How is Multiple Realization Possible?

How is Multiple Realization Possible? Kenneth Aizawa Rutgers University, Newark

The Broader Project (in collaboraAon with Carl GilleD): Describing the composiAonal relaAons implicit in theories in the special sciences. Example: Hydrogen Fluoride.

Relata Composi-onal rela-on

Individuals Lower level individuals together cons%tute a higher individual

Powers Lower level powers together comprise a higher level power

Processes Lower level processes together implement a higher level process

ProperAes Lower level properAes together realize a higher level property

Stereotypical features of composiAonal relaAons

They are typically many one. Hydrogen and fluorine consAtute hydrogen fluoride. ElectronegaAviAes and bond length realize the dipole moment of HF.

Lower level enAAes are typically qualitaAvely disAnct from the higher level enAAes.

Hydrogen and Fluorine are qualitaAvely disAnct from HF. ElectronegaAviAes are qualitaAvely disAnct from dipole moments.

ComposiAonal relaAons are similar to causal relaAons. Both relaAons are non-‐logical, non-‐mathemaAcal, determinaAon relaAons. They are relaAons of natural necessitaAon.

ComposiAonal relaAons are disAnct from causal relaAons. I)  ComposiAonal relaAons are synchronic, whereas causal

relaAons are diachronic. II)  ComposiAonal relaAons do not relate wholly disAnct

enAAes, where causal relaAons do.

III)  ComposiAonal relaAons typically do not involve the transfer of energy or the mediaAon of force, where causal relaAons do.

Nearby projects: Grounding explanaAon MDC mechanisAc explanaAon

Grounding Explana-on A number of philosophers have recently become recepAve to the idea that, in addiAon to scienAfic or causal explanaAon, there may be a disAncAve kind of metaphysical explanaAon, in which explanans and explanandum are connected, not through some sort of causal mechanism, but through some consAtuAve form of determinaAon. (Fine, 2012, p. 37).

1.  Both composiAonal and grounding explanaAon are

supposed to differ from causal explanaAon. 2.  Both composiAonal and grounding explanaAon involve

some sort of consAtuAve form of determinaAon. 3.  But, composiAonal explanaAon is taken to be scienAfic,

whereas grounding explanaAon is not: “Ground, if you like, stands to philosophy as cause stands to science.”

PutaAve examples of grounding explanaAons:

(1) The fact that the ball is red and round obtains in virtue of the fact that it is red and the fact that it is round. (2) The fact that the parAcle is acceleraAng obtains in virtue of the fact that it is being acted upon by some net posiAve force; (3) The fact that his acAon is wrong obtains in virtue of the fact that it was done with the sole intenAon of causing harm.

Grounding explanaAons appear to have more types than do composiAonal explanaAons. Grounding explanaAons need not have the “mereological” dimension that is essenAal to composiAonal explanaAon.

MDC Mechanis-c Explana-on Mechanisms are enAAes and acAviAes organized such that they are producAve of regular changes from start or set-‐up to finish or terminaAon condiAons.

Machamer, Darden, & Craver, 2000, p. 3

§1. The question (and answers)

The very existence of the special sciences tesAfies to reliable macrolevel regulariAes that are realized by mechanisms whose physical substance is quite typically heterogeneous. Does anybody really doubt that mountains are made of all sorts of stuff? Does anybody really think that, since they are, generalizaAons about mountains-‐as-‐such won't conAnue to serve geology in good stead? Damn near everything we know about the world suggests that unimaginably complicated to-‐ings and fro-‐ings of bits and pieces at the extreme micro level manage somehow to converge on stable macrolevel properAes.

Fodor, 1997, p. 160

Normal human color vision is a property many humans have. It is realized by mechanisms whose biophysical properAes are heterogeneous. GeneralizaAons about normal human color vision-‐as-‐such conAnue to serve vision science in good stead.

Damn near everything we know about the world suggests that unimaginably complicated to-‐ings and fro-‐ings of bits and pieces at the extreme micro level manage somehow to converge on stable macrolevel properAes On the other hand, the 'somehow' really is enArely mysterious, and my guess is that that is what is bugging [Jaegwon] Kim. He just doesn't see why there should be (how there could be) macrolevel regulariAes at all in a world where, by common consent, macrolevel stabiliAes have to supervene on a buzzing, blooming confusion of microlevel interacAons

Fodor, 1997, p. 160

How is it possible to have a stable property G, given a diversity realizers F1, F2, …, Fn, and F*1, F*2, …, F*m? 1. It is possible when scienAsts use differences in F1, F2, …, Fn, and F*1, F*2, …, F*m to explain individual variaAon among individuals with G. 2. It is possible when scienAsts treat differences in F1, F2, …, Fn, and F*1, F*2, …, F*m as involving “compensaAon”. 3. It is possible when scienAsts treat differences in F1, F2, …, Fn, and F*1, F*2, …, F*m as “orthogonal” to property G.

