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HYLE International Journal for Philosophy of Chemistry, Vol. 18 (!1", #o. , 1$%&1'.Copyri)ht !1 *y HYLE an+ Hinne Hettema.

The Unity of Chemistry and Physics:Absolute Reaction Rate Theory

Hinne Hettema

Abstract:Henry Eyrings absolute rate theory explains the size of chemical re-action rate constants in terms of thermodynamics, statistical mechanics, andquantum chemistry. In addition it uses a number of unique concepts such asthe transition state. !ey feature of the theory is that the explanation it pro-"ides relies on the comparison of reaction rate constant expressions deri"edfrom these indi"idual theories. In this paper, the example is used to de"elop anaturalized notion of reduction and the unity of science. #his characterization

pro"ides the necessary clues to the sort of inter-theoretic lin!ages that are pre-sent in the theory of reaction rates. #he o"erall theory is then further charac-terized as a theory net$or!, establishing connections bet$een non-reducti"enotions of inter-theory connections. #his characterization also sheds ne$light on the unity of science.

Keywords: re+ution of hemistry to physis, unity of siene, hemial -inetis,a*solute theory of reation rates, eplanation.

Introduction#he unity of chemistry and physics should be paradigmatic for the unity ofscience. %ith the ad"ent of atomic theory, quantum theory, and statisticalmechanics, the fields of chemistry and physics ha"e become increasingly in-tert$ined, perhaps e"en up to the point $here, as &eedham '()*)+ argues, it$ould be hard to imagine chemistry $ith the physics remo"ed. Hence it is a"alid question to as! ho$ this unity of science is constituted in terms of theinter-relationship bet$een theories. In the present paper, these inter-relations$ill be considered for theories of chemistry and physics, specifically focusingon Eyrings theory of absolute reaction rates.

#here seems to be a significant di"ergence of approaches bet$een generalphilosophers of science and philosophers of chemistry in the consideration ofthese issues.


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* Hinne Hettema

In the */)s and *)s, many philosophers of science argued that someform of theory re+utionpro"ides the glue that holds the different sciencestogether. Ho$e"er, the exact shape and form that this reduction might ta!ehas been left far from settled, and currently there exist multiple opinions andconfusions about $hat reduction exactly is. 0or instance, $hile the mostpopular notion of reduction is that of &agel '**+, the exact shape and formof theory reduction that $as actually ad"ocated by &agel is commonly mis-understood.

0or many philosophers, &agelian reduction has become identical $ith thestrict "ersion of it ad"ocated in 1ausey '*22+, $hich turns the &ageliantheory into a form of reductionismbased on both ontological reductionismand strict deri"ation. 3ecently, the papers by 0aze!as '())+, 4lein '())+,5izad6i-7ahmani, 0rigg 8 Hartmann '()*)+ and "an 3iel '()**+ ha"e arguedthat this form of reduction $as actually not ad"ocated by &agel, but that&agel instead argued for a more moderate form of reduction that is perhapsbest characterized as a formal paraphrase of the explanation of la$s and theo-ries by other theories.

In addition to reduction, philosophers of siene ha"e de"eloped non-reducti"e notions of the unity of science, often inspired by specific episodesin the history of science. Examples of such non-reducti"e approaches are ad-"ocated by 5arden 8 9aull '*22+, 7o!ulich '()):+, and &eurath '*:;a,b+.#hese approaches to the inter-theory relationship ha"e not been $idely usedin the philosophy of chemistry, but ha"e the potential to pro"ide interestingadditional insights.


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proposals of philosophers of chemistry ha"e largely been o"erloo!ed by thegeneral philosophy of science community.

1omplicating matters is that the $idespread re6ection of reduction byphilosophers of chemistry might ha"e been premature. #he reduction ofchemistry to physics is usually discussed from the "ie$point of fairly simplechemical theories $ith a simplified notion of reduction, usually of the&agel?1ausey type. It is no$ a fairly common contention in the philosophyof chemistry that chemical theories pro"ide little or no support for a strictnotion of reduction of the &agel?1ausey type, and this has been one of themain forces dri"ing philosophers of chemistry to find alternati"e conceptionsof the inter-relationship bet$een theories of chemistry and physics, ap-proaches $hich in turn ha"e not been generalized to pro"ide a more compre-hensi"e theory of the unity of science.

In this paper I argue that the theory of chemical reaction rates, and espe-cially Eyrings theory of absolute reaction rates '$hich is often called abso-lute reaction rate theory to contrast it $ith theories that do not pro"ide in-terpretations for some of the terms in the rrhenius equation or transition

state theory because it introduces a ne$ term in chemical terminology+, pro-"ides a number of ne$ insights into a realistic notion of the sort of unity ofthe sciences that exists bet$een physics and chemistry. It can thereby helpo"ercome the barrier bet$een philosophy of science and philosophy ofchemistry on the one hand, and propose a number of interesting reconcilia-tions bet$een reducti"e and non-reducti"e notions of the unity of science, onthe other hand.

0ocusing on reduction, I in"estigate $hat it ta!es to eplain a particularchemical theory 'rrhenius equation for reaction rate constants+ in terms of'a number of+ physical theories, and ho$ a reduction bet$een these theoriesmight $or!. I then discuss the prospects of non-reducti"e theories of theunity of science. #he conclusion is that Eyrings theory of absolute reaction

rates does not quite fit $ith either reducti"e or non-reducti"e approachesfor t$o reasons.

In the first place, the theory introduces a specific ne$ concept, the transi&tion state, into the lexicon. #his ne$ concept is the result of the addition ofspecific conditions to the reducing theory, as $ell as the detailed formulationof local assumptions about the nature of chemical reactions at a micro le"el.#he transition state is defined $ith a significant degree of conceptual clarityand precision, gi"es the theory considerable explanatory po$er, and is to alarge extent responsible for the continued conceptual success of the theory.#raditional theories of reduction do not usually foresee such introductions ofne$ concepts, though, as I $ill argue, $ith some close reading of its originalintentions, &agels model for reduction can be made to fit the bill.


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*: Hinne Hettema

=econdly, the theory critically depends on multiple candidates for reduc-ing theories $hich each add critical elements to create the final theory ofabsolute reaction rates, and part of the process of the de"elopment of thetheory is that it allo$s for the interpretation of some of its terms in the ter-minology of different reducing theories.

Hence the o"erall explanatory structure is explanation in terms of a net-$or! of theories, in $hich &agelian lin!ages can be characterized as theoreti-cal patches that pro"ide the net$or! connections. #his is a situation that Ibelie"e is fairly common in chemistry, but currently not $idely in"estigatedin theories of reduction. Hence it is important that this structure is charac-terized and discussed in order to ad"ance the debate on the unity of chemis-try and physics.

#he fact that the theory of absolute reaction rates has sufficient complexi-ty to represent a real-life scientific theory, rather than a toy theory, thereforesuggests that it is a good example of realistic inter-theory relations bet$eenchemistry and physics.

It is primarily the aim of this paper to e"aluate the absolute reaction rate

theory as an eample for the unity of sieneso that some long held theories ofreduction, as $ell as non-reducti"e approaches, can be usefully comparedagainst a realistic record.

