explanatory fictions and fictional explanations - umb forum bangu slides.pdf · explanatory...

Explanatory Fictions and

Fictional Explanations

Sorin Bangu

Univ. of Bergen

[email protected]

mailto:[email protected]

Can fictions explain?

- question of perennial interest “one of the main and most controversial roles that fictional assumptions may play” (Suarez 2009, 7)

Fictionalism

- Vaihinger 1920s

- Van Fraassen 1980s (phil of math: H. Field 1980s) - A. Fine 1990s - M. Suarez 2000s: 2009 Bokulich, Elgin, Winsberg, Morrison, etc.: scientists seem fine with a ‘yes’ answer

2


- question of perennial interest “one of the main and most controversial roles that fictional assumptions may play” (Suarez 2009, 7)

Fictionalism

- Vaihinger 1920s

- Van Fraassen 1980s (phil of math: H. Field 1980s) - A. Fine 1990s - M. Suarez 2000s: 2009 Bokulich, Elgin, Winsberg, Morrison, etc.: scientists seem fine with a ‘yes’ answer

3


• No: Vaihinger [Hempel, Salmon,…] • Yes: Bokulich, Elgin… [2009] Cautious ‘yes’: in what circumstances (new) Account: two steps 1. fictional explanations 2. fictional explanations ≈ (genuine) explanations fictions fictional explanations (genuine) explanations role in should be accepted as

2nd part: case study; phase transitions in thermodynamics and SM

4

Can fictions explain? No

5


If SC doesn’t exist, then how is it that there are gifts under the three?

Explanation :: Understanding

6


If vortices don’t exist, then how is it that the Moon moves?


7

Can fictions explain? No. Because falsehoods don’t explain!

If the EXPLANANS are false / fictions, then how is it that the EXPLANANDUM holds / is true?


8




total falsehoods: gross ‘cancellation effect’ Russell syllogism bread is stone / milk stone / milk is nourishing bread is nourishing

9




idealizations / approximations partial falsehoods: subtle ‘cancellation effect’ Scientific modeling

false / idealized explanans

true explanandum


10






true explanandum


11






true explanandum


‘Concerned’ v. ‘unconcerned’ with the truth [Winsberg 2009]

12






true explanandum


Hempel: no explanation Salmon: no explanation

‘Concerned’ v. ‘unconcerned’ with the truth [Winsberg 2009]

13


Hempel Explananas (L + IC) Explanandum Four conditions for an explanation … 2. “empirical condition of adequacy” = the sentences constituting the explanans must be true (1965, 248) …

Salmon

• Fictional entities and fictional processes do not meet the requirements of genuine physical processes capable of transmitting a mark.

• fiction F cannot be the cause of some phenomenon P—and hence explain P—if F does not exist.

14


Hempel Explananas (L + IC) Explanandum Four conditions for an explanation … 2. “empirical condition of adequacy” = the sentences constituting the explanans must be true (1965, 248) …

Salmon

• Fictional entities and fictional processes do not meet the requirements of genuine physical processes capable of transmitting a mark.

• fiction F cannot be the cause of some phenomenon P—and hence explain P—if F does not exist.

Woodward, Strevens, etc. 15


H. Vaihinger

(1924). The philosophy of ‘as if’ (C. K. Ogden, Trans.). London: Kegan Paul. (Original work published 1911)

Explanation involving fictions Understanding

• “…the fiction induces only an illusion of understanding” (p. xv)

• “[F]iction (…) does not create real knowledge” (p. 88)

16

A diagnostic The Main Problem

true explananda

false / fictional explanans

17

A diagnostic The Main Problem

true explananda

false / fictional explanans

Solution: Fictional content is

eliminable dispensable, etc.