Roadmap: §2 Dimensioned realizaAon and mulAple realizaAon. §3.1 MulAple realizaAon through individual differences

VariaAons in cone opsin absorpAon spectra VariaAons in lens and macular pigment opAcal density

§3.2 MulAple realizaAon by compensatory differences VariaAons in lens and macular pigment opAcal density VariaAons in lens shape and internal structure

§3.3 MulAple realizaAon by orthogonal realizers VariaAons in G proteins VariaAons in the structure of the cone mosaic

§4. The value of realized properAes §5. Conclusion

§2. Dimensioned Realization and Multiple Realization

Dimensioned realizaAon: Property/relaAon instance(s) F1-‐Fn realize an instance of a property G, in an individual s under condiAons $, if and only if, under $, F1-‐Fn together contribute powers, to s or s’s part(s)/consAtuent(s), in virtue of which s has powers that are individuaAve of an instance of G, but not vice versa.

Realized property: Dipole moment of 1.82 D Realizer properAes: ElectronegaAvity of H ElectronegaAvity of F Bond length between H and F.

Hydrogen fluoride: 1.82 D

A property G is mulAply realized if and only if

(i) under condiAon $, an individual s has an instance of property G in virtue of the powers contributed by instances of properAes/relaAons F1-‐Fn to s, or s’s consAtuents, but not vice versa;

(ii) under condiAon $* (which may or may not be idenAcal to $), an individual s* (which may or may not be idenAcal to s) has an instance of a property G in virtue of the powers contributed by instances of properAes/relaAons F*1-‐F*m of s* or s*’s consAtuents, but not vice versa;

(iii) F1-‐Fn ≠ F*1-‐F*m and (iv), under condiAons $ and $*, F1-‐Fn of s and F*1-‐F*m of s* are at the same scienAfic level of properAes

Hydrogen fluoride: 1.82 D Chlorofluoromethane: 1.82 D

Realized property: Dipole moment of 1.82 D

Realizer properties: Realizer properties Electronegativity of H Electronegativity of H Electronegativity of F Electronegativity of H Bond length between H and F. Electronegativity of F

Electronegativity of Cl Bond length between H and C

Bond length between H and C Bond length between C and F Bond length between C and Cl

§3 Case Studies

§3.1 Individual Differences


Let G be the property of having normal color vision. “Normal color vision” here refers only to making normal color discriminaAons. It does not refer to other properAes, such as rapidity of processing, luminance sensiAvity, etc. We know this because of the types of tests invoked.

Ishihara test


ScienAsts someAmes use differences in F1, F2, …, Fn, and F*1, F*2, …, F*m to explain individual variaAon among individuals with G. Case 1: Let F1, F2, …, Fn, and F*1, F*2, …, F*m be properAes of cone opsins. Case 2: Let F1, F2, …, Fn, and F*1, F*2, …, F*m be properAes of lens and macular pigment.


Polymorphisms: ~44% of the populaAon has a red cone opsin that has an alanine at posiAon 180. (This is Red(ala180).) ~56% of the populaAon has a red cone opsin with a serine at posiAon 180. (This is Red(ser180).)

These disAnct molecules have disAnct absorpAon spectra. λmax for Red(ala180) is 552.4 nm. λmax for Red(ser180) is 556.7 nm.


Vision scienAsts could postulate G or G1 and G2: G = normal color vision G1 = normal color vision Red(ala180) G2 = normal color vision Red(ser180). They sAck with G.


Polymorphisms: ~94% of the populaAon has a green cone opsin that has an alanine at posiAon 180. (This is Green(ala180) ) ~6% of the populaAon has a green cone opsin with a serine at posiAon 180. (This is Green(ser180) )

These disAnct molecules also have disAnct absorpAon spectra.


Vision scienAsts could postulate G or G1, G2, G3, and G4: G = normal color vision G1 = normal color vision Red(ala180), Green (ala180) G2 = normal color vision Red(ala180), Green (ser180) G3 = normal color vision Red(ser180), Green (ala180) G4 = normal color vision Red(ser180), Green (ser180) They sAck with G.


There are differences among realizers. These differences will make for differences among realized properAes. ScienAsts will care about these differences among realized properAes. So, they will subtype G.


