TEORIE VĚDY / THEORY OF SCIENCE / XLI / 2019 / 1 MATEJ DROBŇÁK Department of Philosophy and Social Sciences Philosophical Faculty, University of Hradec Králové nám. Svobody 331, 500 03 Hradec Králové Czech Republic email / matej.drobnak@gmail.com ////// studie / article //////////////////////////////////////////// NATURALNESS OF PROPERTIES AND SIMPLICITY OF THEORIES Abstract: In this paper, I discuss a specifi c approach to measuring and comparing the simplicity of theories that is based on Lewis's notion of fundamental properties. In particular, I discuss the criterion of simplicity as stated by Williams. According to Williams, the best candidate for a theory is the one which has the shortest defi nition in terms of fundamental properties. Th e aim of this paper is to show that the criterion thus specifi ed has two constraints. First, the criterion is not applicable to cases in which candidates for theories that specify fundamental properties are compared. Secondly, the applicability of the criterion in social sciences seems to be unwarranted. Keywords: naturalness; simplicity; David Lewis; fundamental properties Přirozenost vlastností a jednoduchost teorií Abstrakt: V tomto příspěvku se zabývám specifi ckým přístupem k měření a porovnání jednoduchosti teorií, který je založen na Lewisově pojetí fundamentálních vlastností. Zejména se zabývám kritériem jednoduchosti, jak ho prezentuje Williams. Podle Williamse nejlepší kandidát na teorii je ten, který má nejkratší defi nici z hlediska fundamentálních vlastností. Cílem tohoto příspěvku je ukázat, že takto specifi kované kritérium má dvě omezení. Zaprvé, kritérium není použitelné v případech, kdy porovnáváme kandidáty na teorie, které stanovují fundamentální vlastnosti. Zadruhé, aplikace tohoto kritéria v sociálních vědách se zdá být neopodstatněná. Klíčová slova: přirozenost; jednoduchost; David Lewis; fundamentální vlastnosti Th is work is licenced under the Creative Commons Attribution 4.0 International License. 4 Th e idea that simplicity of theories should play some role in the theoretical refl ection of scientifi c practice is a part of the philosophy of science since its beginning. While basically no one believes that simplicity plays no role at all, positive answers are varied. In this paper, I will focus on a specifi c view on simplicity of theories which is based on David Lewis's1 notion of fundamental properties and advocated by Williams.2 Williams believes that we should understand Lewis's ranking of properties (based on the notion of fundamental properties) as an "instrument" for stating the criterion of simplicity of theories. According to Williams, the simplest theory is the one with the shortest defi nition when stated in terms of fundamental properties. While Williams's proposal settles an interesting line of an interpretation of Lewis, the suggested connection of two normally independent topics – metaphysics of properties and simplicity of theories – may be hard to see. A partial aim of this paper is therefore to clarify the connection between Lewis's views on naturalness of properties and simplicity of theories. Th e main aim of this paper is to provide a critical reconsideration of the criterion of simplicity, as proposed by Williams, and of its general applicability to a comparison of simplicity of any two theories. While I believe that to understand simplicity in terms of naturalness may sound reasonable in case of some theories, I do not agree that this criterion can be used as a general principle for measuring/comparing simplicity of theories. In the fi rst part of the paper, I will present Lewis's view on naturalness of properties, as well as its connection to the topic of simplicity of theories as advocated by Williams. In the second part of the paper, I will present a critical reconsideration of Williams's criterion of simplicity of theories if used as a generally applicable criterion. 1 David Lewis, "New Work for a Th eory of Universals," Australasian Journal of Philosophy 61, no. 4 (1983): 343–77; David Lewis, "Putnam's Paradox," Australasian Journal of Philosophy 62, no. 3 (1984): 221–36. 