18

A role for fictions in explanation Key-question:

can fictions explain?

why / when do scientists accept explanations in which the fictional content of the explanans is (seems) ineliminable?

starting point: the explanandum has fictional content too

- this situation manifests in a variety of ways

- not always explicit

- some clear example later

19

A role for fictions in explanation Key-question:

can fictions explain?

why / when do scientists accept explanations in which the fictional content of the explanans is (seems) ineliminable?

starting point: the explanandum has fictional content too

- this situation manifests in a variety of ways

- not always explicit

- a clear example in 2nd part

20

A role for fictions in explanation

• indirect, two steps

1. Fictional explanation

2. (Good) fictional explanation genuine explanation

Fictional explanation

21


Fictional explanations • Cases when both the explanans and the explananda involve fictions

explananda too involve fictions

Explananda = ? ‘Phenomena’ – the Woodward & Bogen sense

Data v. phenomena

- ‘constructed’ out of measurement data

-’shaped’ into such as to be invariant

phenomena - not out there, but posited ‘fictional’

Bogen, J., and J. Woodward (1988) Saving the phenomena The Philosophical Review 97: 303-352.

22


Fictional explanations • Cases when both the explanans and the explananda involve fictions

explananda too involve fictions

Explananda = ? ‘Phenomena’ – the Woodward & Bogen sense

Data v. phenomena

- ‘constructed’ out of measurement data

-’shaped’ into such as to be invariant

phenomena - not out there, but posited ‘fictional’

Bogen, J., and J. Woodward (1988) Saving the phenomena The Philosophical Review 97: 303-352.

Data ‘Shaped’ into phenomena

Phenomena ‘Constructed’ from data (such as to be invariant) Not out there, but posited “phenomena (…) cannot be reported by observational claims.” (p. 343, 306). Fictions (concerned with the truth)

23


Key-question why / when do scientists accept explanations in which the fictional content of the explanans seems (is) ineliminable?

A: - When the explananda are

‘phenomena’ = also have ineliminable fictional content.

- So not a worrisome case of [false true]

Fictionalist principle ‘fictions in the explananda allow fictions in the explanans’ 24


Key-question why / when do scientists accept explanations in which the fictional content of the explanans seems (is) ineliminable?

A: - When the explananda are

‘phenomena’ = also have ineliminable fictional content.

- So not a worrisome case of [false true]

Fictionalist principle ‘fictions in the explananda allow fictions in the explanans’

Monopoly principle ‘buy fictional property with

fictional money’

25


true explananda

[phenomena]

fictional/false explanans

26


fictional/false explananda [‘phenomena’]


true explananda

[phenomena]


27




fictional explanation

true explananda

[phenomena]


28





acceptable when no genuine explanation exists = one in which the explananda are phenomena, not ‘phenomena’

Fictionalist principle ‘fictions in explananda allow fictions in the explanans’

true explananda

[phenomena]


29

Example of fictional explanation

• Why does water boil?

30

Explanandum = ‘undergoing a phase transition’

the property of ‘changing state’: liquid vapor (gas)

ice (solid)

- water’s capacity to undergo a ‘phase transition’

- water’s capacity to ‘cross coexistence line’

2. Find realizers + theory

Water (H20) molecules

Statistical Mechanics (QSM)

“When all of this is in, we are entitled to the claim that [boiling] has been

reduced to the [behavior of molecules].”

31



ice (solid)








32

“So, here is a problem for the theoretical physicist: prove that as you raise or lower the temperature of water you have phase transitions to water vapor or to ice. Now, that’s a tall order! We are far from having such a proof. In fact there is not a single type of atom or molecule for which we can mathematically prove that it will crystallize at low temperature. These problems are just too hard for us.” (D. Ruelle 1991: 123-4)



ice (solid)








33


1. Functionalize

- Water’s capacity to undergo a phase transition = cross ‘coexistence line’

More precisely:

- Define a quantity called ‘free energy’: G = H – TS

- Crossing takes place if G behaves in a certain way = its derivative (tangent) varies discontinuously (Zemansky 1968, 347)

34

H = enthalpy of the system = total energy = internal energy + pV


1. Functionalize


More precisely:


- Crossing takes place if G behaves in a certain way = its derivative (tangent) varies discontinuously (Zemansky 1968, 347)

35

H = enthalpy of the system = total energy = internal energy + pV

T = temperature of the system

S = entropy of the system = system's ability to do work


1. Functionalize


More precisely:


- Crossing iff G behaves in a certain way =

its derivative (tangent) varies discontinuously (Zemansky 1968, 347)

36

-‘singularity’ -‘kink’ -‘sharp corner’ (Stanley 1971, 31)


1. Functionalize

- phase transition = cross ‘coexistence line’ = G has a singularity (kink)

Explanans: water molecules + Statistical Mechanics (QSM)






