Intro Explanatory Asymmetries Asymmetries and Mathematical Explanation What the parallel unveils References

A Symmetry in the Asymmetry: How explanatoryasymmetries might shed light on explanations

(in science and in society)

Daniele MolininiRehseis, Universite Paris 7

4th conference of the Societe de Philosophie des Sciences (SPS)June, 2012, Montreal

Daniele Molinini Rehseis, Universite Paris 7 A Symmetry in the Asymmetry: How explanatory asymmetries might shed light on explanations (in science and in society)

Intro Explanatory Asymmetries Asymmetries and Mathematical Explanation What the parallel unveils References

Explanations in science, society ... philosophy!

• Why did the the Halley’s comet pass through its perihelion in April1910? (perihelion is the point in the comet’s orbit at which it isclosest to the Sun)

• Why do people like Jason Pollock’s artwork?

• Why was the metro station flooded last tuesday?

Daniele Molinini Rehseis, Universite Paris 7 A Symmetry in the Asymmetry: How explanatory asymmetries might shed light on explanations (in science and in society)

Intro Explanatory Asymmetries Asymmetries and Mathematical Explanation What the parallel unveils References

Explanatory Asymmetries

Explanatory asymmetries (Bromberger 1966) arise when we have pairs ofdeductively valid arguments which rely on the same laws (e.g. the laws ofoptics and those of trigonometry) but which differ radically inexplanatory potential.

Flagpole (height y)

Shadow(length x)

Flagpole (height y)

Shadow(length x)

YES!NODoes y explain x?Does x explain y?

Figure: Explanatory Asymmetry: flagpole-shadow example

Daniele Molinini Rehseis, Universite Paris 7 A Symmetry in the Asymmetry: How explanatory asymmetries might shed light on explanations (in science and in society)

Intro Explanatory Asymmetries Asymmetries and Mathematical Explanation What the parallel unveils References

(a possible) Solution: CAUSAL CONSIDERATIONS

CAUSAL CONSIDERATIONS: the height of the flagpole causes thelength of the shadow, while the converse is not true.

This idea well fits well with a conception according to which the natureof scientific explanation is essentially causal. However, it seems that theadoption of this ‘causalist attitude’ towards scientific explanation quicklyleads to some problems (Norton 2003; Woodward 2011)

Daniele Molinini Rehseis, Universite Paris 7 A Symmetry in the Asymmetry: How explanatory asymmetries might shed light on explanations (in science and in society)

Intro Explanatory Asymmetries Asymmetries and Mathematical Explanation What the parallel unveils References

Asymmetry in the context of Mathematical Explanation

(Kitcher, 1989): one particular axiomatization of the theory of finitegroups, containing the existence of the inverse and idempotent elements,is preferred by the mathematicians in order to explain why finite groupssatisfy the division property. On the other hand, the reverse derivation,i.e. the derivation of the existence of an idempotent element and ofinverses from the division property, is regarded as a less natural andnon-explanatory derivation (although formally valid).

the derivation of the existence of an idempotent element and ofinverses from the division property is nonexplanatory, and, I think,nonexplanatory in just the same way as the derivation of heightsfrom shadowlengths (Kitcher, 1989, p. 425)

it is not hard to see a reason for the distinguishing of the derivations:the preferred derivation can be generalized to achieve morewide-ranging results [...] the explanatory derivation is similar toderivations we could provide for a more general result; thenonexplanatory derivation cannot be generalized, it applies only tothe local case (Ibid.)

Daniele Molinini Rehseis, Universite Paris 7 A Symmetry in the Asymmetry: How explanatory asymmetries might shed light on explanations (in science and in society)

Intro Explanatory Asymmetries Asymmetries and Mathematical Explanation What the parallel unveils References

Examples of non causal explanations provide, according to Kitcher,sufficient reasons to switch the focus from causal explanation to“theoretical” explanation, and consider the latter as primary to the former

By suggesting that it is not causality the ingredient which permits toaccount for the directional features of asymmetric explanations, heprovided a good reason to reject causality as the basic and uniqueingredient of a monistic approach to scientific explanation (explanation inmathematics and in empirical sciences).

No “philosophical” attention has been devoted to this parallel!

Daniele Molinini Rehseis, Universite Paris 7 A Symmetry in the Asymmetry: How explanatory asymmetries might shed light on explanations (in science and in society)

Intro Explanatory Asymmetries Asymmetries and Mathematical Explanation What the parallel unveils References

New Perspective

I suggest that Kitcher’s parallel unveils a potential approach to thenotion of scientific explanation.

According to this new perspective, which is only sketched here, there arepragmatic constraints which operate in scientific explanation. Thesepragmatic constraints are specific abilities to reason (for instance, theability to reason analogically, or the ability to reason causally) which areused in non-scientific explanations as well.

Daniele Molinini Rehseis, Universite Paris 7 A Symmetry in the Asymmetry: How explanatory asymmetries might shed light on explanations (in science and in society)

Intro Explanatory Asymmetries Asymmetries and Mathematical Explanation What the parallel unveils References

We can solve the asymmetry problem because in one direction we dispose(with respect to the deduction the other way around) of some extrautility which comes into play and permits us to discriminate between thetwo putative explanations (and pick out the explanatory direction).

This extra utility is our ability to reason causally, i.e. our ability torecognize that there is a functional dependency between two or moredetermining elements.

Our ability to reason causally contributes to the acceptance of oneparticular direction of the deduction as explanatory.

