What is physically possible?
Balázs Gyenis
Department of History and Philosophy of Science
University of Pittsburgh
Honoring Hajnal Andréka and István Németi
September 12, 2012
Two components of physical descriptions
FIXED
“Law of the theory”
vs.
VARIABLE
“physically possible worlds”
Two components of physical descriptions
FIXED
vs.
VARIABLE
“Law of the theory”
“physically possible worlds”
Differential equation
solution of differential equation
Three assumptions
1. Fixed component: differential equation
2. Variable component: solution of a differential equation
3. ‘Mathematical compatibility’ of fixed and variable components
is sufficient for a plausible notion of physical possibility
solution of diff. eq.
initial value
initial value problem
solution of diff. eq.
initial value
initial value problem
→
‘bolution’ of diff. eq.
solution of diff. eq.
→
‘bolution’ of diff. eq.
initial value
→
‘binitial value’
initial value problem
solution of diff. eq.
→
‘bolution’ of diff. eq.
initial value
→
‘binitial value’
initial value problem
→
‘binitial value problem’
What is required of a ‘bolution’ ?
I
makes sense
What is required of a ‘bolution’ ?
I
makes sense
I
can be interpreted
What is required of a ‘bolution’ ?
I
makes sense
I
can be interpreted
I
can be motivated
What is required of a ‘bolution’ ?
I
makes sense
I
can be interpreted
I
can be motivated
I
under ‘typical’ circumstances reduces to the notion of a
solution
What is required of a ‘bolution’ ?
I
makes sense
I
can be interpreted
I
can be motivated
I
under ‘typical’ circumstances reduces to the notion of a
solution
Physically possible worlds: set of all bolutions
What is required of a ‘bolution’ ?
I
makes sense
I
can be interpreted
I
can be motivated
I
under ‘typical’ circumstances reduces to the notion of a
solution
Physically possible worlds: set of all bolutions
(some) solutions: mere representational short-hands for bolutions
Potential benefit
The set of all solutions which are representational short-hands for
bolutions might be narrower than the set of all solutions.
Two readings of physical possibility
(A) A possible world is physically possible according to a theory T
if it satisfies the physical laws L of T .
Two readings of physical possibility
(A) A possible world is physically possible according to a theory T
if it satisfies the physical laws L of T .
(B) A possible world is physically possible according to a theory T
if it has the same physical laws L as does T .
Best true system account of laws
(BTS) Laws are propositions of the true deductive systems which
best balance informativeness and simplicity.
Best true system account of laws
Under (BTS) and reading (B) the set of physically possible worlds
may be narrower.
Example: empty spacetime.
Well posed problems
1. solution exists
2. solution is unique
3. solution depends continuously on given data
Best approximately true input-output system account of
laws
(BATIS) Laws are propositions of the deductive systems which
best balance approximation to truth, informativeness, simplicity,
and the ability to entail further informative and simple approximate
truths when they are supplemented by accessible informative and
simple approximate truths.
Potential consequence of reading (B) and (BATIS)
Only solutions of well posed initial value problems of a theory T
are physically possible according to T .
Thanks.