Physics Research - Wave Mechanics
- Discrete Quantum Theory
- Lorentzian Ether Theory
- Potential Continuity Equation
- Magnetism is Not Fundamental
- Schrodinger's Equation
- Derivation of Maxwell Eqns
- Momentum Operator
- Quantum Field Theory
- Gravitomagnetism
- Radial Force Deflection
Physics Notes - Interference Patterns
- Calculus of Units
- Physics Questions
- Physics Derivations
- Electrostatics Derivations
- Green's Functions
- Lagrange's Equation
- First Year Graduate Physics
- Units and Dimensions
- Fermi's Golden Rule
- Geometrical Optics
- Work-Energy Theorem
- The Carnot Heat Engine
Mathematics - Formula Functions
- Knot Theory
- Pythagorean Theorem
- Monte Carlo Integration
- Fibonacci Primes
- Error Analysis
- Fourier Delta
- Lie Groups
- De Moivre's Theorem
- The Total Derivative
Resources |
## Curry's ParadoxSetup: (S) If it is true that S, then Paris is the capital of Italy. Self-referential statements of this form seem to be able to prove that any statement placed in the consequent is true. If we assume S is true, then the antecedent is true by the assumption, and so the consequent follows since the implication is true by the assumption. If we assume S is false, then by the negation of material implication, we obtain "It is true that S and Paris is not the capital of Italy." But this contradicts that S is false, so this case can't happen. The contradiction step can be avoided, while still showing the consequent is true by noting that assuming S is true, Paris is the capital of Italy, as was shown in the last paragraph. But this is exactly the statement made by S, so S is true, and therefore Paris is indeed the capital of Italy whether or not S is true. The problem is that not all statements can be assigned a truth value. Statement S is self-referential, and this property causes problems for whichever truth value is assigned to it. |