Human color vision encompasses a range of individual variaAons, including … subtle variaAons among individuals whose color vision is considered to be normal. One of the principal causes of these color vision differences is variaAon in the spectral posiAoning of the cone photopigments.

Neitz, Neitz, & Jacobs, 1991


G = Normal color vision G11 = Normal color vision lens density1, macular density1 G12 = Normal color vision lens density1, macular density2 … G21 = Normal color vision lens density2, macular density1 G22 = Normal color vision lens density2, macular density2 … G31 = Normal color vision lens density3, macular density1 G32 = Normal color vision lens density3, macular density2 …


There are significant variaAons in colour matches made by individuals whose colour vision is classified as normal. Some of this is due to individual differences in prereAnal absorpAon …, but some is also believed to arise because there is variaAon in the spectral posiAoning of the cone pigments among those who have normal colour vision.

Neitz & Jacobs, 1986


The color matches of normal trichromaAc observers show substanAal and reliable individual differences. This implies the populaAon of normal trichromats is not homogeneous, an observaAon that leads to the quesAon of how one normal trichromat differs from another. In general, the physiological mechanisms that contribute to color-‐matching differences among normal observers may be classified as either pre-‐receptoral or receptoral.

He & Shevell, 1994, p. 367


Summary: One way to get mulAple realizaAon is through recognizing properAes that admit of individual variaAon within them. Case 1: Individual variaAon due to differences in cone opsins. Case 2: Individual variaAon due to differences in lens pigment and macular pigment opAcal densiAes.

§3.2 “Compensatory” Realizers


ScienAsts someAmes treat differences in F1, F2, …, Fn, and F*1, F*2, …, F*m as involving “compensaAon”. Case 1: Let F1, F2, …, Fn, and F*1, F*2, …, F*m be properAes of lens and macular pigment. Case 2: Let F1, F2, …, Fn, and F*1, F*2, …, F*m be properAes of the lens.


Let G = specific sensitivity to 450 nm light.


G = SensiAvity to 450 nm light G11 = SensiAvity to 450 nm light lens density1, macular density1 G12 = SensiAvity to 450 nm light lens density1, macular density2 … G21 = SensiAvity to 450 nm light lens density2, macular density1 G22 = SensiAvity to 450 nm light lens density2, macular density2 … G31 = SensiAvity to 450 nm light lens density3, macular density1 G32 = SensiAvity to 450 nm light lens density3, macular density2 …


The “lens paradox”: The human lens changes shape with ageing. This change in lens shape suggests that humans should typically become more near-‐sighted with age. But, humans typically become more far-‐sighted with age.


SoluAon 1: The eye changes shape to overcompensate for the lens changing shape. SoluAon 2: The internal structure of the lens changes to overcompensate for the lens changing shape.


G = emmetropic vision G11 = Emmetropic vision with lens shape1, refracAve index1 G12 = Emmetropic vision with lens shape1, refracAve index2 … G21 = Emmetropic vision with lens shape2, refracAve index1

G22 = Emmetropic vision with lens shape2, refracAve index2 … G31 = Emmetropic vision with lens shape3, refracAve index1

G32 = Emmetropic vision with lens shape3, refracAve index2 …


Summary: One way to get mulAple realizaAon is through having differences between two sets of properAes “offset” or “compensate” for each other. Case 1: Trading off absorpAon of the lens pigment and the macular pigment. Case 2: ResoluAon of the “lens paradox” offsexng changes in lens shape with changes in the internal structure of the lens.

§3.3 “Orthogonal” Realizers


ScienAsts someAmes treat differences in F1, F2, …, Fn, and F*1, F*2, …, F*m as “orthogonal” to property G. Case 1: Let F1, F2, …, Fn, and F*1, F*2, …, F*m be properAes of the phototransducAon molecules. Case 2: Let F1, F2, …, Fn, and F*1, F*2, …, F*m be properAes of the cone mosaic.


Parallel realizers = small differences in these lower level realizers lead to parallel differences in higher level realized property G. Orthogonal realizers = small differences in these lower level realizers do not lead to parallel differences in higher level realized property G.


Suppose that the G proteins vary in their amino acid sequences. Further, suppose that these variaAons influence the properAes the G proteins contribute to color vision.


G = normal color vision G1 = normal color vision with G protein1 G2 = normal color vision with G protein2 G3 = normal color vision with G protein3 G4 = normal color vision with G protein4 …


Differences in properAes of G proteins do not lead to differences in color discriminaAon. Differences in properAes of G proteins may lead to differences in how quickly the G proteins are acAvated and how quickly they acAvate cGMP phosphodiesterase molecules.


