You Can Always Be Right
Using precise quantifiers and qualifiers (e.g., 'In my opinion,' 'sometimes,' 'there is a sense in which') allows you to avoid being wrong by making statements more nuanced and context-dependent. This approach encourages looking for the sense in which something is true rather than judging it as simply true or false.
THE IDEA
YOU CAN ALWAYS BE RIGHT
If you are very precise about how you quantify your statements you can ensure that you are never wrong about anything. This is one of the reasons I as a mathematician might be quite annoying to argue with: I am careful to use enough quantifiers that it’s almost impossible for me to be wrong. We’ve seen a few ways of doing this with phrases like
In my opinion ...
In my experience ...
Maybe we could add some more, like
Maybe ...
Sometimes ...
Apparently ...
It seems to me ...
I recently did an interview in which I lamented that some maths lessons leave little lasting effect on people except maths phobia – the students don’t remember much actual maths, and mostly only remember fear. In that case, teaching them maths has been a waste of time and money, and worse, has actually had a negative effect. Thus we might have achieved a better result by teaching them no maths at all, because that would have been a zero effect, which is better than negative. Unfortunately various tweets went out declaring that I said “Teaching maths is a waste of time and money” and “We would be better off not teaching maths at all.” In fact, what I said is that in some cases teaching maths is something of a waste of time and money, and in those cases, we might be better off not teaching it at all. Qualifiers abound.
My wonderful, wise, precise and illuminating PhD supervisor, Martin Hyland, is well known among his students for prefacing statements with “There is a sense in which”. “There is a sense in which Mozart is more boring than Brahms” is another way of correcting my sweeping statement “Mozart is more boring than Brahms”. “There is a sense in which teaching maths can be a waste of time and money.” The phrase has a wonderful way of focusing one’s attention on exactly what is the sense – or what are the possible senses – in which something is true. It reminds us all that mathematics is not just about finding the right answer, but is about finding the sense in which things might or might not be true.
I believe that a useful way to be a rational person is to look for the sense in which things are true rather than simply deciding if they are true or false. Someone might say something that is untrue in strictly logical terms, but perhaps they were really trying to say something else, perhaps something with strong emotional content that we should listen to if we are intelligent humans rather than intelligent emotionless robots.
1 Basic quantifiers only quantify over sets, that is, you can only say “For all objects in a certain set”. You can’t quantify over sets of objects, as that is a higher-order level of expressivity and would cause problems of self-reference. The difference is a bit technical, but the idea is one that we’ll come back to when discussing paradoxes in Chapter 9.
When to use it
When providing feedback to colleagues or students, use qualifiers to soften criticism and focus on specific aspects, avoiding blanket statements.
In debates or discussions, preface strong claims with 'In my experience' or 'Sometimes' to make the argument more defensible and nuanced.
In scientific or academic writing, precise quantification and qualifiers (e.g., 'these results suggest,' 'under certain conditions') help avoid overgeneralization.
When summarizing complex topics for a general audience, use phrases like 'There is a sense in which' to encourage critical thinking and multiple perspectives.
FROM THEORY TO EVERYDAY LIFE
In practice
Misunderstood Interview on Maths Teaching
In an interview, the author said that in some cases teaching maths is a waste of time and money and that we might be better off not teaching it at all. However, tweets misquoted the statement as an absolute, claiming the author said 'Teaching maths is a waste of time and money' and 'We would be better off not teaching maths at all.' The qualifiers ('some cases', 'might') were lost, leading to a distortion of the intended meaning.
There Is a Sense in Which
Using the phrase 'There is a sense in which' before a statement, as Martin Hyland does, forces the listener to consider the specific context or interpretation that makes the statement true, as in 'There is a sense in which Mozart is more boring than Brahms' instead of the absolute 'Mozart is more boring than Brahms.'
A MOMENT TO REFLECT
Put it to work.
Think of a recent argument or disagreement. How could adding qualifiers have changed the outcome?
What is a common absolute statement you hear (e.g., 'Everyone knows...') that might benefit from a 'There is a sense in which' rephrasing?
When is it appropriate to avoid over-qualifying? Can too many qualifiers weaken a message?
How does the concept of 'You Can Always Be Right' relate to intellectual honesty and humility?
CONTINUE THE CONVERSATION
Source texts
- The Art of Logic How to Make Sense in a World that Doesn’t (Eugenia Cheng)