#his paper is structured as follo$s. In the next section, =ection (, I lay outthe mathematical and conceptual structure of reaction rate theory. =ection ;outlines in some detail the rele"ant aspects of the theory of reduction, fromthe "ie$point of &agel and his critics. #his section contains my reasons forthe proposed liberal reading of &agel, but other$ise contains little ne$ mate-rial and may be s!ipped by readers that are familiar $ith the literature on re-duction. In =ection ;.(, I pro"ide an introduction to some non-reducti"e ap-proaches. I ma!e a proposal for naturalized reduction in section ;.;. #hen Icontinue, in =ection , $ith a characterization of Eyrings theory of absolute

reaction rates as an example of naturalized reduction. =ection / contains aconclusion that dra$s the main lines together.

#he treatment of the material in this paper is informal, focusing on theo"erall structure of the theory of absolute reaction rates. formal renderingof naturalized reduction relationships is presented in Hettema ()*(.

(. 3eaction 3ate #heory@ its history and structure#he theory of absolute reaction rates $as de"eloped by Henry Eyring '*;/+,and $as discussed in detail in a boo! by Alasstone, >aidler 8 Eyring '**+.

Eyring, %alter 8 4imball '*+ discussed the theory in a single chapter,


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adding a quantum mechanical formulation of the theory. #he historical de-"elopment of the theory is presented in >aidler 8 4ing *:; as $ell as in 9il-ler *:. I follo$ primarily Alasstone et al. **, and note that >aidler 84ing *:; contains a number of useful additions to my presentation. In thissection it is my aim to trace the de"elopment of the theory of absolute reac-tion rates from the rrhenius equation to the formulation in Eyring *;/ andAlasstone et al. ** in a limited "ersion.

If $e consider a chemical reaction

B 7 B ...1 B 5 B ...

the rate of the reaction is gi"en by rrhenius la$, $hich is the main explana-tory target of absolute reaction rate theory. It $as de"eloped in *:: 'thearticle appeared in English translation in 7ac! 8 >aidler *2+ and definesthe rate constant-@

-C2 exp'-E2?30+

expressing the rate constant for a chemical reaction in terms of a frequencyfactor2and an acti"ation energyE2.

rrhenius concept of acti"e cane sugar contains three important com-ponents of the theory of reaction rates, $hich can be reconstructed as thefollo$ing set of claims@

* #here is some acti"e component of the reactants in"ol"ed in the reac-tion, $ithout $hich the reaction $ould not occur.

( #he acti"e and inacti"e components are in equilibrium.; #he acti"e form of the reactants is continuously remo"ed by the reac-

tion.1onditions *-; are, in generalized form, the basic assumptions of all reac-tion rate theories.

rrhenius la$ posed the question of ho$ to account for both the fre-quency factor and the acti"ation energy, and, as described in >aidler 8 4ing*:;, a number of candidate theories appeared.

In the ollision theory the frequency factor 2 in rrhenius equation isinterpreted as equal to the frequency of collisions 4 bet$een the reactants.#he collision theory assumes that all the reactants are hard spheres, and thatany collision that has sufficient energy to reach the acti"ated state $ill pro-ceed to complete the reaction.

modified collision theory often introduces a probability factor P$hich measures the probability that a collision $ill lead to a completed chem-ical reaction. Hence, in the modified collision theory@

-CP4 exp'-E2?30+


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#he fudge factor Pis introduced since the collisional cross section of a mol-ecule bears no clear relationship to the probability for a chemical reaction.

%hile the collision theory $or!s $ell for reactions bet$een mono-atomicgases, it brea!s do$n for reactions bet$een more complex molecules. In thisrespect, the collision theory is not capable of clarifying the internal mecha-nisms of chemical reactions in the necessary detail.

nother candidate is the thermo+ynami formulation, in $hich the reac-tion rate constant is expressed in thermodynamic quantities as

k=kT

hK

t

=ince the equilibrium bet$een the acti"ated state and the reactants is a nor-mal chemical equilibrium, the equilibrium constant 5 can be related to thethermodynamic theory of chemical reactions, and hence, it can be related tothe normal thermodynamic concepts of free energy, enthalpy 'heat con-tent+, entropy, and so forth. #his yields a measure of the entropy changes

associated $ith the reaction.

(.* bsolute reaction rate theory

bsolute reaction rate theory is a theory that aims to pro"ide explanationsfor both the acti"ation energy and the pre-exponential factor 'the fre-quency factor+ in the rate equation from first principles. Its underlying theo-ries are quantum mechanics and statistical mechanics. #he success of the the-ory depends on an accurate calculation of the potential energy surface of thereaction, as $ell as a detailed consideration of the initial and final states of themolecules.

#he theory also introduces a precise concept of a transition state$hich isli!e a normal molecule. #he transition state has a definite structure, mass,

and so forth. #he only exception is that there is one particular direction ofmotion 'the reaction coordinate+ $hich causes the molecule to brea! upinto the end products of the reaction.

#he situation is s!etched in 0igure *. Dn the right is a channel of reac-tants $hich transforms along a reaction coordinate into a channel of prod-ucts. t the height of the energetic barrier bet$een the reactants and theproducts lies the transition state, $hich is thus specified as a particular typeof molecule, $ith the structural property that there is one particular internalcoordinate $hich leads to a decomposition of the molecule.

#he further de"elopment of absolute reaction rate theory is based on thestatistical mechanics of the equilibrium bet$een the reactants and the transi-tion state. Eyrings introduction of statistical mechanics into the expression

of the rate equation is based on the idea that the potential energy surface can


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be calculated $ith quantum mechanics, and the motion of the nuclear framecan subsequently be treated classically $ith statistical mechanics.

0igure *@ #he potential energy surface for a three-atom reac-tion, indicating the reaction coordinate and the transition stateat the saddle point.

It is therefore clear that the absolute theory of reaction rates requires accu-rate calculations of the potential energy surface for the reaction. =uch precisecalculations $ere not possible in the *;)s, and hence Eyring de"eloped asemi-empirical form of quantum mechanics that gi"es access to the potentialenergy surface $ith sufficient precision to allo$ predictions from the theory.

Eyrings formulation of absolute reaction rate theory uses the follo$ingassumptions@E* #he potential energy surfaces can be calculated $ith quantum mechan-

ics 'or a semi-empirical form of quantum mechanics+.E( #he beha"ior of the nuclear frame on the potential energy surface

'note that this therefore includes the 7orn-Dppenheimer approxima-tion+ can be described $ith statistical mechanics.

E; #he decomposition of the transition state into the reactants can be de-scribed as a translational motion along the reaction coordinate.

>et us reconstruct the remainder of the argument in the form in $hich it isgi"en in Alasstone et al. **. #he !ey element of statistical mechanics is thepartition function '4ustan+ssumme+ 4@


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*/( Hinne Hettema

z=giexp(

ei

kT)$here )iis the degeneracy of the state corresponding to energy ei. #he com-plete partition function for any system is complex to calculate, since it in-

"ol"es all electronic, translational, "ibrational and rotational motions of thesystem $ith their degeneracies and corresponding energy le"els. #he rateformula of the absolute theory of reaction rates is gi"en in terms of the parti-tion functions of the reactants and the transition state by

k=kT

h

Z

ZAZ

BZ. ..

exp( E0

RT)#he ad"antage of this formulation is that the partition functions for all com-pounds featuring in the reaction '42, 46, et.+ can be calculated using statisti-cal mechanics for "ibrational and rotational motion of mechanical systems.

