Where Do Implications Start?
Logical arguments face an infinite regress when each premise requires prior justification. The chain continues endlessly unless foundational assumptions are accepted, as in the 'turtles all the way down' story.
THE IDEA
WHERE DO IMPLICATIONS START?
There is a story that Stephen Hawking tells in A Brief History of Time, about an audience member who came up to a “well-known scientist” after a talk on cosmology, and declared “What you have told us is rubbish. The world is really a flat plate supported on the back of a giant tortoise.” The scientist asks what that tortoise is standing on, whereupon the audience member supposedly replies, “You’re very clever, young man, very clever, but it’s turtles all the way down!”
Even if we are using logic instead of turtles to hold our arguments up, we still need to wonder what is holding up each level of our argument. It is important to remember that logical implication only enables us to deduce something from something else. “X implies Y” only tells us that Y is true if X is true. It doesn’t tell us whether or not X is true. In order to know that X is true we need something to imply it, perhaps “W implies X”. But what tells us that W is true? Perhaps V implies W. But what implies V? Where does all this originate from?
As I have mentioned, I think this process of working backwards is just like small children who ask “Why?” repeatedly. Every time you give them an answer they proceed to ask “Why?” to that. Children have apparently infinite curiosity and infinite tolerance for doing the same thing over and over again, so are likely to keep asking “Why?” until the adult gets frustrated and puts a stop to it. I personally carried on asking why all the way through science and mathematics until I was doing my own research in abstract mathematics because I was still asking “Why?”. Pragmatism and worldly responsibilities cause adults (most of them anyway) to stop asking why, accept some things, and get on with daily life. I like to think that we still all have that infinite curiosity inside us, which is why Wikipedia is so popular and why so many of us are prone to falling down Wikipedia wormholes. You know the kind, where you keep clicking on more links to read more articles and understand more things. (I have done my fair share of cat video wormholes too.)
When to use it
When building a scientific theory, deciding on axioms that cannot be further justified without infinite regress.
In legal reasoning, establishing a chain of evidence that must eventually rest on a foundation of accepted facts or testimony.
In everyday decision-making, recognizing when you are accepting a premise as 'common sense' to avoid endless questioning.
In philosophical debates, using the infinite regress argument to challenge opponents to provide a foundation for their claims.
FROM THEORY TO EVERYDAY LIFE
In practice
The Flat Earth and the Giant Tortoise
In Stephen Hawking's story, an audience member claims the world is a flat plate on the back of a giant tortoise. When asked what supports the tortoise, the reply is 'turtles all the way down,' illustrating an infinite regress of foundational assumptions.
Children Asking Why
Children naturally ask 'why' repeatedly, seeking ever deeper explanations. This mirrors the logical problem of infinite regress, where each answer leads to a new premise requiring justification, until frustrated adults halt the chain.
A MOMENT TO REFLECT
Put it to work.
Identify a belief you hold. Can you trace a chain of 'why' questions back to a fundamental assumption? What would happen if you kept asking why beyond that point?
In what areas of your life do you pragmatically stop asking why? Are those stopping points justified or arbitrary?
How does the infinite regress problem affect the validity of logical arguments you encounter? Can you spot when an argument relies on an unproven premise?
References
- A Brief History of Time — Stephen Hawking (1988)
CONTINUE THE CONVERSATION
Source texts
- The Art of Logic How to Make Sense in a World that Doesn’t (Eugenia Cheng)