Isomorphisms Induce Meaning, p 50
The perception of an isomorphism between two known structures is a significant advance in knowledge --and I claim that it is such perceptions of isomorphism which create meanings in the minds of people.
Recursively Enumerable Sets vs. Recursive Sets, p 72
I was quite convinced that not only the primes, but any set of numbers which could be represented negatively, could also be represented positively [...] How could a figure and its ground not carry exactly the same information?
[...]
There exists formal systems whose negative space (set of non-theorems) is not the positive set (set of theorems) of any formal system. [...]
There exists recursively enumerable sets which are not recursive.
Implicit and Explicit Meaning, p 82
We see the meaning without seeing the isomorphism. The most blatant example is human language, where people often attribute meaning to words in themselves, without being in the slightest aware of the very complex "isomorphism" that imbues them with meanings. This is an easy enough error to make. It attributes all the meaning to the object (the word), rather than to the link between that object and the real world.