Any text is given meaning by its context. A text, or body of texts, might
plausibly contain enough information for the diligent reader to infer, from the
text, enough about the context presumed by the text to be able to make sense of
the text. A sufficiently careful text (perhaps the Algol 68 Report) may even
aspire to contain enough structure, in the ways it refers to itself, that it can
be viewed as having meaning out of context
- but still each part of it is
read in the context of the rest, the whole being read in the notional
empty
context which tells us nothing (but, in fact, assumes at least the
reader's diligence).
I shall presume that you are reading this text: if you are hearing it read
to you, please interpret read
as hear
; if it is coming to you in
some other form, I trust you to interpret read
appropriately. At the
start of a text, your context and mine differ: the text introduces notions which
we understand in terms of those contexts, along with forms of expression for
those notions and ways of manipulating truths about them; from these, each
reader builds up a new context in which to read subsequent text; if the notions
and etc. have been introduced with care, our contexts soon enough have
enough in common that the text can presume tight overlap of our contexts, at
least in so far as they address the notions being discussed by the text.
Text need not be wholly linear (at least, given hyperlinks): and even where
it is, the reader may well gain by re-reading a text with a re-considered prior
context adopted in the light of a first read-through. In any case, the context
of one part of a text can make reference to another; which may be in another
text (eg via a hyperlink); if in the same text it will usually be
earlier, but see below
has its place. Care is always needed in such
references, at least where proofs are concerned, to avoid proof by circular
cross-reference
; with definitions, similar care is also needed for
circular
definitions to be well-behaved, where they arise (eg a
natural number is a finite collection of natural numbers, each of which it
subsumes
can make sense, but defining exp as the inverse of log and defining
log as the inverse of exp would fail to say enough about these functions).
A text can introduce notions, statements and namings (to which I'll return)
to be included in some subsequent contexts. These may be for the rest of
the text or only for some definite portion (eg when a proof names some
party to the statement being proved, the better to manipulate it, but the name
is only bound to that party for the duration
of the proof; it may
subsequently be used, outside the proof, to name some other entity; similar
remarks apply to dummy variables
when specifying mappings).
I think I'm writing my pages in a manner for which the relationship between text and context revolves around:
which may have been supplied by context or may be
constructed
during the discourse, possibly from other values. I assume
that context also provides a notion of sameness
for which any value is
equal to
itself and everything true of a value is also true of any value
equal to it: equal values are indistinguishable.
The purpose of this ground-work is to discuss what a discourse may do with
values (once it has introduced any, by whatever means satisfy its criteria of
explanative adequacy) and I see no need to constrain your freedom to use the
tools I build to only such values
as I know how to characterise: the same
applies to much else in this discourse.
which are fragments of the text which the context interprets as values.
which are statements in the text in which a fragment of
text, called a name
, is given meaning as a value: it may retain that
meaning for the duration of some sub-text only or for the rest of the text; it
may even be exported
by the text for use in other contexts. Generally,
the broader the expanse of text over which a name is given meaning, the longer
the name will be: but some large-scope names are short, eg π and &on;.
I shall generally use single characters, English words and &...; tokens
(some of which will be recognised as HTML character entities and displayed as
single characters) for names.
which are fragments of the text which (in their
contexts) introduce terms and denotational forms for use by contexts, notably my
basic denotational forms for plaintext. Namings
are a particular kind of definition; another common kind has the form I shall
describe a donkey which has no tail as an
eyeore
in which a new notion is introduced
in terms of some previously defined notions.
Beyond this, I must trust to your ability to make such sense as you can of the things I write when I try to express the ideas which form the context in which I'm writing this.
Written by Eddy.