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8/19/2019 Bangu _Fiction and Explanation.pdf
http://slidepdf.com/reader/full/bangu-fiction-and-explanationpdf 1/49
Explanatory Fictions
and
Fictional Explanations
Sorin Bangu
Univ. of [email protected]
8/19/2019 Bangu _Fiction and Explanation.pdf
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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
8/19/2019 Bangu _Fiction and Explanation.pdf
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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
3
8/19/2019 Bangu _Fiction and Explanation.pdf
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Can fictions explain?
• No: Vaihinger [Hempel, Salmon,…]
• Yes: Bokulich, Elgin… [2009]
Cautious ‘yes’: in what circumstances (new)
Account: two steps
1. fictional explanations2. fictional explanations ≈ (genuine) explanations
fictions fictional explanations (genuine) explanations
role in should be accepted as
2nd part: case study; phase transitions inthermodynamics and SM
4
8/19/2019 Bangu _Fiction and Explanation.pdf
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Can fictions explain? No
5
8/19/2019 Bangu _Fiction and Explanation.pdf
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Can fictions explain? No
If SC doesn’t exist, then how is it that there are giftsunder the three?
Explanation :: Understanding
6
8/19/2019 Bangu _Fiction and Explanation.pdf
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Can fictions explain? No
If vortices don’t exist, then how is it that the Moonmoves?
Explanation :: Understanding
7
8/19/2019 Bangu _Fiction and Explanation.pdf
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Can fictions explain? No.
Because falsehoods don’t explain!
If the EXPLANANS are false / fictions, then how is itthat the EXPLANANDUM holds / is true?
Explanation :: Understanding
8
8/19/2019 Bangu _Fiction and Explanation.pdf
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Can fictions explain? No.
Because falsehoods don’t explain!
If the EXPLANANS are false / fictions, then how is itthat the EXPLANANDUM holds / is true?
Explanation :: Understanding
total falsehoods: gross ‘cancellation effect’
Russell syllogism
bread is stone / milk
stone / milk is nourishing
bread is nourishing
9
8/19/2019 Bangu _Fiction and Explanation.pdf
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Can fictions explain? No.
Because falsehoods don’t explain!
If the EXPLANANS are false / fictions, then how is itthat the EXPLANANDUM holds / is true?
Explanation :: Understanding
idealizations / approximationspartial falsehoods: subtle ‘cancellation effect’
Scientific modeling
false / idealized explanans
true explanandum
total falsehoods: gross ‘cancellation effect’
Russell syllogism
bread is stone / milk
stone / milk is nourishing
bread is nourishing
10
8/19/2019 Bangu _Fiction and Explanation.pdf
http://slidepdf.com/reader/full/bangu-fiction-and-explanationpdf 11/49
Can fictions explain? No.
Because falsehoods don’t explain!
If the EXPLANANS are false / fictions, then how is itthat the EXPLANANDUM holds / is true?
Explanation :: Understanding
idealizations / approximationspartial falsehoods: subtle ‘cancellation effect’
Scientific modeling
false / idealized explanans
true explanandum
total falsehoods: gross ‘cancellation effect’
Russell syllogism
bread is stone / milk
stone / milk is nourishing
bread is nourishing
11
8/19/2019 Bangu _Fiction and Explanation.pdf
http://slidepdf.com/reader/full/bangu-fiction-and-explanationpdf 12/49
Can fictions explain? No.
Because falsehoods don’t explain!
If the EXPLANANS are false / fictions, then how is itthat the EXPLANANDUM holds / is true?
Explanation :: Understanding
idealizations / approximationspartial falsehoods: subtle ‘cancellation effect’
Scientific modeling
false / idealized explanans
true explanandum
total falsehoods: gross ‘cancellation effect’
Russell syllogism
bread is stone / milk
stone / milk is nourishing
bread is nourishing
‘Concerned’ v. ‘unconcerned’ with the truth
[Winsberg 2009]
12
8/19/2019 Bangu _Fiction and Explanation.pdf
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Can fictions explain? No.
Because falsehoods don’t explain!
If the EXPLANANS are false / fictions, then how is itthat the EXPLANANDUM holds / is true?
Explanation :: Understanding
idealizations / approximationspartial falsehoods: subtle ‘cancellation effect’
Scientific modeling
false / idealized explanans
true explanandum
total falsehoods: gross ‘cancellation effect’
Russell syllogism
bread is stone / milk
stone / milk is nourishing
bread is nourishing
Hempel: no explanation
Salmon: no explanation
‘Concerned’ v. ‘unconcerned’ with the truth
[Winsberg 2009]
13
8/19/2019 Bangu _Fiction and Explanation.pdf
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Can fictions explain? No.
