Varie\u0026es of structural explana\u0026ons and the no\u0026ons of explanatory pluralism

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Varie&es of structural explana&ons and the no&ons of explanatory

pluralism

DÜsseldorf, EPSA conference 2015 Philippe Huneman

(IHPST (CNRS/Université Paris I Sorbonne), Paris). hKp://philippehuneman.wordpress.com

Context of the overall project

• Biology explains by uncovering mechanisms • Molecular biology

• Neuroscience • EvoluSonary biology & ecology

• Mechanis)c vs phenomenological models; processes vs pa7erns.

Context of the overall project

• Many explanaSons are using topological and generally formal properSes of abstract spaces in ecology and evoluSonary biology

• They are well fit to explain robustness (Huneman 2010)

• They abstract away from mechanisms

BaKerman (2010), Jackson and PeXt (1998), Sober (1983)

Outline

• Considering mechanisms • Explaining without mechanisms • DemarcaSng a family of structural explanaSons • AccounSng for the explanatory capacity of mathemaScal properSes – The constraint account

• VarieSes of structural explanaSons – Homogeneous and heterogeneous pluralism

• Explanatory pluralism and its kinds

• A complex and fuzzy noSon with a long history • Anything should be explained/ruled by the laws of mechanics (les mécaniciens)

• Explaining from parts to wholes (Kant, mechanism vs teleology)

• Analogy with a machine (les animaux machines)

– The new mechanicism, Craver Machamer, Darden..

Mechanisms: philosophical idea


• Not obvious that all “mechanicism” yields an idea of realizaSon

• Physicalism & mechanicism are different • parts at the quantum level???? Part/wholes may be only macroscopic noSon


• New mechanicism: – Proximity with the scienSsts’ talk (“the mechanism of the spread of radical ideas is…”, “the mechanism of ion channels...” etc.).

– Bypass the reducSonism issue – Avoid metaphysical puzzles proper to ideas of laws (eg in DN explanaSon views) or causa=on

– -‐Salmon (onSc explanaSons), WimsaK (models)

Mechanisms: ScienSfic contexts

• Mechanism: Most trivial term in scienSfic literature

• Oien synonymous of “explanaSon”, “cause” • “Mechanism of X”

Mechanisms: ScienSfic contexts

• Models – phenomenological vs. mechanisSc.

• PaKerns vs. processes.

– SAD vs. niche model – clades distribuSon vs. macroevoluSonary models

– Etc.

2 longstanding assump)ons in theories of explana)on

• Pinpointed by Salmon: If E explains A, you can’t use E to explain non-‐A

– Issue of low probability events

• “ideal explanatory text” (Railton). • See Hempel, “explanatory sketches”, “parSal explanaSons” etc.

• ManipulaSonism,neomechanicism etc. : opening black boxes

• Some explanaSons don’t fulfill the IET condiSon

• In general they are indifferent to mechanisms

EXPLAINING, NOT WITH MECHANISMS

• Mathema=cal explana=ons – (BaKerman 2010)-‐ cicadas

• “Minimal model explana=ons” – BaKerman and Rice 2014

• Sta=s=cal explana=ons • Casinos -‐ see also (Lange 2013: regression towards the mean)

• Variance explanaSons • Walsh2013

• Equilibrium explana=ons • Op=mality explana=ons • Topological explana=ons

• Example: ice cream vendors (Nash equilibirum)

Equilibrium / op)ma

Note – explanatory role of maths (odd/ even )

OpSmality explanaSon in ecology: foraging Sme

Topological explanation • an explanation in which a feature, a trait, a

property or an outcome X of a system S is explained by the fact that it possesses specific topological properties Ti. – i.e. properties about its invariances through

continuous transformations, or graph theoretical properties.

Stability regarding exSncSons of random species

Huneman 2010, 2015

Major Instance of topological explanaSons: Networks

How can networks of unreliable elements perform reliably? We here address this quesSon in networks of autonomous noisy elements with fluctuaSng Sming and study the condiSons for an overall system behavior being reproducible in the presence of such noise. We find a clear disSncSon between reliable and unreliable dynamical aKractors. In the reliable case, synchrony is sustained in the network, whereas in the unreliable scenario, fluctuaSng Sming of single elements can gradually desynchronize the system, leading to nonreproducible behavior. The likelihood of reliable dynamical aKractors strongly depends on the underlying topology of a network. Comparing with the observed architectures of gene regulaSon networks, we find that those 3-‐node subgraphs that allow for reliable dynamics are also those that are more abundant in nature, suggesSng that specific topologies of regulatory networks may provide a selecSve advantage in evoluSon through their resistance against noise.