%hile this is still a difficult problem, a detailed consideration of different re-

acting systems yields a mechanistic insight in ho$ the reaction occurs on amolecular le"el. 0igure ( presents a s!etch of the situation.

0igure (@ #he potential energy surface for reaction seen alongthe reaction coordinate. #he parabolic cur"es $ith energeticle"els in them should be read as being perpendicular to the re-action coordinate.

(.( %igners three threes

detailed summary of absolute reaction rate theory $as gi"en in %igners'*;:+ presentation at the *;2 0araday conference '>aidler 8 4ing *:;

contains a brief discussion of this conference and the role it played in the


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subsequent adoption of the theory+, $here he summarized the challenges,types of reactions, and assumptions of the theory as a set of three threes.#hese are presented in #able * and translated into a specific set of steps'%=+, groups '%A+ and assumptions '%+.

#able *@ %igners three threes that characterize transition state theory 'after9iller *:+.

Three steps in the theory of kinetics%=* 5etermine potential energy surfaces%=( 5etermine elementary reaction rates%=; =ol"e rate equations for complex reaction mechanismThree groups of elementary reactions%A* ibrationally?rotationally inelastic collisions 'not a chemical reaction+%A( 3eacti"e collisions on a single potential energy surface%A; Electronically non-adiabatic reacti"e collisionsThree assumptions%* Electronic adiabaticity@ the electronic configuration is in the lo$est quantum

state for each configuration of the nuclei%( #he "alidity of classical mechanics for the nuclear motion%; Existence of a di"iding surface that tra6ectories do not re-cross

%igner referred to the theory in this paper as #he #ransition =tate 9ethodand distinguished three steps. %=*@ #he determination of potential energysurfaces, $hich gi"es Fthe beha"iour of all molecules present in the systemduring the reaction, ho$ they $ill mo"e, and $hich products they $ill yield$hen colliding $ith definite "elocities, et.G '%igner *;:, p. (+. #he solu-tion of this problem requires the calculation of a potential energy surface,$hich is a quantum chemistry problem. %=(@ #he next step is the calculationof elementary reaction rates. %=;@ #he third problem is to combine theseelementary reactions into a series of reactions $hich ma!e up the o"erallchemical transformation. Df these, the elementary form of reaction ratetheory only considers %=* and %=( and ignores %=;.

%igner classified the elementary reactions in three groups@ inelastic colli-sions, in $hich the molecules exchange "ibrational and?or rotational energybut do not change their chemical composition, reactions on a single potentialenergy surface $hich in"ol"e no change in electronic quantum numbers, andreactions in"ol"ing multiple potential energy surfaces 'non-adiabatic reac-tions+. Dnly the second type of elementary reactions can be treated $ithtransition state theory, hence, only %A( is considered in the theory. 0inally,

%igner discussed three assumptions. #he first one is the adiabatic assump-tion '%*+, $hich assumes that during the reaction the molecular systemstays on the lo$est possible potential energy surface and there is no changeof electronic configuration. #he second assumption is that the motion of the


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calculation of absolute rates but are helped by gaining some insight into chem-ical and physical processes. #he theory pro"ides both a statistical-mechanicaland a thermodynamic insight M one can ta!e ones choice or use both formula-tions. >aidler 8 4ing *:;, p. (K

#hus, in the final analysis, the achie"ement of the theory $as primarily con-ceptual@ it pro"ided "aluable insights into the mechanisms that dri"e chemicalreactions at a molecular le"el. Hence, the absolute theory of reaction rates is a"ery strong example for the unity of science M it is precisely one of those ex-amples $here it is hard to imagine chemistry $ithout physics, but at the sametime it is a chemical theory in that it focuses on molecules, molecular struc-tures, and transformations.

#he remainder of this paper $ill be concerned $ith ho$ the absolute the-ory of reaction rates fits philosophical conceptions of the unity of science.0rom the "ie$point of reduction and unity of science, the theory has a num-ber of unique features@

*. #he introduction and specification of the transition statein terms of aspecific location on the potential energy surface of the reaction and itscharacterization as a molecule $ith specific propertiesL

(. #he degree to $hich explanation depends on omparisonbet$een thecollision, thermodynamic, and quantum mechanical?statistical me-chanical formulations of molecular quantities.

If it is the case that the unity of science is the end product of some process oftheory reduction, then this case should fit a reducti"e model. =imilarly, if theunity of science is not based on a reducti"e model, there should be a fit $ithone of the non-reducti"e proposals.

In the next section it is my aim to discuss some approaches to the topic ofreduction before returning to the question ho$ the theory of absolute reac-tion rates might fit a reducti"e model and $hat the consequences of such a fitmight be.

;. #he unity of science@ reducti"e, non-reducti"e, andnaturalized approachesIn this section, it is my aim to present the &agelian approach to reduction asa close reading of the form in $hich it $as originally gi"en by &agel '**+,as $ell as to outline some aspects of the recent interpretation of &agels the-ory. I then discuss a number of non-reducti"e approaches, and conclude $itha proposal for a naturalized &agelian reduction model that combines im-

portant aspects of a defensible &agelian model $ith non-reducti"e approach-es, and $hich is adaptable to interesting cases of scientific explanation. #he


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!ey concept of naturalized &agelian reduction is that the philosophical no-tion of reduction should be a paraphrase, in some formal language, of $hathappens $hen scientists claim that one theory explains another. #he conceptis discussed in more detail in =ection ;.;.

;.* &agelian 3eduction

&agels formal requirements for reduction are $ell !no$n and are generallyta!en to be the requirements of connectibility and deri"ability, stating that alinguistic connection bet$een the languages of the reduced and reducing the-ory has to exist, and that the reduced theory has to be deri"able from the re-ducing theory umreduction postulates. Df the formal conditions, especial-ly the notion of connectibility requires further consideration.

#o begin $ith, the reduced and reducing sciences usually ha"e a numberof terms in common '&agel **, p. ;/*-(+. %hile the meaning of theseterms is fixed by procedures internal to both sciences, the meanings of termsof a certain common "ocabulary $ill coincide sufficiently to pose no further

problems for deri"ability. Dn the other hand, there is also a class of terms$hich occur in the reduced science but not in the reducing one. Hence, de-ri"ability can only be achie"ed $hen the concepts nati"e to the reduced sci-ence can be explicated in terms of the reducing one.

#o achie"e connectibility, &agel introduced, in addition to the formalrequirements, the notion of coordinating definitions 'here called reductionpostulates+ as an additional assumption. #he reduction postulates modifiesthe reducing science to o"ercome the issue that, as &agel states, deri"ation isimpossible if the premise of the argument 'i.e.the reducing science+ does notalready contain the necessary concepts of the reduced science. Hence, thereducing science has to state, in some meaningful sense, $hat the concepts ofthe reduced science are. #he reduction postulates stipulate

suitable relations bet$een $hate"er is signified by and traits representedby the theoretical terms already present in the primary science i*i+., pp. ;/;-K.

%hile the role of the reduction postulates is simple enough, the exact formu-lation of the reduction postulates themsel"es is far from simple. 0or instance,&agel discussed three possible !inds of lin!ages postulated by reduction pos-tulates 'i*i+.+, $hich can be paraphrased as follo$s@

*. #he lin!s are logical connections, such that the meaning of 2 as fixedby the rules or habits of usage is explicable in terms of the establishedmeanings of the theoretical primiti"es in the primary discipline.