2 J. Robert G. Williams, "Eligibility and Inscrutability," Philosophical Review 116, no. 3 (2007): 361–99; J. Robert G. Williams, "Lewis on Reference and Eligibility," in A Companion to David Lewis, eds. Barry Loewer and Jonathan Schaff er (Oxford: Wiley–Blackwell, 2015), 367–81. Th is work was supported by Philosophical Faculty, University of Hradec Králové, where the author currently holds the position of Junior Researcher. I would like to thank the anonymous reviewers for their valuable comments and eff orts towards improving this manuscript. Matej Drobňák 5 David Lewis on Naturalness Before I proceed to a critical reconsideration of Williams's proposal, I try to present Lewis's views on naturalness of properties in detail and to elucidate the relation between the naturalness of properties and simplicity of theories. Lewis introduced the idea of the naturalness of properties in his paper "New Work for a Th eory of Universals."3 Th e most basic motivation behind the idea was to fi nd a criterion which would allow us to compare objective distinctions and similarities between properties (understood more or less as classes of things). Th e idea that there are objective similarities between things is intuitively acceptable for philosophers as well as for lay persons. Most people would agree that the class consisting of all the occurrences of water on Earth is in some way more uniform than the class consisting of all animals on Earth. And the class consisting of all animals on Earth is still in some way more uniform than the class consisting of water, dogs, aeroplanes and revolutions. Th e philosophically interesting question is on the basis of what we can compare classes of such radically dissimilar objects. Th e answer to this question leads us to a reconsideration of what all those objects have in common. If we talk about such a gerrymandered class, then physical reality seems to be a reasonable candidate for a common ground of comparison. What water, dogs, aeroplanes, and even revolutions have in common is that they "are part of" the same physical world. In fact, if we follow physics, then at the most basic level everything in the world consists of the same physical particles – quarks and electrons. Lewis decided to follow the idea that the most fundamental parts of the world are those proposed by current physics (quarks and electrons) and subsequently that the most fundamental properties in the world are also physical – mass, charge, and spin. Th is is, to some degree, a consequence of his acceptance of the Ultra–sparse theory of universals (or properties as their equivalent) and, to some degree, a consequence of his reductive approach to properties. Moreover, Lewis proposed to ascribe a specifi c privileged status to the properties at the most basic microphysical level. Th e privileged status of the fundamental microphysical properties resulted from the fact that those properties had a potential to be used to explicate all other properties (e.g., macroscopic properties such as being animal or being wooden). In fact, Lewis's strategy is a version of reductionism of macroscopic properties to 3 Lewis, "New Work for a Th eory of Universals," 343–77. Naturalness of Properties 6 microscopic ones. In Lewis's terminology fundamental microphysical properties are perfectly natural and all other properties should be explicated in terms of those perfectly natural ones.4 Furthermore, Lewis used the idea of fundamental microphysical properties to state an objective criterion for "ranking" properties. Fundamental microphysical properties, such as mass, charge, and spin, are at the bottom of the ranking as perfectly natural properties and they serve as a unit of measurement of relative naturalness of other properties. Relative naturalness of other properties is ranked on the basis of their "distance" from perfectly natural ones. Th e question is how we can measure the distance of a property from perfectly natural ones. Lewis proposed to measure the distance on the basis of the length of their defi nitions if stated in terms of fundamental properties. Lewis's writings give us a little clue on how to spell out the idea of defi nitions in fundamental properties, but a good example of how such a defi nition may look like is provided by Th eodore Sider.5 Sider demonstrates such defi nition on a simplifi ed defi nition of a hydrogen atom: "ƎxƎy(ExPyRxy), which should be read as: 'Th ere exist an electron and a proton, the fi rst of which orbits the second'."6 Th e idea is that, in one way or another, we should be able to state a chain of defi nitions which links the property being defi ned to some fundamental properties even for more complex properties (such as being an animal). Th e criterion for ranking properties on the scale from the perfectly natural ones to very unnatural ones is then rather straightforward: the longer the defi nition, the less natural the property. For example, we can stipulate that the defi nition of a property being a molecule of water is considerably shorter than the defi nition of a property being an animal. To defi ne a molecule of water we need only to double the defi nition of a hydrogen atom and to add the defi nition of an atom of oxygen, but the defi nition of the property being an animal consists of defi nitions (i.e., microphysical descriptions) of all the atoms and molecules which form objects that we call animals. 4 See Lewis, "New Work for a Th eory of Universals," 357–68. 