In the reliable scenario, the elements cooperaSvely suppress fluctuaSons and tend to syn-‐ chronize their operaSons. In the unreliable scenario, in contrast, networks desynchronize and show irreproducible behavior when response Smes fluctuate.The occurrence of the two dynamical classes is strongly biased by the topology. Whether or not the system shows reliable dynamics can to a large degree be deduced from the unlabeled wiring diagram without informaSon on the type of couplings and funcSons of switches.

• “This network, more than recovering a biological process, give us a conceptual picture”

“recovers the informaSon of those pair of gene that simultaneously mutated lead to lethality but not when they are individually mutated.”

Many consequences about the robustness of the system and its evoluSon

Classical problem: popula=on stocked on a low local fitness peak. Wright. ShiPing balance theory. Mathema=cal and empirical problems (i.e. Barton et al. 1987)

Other instances: topological proper&es of system’s phase space/ landscapes etc.

• Concept of “Neutral spaces” – Gavrilets 1997.

• Idea: in hyperspaces high dimensional the problem is not the same

• There may be “fitness tunnels” in which mutaSon is neutral, but which connect different fitness zones.

SelecSon, drii, etc. are forces or “mechanisms”. The topology of the landscape clearly determines what drii can do.

DEMARCATING A FAMILY OF STRUCTURAL EXPLANATIONS.

Common features

• knowing the trajectory of the system is not necessary to explain the explanandum

• Generality and genericity • A formal property plays a role in explaining

Defining the demarcaSon

• Using maths ?

• MathemaScs are always used as modeling tools in explanaSon

• But here: explanatory role of mathemaScs (and not representa=onal)

• Don’t confuse with mechanisSc/phenomenological models ! (eg Kaplan & Craver 2011)

• Namely: A mathema=cal property accounts for the fact that the explanandum is the case

Explanatory use ?

• Bergmann’s rule: “animals of a given clade/species/family increase in size while going north”

Why ? Because different disposiSons to radiaSng heat vary in funcSon of size

Contrast

Bergmann’s rule • (Principle of natural selecSon:) beKer

adapted animals that face heat loss beKer than others are more adapted (other things being equal);

• animals reproducSvely overcome less adapted animals, in general ;

• temperature decreases when going North (in the northern hemisphere, of course).

• the law of heat loss is • where A is the area of the organism and e is

the emissivity of its surface; • the variaSon of the surface area to volume

raSo decreases when the radius increases (in a sphere), so the larger animal loses as much heat as a smaller animal while having more volumes, hence more remaining heat. In other words the larger animal needs much more Sme to radiate all the heat stored in its volume. (P)

“Pseudo Bergmann’s” rule • (Principle of natural selecSon:) beKer

adapted animals that face heat loss beKer than others are more adapted (other things being equal);

• animals reproducSvely overcome less adapted animals, in general ;

• temperature decreases when going North (in the northern hemisphere, of course).

• the law of heat loss is • where A is the area of the organism and

e is the emissivity of its surface; • Stuff X has a an emissivity index e’

lower than mammalian the emissivity e of the surface of mammals. (P’)

Lesson

• Both rules include mathemaScal descripSon (esp. the law of heat radiaSon) of a mechanism

• Though (P’) is a physical fact -‐> pseudo-‐Bergmann’s rule does not use any explanatory mathemaScal property

• But Bergmann’s rule does : P is a mathema=cal fact

Lesson

• Both rules include mathemaScal descripSon (esp. the law of heat radiaSon) of a mechanism

• Though (P’) is a physical fact -‐> pseudo-‐Bergmann’s rule does not use any explanatory mathemaScal property

• But Bergmann’s rule does : P is a mathema=cal fact

NoSce: this is a very usual feature of evoluSonary biology, unlike cicadas, beehives’ hexagons, etc. Though it works the same way (Baker 2009, BaKerman 2009, Colyvan 009etc.)

• Yet the whole explanaSon is not consStuted by (P) !

• Check the casino example

{0…..36}

MECHANISTIC EXPLANATION

{0…..36} CASINO WINS

LAW OF LARGE NUMBERS


MATHEMATICAL EXPLANATION

{0…..36} CASINO WINS

LAW OF LARGE NUMBERS


MATHEMATICAL EXPLANATION

CASINOS EXIST

• Yet the whole explanaSon is not consStuted by (P) !