(. #he lin!s are con"entions or coordinating definitions, created by de-liberate fiat, $hich assigns a meaning to the term 2 in terms of the


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primary science, sub6ect to a criterion of consistency $ith other as-signments.

;. #he lin!s are factual or material, or physical hypotheses, and assertthat existence of a state 6 in the primary science is a sufficient 'ornecessary and sufficient+ condition for the state of affairs designatedby 2. In this scenario, the meanings of 2 and 6 are not related ana-lytically.

It is thus important to realize that &agels criteria for reduction postulatesare open to a number of interpretations, and can be instantiated in actualpractice in a number of $ays. =pecifically, as also 4lein '())+ has argued, thereduction postulates refer to the representational po$er of the reducing the-oryL its ability to introduce the terms present in the reduced science. &otethat &agels second formal requirement states that the terms are fixed bymeanings and use local to the rele"ant theory and hence this sort of represen-tational po$er is not a tri"ial requirement.

#he &agelian deri"ability condition states@

JK a reduction is effected $hen the experimental la$s of the secondary sci-ence 'and if it has an adequate theory, its theory as $ell+ are sho$n to be thelogical consequences of the theoretical assumptions 'inclusi"e of the coordi-nating definitions+ of the primary science. &agel **, p. ;/(K

In addition to the formal requirements, &agel specified a number of informalrequirements. #hese introduce many qualifications and conditions that $illpro"e to be rele"ant in $hat follo$s. 9oreo"er, the informal requirementscontain many qualifications to the reduction scheme that are commonlyo"erloo!ed.

#he main reason for introducing the informal requirements is that theformal requirements are, by themsel"es, incapable of distinguishing bet$een$orth$hile and $orthless theory reductions. s &agel noted, the formal

conditions could in many cases be satisfied rather tri"ially $ith some a+ hoassumptions. #he informal conditions are there to bloc! this sort of tri"ialreduction.

#he first informal requirement is that of 'external+ corroboration of thereducing theory. #hat helps in the unification of the sciences by expandingtheir domains of applicability, and strengthens the case for the corroborationof the reducing theory.

#he second informal requirement is that of maturity of the reducing theo-ry. s &agel notes, the ideal gas la$ could be reduced to the !inetic theory ofgases only after the formulation of 7oltzmanns statistical interpretation ofthe second la$ of thermodynamics, and similarly the reduction needs a suffi-ciently mature mechanics to be counted as a success.


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*/: Hinne Hettema

is the third one. &agel claimed that it is frequently a mista!e to assume thatreduction amounts to the deri"ation of the properties of one sub6ect matterfrom the properties of another, and therefore denies that the reduced sciencecan be eliminated on the basis of such property reduction, and that, in fact,Fthe conception of reduction as the deduction of properties from other prop-erties is potentially misleading and generates spurious problemsG 'i*i+., p.;+. Instead, &agel argued that the "arious properties ascribed to chemicalelements, for instance, are the end result of theories about chemical elements.If such theories are later sho$n to be reducible to theories of atomic physics,then this pro"es the existence of a logical relationship bet$een theories, butdoes not pro"ide an argument for the reduction of the essential natures ofthe concepts that function in these theories.

It is thus important to note that &agel did not defend a form of reduc-tionism that allo$s for a nothing but approach to reduction. =pecifically, hedid not defend a "ie$ $here for instance an atom can be said to be nothingbut a collection of a nucleus $ith a certain number of electrons. %hile it isformally required to ma!e such a statement in order for the reducing theory

to be able to say something about atoms in the first place, the requirement isa formal and not an ontological one.

#his is an important point precisely because this third informal require-ment establishes the ontological independence of the reduced science@ inmany cases of reduction, the existence of reduction is a matter of the exist-ence of a logical or formal relationship bet$een the reduced theory and thereducing theory umthe reduction postulates, $here the latter allo$ a formalderi"ation relationship but do no ontologically hea"y lifting.


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used as connecting sentences JK then $e do not explain #( in terms of thela$s of #* but rather in terms of #* plus these mysterious correlation la$s.I*i+., p. :K

Hence 1ausey concluded that adequate correlations of the form '2+ requireFthing-identitiesG and Fattribute identitiesG 'i*i+., p. 2+.

3ecently, the pendulum on &agelian reduction has s$ung the other $ay.4lein '())+ and "an 3iel '()**+ ha"e argued that &agelian reduction shouldnot be read as a defense of ontological reductionism. 4lein argues that&agels condition of connectibility focuses on the degree to $hich the reduc-ing theory can represent notions of the reducing theory. =imilarly, "an 3ielargues that the $ay in $hich &agels frame$or! for reduction is commonlyread does not correctly represent the careful remar!s about the inter-theoretic relationships that accompanied it.

5izad6i-7ahmani, 0rigg 8 Hartmann '()*)+ argue that a generalized&agel-=chaffner model, in $hich the reduction postulates are factual claims,is ali"e and $ell. n o"er"ie$ of their proposal is presented in 0igure .

#hey defend the generalized &agel-=chaffner model against se"en specificob6ections, concluding that none of them apply. In their terminology, thegeneralized &agel-=chaffner model consists of a theory 0Preducing to a the-ory 07through the follo$ing steps@

*. #he theory 07 is applied to a system and supplied $ith a number ofauxiliary assumptions, $hich are typically idealizations and boundaryconditions.

(. =ubsequently, the terms in the specialized theory 07are replaced $iththeir correspondents "ia bridge la$s, generating a theory 0P.

;. successful reduction requires that the la$s of 0Pare approimatelythe same as the la$s of the reduced theory 0Pand hence bet$een 0

P

and 0Pthere exists ananalo)yrelation.

0igure @ D"er"ie$ of the generalized &agel-=chaffner reduc-tion proposed by 5iza6e et al. ()*).

=pecifically, t$o features of the generalized &agel-=chaffner model are $orthnoting. #he first one is that in this model the reduction postulates are part ofthe reducing theory, rather than some auxiliary statements that ha"e a pri-marily metaphysical import. =pecifically, 5izad6i-7ahmani et al. argue that ofthe three types of lin!ages that may be expressed by reduction postulates, thefirst t$o can be discarded and reduction postulates express matters of fact.#his is so, because the aim of scientific explanation is neither Fmetaphysical


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*) Hinne Hettema

parsimonyG nor Fthe defense of physicalismG 'i*i+., p. )/+. #hey argue for anaturalized reading of &agel, in $hich the aim of reduction is consistencybet$een the reduced and reducing theory, and confirmation of 0P entailsconfirmation of 07for domains $here there is significant o"erlap.

In this manner, 5izad6i-7ahmani et al. claim that reductions ha"e a highli!elihood of occurring in situations, such as the present case of the unitybet$een chemistry and physics, $here theories ha"e an o"erlapping targetdomain@

%e are committed to the claim that if $e ha"e a situation of the !ind de-scribed abo"e 'in $hich the t$o theories ha"e an o"erlapping target domain+,then one must ha"e a reduction. I*i+., p. *)K

;.( &on-reducti"e approaches to the unity of science

In this section, I $ill discuss some of the non-reducti"e approaches that mayassist in understanding and characterizing the relationship bet$een theories

of physics and theories of chemistry. #he examples are 5arden and 9aullsnotion of an interfield theory, and "arious approaches to accommodationand structural similarity. I $ill not focus on non-reducti"e theories, such asthe approach by 5uprN '*;+, $hich ad"ocate disunity.

