Let F be some property had by and only by the sequence of symbols:
- The sequence of symbols with property F is not a sentence expressing a truth, and 2+2=4.
- The sequence of symbols with property F is not a sentence expressing a truth.
In my previous post, I tried to create space for the idea that in natural language not every pair of sentences can be conjoined. The above argument extends this to sufficiently rich artificial languages, since the above case could be formulated in an artificial language.
We can keep classical logic rules such as:
- If c is the conjunction of a and b, and a and b are both true, then c is true,