• What would be a structural explana=on per se ?

ACCOUNTING FOR THE EXPLANATORY CAPACITY OF MATHEMATICAL PROPERTIES

Example: the CLT

• Why so many normal paKerns in nature ? » Frank 2009 JEB, Lyon BJPS 2013

-‐ Height -‐ Measures -‐ Exam scores -‐ PoliScal opinions

-‐ Etc.

• One answer: because of the central limit theorem. – Adding independent random variables with the same (finite) mean and variance produces a normal distribuSon

– (see Lyon 2013 for a criSque)

importance

• All phenomena made up by many independent random processes will probably exhibit a normal “law” – Example: stochasSc gene expression.

– One cell (with gene G) expresses a random value of protein – But through this variaSon/averaging the average value of the protein expressed by a group of cells seem robust.

Conclusion

features

• The CLT does not depend on any distribuSon-‐yielding mechanisms

• It enunciates a necessary fact about a mathemaScal operaSon (aggregaSon) on mathemaScal enSSes (random variables)

What it takes for a mathema&cal property to be explanatory ? • SuggesSon:

– “refer” to mathemaScal enSSes and operaSons ?

– Indifference to mechanisms ?

STRUCTURAL EXPLANATION: THE CONSTRAINT ACCOUNT

In general

• F (x1… Xn) = Y describes a mechanism • F belongs to a space of funcSons (eg the space of funcSons

derivable once, C1 , or twice, C2 , or etc. Ci , unSl C∞)

• ProperSes of this space holds for subclasses of funcSons: funcSons are the values of variables in their expression.

• Those general properSes of funcSons characterize the behaviour of all funcSons in the subclass

• They entail properSes shared by all these funcSons • Some of these properSes may be the explanandum of an

explanaSon • Then the mathemaScal properSes is explanatory

-‐> “constraint account’”

• P is a mathemaScal property playing an explanatory role regarding an explanandum in a stem S iff P is a mathemaScal proposiSon holding of a space of mathemaScal enSSes, that constrains any mathemaScal representaSons of the mechanisms or trajectories of S.

Example of this “constraint account”

• Fixed point theorems: • In the subspace C’ of C**, funcSons have point such that f (x) = x

• •

Example of this “constraint account”

• Fixed point theorems: • In the subspace C’ of C**, funcSons have point such that f (x) = x

• Used by Nash to derive the existence of equilibria in n-‐players zero sum game

• The property of a func=onal space accounts for the fact of the game

• MathemaScal structures are transworldly constraints, to which any mechanism must comply

• Some features of systems instanSated by their mechanism directly derive from them

» Unanswered quesSon: relaSon to structural realism

Consequences

• Genericity: any system instanSaSng a funcSon (resp. a matrix etc.) of the domain in which P holds will display the explanandum – -‐> transworldly validity – strong counterfactual robustness

• Very abstract properSes play a role – abstractness = reference to mathemaScal enSSes as variables

Concurs with accounts by Lange, etc.

contrast Mathema&cal fact used explanatory • Theorem T about a funcSonal

class C

• f belongs to C

• ProperSes, e.g. fixed point, monotonicity, steady states E* of f are derived from T

• E* mapped onto E, the explanandum

Representa&onal use

• f describes mechanism M in S

• Use T to compute the value of f at x°

• Describe the trajectory of the system with values of f

Dependence upon the explanandum

VARIETIES OF STRUCTURAL EXPLANATION

DisSncSon #1

• Structure: mathemaScal set or space (funcSonal spaces, topological spaces, algebraic spaces, etc.)

• Structural properSes : properSes of this structure

• VarieSes of structures -‐ > kinds of structural explanaSons


DisSncSon #2

• Cases like Bergmann’s rule

• Cases like CLT explanaSons

DisSncSon #2

• Cases like Bergmann’s rule

• Cases like CLT explanaSons

Consider the raSo of explanatory structural properSes vs explanatory physical laws or facts -‐> degree of structuralism

THE QUESTION OF EXPLANATORY PLURALISM

• Pluralism #1. Heterogeneous Between structural explanaSons and mechanisms

Pluralism #2: Homogeneous

Between kinds of structural explanaSons

HETEROGENEOUS PLURALISM

Two types of heterogeneous pluralism

• Heterogeneous Pluralism: it exists both a structural and a mechanism explanaSon for P.