Males with normal color vision varied in the raAo of L to M cones from 1.1:1 to 16.5:1.


G = normal color vision G1 = normal color vision with cone mosaic1 G2 = normal color vision with cone mosaic2 G3 = normal color vision with cone mosaic3 …


Differences in properAes of cone mosaic do not lead to differences in normal color discriminaAon (property G). Differences in properAes of the cone mosaic do lead differences in “islands of color-‐blindness” (property H). Differences in properAes of the cone mosaic lead to differences in color discriminaAons in paDerns with high spaAal frequency (property J).

Roorda & Williams, 1999


One confusion to avoid: •  Both parallel and orthogonal realizers are in fact realizers. •  Being a parallel or orthogonal realizer is relaAve to both the higher level and lower level properAes in quesAon. •  Cone mosaic properAes are orthogonal to normal color vision •  Cone mosaic properAes are parallel to spaAal frequency discriminaAon capaciAes.

§4. The Value of Realized Properties


we could, if we liked, require the taxonomies of the special sciences to correspond to the taxonomy of physics by insisAng upon disAncAons between the natural kinds postulated by the former wherever they turn out to correspond to disAnct natural kinds in the laDer.

Fodor, 1974, p. 112


Normal color vision Red(ala180), Green (ala180) Normal color vision Red(ala180), Green (ser180) Normal color vision Red(ser180), Green (ala180) Normal color vision Red(ser180), Green (ser180)

Trichromacy Red(ala180), Green (ala180) Trichromacy Red(ala180), Green (ser180) Trichromacy Red(ser180), Green (ala180) Trichromacy Red(ser180), Green (ser180)


we could, if we liked, require the taxonomies of the special sciences to correspond to the taxonomy of physics by insisAng upon disAncAons between the natural kinds postulated by the former wherever they turn out to correspond to disAnct natural kinds in the laDer. .... But it would also lose us precisely the generalizaAons which we want the special sciences to express.

Fodor, 1974, p. 112


Physics develops the taxonomy of its subject-‐maDer which best suits its purposes … But this is not the only taxonomy which may be required if the purposes of science in general are to be served

Fodor, 1974, p. 114


Human color vision enables us to express certain generalizaAons about what individual are likely to perceive.

For example, this is important insofar as color discriminaAon capaciAes may maDer for job performance.

§4. Normal color vision and trichromacy

ObjecAon: Normal color vision is not a natural (kind) property. It is a convenAonal category. Reply: The foregoing arguments that use normal color vision can run on trichromacy. That is, the property of having trichromaAc vision is treated in just the way as is the property of having normal color vision.

Diversity in cone opsins and pre-‐receptoral elements is used to explain individual differences among trichromats.

§4. Normal color vision and trichromacy

The color matches of normal trichromaAc observers show substanAal and reliable individual differences. … In general, the physiological mechanisms that contribute to color-‐matching differences among normal observers may be classified as either pre-‐receptoral or receptoral.

He & Shevell, 1994, p. 367


Trichromacy seems to be an explanatorily relevant property for vision science.

For example, trichromacy seems to be the property relevant to explaining how the visual system overcomes the “univariance principle”.


Univariance Principle: “Each visual pigment can only signal the rate at which it is effecAvely catching quanta; it cannot also signal the wave-‐length associated with the quanta caught”

Naka & Rushton, 1966, p. 538.


Trichromacy seems to be the property that is relevant to the explanaAon of how the visual system overcomes the univariance principle. Specific cone opsin absorpAon spectra, specific transmission properAes of the lens and macula, the binding constants of the G proteins, the detailed structure of cone mosaic,

that realize the trichromacy appear to be irrelevant to the explanaAon of how the visual system overcomes the univariance principle.


Maybe this is what Fodor has in mind when he claims that postulaAng as many different properAes as there are realizers would “lose us precisely the generalizaAons which we want the special sciences to express”.

§5. Conclusions

§5. Conclusions

So, how is mulAple realizaAon possible? 1. It is possible when scienAsts use differences in F1, F2, …, Fn, and F*1, F*2, …, F*m to explain individual variaAon among individuals with G. 2. It is possible when scienAsts treat differences in F1, F2, …, Fn, and F*1, F*2, …, F*m as involving “compensaAon”. 3. It is possible when scienAsts treat differences in F1, F2, …, Fn, and F*1, F*2, …, F*m as “orthogonal” to property G. And these are possible, when the property G is an explanatorily relevant property.

How is Multiple Realization Possible?

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