometimes honest,” it’s the adjective “honest” that’s being modified (or quantified), which creates an entirely different proposition.

I would, of course, agree that “Men are sometimes honest” is logically consistent with “Men are sometimes dishonest.”

As I mentioned, I’m an English teacher in Japan. Therefore, I view language from the perspective of a teacher. In terms of context, Japanese language is what would be considered high-context. By that, I mean that the context is a much greater part of communication when speaking Japanese than it is when using English. This stems from the fact that overall, Japan remains a very culturally homogenous country. They simply don’t need actual language as much to understand each other.

For example, in Japan when a boss responds to an employee’s request (in Japanese, of course) with “Hmmm… That might be difficult,” the Japanese employee understands that this is essentially the same as “no”. Part of my job is to teach students that because English is used by such a culturally diverse group of people, a response of “Hmmm… That might be difficult” will not necessarily be received as the same as “no”.

I’m trying to help them have a better command of the old “say what you mean, mean what you say” approach. I, of course, try to make sure I do the same. Thus, my challenges to your examples.

Finally, you mention that translation is “rather art than science”. I couldn’t agree more. In fact, I’m convinced that language in general is more art than science. In strict terms, though, I view logic as science, not art. Am I incorrect in thinking so?

Dean

[gerard.casey]

Dear Dean,

I’m glad you like the idea of a ‘principle of charity’. It’s a sure fire way of being consistently fair to your opponents. As faulty human beings, it’s hard to do this, especially when the argument concerns something you’re passionate about and the temperature rises!

Your write: “I’m in agreement when you say that “Some men are honest” is logically consistent with “Some men are not honest.” However, neither of these sentences is at all consistent with “Men are sometimes honest.” In the first two examples, the quantifier “some” modifies the noun “men”. In “Men are sometimes honest,” it’s the adjective “honest” that’s being modified (or quantified), which creates an entirely different proposition.”

In fact, “Some men are honest” and “Some men are not honest” are consistent with one another and both of them are consistent with “Men are sometimes honest.” Consistency is simply a matter of its being possible for proposition A and proposition B to be simultaneously true and all three of these propositions can be true at the same time.

Grammatically, these sentences are distinct. Logic and grammar, however, are not coterminous. The difficulties you are having and with which I sympathise, are the result of the fact that natural language and formal languages don’t have the same boundaries, so that some things that are easy in natural languages are difficult to capture in a formal language; meanwhile, the simplicity, clarity and rigour of formal languages find little resonance in natural languages, which are wonderfully messy, rich, and redundant (in the formal, not pejorative, sense of that term.)

You write: “As I mentioned, I’m an English teacher in Japan. Therefore, I view language from the perspective of a teacher. In terms of context, Japanese language is what would be considered high-context. By that, I mean that the context is a much greater part of communication when speaking Japanese than it is when using English. This stems from the fact that overall, Japan remains a very culturally homogenous country. They simply don’t need actual language as much to understand each other.”

The matters you mention which are very familiar to you as a teacher of a foreign language are not, in the end, an issue for a formal system, except in the opening stages of translation. They will, however, concern us rather more when we come to consider briefly (perhaps all too briefly) logic in an informal context.

And yes, logic is more a science than an art, though even as a science it requires insight and, in practice, a modicum of ingenuity.

[Brendan.clarke]

I had made almost all the same observations and come to the same conclusions before reading this post. Amusingly enough I am also an English teacher.min my case in Spain. So of course the fact of the adjective modifying the word “men” and “honest” also bothered me. The search for what the speaker is actually attempting to assert is indeed an art for the reasons you stated. The speaker sometimes is not gramatically rigorous and would express one thing in a manner that I would mark as incorrect on a students exam. This puts us in a quandry doesnt it? Shouldnt we depend upon the speaker expressing himself clearly? Doesnt our whole logical game depend upon the speaker clearly defining the terms, the propositions and indeed everything that we are to assess? Otherwise we are throwing a spanner into our logical works. Well that sId… I am only three videos into the logic course so perhaps I can take it easy. I have one of the books from the reading list and am plodding through it in an attempt to grasp it all. Kim still getting the exercises wrong so… Guess Ill repeat the last two classes before going on.

[gerard.casey]

Dear Brendan,

In formal English, two negatives = affirmative. But in colloquial English, if some says “I’m never going to do nothing, nohow, noway….” what they are doing is asserting a very strong negative. and in some language, a double negative is routinely a way of making a strong denial.

In serious disputation, it is indeed necessary to be clear, to define your terms and so on. Often, however, a substantial portion of any discussion involves getting to that stage. That’s human nature, I’m afraid, and also the nature of language.

If I may make a suggestion? I would recommend moving on through the logic lectures until the level of understanding really starts to drop, then go back and repeat the viewing. If you do this, you will find that some at least of what was earlier problematic is no longer so. I can’t guarantee that this will happen but that has been my experience over the years.

Keep up the study and thank you for your interesting posts.

[hollenbeck2]

First i want to say how much i am enjoying your course on logic and indeed, all the courses here at Liberty Classroom.
But I too am having trouble understanding why “women can’t drive” isn’t understood to mean “all women can’t drive”. Is this a convention we will use for the purpose of this course or is it something all logicians adhere to? If the latter is the answer why is it different in mathematical logic?
Thank you in advance for any clarity you can provide.

[gerard.casey]

Thank you for the kind compliment, Kristopher.

In English (and, I presume, in other natural languages also), expressions such as “Women can’t drive” or “Men can’t navigate” have no explicit quantifiers on them. If such propositions have categorical import, they must be either universal, particular or singular. Now, it seems reasonably clear that they are not singular so that leaves us with a choice between universal or particular. It’s possible that someone might say this and intend by it a universal proposition. It’s also possible they might not. Where it’s not possible to receive clarification on intent, then we have a hermeneutical principle of charity which says that we should take a proposition in its most defensible form; and particulars are always easier to defend than universals. If the context indicates that a universal is the only sensible way to take a proposition, then take it as universal; otherwise the default in cases of ambiguity is particular. {I’m assuming you’ve read the exchanges above?}

You ask: “If the latter [taking the proposition particularly] is the answer why is it different in mathematical logic?”

I don’t know that it is different in mathematical logic. If I were using this example in the context of the predicate calculus, I would counsel translation in exactly the same way.

Remember, as I’ve said elsewhere on the forum, translation is an art not a science and our guiding principle, as in all translation, is to be as faithful as we can to what is being said and as accommodating as we can be to our interlocutors.

Let me know if this helps or if you’re still unpersuaded.

[hollenbeck2]

Thank you for responding. I don’t recall where I got the idea that without modifiers proposition were understood to be universal by default. However it does seem to me you are correct.
In order to ensure I do grasp this concept correctly i would be grateful if you could tell me if the following is correct:

If one made the statement “triangles have three sixty degree angles”. We would be obliged by the principle of charity to conclude that the person was referring to equalateral triangles and conclude that this was a true statement as opposed to offering right triangles as a counter example and conclude the statement was false.

Once again thank you for taking the time to respond. It is greatly appreciated.

[gerard.casey]

Remember, definitions are invariably universal, so, “triangles are plane figures bounded by three straight lines” and “gold is a metal” can only sensibly be taken as universal. If someone said to me “triangles have 3 x 60 degrees angles” I’d say, “You are talking about equilateral triangles, aren’t you?” If there’s no way on interviewing your interlocutor, you could take this proposition (as I think you are suggesting) as being an elliptical “(Some) triangles have 3 x 60 degree angles” and thus true or, alternatively, as a quasi-definition and thus false.

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