#he first model $e $ill consider is that of interdisciplinarity. #he prom-ise of the interdisciplinarity or interfield theory approach is that it can pro-"ide a non-reducti"e model for the unity of science, in $hich both chemistryand physics play an equal part in the relationship.

Dne of the theories proposed to this end is the concept of an inter-fieldtheory proposed by 5arden 8 9aull '*22+. #he notion of a field is basicto the model. field is characterized 'along the lines de"eloped in =hapere*22+ as based on an ordered domain of phenomena, to $hich it introduces

a specific set of practices and techniques, perhaps $ith some local theories@>ocal theories that are specific to a field are called intrafield theories. 0ieldsand intrafield theories cannot be equated. =e"eral, sometimes competing, theo-ries are possible@ field at one point in time may not contain a theory, or mayconsist of se"eral competing theories, or may ha"e one rather successful theo-ry. 5arden 8 9aull *22, p. :K

In this manner, fields are not competing in the same $ay as theories, and it isalso not possible to say that one field may reduce another@ the necessary'&agelian+ relationships for theory reduction cannot obtain bet$een fields.Interfield theories are specific theories $hich use concepts and data fromneighboring fields. #he definition of an interfield theory is a theory that doessome or all of the follo$ing 'i*i+., p. /+@


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0he nity of Chemistry an+ Physis **

*. #o sol"e 'perhaps correctly+ the theoretical problem $hich led to its gen-eration, that is, to introduce a ne$ idea as to the nature of the relations be-t$een fieldsL

(. #o ans$er questions $hich, although they arise $ithin a field, cannot beans$ered using the concepts and techniques of that field aloneL

;. #o focus attention on pre"iously neglected items of the domains of one orboth fieldsL. #o predict ne$ items for the domains of one or both fieldsL/. #o generate ne$ lines of research $hich may, in turn, lead to another in-

terfield theory.

Oet it is hard to see that the interfield concept $ould be incompatible $ith alocal "ersion of the naturalized &agelian reduction $e de"eloped in the pre-"ious section. 0ields can be populated by theories, and reduction relation-ships in a &agelian sense may exist bet$een theories in different fields. Inthis regard it is especially $orth noting that the reading of the reduction pos-tulates as matters of fact plays the role of establishing the interfield theoryto a significant degree.

In a recent paper, Harris '()):+ has argued that the early theories of thechemical bond are best concei"ed as an interdisciplinary entity, $hich dra$sequally on physics and chemistry. ccording to Harris, the hallmar! of thisinterdisciplinary entity is the cooperation bet$een chemists and physicists onproblems of common interest@

JK physics and chemistry $ere disco"ering problems of collaborati"e "alue$ithin a common theoretical frame$or!. #here is no a"oiding the fact that un-til physical methods $ere a"ailable to chemists, there $as no real possibility ofdisco"ering the mechanism of bonding. Harris ()):, p. ::K

Harris argues that from this perspecti"e, the claim that chemistry $as re-duced to physics has to be re"ised, since the assumption that a successful re-duction $as the prime consequence of this interdisciplinarity does not

properly assess the historical facts and the "alue of the interdisciplinarity toboth physicists and chemists. Harris argument is primarily historic. =he con-trasts the interdisciplinary relationship $ith a reducti"e relationship $hichshe does not flesh out in a lot of detail but describes in terms of an attemptedta!eo"er, quoting 7orn $here he expressed Fa belief that the "ast territory ofchemistry $as not only important for physicists to explore, but that this$or! $as necessary in order for physicists to impose her la$s upon her sisterscienceG '7orn as quoted in i*i+., p. :*+.

3ecently, there has also been rene$ed interest in the &eurathian programfor the unity of science. #he program $as discussed by 1art$right et al.'*+ and


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*( Hinne Hettema

tional in character. characteristic of &euraths concept of the unity of sci-ence is that it has room for multiple explanations for a single phenomenon.&eurathian unity of science is closely lin!ed to 5uhemian holism, in thesense that hypotheses are tested in a holistic manner, against a unified $holeof theoretical statements.

In this context, it is interesting to note that =pector '*2:+ has ad"ancedclaims "ery similar to those of Harris to argue precisely that the relationshipis one of reduction, in fact, an entire branch reduction of chemistry to phys-ics $hich seems to dra$ into question the notion of non-reducibility, as $ellas that of a further specification of the reduction relation in question.

In practice, the encyclopedic approach builds on $hat the initial sciencesha"e to offer, and then starts loo!ing at the sort of relationships that mighthold bet$een them. In his *;2 essay #he 5epartmentalization of nified=cience, &eurath described the follo$ing approach to unification@

If one starts $ith a great many special disciplines JK o"erlapping one anoth-er, one might axiomatize all groups of statements ready for it. Dne might se-lect all cases in $hich the logical structure of a group of statements is identical$ith the logical structure of another group. &eurath *:;a, p. ()(K

&eurath called this approach to the unity of science encyclopedism andcontrasted it to pyramidism. He "ie$ed the latter as inspired by metaphysi-cal "ie$s on the unity of science, in $hich@

&ot a fe$ classifications and arrangements of the sciences can be regarded asderi"ates from the architectonic structure of such metaphysics, e"en if theircreators $ere interested in empiricism. I*i+., p. ();K

=uch a metaphysical commitment is a bad idea according to &eurath. Hence,the unity of science is not based on a hierarchical structure of nature, but ra-ther on an encyclopedic model, in $hich one is

JK satisfied $ith a rough bibliographic order for an initial orientations, madeby librarians. DneK accepts the fact that the "ast mass of the groups of state-ments are, as it $ere, in one place. 1ertain coherent forms could be arri"ed atby means of axiomatization or other procedures and a complicated net$or!gradually createdL there is no symmetrically pyramidical edifice. I*i+., p. ()K

&euraths model is thus best characterized as anti-reductionist@ the holisticcriterion for acceptance of statements is $hether they fit $ith an existing$hole, and once constructed, many $holes might structurally connect $itheach other. In this $ay, &eurath allo$ed se"eral competing explanatory sys-tems to co-exist, and argued that some systems are better suited to pro"ideexplanations in gi"en situations.


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0he nity of Chemistry an+ Physis *;

lisa 7o!ulich '()):+, in a study of the relationship bet$een classical andquantum mechanics, de"elops a notion of 'non-reducti"e+ interstructural-ism@

Interstructuralism is an approach to inter-theory relations that emphasizes the

importance of structural continuities and correspondences in gi"ing an ade-quate account of the relation bet$een t$o theories. It recognizes a richer di-"ersity of correspondence relations than does any form of reductionism orpluralism. 7o!ulich ()):, p. *2;K

7o!ulich claim concerns specifically +ynamial structures. 0rom this per-specti"e, she argues that there may be some question as to ho$ this model$ould apply to different theory pairs, though she does mention chemistry asa potential candidate for such a relationship 'i*i+., p. *2;+. =he presents in-terstructuralism as a middle path bet$een reductionism and theoretical plu-ralism, $hich ta!es important lessons from either approach.

