Programming and Meaning - Natural and Artificial Reasoning - page 110

3. T2.0123 , If I know an object I also know all its possible occurrences in states
of affairs.
1. (every one of these possibilities must be part of the nature of the object)
2. A new possibility cannot be discovered later.
a. T2.01231 , If I am to know an object, though I need not know its external
properties, I must know all its internal properties.
4. T2.03, In a state of affairs objects fit into one another like links of a chain.
1. T2.033 , Form is the possibility of structure.

These referents (objects) are intended to be more than just elements of description;
they form the real world:

T2.04 , The totality of existing states of affairs is the world.
T2.06 , The existence and non-existence of states of affairs is reality. (We also call the
existence of states of affairs a positive fact, and their non-existence a negative fact).

From these referents, the full force of logic, predicate and propositional calculus
retains stability of meaning and sense. Such a stance results in the position that
everything is potentially unambiguously describable:

T2.225 , There are no pictures that are true a priori.
T2.224 , It is impossible to tell from a picture alone whether it is true or false.
T7 . What we cannot speak about we must pass over in silence.

8.3.2 A Rational Set

I now introduce here the idea of a 'rational' set. The idea of rational and irrational sets
was proposed first by Jan Townsend Addis (private communication February 2004),
who related the irrational sets to Cantor's (1845-1918) irrational numbers. In the
case of rational numbers the rule was that a member number could be expressed as a
ratio of integers. Examples of irrational numbers are √ 2 and . There are infinitely

more irrational numbers than rational numbers. So we will define a 'rational' set is
a set where there is a finite set of rules that unambiguously includes any member of
that set and unambiguously excludes any non-member of that set .
It should be noted that all the sets referenced by the Tractatus are rational, where
set membership is always specifiable and context independent or has an explicit
context that is also rational. This, as discussed above, was the formal limitation
imposed on the Tractatus .
The Tractatus provides an extensive and useful description of computer program-
ming languages. The argument is that signs (the visible part of an expression) in
propositions do not always refer to primitive objects but are themselves referencing
propositions. This is expressed by the following Tractatus statements:

π

T3.14, What constitutes a propositional sign is that in its elements (the words) stand in a
determinate relation to one another.
A propositional sign is a fact.