Daniele Molinini Rehseis, Universite Paris 7 A Symmetry in the Asymmetry: How explanatory asymmetries might shed light on explanations (in science and in society)

Intro Explanatory Asymmetries Asymmetries and Mathematical Explanation What the parallel unveils References

Flagpole (height y)

Shadow(length x)

Flagpole (height y)

Shadow(length x)

YES!NODoes y explain x?Does x explain y?

...

Abilities to reason

...A (ability to reason causally)

B C

...

Conceptual Resources

Figure: My framework for the case of the asymmetry problem of explanation.Our ability to reason causally is used through conceptual resources

Daniele Molinini Rehseis, Universite Paris 7 A Symmetry in the Asymmetry: How explanatory asymmetries might shed light on explanations (in science and in society)

Intro Explanatory Asymmetries Asymmetries and Mathematical Explanation What the parallel unveils References

An ability to reason which operates in explanation is not a relativenotion because, although psychological because it has to do withindividual beliefs and attitudes of persons, it is constant for a group ofpersons (for instance a community sharing a system of beliefs).

A solution to the problem of explanatory asymmetries may require adifferent answer in empirical sciences and in mathematics, although inboth the cases the answer can be given in terms of an ability to reason.Our ability to reason causally acts as a pragmatic constraint in the caseof the flagpole and the shadow, thus permitting us to discriminatebetween the two putative explanations.

Daniele Molinini Rehseis, Universite Paris 7 A Symmetry in the Asymmetry: How explanatory asymmetries might shed light on explanations (in science and in society)

Intro Explanatory Asymmetries Asymmetries and Mathematical Explanation What the parallel unveils References

Such pragmatic constrainst are not exclusive of explanations inscience

Consider here the example of the ability to reason analogically, i.e. theability to reason and learn about a new situation -the target analog- byrelating it to a more familiar situation -the source analog- that can beviewed as structurally parallel (Holyoak and Thagard, 1997). This abilityto reason is extensively used in scientific explanations (Hesse 1966;Cartwright 1983) as well as in our everyday-explanations. For instance, itis used in morality: why is it wrong to do something in situation B?Whether it is wrong to do something in a situation A, and situation B isanalogous to A in all relevant features, then it is also wrong to performthat action in situation B. Such an explanation uses the the ability toreason analogically, however it is not scientific.

Daniele Molinini Rehseis, Universite Paris 7 A Symmetry in the Asymmetry: How explanatory asymmetries might shed light on explanations (in science and in society)

Intro Explanatory Asymmetries Asymmetries and Mathematical Explanation What the parallel unveils References

Conclusions

Kitcher’s parallel shows that explanatory asymmetries also arise inmathematics and therefore explanatory asymmetries in empirical sciencesand in mathematics do not share a common ‘causal solution’. However,it might be thought that the nature of the ‘asymmetry’ is the same inboth cases (as Kitcher seems to suggest).

My idea is that there are pragmatic ingredients (abilities to reason) whichoperate in scientific explanation. And the same pragmatic ingredients areused in explanations which are given outside a scientific context.

The difference between an explanation in science and an explanationoutside science resides in the way in which an ability to reason is used.To say that we can use an ability to reason (for instance analogicalreasoning) is not enough and more should be said on the conditions ofadecuacy (the adequate physical or mathematical reconceptualization)which permit its use in explanation.

Daniele Molinini Rehseis, Universite Paris 7 A Symmetry in the Asymmetry: How explanatory asymmetries might shed light on explanations (in science and in society)

Intro Explanatory Asymmetries Asymmetries and Mathematical Explanation What the parallel unveils References

Acknowledgements

... THINK IN PROGRESS

Thank you!

Presentation [with Bibliography] available here:

http://www.rehseis.univ-paris-diderot.fr/IMG/pdf/Montreal.pdf

Daniele Molinini Rehseis, Universite Paris 7 A Symmetry in the Asymmetry: How explanatory asymmetries might shed light on explanations (in science and in society)

Intro Explanatory Asymmetries Asymmetries and Mathematical Explanation What the parallel unveils References

Bromberger, S. (1966). Why-questions. In Colodny, R., editor, Mind andCosmos. Pittsburgh: University of Pittsburgh Press.

Cartwright, N. (1983). How the laws of physics lie. Clarendon Press,Oxford.

Hesse, M. (1966). Models and Analogies in Science. Indiana: Universityof Notre Dame Press.

Holyoak, K. J. and Thagard, P. (1997). The analogical mind. AmericanPsychologist, 52:35–44.

Kitcher, P. (1989). Explanatory unification and the casual structure ofthe world. In Kitcher, P. and Salmon, W., editors, ScientificalExplanation, volume XIII of Minnesota Studies in the Philosophy ofScience, pages 410–505. University of Minnesota Press, Minneapolis.

Mancosu, P. (2008). Mathematical explanation: Why it matters. InMancosu, P., editor, The Philosophy of Mathematical Practice, pages134–150. Oxford: Oxford University Press.

Norton, J. (2003). Causation as folk science. Philosopher’s Imprint,3(4):1–22.

Woodward, J. (2011). Scientific explanation. In Zalta, E. N., editor, TheStanford Encyclopedia of Philosophy. Winter 2011 edition.

Daniele Molinini Rehseis, Universite Paris 7 A Symmetry in the Asymmetry: How explanatory asymmetries might shed light on explanations (in science and in society)