– Concilia=ng pluralism (whatever x in domain S) there exists One mechanisSc and one structural explanaSon for x (Leibniz!)

– Divergent pluralism : in S, some x have mechanisSc explanaSon, others have structural explanaSon

Divergent pluralism of explanatory modes Example of COMMUNITY STABILITY

• Mechanistic explanation Topological explanation

• A ->B->C->D

• A ->B- / D C extinct, B decreases in frequency, D increases Vacant niche appears Other species C’ replaces C A->B-> C’ -> D

• The food web is a scale free network

• Probability that a random species extinction alters the community structure is therefore low

ConciliaSng pluralism

Mechanis=c explana=on of the posiSon of B below: its trajectory (newtonian mechanics of forces etc.)

Topological explana=on: the existence of an aKractor

• ConciliaSng pluralism:

Levins : robust theorems lie at the intersecSon of various models

HOMOGENEOUS PLURALISM

Two types of homogeneous pluralism

• ConciliaSng • divergent

Key issue: Rela=on between mathema=cal proper=es of dis=nct domains.

concilia&ng

• Example 1: graph theory and algebra

divergent

• Example 2: opSmality and topology – EvoluSonary biology

Matrixes of rela=ons: algebraic properSes entail features of a class of explanandum (e.g. condiSons on eigenvector and eigenvalues, etc.)

Network of interac=ons: topological properSes entail general features of equivalence classes of graphs

Mechanis&c explana&ons

Structural explana&ons

Topological explana&ons Algebraic explana&ons Sta&s&cal explana&ons

S Kind of system

S1 S2S3 …Si Si+1… Sp

…………..

Heterogeneous pluralism

Divergent hetero. pluralism

Conciliating het. pluralism

Mechanis&c explana&ons

Structural explana&ons

Topological explana&ons Algebraic explana&ons Sta&s&cal explana&ons

S Kind of system

S1 S2S3 …Si Si+1… Sp

…………..

Heterogeneous pluralism

Divergent pluralism

Conciliating pluralism

Homogeneous pluralism

Example of concilia)ng pluralism: popula)on gene)cs

Role of algebraic proper&es and theorems of func&onal analysis as explanatory

• Dynamics of allele frequencies

• Some equaSons (Price equaSon:

Example of concilia)ng pluralism: popula)on gene)cs

• Dynamics of allele frequencies

• Some equaSons (Price equaSon: ,

Topological explana&ons

• Climbing landscapes.

Possibly divergent pluralism: popula=on gene=cs and behavioural

ecology. Popula&on gene&cs

• How does selec=on proceeds? – Which dynamics can account

for specific frequency paKerns?

• Genes (alleles) are evoluSonary agents.

Behavioural ecology • Why did selec=on happen ?

– Why does the duck have webbed feet ? Because this copes beKer with the environmental demands.

• Organisms are evoluSonary agents – Op)miza)on is presupposed:

“phenotypic gambit” (Grafen 1984) = in the long run gene frequencies mirror the op=miza=on of the phenotype.

The divergence

• PopulaSon geneScs: selecSon is one among several forces, its dominaSon over other forces happen under several condiSons

• Behavioural ecology: opSmisaSon, ie maximisaSon of fitness by selecSon, is the methodological norm

The divergence

• PopulaSon geneScs: selecSon is one among several forces, its dominaSon over other forces happen under several condiSons

• Behavioural ecology: opSmisaSon, ie maximisaSon of fitness by selecSon, is the methodological norm

Is it really divergent ?

Can we derive behavioural ecology’s assumpSon from populaSon geneScs ?

• Climbing landscapes.

Fisher’s Fundamental theorem of natural selec&on: Maximising fitness is the rule. Empirically wrong.

Formal Darwinism (Grafen 2002, 2006, 2008) : there exists an isomorphism between dynamics of gene frequencies and opSmizing agents.

A story about the relaSons between dynamics and opSmisaSon, but not only…

Explanatory pluralism in evoluSonary biology

• Requires to arSculate:

– Algebraic property (properSes of matrixes used in modeling Markov processes)

– OpSmisaSon theory – Topology

– The extent to which some properSes overlap other properSes in another domain define the core of convergence of the theory

Varie\u0026es of structural explana\u0026ons and the no\u0026ons of explanatory pluralism

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