## Identifying Arguments

We encounter
inferences and recommendations all the time in our ordinary lives.
Generally, to infer is
to show that a conclusion follows
from some evidence. In the parallel case of mathematics, we say that
one step in an equation follows
from a previous step when the “gap” between them is sufficiently
small that the next step is obvious. In this case, this obviousness
is equivalent to our use of the word “reasonable”.

For example,
those minimally competent with algebra can move from 3x = 9 to x = 3
without showing the need to divide both sides by 3 to isolate x. When
learning algebraic techniques, “showing your work” is important,
but with competence comes license to declare that the later step
*follows* the previous
without the burden of an overly-detailed expression of the progress.
This is a model of how we move from premises to conclusions in logic,
and it is similarly a model for how we talk about the relationship
between *reasons to think*
and *explanations*,
which is the first relationship we’ll investigate here.

In this we see
the fundamental importance of making analogies and comparisons in our
ordinary commerce with one another. We say this step is *like*
the previous step, but for __
X__* *.

*Following*depends on comparison between steps in a sequence, and when we judge that one step follows another, the X in the blank

*goes without saying*.

When
one thing *follows*
another, the steps in between *go without saying*.
We need to be sensitive to the competence of our audience when we
judge how much or how little we ought to make explicit.