Because falsehoods don’t explain!
Hempel
Explananas (L + IC)
Explanandum
Four conditions for anexplanation
…
2. “empirical condition of
adequacy” = the sentencesconstituting the explanans mustbe true (1965, 248)
…
Salmon
• Fictional entities and
fictional processes do not
meet the requirements ofgenuine 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
8/19/2019 Bangu _Fiction and Explanation.pdf
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Can fictions explain? No.
Because falsehoods don’t explain!
Hempel
Explananas (L + IC)
Explanandum
Four conditions for anexplanation
…
2. “empirical condition of
adequacy” = the sentencesconstituting the explanans mustbe true (1965, 248)
…
Salmon
• Fictional entities and
fictional processes do not
meet the requirements ofgenuine 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
8/19/2019 Bangu _Fiction and Explanation.pdf
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Can fictions explain? No.
Because falsehoods don’t explain!
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
8/19/2019 Bangu _Fiction and Explanation.pdf
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A diagnostic
The Main Problem
true explananda
false / fictional explanans
17
8/19/2019 Bangu _Fiction and Explanation.pdf
http://slidepdf.com/reader/full/bangu-fiction-and-explanationpdf 18/49
A diagnostic
The Main Problem
true explananda
false / fictional explanans
Solution:
Fictional content is
eliminable
dispensable, etc.
18
8/19/2019 Bangu _Fiction and Explanation.pdf
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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
8/19/2019 Bangu _Fiction and Explanation.pdf
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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
8/19/2019 Bangu _Fiction and Explanation.pdf
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A role for fictions in explanation
• indirect, two steps
1. Fictional explanation
2. (Good) fictional explanation genuine explanation
Fictional explanation
21
8/19/2019 Bangu _Fiction and Explanation.pdf
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A role for fictions in explanation
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
8/19/2019 Bangu _Fiction and Explanation.pdf
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A role for fictions in explanation
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
8/19/2019 Bangu _Fiction and Explanation.pdf
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Can fictions explain?
Key-question
why / when do scientistsaccept explanations inwhich the fictional content
of the explanans seems (is)ineliminable?
A:
- When the explananda are‘phenomena’ = also haveineliminable fictional
content.- So not a worrisome caseof [false true]
Fictionalist principle
‘fictions in the explanandaallow fictions in theexplanans’
24
8/19/2019 Bangu _Fiction and Explanation.pdf
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Can fictions explain?
Key-question
why / when do scientistsaccept explanations inwhich the fictional content
of the explanans seems (is)ineliminable?
A:
- When the explananda are‘phenomena’ = also haveineliminable fictional
content.- So not a worrisome caseof [false true]
Fictionalist principle
‘fictions in the explanandaallow fictions in theexplanans’
Monopoly principle
‘buy fictional property with
fictional money’
25
8/19/2019 Bangu _Fiction and Explanation.pdf
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Can fictions explain?
true explananda[phenomena]
fictional/false explanans
26
8/19/2019 Bangu _Fiction and Explanation.pdf
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Can fictions explain?
fictional/false explananda[‘phenomena’]
fictional/false explanans
true explananda[phenomena]
fictional/false explanans
27
8/19/2019 Bangu _Fiction and Explanation.pdf
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Can fictions explain?
fictional/false explananda[‘phenomena’]
fictional/false explanans
fictionalexplanation
true explananda[phenomena]
fictional/false explanans
28
8/19/2019 Bangu _Fiction and Explanation.pdf
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Can fictions explain?
fictional/false explananda[‘phenomena’]
fictional/false explanans
fictionalexplanation
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]
fictional/false explanans
29
8/19/2019 Bangu _Fiction and Explanation.pdf
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Example of fictional explanation
• Why does water boil?
30
8/19/2019 Bangu _Fiction and Explanation.pdf
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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
8/19/2019 Bangu _Fiction and Explanation.pdf
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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].”
32
“So, here is a problem for the theoreticalphysicist: 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)
8/19/2019 Bangu _Fiction and Explanation.pdf
http://slidepdf.com/reader/full/bangu-fiction-and-explanationpdf 33/49
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].”
