Information Technology Reference
In-Depth Information
It was from
Tractatus
that predicate calculus emerged. This is a formal language
for describing states of affairs or facts. Pure functional programming languages,
such as ML and LISP, have evolved from predicate calculus. Wittgenstein describes
predicate calculus in the
Tractatus
. His early work encapsulated a formal and logical
representational schema into a descriptive form that was based upon denotational (or
referential) semantics. Such a semantics link the meaning of a symbol to an object in
the world. A 'symbol' can only have one meaning and a 'sign' can represent two or
more symbols. The distinction between symbols is inferred by how the sign is used.
•
T3.32,
A sign is what can be perceived of a symbol
•
T3.321
, So one and the same sign (written or spoken) can be common to two
different symbols—in which case they signify in different ways.
Thus, a symbol's physical representation is a sign and it is usually a recognisable
mark on the page such as a word or character, but it can be a spoken word or any
other physical display. This display (the sign) refers through a symbol to an object
in the world. Wittgenstein also referred to these signs presented in some kind of
relationship as 'pictures'.
•
T3.221
, Objects can only be
named
. Signs are their representatives. I can only
speak
about
them: I cannot
put them into words
. Propositions can only say how
things are, not what they are.
•
T3.27
, A name cannot be dissected any further by means of a definition: it is a
primitive sign
•
T3.3,
Only propositions have sense: only in the nexus of a proposition does a
name have meaning.
•
T3.32
, A sign is what can be perceived of a symbol.
The idea here is that the meaning of the symbol is to what it points (its referent), and
so it can only have one meaning. A sign can represent more than one symbol and its
distinction may be inferred as to how it is used. A 'name' is a primitive sign.
A sign may also represent other signs in relationship; these are signs that represent
propositions, or states of affairs. For example, the sign 'father' refers to a sign that
refers, in turn, to the proposition 'A man who has an offspring'. Thus, the sign 'father'
refers to the symbol that is the object of being a father. These are propositions and
refer to a state of affairs.
8.3.1
Objects
Wittgenstein was after a set of primitive and simple objects in the world. These
objects would form the base from which everything else could be expressed in terms
of propositions. In this case, the referents (the objects) will have some logically
strange properties. Objects must be:
