What this math problem illustrates is why one procedure works in problem solving and others don't.
Context and issue framing are key issues in math and in everyday life.
When "facts" are presented in a particular way they can seem compatible with reality and yet not add up.
It is as true for religion as for a math problem.
Bertrand Russell discovered this to his dismay. Read below a quote from Wikipedia:
Russell continued to defend logicism, the view that mathematics is in some important sense reducible to logic, and along with his former teacher, Alfred North Whitehead, wrote the monumental Principia Mathematica, an axiomatic system on which all of mathematics can be built. The first volume of the Principia was published in 1910, which is largely ascribed to Russell. More than any other single work, it established the specialty of mathematical or symbolic logic. Two more volumes were published, but their original plan to incorporate geometry in a fourth volume was never realised, and Russell never felt up to improving the original works, though he referenced new developments and problems in his preface to the second edition. Upon completing the Principia, three volumes of extraordinarily abstract and complex reasoning, Russell was exhausted, and he never felt his intellectual faculties fully recovered from the effort. Although the Principia did not fall prey to the paradoxes in Frege's approach, it was later proven by Kurt Gödel that neither Principia Mathematica, nor any other consistent system of primitive recursive arithmetic, could, within that system, determine that every proposition that could be formulated within that system was decidable, i.e. could decide whether that proposition or its negation was provable within the system ( Gödel's incompleteness theorem ).
What lesson did Russell learn that Godel understood which is applicable to our simple Math Problem?
Any system which is self-referential is recursive and leads to Paradox.
Terry
