Reply To: All or some


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.