Externalism - that having or not having true beliefs are dependent on
the environment.

Putnam's classic argument for externalism starts with a thought
experiment: imagine that water comes in two forms - H2O on earth, and
XYZ on twin-earth. So, when both earthmen and twin-earthmen (who are
physically alike) say that 'water quenches thirst' they are expressing
different beliefs. This is externalism's claim.

There are many arguments against this idea - that the content of a
belief is dependent on external factors. The opposite argument is
internalism - that beliefs are an intrinsic property of the individual.

Both externalism and internalism are wrong, it seems to me. First, for
the externalist, there is no way that either H2O or XYZ can be
identified except by water. It is water that allows us to distinguish
H2O or XYZ from the cup that holds it, or the river from the river-bed.

For the internalist position, we have simply an environmental
minimalism, veiled by the term 'psychological'. The internalist merely
limits the extent of the externalist environment to the body. The body
then, inexplicably, becomes the receptacle of thoughts (as a
'psychological' condition), yet the problem of the mind-matter,
internal-external interface, remains.

But we can deliver a double-whammy against both positions. Both
internalism and externalism rest on classical notions of belief. The
ontological ambiguity of the term 'belief' is historically entrenched,
and you will be hard put to make sense of it. All we need claim is that
a 'belief' is neither internal nor external but is a public document. An
ontological or physical placement of that document is irrelevant to the
use we make of it. Where there is only one proposition publically or
individually presented, such as 'this is water', then we can have no
belief about the matter.

For example, we have no belief or knowledge that one and one are two -
they simply are two, for no alternative is on offer. Granted, we may
create an alternative - that, for example, in quantum reality one and
one may not be two; or that we are mad and cannot make sense of
addition. But whether the alternatives we create are ontological, or
mental, etc., one and one are two per se is neither an internal belief,
nor an external truth. However, once we are given another alternative -
that one and one are not two, then we may decide on the evidence which
is right - we would come to a pragmatic decision, i.e. have a belief,
about which is right. But coming to a pragmatic decision, or believing
which of two or more propositions are the right ones, is not a property
of the propositions that make up the belief.