Irrational Reasoning - Natural and Artificial Reasoning - page 115

9.2 The Paradigm Leap

The Tractatus is a magnificent piece of work and is an effective description of how
programming languages should be linked to a computer through 'sense' (as with
meaning) assignment. There is no problem with the engineering necessity of this
approach to 'sense and meaning'. On a broader scale, it sidesteps many of the
paradoxes of the linguistic philosophy of the day. However, it has one fatal flaw
when applied to the human use of language. Wittgenstein eventually exposed this
flaw. He noted that it is not possible to unambiguously describe everything within the
propositional paradigm . He found that the normal use of language is riddled with
example concepts that cannot be bounded by logical statements that depend upon a
pure notion of referential objects. So I now turn to Wittgenstein's second great work
where he explores the issues this raises (Wittgenstein 1953 ).
Wittgenstein illustrates this problem of defining concepts, using a propositional
framework, in his P hilosophical I nvestigations. We will refer to paragraphs in this
work as PI n where n is an integer. In his illustration, he attempts to define a 'game'( PI
69- PI 71). He makes clear that such an unambiguous definition cannot be achieved.
If you try to create such a definition then you will always fail both to exclude all
examples that are not games and to include all examples that are.
It is through such considerations that Wittgenstein proposed a new linguistic phi-
losophy that was based upon what I will call 'inferential semantics'. David Gooding
(University of Bath, private communication 2004) notes that:

• The view epitomised by Wittgenstein's Philosophical Investigations is that mean-

ing, grammar and even syntactic rules emerge from the collective practices (the
situated, changing, meaningful use of language) of communities of users.

It is because of this observation by Wittgenstein that we make the distinction between
rational and irrational sets (see Chap. 8-A Rational Set).

An irrational set is where no finite set of rules can be constructed that can include unambigu-
ously any member of that set and, at the same time, unambiguously exclude any non-member
of that set.

By way of illustration, consider the set of chairs and a possible specification
(Fig. 9.3 ). Here we have a typical chair (1), a high chair (2), a bar stool (3), a
shooting stick (4) and a shooting stick that is also an umbrella (5) and finally a chair
that is a maze that cannot even be sat upon. Each of these stages eliminates a rule
in the original specification of a chair. It is always possible to find some exception
to a finite set of rules that attempts to identify a member of the set 'chair'. Even if
every exception were added to a membership list this would break down by simply
discovering a context in which at least one member would cease to be identified as
a member through the use of the rules. The more additions made of extreme cases
to the set, the more opportunities there will be for finding situations that exclude
accepted members of the set.