Mathematics – General Mathematics
Scientific paper
2003-04-21
Mathematics
General Mathematics
v2; revised para 5(xviii); introduced standardised ACI compliant notation for citations; 15 pages; an HTML version is availabl
Scientific paper
We formally define a "mathematical object" and "set". We then argue that expressions such as "(Ax)F(x)", and "(Ex)F(x)", in an interpretation M of a formal theory P, may be taken to mean "F(x) is true for all x in M", and "F(x) is true for some x in M", respectively, if, and only if, the predicate letter "F" is a mathematical object in P. In the absence of a proof, the expressions "(Ax)F(x)", and "(Ex)F(x)", can only be taken to mean that "F(x) is true for any given x in M", and "It is not true that F(x) is false for any given x in M", respectively, indicating that the predicate "F(x)" is well-defined, and effectively decidable individually, for any given value of x, but that there may be no uniform effective method (algorithm) for such decidability. We show how some paradoxical concepts of Quantum Mechanics can then be expressed in a constructive interpretation of standard Peano's Arithmetic.
No associations
LandOfFree
Is there a "loophole" in Goedel's interpretation of his formal reasoning and its consequences? does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Is there a "loophole" in Goedel's interpretation of his formal reasoning and its consequences?, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Is there a "loophole" in Goedel's interpretation of his formal reasoning and its consequences? will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-551174