272
Appendices
Fig. A.6 Extract from Whitehead and Russell’s Principia Mathematica
A.3.5 Falsifiability
The concept of falsifiability, or the notion that every physical theory must be
capable, at least in principle, of being proven wrong, was introduced by the
philosopher of science, Karl Popper. In Part 3, we see that there are currently
diverging opinions on whether a lack of falsifiability is sufficient grounds for
rejecting a physical theory. Also in Chap. 4, we see that the logician, Kurt
Gödel, showed that certain propositions inside a system cannot be proved
from within the system itself. In addition, undecidable statements, such as
the famous paradox This sentence is false, obviously cannot be falsified.
A.3.6 Variation of the Fine Structure Constant
A very tight bound on current variations of the Fine Structure Constant α
has been set at one part in 10 17 per year [4]. This result however does not
preclude past variations. Research by a group at the University of New South
Wales has shown a variation in α of approximately one part in 10 5 spanning
∼23% to 87% of the age of the universe [5]. More recent work by this group
claims that the changes in α are different in different directions in the universe
[6].
A.4.1 Russell’s Paradox
Russell discovered the paradox that bears his name in 1901 while using set
theory to formalise the mathematics of arithmetic. A set can be considered
Appendices
Fig. A.6 Extract from Whitehead and Russell’s Principia Mathematica
A.3.5 Falsifiability
The concept of falsifiability, or the notion that every physical theory must be
capable, at least in principle, of being proven wrong, was introduced by the
philosopher of science, Karl Popper. In Part 3, we see that there are currently
diverging opinions on whether a lack of falsifiability is sufficient grounds for
rejecting a physical theory. Also in Chap. 4, we see that the logician, Kurt
Gödel, showed that certain propositions inside a system cannot be proved
from within the system itself. In addition, undecidable statements, such as
the famous paradox This sentence is false, obviously cannot be falsified.
A.3.6 Variation of the Fine Structure Constant
A very tight bound on current variations of the Fine Structure Constant α
has been set at one part in 10 17 per year [4]. This result however does not
preclude past variations. Research by a group at the University of New South
Wales has shown a variation in α of approximately one part in 10 5 spanning
∼23% to 87% of the age of the universe [5]. More recent work by this group
claims that the changes in α are different in different directions in the universe
[6].
A.4.1 Russell’s Paradox
Russell discovered the paradox that bears his name in 1901 while using set
theory to formalise the mathematics of arithmetic. A set can be considered