Lack of awareness of the difference between ‘some’ and ‘any’ as opposed to acute such awareness is what makes some people call themselves ‘humanists’, in the sense of ‘not scientifically-minded’. They shy away from anything connected with mathematics. It is a safe bet that the other lot, those who say they’ve never been good at languages, are not mathematicians either. The distinction between ‘some’ and ‘any’ is the bedrock for logical and mathematical analysis.
In the teaching of English, the problem is explained in terms of positive declarative sentences for ‘some’ and interrogative or negative sentences for ‘any’. That is wholly inadequate, although it may serve the purpose of marking the correct answers on a test paper. Consider the sentence:
(1) If someone is in, the lights are on.
Does this sentence say that there is a person, whoever they may be, such that if that person is in, the lights are on, or does it rather say that if a person, any person, happens to be in, then the lights are on? Clearly the latter. The former interpretation is possible but it makes a very weak sentence, or else it is extremely unlikely for anyone to have uttered such a sentence. It follows then that (1) says in fact that if anyone is in, the lights are on.
Another way of putting it is that if we allowed questions such as, ‘Have you eaten something?’, then we would probably mean, ‘Have you eaten anything?’ anyway. The difference is this: ‘Is there something that you have eaten? as opposed to ‘Is there anything that you have eaten?’
The word ‘some’ means ‘any’ also in a sentence like this:
(2) Someone who doesn’t tell the whole truth is a liar.
Again, I could mean to say that there exists a person who doesn’t tell the whole truth and that person is a liar, but I am more likely to extend this classification to anyone who doesn’t tell the whole truth.
Quantification is key in testing whether a mathematical formula is true or not. (x – 1)(x + 1) > 0 is true for some x, but not for any x we happen to pick in the set of real numbers. Specifically, the formula is false for an x that is greater than – 1 and less than 1.
Negations bring into sharp relief the difference between ‘some’ and ‘any’.
(3) I don’t know something.
(4) I don’t know anything.
Clearly, ‘something’ in (3) must not be interpreted in the same way as ‘someone’ in (1). In (1) the indefinite pronoun ‘someone’ has wide scope, meaning it captures anyone or everyone who happens to be in when the lights are on. In (3) on the other hand, ‘something’ takes narrow scope: it includes at least one thing, but excludes everything else besides.
What is (1) equivalent to? Answer:
(5) I don’t know everything.
Sentence (5) is the reciprocal of (3). Since the universal set U is the disjoint union of A, or the set representing ‘some’ members, and Ac, its complement, that is the set of all those members of U that are not members of A, in both sentences we are focusing on Ac. What changes is the perspective: in (3) we are indicating how much we are short of the full set, while in (5) we are saying what it is that we are a certain amount short of.
The word ‘any’, on the other hand, takes the widest scope possible, in (4) and in negations in general.
In the teaching of English, the problem is explained in terms of positive declarative sentences for ‘some’ and interrogative or negative sentences for ‘any’. That is wholly inadequate, although it may serve the purpose of marking the correct answers on a test paper. Consider the sentence:
(1) If someone is in, the lights are on.
Does this sentence say that there is a person, whoever they may be, such that if that person is in, the lights are on, or does it rather say that if a person, any person, happens to be in, then the lights are on? Clearly the latter. The former interpretation is possible but it makes a very weak sentence, or else it is extremely unlikely for anyone to have uttered such a sentence. It follows then that (1) says in fact that if anyone is in, the lights are on.
Another way of putting it is that if we allowed questions such as, ‘Have you eaten something?’, then we would probably mean, ‘Have you eaten anything?’ anyway. The difference is this: ‘Is there something that you have eaten? as opposed to ‘Is there anything that you have eaten?’
The word ‘some’ means ‘any’ also in a sentence like this:
(2) Someone who doesn’t tell the whole truth is a liar.
Again, I could mean to say that there exists a person who doesn’t tell the whole truth and that person is a liar, but I am more likely to extend this classification to anyone who doesn’t tell the whole truth.
Quantification is key in testing whether a mathematical formula is true or not. (x – 1)(x + 1) > 0 is true for some x, but not for any x we happen to pick in the set of real numbers. Specifically, the formula is false for an x that is greater than – 1 and less than 1.
Negations bring into sharp relief the difference between ‘some’ and ‘any’.
(3) I don’t know something.
(4) I don’t know anything.
Clearly, ‘something’ in (3) must not be interpreted in the same way as ‘someone’ in (1). In (1) the indefinite pronoun ‘someone’ has wide scope, meaning it captures anyone or everyone who happens to be in when the lights are on. In (3) on the other hand, ‘something’ takes narrow scope: it includes at least one thing, but excludes everything else besides.
What is (1) equivalent to? Answer:
(5) I don’t know everything.
Sentence (5) is the reciprocal of (3). Since the universal set U is the disjoint union of A, or the set representing ‘some’ members, and Ac, its complement, that is the set of all those members of U that are not members of A, in both sentences we are focusing on Ac. What changes is the perspective: in (3) we are indicating how much we are short of the full set, while in (5) we are saying what it is that we are a certain amount short of.
The word ‘any’, on the other hand, takes the widest scope possible, in (4) and in negations in general.
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