33
8/19/2019 Bangu _Fiction and Explanation.pdf
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Explanandum = ‘undergoing a
phase transition’
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
8/19/2019 Bangu _Fiction and Explanation.pdf
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Explanandum
= ‘undergoing a phase transition’
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)
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 dowork
8/19/2019 Bangu _Fiction and Explanation.pdf
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Explanandum
= ‘undergoing a phase transition’
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 iff G behaves in a certain way =
its derivative (tangent) varies discontinuously (Zemansky 1968, 347)
36
-‘singularity’
-‘kink’ -‘sharp corner’
(Stanley 1971, 31)
8/19/2019 Bangu _Fiction and Explanation.pdf
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Explanandum = ‘undergoing a
phase transition’
1. Functionalize
- phase transition = cross ‘coexistence line’ = G has a singularity (kink)
Explanans: water molecules + Statistical Mechanics (QSM)
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].”
37
8/19/2019 Bangu _Fiction and Explanation.pdf
http://slidepdf.com/reader/full/bangu-fiction-and-explanationpdf 38/49
Explanandum = ‘undergoing a
phase transition’
1. Functionalize
- phase transition = cross ‘coexistence line’ = G has a singularity (kink)
Explanans: water molecules + Statistical Mechanics (QSM)
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].”
38
)ln
(ln1
V
Z
V Z G
r
E r e Z
8/19/2019 Bangu _Fiction and Explanation.pdf
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Explanandum = ‘undergoing a
phase transition’
1. Functionalize
- phase transition = cross ‘coexistence line’ = G has a singularity (kink)
Explanans: water molecules + Statistical Mechanics (QSM)
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].”
39
)ln
(ln1
V
Z
V Z G
r
E r e Z
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
8/19/2019 Bangu _Fiction and Explanation.pdf
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Explanandum = ‘undergoing a
phase transition’
1. Functionalize
- phase transition = cross ‘coexistence line’ = G has a singularity (kink)
Explanans: water molecules + Statistical Mechanics (QSM)
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].”
40
)ln
(ln1
V
Z
V Z G
r
E r e Z
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 (isanalytic). 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.
8/19/2019 Bangu _Fiction and Explanation.pdf
http://slidepdf.com/reader/full/bangu-fiction-and-explanationpdf 41/49
Explanandum = ‘undergoing a
phase transition’
1. Functionalize
- phase transition = cross ‘coexistence line’ = G has a singularity (kink)
Explanans: water molecules + Statistical Mechanics (QSM)
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].”
41
)ln
(ln1
V
Z
V Z G
r
E r e Z
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 (isanalytic). 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 theoreticalphysicist: 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)
8/19/2019 Bangu _Fiction and Explanation.pdf
http://slidepdf.com/reader/full/bangu-fiction-and-explanationpdf 42/49
• 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
8/19/2019 Bangu _Fiction and Explanation.pdf
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• ‘Solution’ (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 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
8/19/2019 Bangu _Fiction and Explanation.pdf
http://slidepdf.com/reader/full/bangu-fiction-and-explanationpdf 44/49
• ‘Solution’ (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 fin
(taking the ‘thermodynamic limit’)
44
“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 too
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
8/19/2019 Bangu _Fiction and Explanation.pdf
http://slidepdf.com/reader/full/bangu-fiction-and-explanationpdf 45/49
• ‘Solution’ (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 fin
(taking the ‘thermodynamic limit’)
45
“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 too
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
8/19/2019 Bangu _Fiction and Explanation.pdf
http://slidepdf.com/reader/full/bangu-fiction-and-explanationpdf 46/49
• ‘Solution’ (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 fin
(taking the ‘thermodynamic limit’)
46
“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 too
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
8/19/2019 Bangu _Fiction and Explanation.pdf
http://slidepdf.com/reader/full/bangu-fiction-and-explanationpdf 47/49
Wrapping up:
how/when fictions can be explanatoryfictional/false explananda
[‘phenomena’]
fictional/false explanans
fictionalexplanation
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’
47
8/19/2019 Bangu _Fiction and Explanation.pdf
http://slidepdf.com/reader/full/bangu-fiction-and-explanationpdf 48/49
Wrapping up:
how/when fictions can be explanatory
singularity: fictional
infinite system: fictional
fictional/false explananda
[‘phenomena’]
fictional/false explanans
fictionalexplanation
acceptable when no genuine
explanation exists = one in which the
explananda are phenomena, not
‘phenomena’
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)
Fictionalist principle
‘fictions in explananda allow
fictions in the explanans’
48
8/19/2019 Bangu _Fiction and Explanation.pdf
http://slidepdf.com/reader/full/bangu-fiction-and-explanationpdf 49/49
Thank you