An assumption is a claim that is taken to be true—without the need of proof. Most arguments are based to some extent on assumptions, since writers rarely have the time and space to prove all of the conceivable claims on which an argument is based.
For example, someone arguing about the best means of limiting population growth in developing countries might well assume that the goal of limiting population growth is worthwhile. For many audiences, there would be no need to articulate this assumption or to defend it. But in some developing countries, for instance, many children do not survive to adulthood, so population growth has a different meaning and set of assumptions. It is always a good idea to challenge your own assumptions, asking if they are well grounded for all situations.
There is a danger in failing to spell out and prove a claim that is clearly controversial.
Consider the following short argument, in which a key claim is missing.
ARGUMENT WITH MISSING CLAIM
Violent crime is increasing. Therefore, we should vigorously enforce the death penalty.
The writer seems to be assuming both that the death penalty deters violent criminals and that it is a fair punishment—and that most readers will agree. These are not reasonable assumptions.
When a missing claim is an assertion that few would agree with, we say that a writer is guilty of a non sequitur (Latin for “does not follow”).
NON SEQUITUR
Christopher gets plenty of sleep. Therefore, he will be a successful student in the university’s pre-med program.
Does it take more than sleep to be a successful student? The missing claim—that people with good sleep habits always make successful students—would be hard to prove.