37


1. Functionalize








38

)ln

(ln1

V

ZVZG

r

EreZ


1. Functionalize








39

)ln

(ln1

V

ZVZG

r

EreZ

G can’t have a singularity! Impossible to find one in principle (mathematical result) Reduction is blocked at step 2: realizers + theory

Boiling = case of emergence not captured in the Kim-Chalmers model -Not weak emergence -Not strong emergence due to failure at step 1


1. Functionalize








40

)ln

(ln1

V

ZVZG

r

EreZ

G can’t have a singularity! Impossible to find one in principle (mathematical result) G depends on Z, so if G is to have singularities, Z has to have singularities. But Z can’t have singularities (is analytic). Z is a finite sum of analytic functions (not having singularities), and any finite sum of analytic functions is analytic (no singularities) So G can’t have singularities b.c. of Z.


1. Functionalize








41

)ln

(ln1

V

ZVZG

r

EreZ

G can’t have a singularity! Impossible to find one in principle (mathematical result) G depends on Z, so if G is to have singularities, Z has to have singularities. But Z can’t have singularities (is analytic). Z is a finite sum of analytic functions (not having singularities), and any finite sum of analytic functions is analytic (no singularities) So G can’t have singularities b.c. of Z (Kadanoff 2000)

“So, here is a problem for the theoretical physicist: prove that as you raise or lower the temperature of water you have phase transitions to water vapor or to ice. Now, that’s a tall order! We are far from having such a proof. In fact there is not a single type of atom or molecule for which we can mathematically prove that it will crystallize at low temperature. These problems are just too hard for us.” (D. Ruelle 1991: 123-4)

• Proof (!): Yang & Lee 1952, etc.)

• singularity problem

A phase transition = singularity in G

can be derived within QSM

if the system contains an infinite

number of particles

N infinite

N / V finite

(‘thermodynamic limit’)

42

N = number of molecules V = volume

“The existence of a phase transition requires an infinite system. No phase transitions occur in systems with a finite number of degrees of freedom.” (Kadanoff 2000, 238)

Explanandum

Explanans

• ‘Solution’ (Yang & Lee 1952, etc.)





number of particles

N infinite

N / V fin

(taking the ‘thermodynamic limit’)

43

“The existence of phase transitions shows that we have to be careful when we adopt a reductionist approach. Phase transitions correspond to emerging properties.” (Prigogine 1997, 45)

A case of fictional explanation The explanandum has fictional content...

The explanans have fictional content -“no experiments, no matter how finely tuned, can ever determine whether the ‘corners’ which bound [phase transitions] regions are sharp or round” (Liu 2001, 328) - “the transition is neither ‘smooth’ nor ‘singular’” (Liu 1999, 103). -[singularities are] “artifacts”; “fictions”; “do not exist in reality” (Liu 1999, S104) - “the role of a singularity is to represent a phase change phenomenon. Note that the term ‘phenomenon’ is used here in the specific sense of Bogen and Woodward. “ (Bangu 2009, 49)

Explanandum

Explanans






number of particles

N infinite

N / V fin


44


A case of fictional explanation The explanandum has fictional content too


Explanandum

Explanans






number of particles

N infinite

N / V fin


45




Explanandum

Explanans






number of particles

N infinite

N / V fin


46



The explanans have fictional content -“no experiments, no matter how finely tuned, can ever determine whether the ‘corners’ which bound [phase transitions] regions are sharp or round” (Liu 2001, 328) - “the transition is neither ‘smooth’ nor ‘singular’” (Liu 1999, 103) -[singularities are] “artifacts”; “fictions”; “do not exist in reality” (Liu 1999, S104) - “the role of a singularity is to represent a phase change phenomenon. Note that the term ‘phenomenon’ is used here in the specific sense of Bogen and Woodward. “ (Bangu 2009, 499)

Explanandum

Explanans

Wrapping up: how/when fictions can be explanatory






47

Wrapping up: how/when fictions can be explanatory

singularity: fictional

infinite system: fictional





no explanation exists in which the explanandum = phase transition (a real process!) is not represented as a singularity (and the explanans don’t involve an infinite system)


48

Thank you

49

explanatory fictions and fictional explanations - umb forum bangu slides.pdf · explanatory...

Documents