Especially, she argues that interstructuralism lea"es the higher le"el theo-ries 'the reduced theories in a reduction relationship+ intact as explanatory

theoretical entities in their o$n right. Ho$e"er, from reductionism she ta!esthe idea that the domains of phenomena are not entirely distinct, and that inthis sense, an o"erall theory of ho$ these phenomena are related is bound tolead to ne$ insights.

#o the degree that 7o!ulich identifies reductionism $ith the strict inter-pretation of &agelian reduction as identities umstrict deri"ation 'and herboo! suggests that she does+ the approach I am ad"ocating to &agelian re-duction is to a significant degree compatible $ith interstructuralism.

;.; &aturalized reduction

In this paper, my proposal is to de"elop and defend a naturali9e+ &agelianreduction, $hich ta!es the &agelian model as a heuristi model to inter-theory relationships in actual science. 1andidate theories for the naturalized&agelian reduction are those theories $hich claim eplanations of 'aspects+of one theory by another.

&aturalized &agelian approach then proceeds along the follo$ing lines@*. 0irst $e see! out cases of claimed explanations in actual science.(. %e then proceed to rationally reconstruct these cases of explanations.;. =ubsequently, $e see! to formulate a paraphrase of this rational recon-

struction in terms of a 'more or less formal+ specification of both thebasic assumptions and unique features of the explanation.

. =ubsequently, $e establish the necessary lin!ages $hich ma!e the ex-planation $or!.

/. >astly, $e e"aluate the formal structure in terms of either a reducti"e

or suitable non-reducti"e model of the unity of science.


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* Hinne Hettema

#he main reason for ad"ocating a naturalized conception of the &agelianreduction as the correct relation of unity bet$een chemistry and physics isthat this seems to be one of the fe$ conceptions of this relationship that iscapable of dealing $ith the conceptual strength of chemical language.

It is by no$ $ell established in the philosophy of chemistry that the rela-tionships bet$een theories of chemistry and theories of physics do not fit therequirements of the &agelian reduction model $hen it is read in terms ofidentities um strict deri"ation. s the naturalized &agelian reduction con-tends, it is explicitly non-eliminati"eL rather, &agelian reduction aims to be a'logical+ paraphrase of $hat exactly happens $hen one theory explains an-other.

#he percei"ed disunity of the language of chemistry and physics is to alarge degree responsible for the some$hat unfortunate introduction of theconcept of ontological reduction in the philosophy of chemistry, a blan!cheque $ritten to metaphysics in payment for the percei"ed failure of &age-lian reduction. It is the aim of naturalized &agelian reduction to bounce thatcheque, and reclaim room for theoretical explanation $ith ontological inde-

pendence.s stated in the introduction, my treatment of these issues in the present

paper is mostly informal in order to bring out the approach. I ha"e proposeda formal frame$or! for naturalized reduction $hich is based on the structur-alist approach to scientific theories in Hettema '()*(+.

. bsolute reaction rates as a case study for natural-ized reduction

In this section I consider absolute reaction rate theory as a case study fornaturalized &agelian reduction. #he rational reconstruction required for ourdiscussion is largely found in =ection (. #he main aim of this section $ill beto discuss the structure of the theoretical frame$or! and the lin!ages be-t$een the rele"ant components of the net$or!. #he sort of unity of sciencethat is supported by the consideration of the absolute reaction rate theory isdiscussed in the next section.

#he characterization of the lin!ages $ill in"ol"e a number of steps. #hefirst step is the specification of the &agelian connections bet$een the theo-ries that constitute the net$or! of explanation. 0rom these, I $ill dra$ t$omain conclusions $hich allo$ us to characterize the uniqueness of absolutereaction rate theory as a proposed case of reduction@ in the first place, I argue

that some elements of this theory remain unconnected, and hence are uniquefeatures of the theory, and secondly, the &agelian connections, $hen read as


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0he nity of Chemistry an+ Physis */

statements of fact, allo$ us to specify the unique role played by comparisonin the theory. #he last step is the e"aluation of the theory as a case study innaturalized &agelian reduction. #his $ill assist in further specifying some ofthe necessary detail of naturalized &agelian reduction.

s I $ill argue in this section, the theory of absolute reaction rates exhib-its a number of interesting features $hich pro"e to be unique features of thetheory. #hese are a specification of the transition state and the degree to$hich the comparison of the three different approaches M statistical mechan-ics, collision theory, and thermodynamics M pro"ides further insight into thecalculation of the quantities 2andE2. #he combination of these t$o uniquefeatures gi"es rise to a third@ the fact that in the absolute reaction rate theorymultiple theories cooperate in the explanation. #he role played by theseunique features of the theory is specified in detail by the specification of the&agelian connections.

.* 3eduction bet$een theories@ &agelian connections and deri-

"ations#he first step in the naturalized reduction program is to formally paraphrasethe reduction of the rrhenius equation by the "arious theories that consti-tute the net of absolute reaction rate theory. s $e ha"e seen in the pre"iousdiscussion, the theory needs to explain the pre-exponential 'or frequency+factor2and the acti"ation energyE2. #he formal paraphrase of explanationin terms of reduction is &agels formal conditions of onneti*ilityand +eri/&

a*ility. s $as already indicated in the preceding sections, the contention ofnaturalized &agelian reduction is that, of these conditions, connectibilitydoes a significant amount of scientific $or!, $hile deri"ability is a relati"elypedestrian affair.

$.1.1 2ti/ation ener)y#he acti"ation energy may be identified $ith the difference in energy be-t$een the ground state of the reactants and the point on the potential energysurface $hich corresponds to the transition state M a molecular structure$hich can be specified $ith sufficient precision to allo$ its exact calculation'though $ithin the limits of quantum chemical methods and approximationssuch as the 7orn-Dppenheimer approximation+. Hence $e ha"e, I belie"e, arelati"ely non-contentious case for i+entifiation of the acti"ation energy,under the condition that $e define a transition state in terms of its locationon the potential energy surface. #he real $or! of the reduction is, ho$e"er,done precisely by this condition.

#he &agelian identification is thus a t$o-step process, $hich ta!es usfrom 'i+ astipulationof a transition state in terms of a structure located at a


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* Hinne Hettema

particular location on the potential energy surface, to 'ii+ an i+entifiationofthe acti"ation energy in terms of the energy difference bet$een the groundstate and the transition state.

Eyrings theory is note$orthy for the amount of precision it allo$s in thespecification of the transition state at a molecular le"el. s $e ha"e seen, abac!ground postulate $hich has no counterpart in the rrhenius equation isthat the reaction may be "ie$ed as a translational motion along the reactioncoordinate. %hereas the transition state $as foreshado$ed in the $or! ofrrhenius in the postulate of the acti"e form of cane sugar, the absolutetheory of reaction rates is capable of explicating exactly $hat the transitionstate is. In brief, its structural features are@

*. #he motion along the reaction coordinate can be treated as a freetranslational motion.

(. #he transition state lies at the saddle point of the potential energysurface of the reaction.

