= {+ happy smilie, sad smilie, bucked - tooth vampire with one tooth missing,
cross smilie , ate something sour smilie, smilie af ter a bizzare comment}. (7)
Thus six real valued flags replace replace the one integer valued flag
Q = {truth}. (8)
This assignation taken to be the driving force behind the optimization of corre-
spondence between language and the world and hence radical interpretation.
8 Implications for the Philosophy of Mathemat-
ics
8.1 The Continuum Hypothesis and the Segmentation Prob-
lem
In mathematics there is an assumption: the Continuum Hypothesis see for
example Maddy (1993) [27] and Hirsch (1995) [18], that mathematical objects
can have continuous properties. A major place where this hypothesis appears is
that real numbers cannot be constructed from rational numbers necessitating a
new assumption for real number construction. An example of such an assump-
tion is given by Dedekind’s axiom of completeness, see for example Issacs (1968)
[20]. Hirsch (1995) [18] p.146 notes as a possibility that
”(b) Neurologists and psychologists learn enough about cell assem-
blies and cognition to make it scientifically certain that there could
not possibly be any activity in the nervous system which would cor-
respond to a truth value for the Continuum Hypothesis.”
What is about to be advocated here is something along these lines, essentially
it is argued that both truth and meaning are intrinsically real valued. The
segmentation problem is the problem of how to account for the existence of and
meaning attributed to the real numbers. From the point of view of traditional
radical interpretation the number of times truth can be assigned to natural
language statements is integer valued, and so does not allow for real numbers.
There are three parts to this problem:
1. how to account for the fact that real numbers as pure mathematical con-
structs have meaning,
2. how to account for the success, meaning, and use of real numbers in the
physical world,
3. how to account for the success, meaning and use of real numbers in cog-
nitive science.
20