2. “…no
statement
which
refers
to
a
‘reality’
transcending
the
limits
of
all
possible
experience
can
possibly
have
any
literal
significance;
from
which
it
must
follow
that…
those
who
have
striven
to
describe
such
a
reality
have
all
been
devoted
to
the
produc*on
of
nonsense.”
Alfred
Jules
Ayer,
“The
Elimina*on
of
Metaphysics”
4. Problem
No.
1:
“Verifica*on”
is
too
strong
a
criterion.
If
truth
value
requires
verifica*on,
then
some
proposi*ons
can
never
be
considered
conclusively
true.
10. strong
verifiability:
verifica*on
that
makes
the
truth
value
of
a
proposi*on
certain
weak
verifiability:
verifica*on
that
makes
the
truth
value
of
a
proposi*on
probable
12. Problem
No.
2:
The
Problem
of
Induc*on
induc5ve
reasoning:
extrac*ng
a
generaliza*on
from
specific
facts
or
cases.
13. induc*ve
reasoning
1. In
the
past,
most
sheep
have
been
white.
2. Today,
most
sheep
are
white.
3. Therefore,
in
the
future
most
sheep
will
probably
be
white.
14. induc*ve
reasoning
1. In
the
past,
the
future
has
resembled
the
past.
2. Today,
the
future
resembles
the
past.
3. Therefore,
in
the
future,
the
future
will
probably
resemble
the
past.
16. Gödel’s
First
Incompleteness
Theorem
Any
effec5vely
generated
theory
capable
of
expressing
elementary
arithme5c
cannot
be
both
consistent
and
complete.
In
par5cular,
for
any
consistent,
effec5vely
generated
formal
theory
that
proves
certain
basic
arithme5c
truths,
there
is
an
arithme5cal
statement
that
is
true,
but
not
provable
in
the
theory.
17. In
other
words….
An
arithme*c
system,
for
instance
a
finite
set
of
axioms,
cannot
be
BOTH
consistent
and
complete.
18. where….
Consistent
–>
contains
no
logical/mathema*cal
contradic*ons
Complete
–>
describes
all
possible
logical/
mathema*cal
statements.
19. In
other
words….
…there
is
an
arithme*c
statement
that
is
true,
but
not
provable
by
the
theory.
Finite
lists
of
axioms
cannot
describe
a
system
where
all
statements
are
shown
to
be
true/
false.