;. It is a normal molecule in all other rele"ant respects.It is $orth$hile to in"estigate ho$ this specification of the transition state

relates to the basic assumptions of both rrhenius equation and absolutereaction rate theory. It is particularly interesting in this context that the no-tion of the transition state gains additional precision and is in particular byEyrings theory in terms of an

JK ordinary molecule, processing all the usual thermodynamic properties,$ith the exception that motion in one direction, i.e.along the reaction coordi-nate, leads to decomposition at a definite rate. Alasstone et al. **, p. *)-**K

In terms of a &agelian model, it is thus not a case of straightfor$ard identi-ties umderi"ation that leads to the specification of the acti"ated state. 3a-ther, the reduction postulate for the acti"ation energy ta!es the form of astatement of fact, one that has ta!en hard $or! in the reducing theory to ac-

complish.#he fact that the reducing theory is transforme+ during the reduction is

generally recognized in discussions of &agelian reductions, as $e ha"e seen inour discussion of the model of 5izad6i-7ahmani et al. '()*)+. In the presentcase it may be argued, ho$e"er, that the specification of the transitions statesdoes morethan mere a transformation of the reducing theory@ it interprets aspecific feature of the re+ue+ theory in terms of the re+uin) theory as aconcept that does not flo$ naturally from the reducing theory, and can onlybe properly understood from the "ie$point of the reducing theory itself.

0urthermore, this specification relies on se"eral further theoretical con-cepts@ the idea of a reaction as a translational motion along the reaction coor-dinate, as $ell as a structural characterization of the acti"e complex as a par-

ticular type of molecule.


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0he nity of Chemistry an+ Physis *2

$.1. 0he Pre&eponential fator

In the statistical formulation of the theory, the frequency factor is identi-fied 'apart from the factor-0:h+ $ith a quotient of the partition functions ofthe acti"ated state and the reactants. 7ut this identification is not the compel-

ling point of absolute reaction rate theory.s in the case of the acti"ation energy, the real $or! is done by the sci-ence itself. #he compelling point is that this identification allo$s for amehanistiinsight into the dynamics of a chemical reaction. #he mechanismfor this mechanistic insight is the comparison of se"eral contending explana-tory theories for the pre-exponential factor, $hich pro"ide mechanisms interms of intermolecular collisions or thermodynamic quantities.

#he mechanistic features are quite easy to see for the simple collision the-ory. 7ut since the collision theory needs to introduce a fudge factor in theform of a reacti"e probability P its predicti"e po$er is some$hat limited.#he statistical mechanical theory fares better in this regard. %ith some sim-plifying assumptions, it is possible to construct explicit partition functions in

terms of translational, rotational, and "ibrational motion for the reactants andproducts, and hence gain significant insight into "arious types of reactions.Indeed, a large part of the boo! by Alasstone, >aidler 8 Eyring '**+ doesprecisely that.

#he thermodynamic formulation of the reaction rate is another interest-ing feature of the theory. #hermodynamic quantities are in general macro-scopic quantities, and Eyrings thermodynamic formulation alongside thestatistical mechanical formulation of the theory allo$s for a specification ofthermodynamic energies and entropies of acti"ation in terms of a mechanicalmodel at the micro le"el.

#he interpretation of the partition function can be seen, along the lines of=pectors '*2:+ di"ision of labor bet$een the theoretical chemist and the

theoretical physicist, as falling $ithin the realm of Faccounting for the ar-rangement and beha"ior of atoms and molecules JK on the basis of currentphysical theories regarding the structure of the atom and the la$s concerningthe beha"ior of its constituentsG 'e"en though =pectors final conclusion, thatthis is e"entually done $ith quantum mechanics, is incorrect in this context+.

#he fact that $e can express2in terms of statistical mechanics or reinter-pret it in terms of the collision theory forms an interesting 'and complicat-ing+ feature of the classification of the present case as one of &agelian reduc-tion. #hese re-interpretations form an important component of the attrac-ti"eness of the theory, since they allo$ chemists to shift perspecti"e on thetheoretical model $here required, and cannot be ignored as a feature of re-duction. It is in this context note$orthy that explanatory theories of $ea!erstrength, such as for instance the collision theory, are not discarded in theexplanation. Hence, the theory of absolute reaction rates forms a !ey exam-


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*: Hinne Hettema

ple of cooperation bet$een se"eral reducing theories, $hich turns the reduc-tion relation from one bet$een t$o theories into an explanatory and compar-ati"e relation on a net$or! of theories.

#he comparison of different approaches in the calculation of the pre-exponential factor therefore has significant consequences for the philosophyof science@ it establishes net;or- of reducing theories that can be e"aluatedon a criterion of explanatory strength. #he refinement and e"aluation of theexplanatory strength forms an important addition to the concept of &agelianreduction, and moreo"er, is one that allo$s for disciplinary autonomy.

$.1. 2 theory net ;ith loal re+utions

#he explanation of reaction rates thus proceeds in the context of a netof the-ories, $hich is depicted in 0igure ;. %hile connecti"e and deri"ati"e lin!s of a&agelian sort exist bet$een all these theoretical approaches, the reductioncannot be summarized as a relationship bet$een t$o theories@ the strength ofthe theory results from the detailed specification of the transition state $hich

ma!es the identification possible, and the comparison it allo$s bet$een thedifferent approaches.Hence in the case of absolute reaction rate theory the explanation pro-

ceeds in terms of multiple underlying theories, $hich in turn can be e"aluatedand compared on the amount of reducti"e strength that they are capable ofpro"iding.

In this sense, the intertheory relationships bet$een chemistry and physicsrequire a net$or! of theories for their specification. #his has a number ofimportant consequences. In particular, it lends support to the characteriza-tion of absolute reaction rate theory as an interfiel+ theory in the sense of5arden 8 9aull '*22+, $here the theories comprising the interfield are inturn reducti"ely connected. In this context, it is crucial that the reduction

postulates carry limited, context-free information, so that the theoreticalcontext is lost $hile the reducti"e connection is made.#his circumstance allo$s us to argue that, $hile the indi"idual theories

ma!e up the field, &agelian reduction relationships bet$een these indi"idualtheories do not in turn amount to tout ourtre+utionof the field. s is thecase in the reduction bet$een chemistry and physics, &agelian reductionthus allo$s theoretical independence of the field.

In the concept of naturalized reduction I ha"e de"eloped, theoretical con-cepts may be freely borro$ed from other fields, and reused as theoreticalpatches in the de"elopment of further theories. =uch theoretical patchingin"ol"es a loss of context. s an aside, the loss of context that may accom-pany intertheory reduction may formally be specified in terms of the chun!and permeate approach to theories de"eloped for instance by 7ro$n 8


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0he nity of Chemistry an+ Physis *

structures are e"en present in indi"idual theories. lternati"ely, these con-cepts can also be logically de"eloped as part of a semantic or structuralistmodel of theory nets and intertheoretic lin!s. 0or no$, $e $ill forgo theseformal specifications.

.( #he unity of science@ reducing theories and disciplinary au-tonomy

#he last step in my naturalized approach is e"aluating the reconstruction interms of a naturalized &agelian approach to the unity of science. p to thispoint, I ha"e argued that considering the absolute reaction rate theory as acase of naturalized &agelian reduction has gi"en us additional insight into thestructure and nature of the intertheory relationship that applies in this case.

%e no$ turn to the last step of the naturalized approach, $hich is the classi-fication of the case study in terms of either a reducti"e 'or non-reducti"e+model.

