Where Do We Stop?
The concept of knowing when to stop asking 'why' and accepting basic assumptions or axioms as starting points in reasoning, which helps avoid infinite regress and clarifies the nature of disagreements.
THE IDEA
WHERE DO WE STOP?
Knowing where we start is important. But in a way this comes down to knowing when to stop, that is, knowing when to stop asking why and stop trying to justify ourselves further. When should we stop filling in gaps in the logic? Eventually we have to close Wikipedia and get on with something else. Eventually we have to tell the inquisitive child that it’s time to go to bed, or get ready for school. If I imagine an adult who has not developed the ability to stop asking those “why” questions and get on with daily life, I imagine a tortured philosopher, endlessly questioning everything and searching for meaning instead of eating, sleeping or earning money. Do I exist? What is the meaning of life? Why are we here? Why is there so much suffering in the world? What is love? Why do people hate each other? Why do people hurt each other? To be a moderately functioning adult, we have to stop asking those questions at some point – not necessarily permanently, but at least for some part of every day.
In logic we also have to stop asking questions at some point, and accept some facts, otherwise we’ll never get anywhere. We can work out that Y is implied by X, which is implied by W, which is implied by V, and so on, but at some point we need to stop working backwards and decide that we have explained enough for now. The place where you stop trying to work backwards is the place where you have basic assumptions or beliefs that you don’t try to justify at the moment. It doesn’t mean that you won’t ever try, and that nobody else will, it’s just that right now you’ve decided this is your starting point and is the basis of your logical system, or your belief system.
In logic and mathematics these are called axioms, and we will discuss them further in Chapter 11. We need a starting point in logic because we can only deduce things from other things – we can’t deduce something from nothing. We’re not magicians, and even magicians don’t really produce something from nothing, they’re just very successfully fooling us. If a logician claims to be deducing something from nothing they’re fooling us too.
Looking for axioms, or starting points, in my own system of beliefs has led me to a much clearer understanding of my own thinking. It has enabled me to identify basic beliefs that some other people don’t hold. For example, when it comes to prejudice, I fundamentally believe that prejudice of those with more power towards those with less power is much more harmful than the other way round. This means that if I can trace someone else’s axioms down to different ones then I know we have a disagreement at the very beginning of the argument, and there’s no point trying to resolve a later implication without trying to resolve this starting point. But crucially it is possible to reach a different conclusion from me by applying logic perfectly soundly but starting from different basic beliefs. So two people can both be logical but still disagree about things.
Working out what the basic starting points in an argument are is an important part of analysing it logically, and is an important part of understanding the nature of disagreements. The logic must all flow out of that starting point.
When to use it
In a debate or argument, identify the foundational assumptions of each side to understand the root of disagreement and avoid unproductive debates on later implications.
In mathematics or logic, explicitly state the axioms you are building upon to ensure sound reasoning and allow others to verify the chain of deduction.
In personal decision-making, define core values as axioms to stop overanalysis and act decisively when faced with complex choices.
In scientific theorizing, stating the assumptions a model relies on and examining which can be tested, revised, or replaced.
FROM THEORY TO EVERYDAY LIFE
In practice
The Inquisitive Child
A child keeps asking why it is time for bed. At some point, the adult ends the discussion so they can act. This is a practical stopping point; it does not mean that every further question has been answered or that the starting assumptions can never be reconsidered.
Prejudice and Power
The author gives the example of a fundamental belief that prejudice from those with more power towards those with less power is more harmful than the reverse. This serves as an axiom in their belief system. If someone else starts from a different axiom, they might reach different conclusions even while being perfectly logical.
A MOMENT TO REFLECT
Put it to work.
Identify a deeply held belief. Can you trace it back to a fundamental axiom that you accept without justification?
Think of a disagreement you have with someone. What basic assumptions might each of you be starting from that lead to different conclusions?
In a situation where you are tempted to keep asking 'why,' how do you decide when to stop and take action?
Often confused with
CONTINUE THE CONVERSATION
Source texts
- The Art of Logic How to Make Sense in a World that Doesn’t (Eugenia Cheng)