When Logic Causes Contradictions
Cheng uses everyday loops and conflicting rules to explore paradoxes. Some reveal inconsistent requirements; others challenge intuition or raise questions about self-reference without necessarily producing a formal logical contradiction.
THE IDEA
WHEN LOGIC CAUSES CONTRADICTIONS
I AM AN AVID writer of to do lists. I find it an excellent way to procrastinate in a mildly useful way. Sometimes if I’m feeling particularly tired or stressed I will put some very easy things on my to do list so that I can easily declare that I’ve achieved something. This might be something like “eat breakfast” or “check email”. I went through a phase of putting “get up” on my to do list, so that I could immediately cross that off. It suddenly occurred to me to put “Do something on this list” on my list. Could I then immediately cross that off? I got quite confused wondering about that.
I often get intrigued by looped-up thoughts like this. For example, I really want to go round telling everyone not to give unsolicited advice, but I fear that this would constitute unsolicited advice. Then there’s the fact that I can’t keep ice cream in the house because if there is any, I will immediately eat all of it, and then there won’t be any. A more serious contradiction happened to me when I was filling in a form online for a visa application. It sternly told me that I had to fill in my full name and it had to match my name in my passport. However, my middle name in my passport has a hyphen, and the online form would not allow me to input a hyphen. “Invalid name: only alphabetic characters are allowed.” So I found myself stuck – I had to fill in my name exactly as it appeared in my passport, but was not allowed to. I am surely not the only person with a hyphenated name ever to have applied for a visa, not to mention those with apostrophes or accents.
I think of these loops and contradictions as paradoxes of life. Paradoxes occur when logic contradicts itself or when logic contradicts intuition. Both cases show us some of the limitations of strictly logical thinking. In the first case we see how we may need to take more care over how we set up our logic, our definitions, or the scope of our thinking. In the second case we see that we shouldn’t necessarily trust our intuition, or that we should take some time to understand quite where that intuition is coming from. The first type illuminates our treatment of logic and the second illuminates our view of the world.
When to use it
When setting rules for automated systems, anticipate paradoxes from self-referential constraints.
When analyzing arguments, watch for contradictions that indicate flawed premises or definitions.
In personal decision-making, recognize paradoxes that arise from conflicting desires (e.g., wanting to eat ice cream but also wanting to save it).
FROM THEORY TO EVERYDAY LIFE
In practice
To-Do List Paradox
Putting 'Do something on this list' on a to-do list creates a self-referential loop: if you cross it off, you've done something on the list, but that action is the crossing off itself.
Unsolicited Advice Paradox
Telling people not to give unsolicited advice may itself be unsolicited advice. The instruction can conflict with the speaker’s own conduct, even though the situation need not be a formal logical contradiction.
Ice Cream Paradox
You cannot keep ice cream in the house because if there is any, you will eat it all, resulting in none left.
Visa Application Paradox
A form requires your name exactly as in your passport, but does not allow hyphens, making it impossible to comply if your name contains a hyphen.
A MOMENT TO REFLECT
Put it to work.
Does the to-do-list example create a contradiction, or does it simply allow an action to satisfy its own instruction? How would you decide?
What does the visa application paradox reveal about the limitations of rule-based systems?
Can you identify a paradox in your own reasoning that stems from conflicting rules?
CONTINUE THE CONVERSATION
Source texts
- The Art of Logic How to Make Sense in a World that Doesn’t (Eugenia Cheng)