#he analysis of absolute reaction rate theory in terms of the naturalized

&agelian model has illuminated t$o unique features of the theory $hich areof further interest for the philosophy of science. #hese are@

*. #he specification of the transition state as a uni


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*2) Hinne Hettema

rhenius condition. s $e ha"e seen, 5izad6i-7ahmani et al. '()*)+ argue thatthe specialization, application, and transformation that characterize their "er-sion of &agelian reduction yields a final theory that stands in such an analogyrelation to the theory to be reduced. 0or the present case that implies thatthe precise specification of the transition state $hich is furnished by absolutereaction rate theory is analogous to rrhenius acti"e form of cane sugar.

n important consequence of this conceptual patching of the reducingtheory is that in the reduction the reduced theory cannot be eliminate+@ itretains its o$n status as a "alid theory of a phenomenon.

#he omparison 'and to some degree competition+ of se/eral reducingtheories is the second important feature of this particular test case. =pecifical-ly, the three formulations of the Eyring equation that are of interest are thecollision theory, the thermodynamic formulation, and the statistical mechan-ical formulation. ll of these three theories remain "alid in the explanation.In this $ay, omparisonof the "arious approaches is used to illuminate "ari-ous aspects of the mechanisms of chemical reactions.

It is harder to read this second feature as one that is inherent e"en in a

liberal reading of &agels model, e"en though it does pro"ide clues as to ho$one might go about e"aluating the reducti"e strength of the three theoriesin"ol"ed. #he e"aluation of such a reducti"e strength, combined $ith the as-sociated theory sur"i"al, $ould form an interesting extension to &agelsmodel. E"en $hile it seems possible to extend it in this particular $ay, it isinteresting at this point to in"estigate $hether non-reducti"e theories pro-"ide us $ith an a"enue to accommodate this feature more naturally.

5arden and 9aulls concept of interfield theories 'or Harris interdisci-plinarity+ as an approach to the explication of absolute reaction rate theoryare certainly promising in this regard. bsolute reaction rate theory fits $iththe idea of an interfield theory in the sense that it pro"ides ne$ connectionsbet$een not only chemistry and statistical mechanics, but also bet$een can-

didate reducing theories from different fields such as thermodynamics. =imi-larly, the theory necessarily dra$s on concepts from chemistry, physics, andthermodynamics to pro"ide its o"erall explanation, since the insights offeredby the absolute theory depend in significant measure upon the comparisonsbet$een the different reducing candidate theories.

#he fulfillment of the remainder of 5arden and 9aulls criteria seems abit more problematic, in the sense that the theory does not refocus our atten-tion on pre"iously neglected items or domains or predicts ne$ such items ordomains. #he theory is open to further concretization, and has to some de-gree initiated ne$ areas of research. Ha"ing said that, the first t$o criteriaseem to be the !ey criteria that allo$ us to classify the theory as an inter-field theory, so that 5arden and 9aulls model is at least partially successful.

Ho$e"er, $hile the case at hand fits some of the criteria for such an inter-


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0he nity of Chemistry an+ Physis *2*

field theory or interdisciplinary entity, it lea"es the issue of reductionsome$hat unsatisfactorily unresol"ed.

5arden and 9aulls notion of interfield theories is usually ad"ertised as anon-reducti"e theory, and its use seems to prompt us to come up $ith a ne$model for the unity of science. It can be argued, ho$e"er, that their model ofinterfield theories is reductionist in the sense that it ascribes to some sort ofderi"ation or explanation and at the same time liberalizes &agels reductionpostulates to include constituti"e theories. #his seems to me a defensibleclassification to the extent that 5arden and 9aull seem to ha"e an issue $ithreductionism and elimination rather than reduction as a more liberal theoryof explanation.

#he &eurathian model, li!e that of 7o!ulich, is based on structural rela-tionships bet$een the "arious constituting theories. =uch structural relation-ships do exist, as $e ha"e already argued, bet$een the notion of the transi-tion state and the acti"e form of cane sugar studied by rrhenius. #hey alsoexist bet$een the three competing theories@ the form of the mathematicalequations for the reaction rate constant is similar.

&one of the non-reducti"e models, moreo"er, are incompatible $ith the"ie$ of the net$or! of intertheory relations $e ha"e s!etched in 0igure ;,$here &agelian connections exist bet$een the different theories that formthe net$or!, and $here the o"erall reduction is specified in terms of thisnet$or!. #herefore at this stage there seem to be no good reasons to con-clude that a &agelian model cannot fruitfully deal $ith the complexities oftheory comparison in the present case.

/. 1onclusion@ the unity of chemistry and physics&aturalized &agelian reduction has yielded interesting perspecti"es on thecase of absolute reaction rate theory. 9y aim in this conclusion $ill be togather up some of the gains and suggest a"enues for further $or!.

#he heuristic approach to &agelian reduction follo$ed in this paper hassuggested that the t$o salient features of absolute reaction rate theory M thespecification of the transition state and the explanation by comparisonthrough the "arious reducing theories M necessitate a realignment of &agelsmodel of reduction along the lines suggested by 4lein '())+ and 5izad6i-7ahmani et al. '()*)+, and more formal $or! to extend this model to the no-tion of a theory net;or-.

#he explanation by comparison feature of absolute reaction rate theoryalso suggests interesting additional formal $or! in the philosophy of science,

in $hich se"eral candidate reducing theories can be e"aluated on their explan-


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*2( Hinne Hettema

atory strength. feature of such a 'future+ formal de"elopment $ill ha"e tobe that it accounts for the insights offered by the "arious candidates for thereducing theories. It also needs to clarify $hy these candidates are not elimi-nated.

s the current example suggests, the unity of science is most properlyconcei"ed as a net$or! of interloc!ing theories, $hich pro"ide mutual sup-port to each other. #his seems at first sight more compatible $ith the "ariousnon-reducti"e theories $e ha"e discussed than $ith the &agelian model.Ho$e"er, a large dra$bac! of the non-reducti"e schemes is that they do notallo$ for further specification and e"aluation of the consequences of this fact.#he reducti"e model, e"en in places $here strict &agelian reduction fails, atthis point appears to be the superior science of science.

3eferences

7ac!, 9.H. 8 >aidler, 4.P.@ *2, =elete+ 3ea+in)s in Chemial 5inetis, Dxford@. 8 ebel, #.@ *, Dtto #eurath? Philosophy *et;eensiene an+ politis, 1ambridge@ 1ambridge ni"ersity aidler, 4.P. 8 Eyring, H.@ **, 0he 0heory of 3ate Proesses? 0he 5i&

netis of Chemial 3eations, Visosity, iffusion an+ Eletrohemial Phenome&na, &e$ Oor!@ 9cAra$-Hill.

Harris, 9.>.@ ()):, 1hemical reductionism re"isited@ >e$is,


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0he nity of Chemistry an+ Physis *2;

Hendry, 3.0.@ ()*), Dntological reduction and molecular structure, History an+Philosophy of =iene Part 6? =tu+ies In History an+ Philosophy of Do+ern Phys&is, "'(+, *:;-**.

Hettema, H.@ ()*(,3e+uin) Chemistry to Physis? Limits, Do+els, Conseaidler, 4.P. 8 4ing, 9.1.@ *:; 5e"elopment of #ransition-=tate #heory, Journal

of Physial Chemistry, &!'*/+, (/2-(.>e

absolut chemistry.pdf

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