5 Th eodore Sider, Writing the Book of the World (Oxford: Oxford University Press, 2011). 6 Sider, Writing the Book, 120. Sider is generally sceptical about eff ective ways of defi ning ordinary properties such as being an animal, but he believes that, theoretically, such defi nitions could be stated. See Th eodore Sider, "Sparseness, Immanence, and Naturalness," Noûs 29, no. 3 (1995): 360–77. Matej Drobňák 7 Rival Interpretations While the way how to state defi nitions of properties in terms of fundamental properties is basically taken for granted, the role of the ranking of properties in Lewis's broader views in metaphysics and philosophy of science has been an object of a lively debate in the recent years. Most of the commentators agree – and Lewis was explicit about it – that one of his aims was to use naturalness of properties to answer some of the sceptical challenges in philosophy (e.g., Putnam's7 model theoretic argument or Goodman's8 riddle of induction). However, opinions of commentators vary in how exactly the idea of naturalness of properties should be used to answer the challenges and how it should fi t his broader views on language.9 Weatherson10 and Schwarz11 believe that the criterion for ranking properties is primarily meant to co– determine mental content and by doing so it helps to determine semantic content. On the other hand, Sider12 believes that the criterion is meant to be used to directly determine the semantic content of particular predicates (taken into account their use). Th e third line of interpretation is advocated by Williams, who suggests that the criterion for ranking properties should be primarily used for the comparison of (simplicity of) theories and only indirectly as a meaning-determining criterion. Even though it could be interesting to compare the viability of particular proposals with regard to Lewis's writings, it is not in the primary scope of this paper to follow exegetical discussions. 7 Hilary Putnam, Reason, Truth, and History (Cambridge: Cambridge University Press, 1981). 8 Nelson Goodman, Fact, Fiction and Forecast (Cambridge, MA: Harvard University Press, 1955). 9 See David Lewis, Convention: A Philosophical Study (Cambridge, MA: Harvard University Press, 1969); David Lewis, "Languages and Language," in Language, Mind, and Knowledge, ed. Keith Gunderson (Minneapolis: University of Minnesota Press, 1975), 3–35. 10 Brian Weatherson, "Th e Role of Naturalness in Lewis's Th eory of Meaning," Journal for the History of Analytical Philosophy 1, no. 10 (2013): 1–19. However, see a critical reassessment of Weatherson's view: Matej Drobňák, "Epistemological Naturalness: What is a Good Heuristic Strategy Good For?," Logic and Logical Philosophy 27, no. 1 (2018): 85–104. 11 Wolfgang Schwarz, "Against Magnetism," Australasian Journal of Philosophy 92, no. 1 (2013): 17–36. 12 Th eodore Sider, "Ontological Realism," in Metametaphysics, eds. David Chalmers, David Manley, and Ryan Wasserman (Oxford: Oxford University Press, 2009), 384–423; Sider, Writing the Book. Naturalness of Properties 8 With regard to the main aim of this paper, I will focus on the interpretation of Lewis's views on naturalness as provided by Williams13 and I will take it for granted. In any case, I believe, that the fact whether Williams off ers accurate interpretation of Lewis does not have any infl uence on the main argument presented in this paper. Th is is mainly because Williams's proposal can be assessed on its own. Regardless of the fact whether Lewis would agree with Williams, Williams's attempt to defi ne the simplicity of theories in terms of naturalness of properties can be seen as a cornerstone of an interesting and original view on similarity of theories. And it is the assessment of a general viability of this view that is in the main focus of this paper. Williams on Naturalness and Simplicity Th e most controversial and original point of the Williams's interpretation of Lewis is his conviction of the specifi c role naturalness should play in Lewis's views on language. In the line with other commentators, Williams admits that the idea of naturalness of properties can be used to determine meaning, but this is only its secondary function. As Williams argues, the criterion of naturalness is primarily meant to be used as the criterion of simplicity of theories and so its primary function should be to determine which of the candidate theories is the best one – the best theory is the one which best fi ts the data and if there are more theories which fi t the data equally well, then the criterion of simplicity should step in. In his paper, Williams focuses on one particular application of the criterion – to determine the best candidate for a semantic theory of some language. Th e secondary feature of the use of the criterion is that by determining the best candidate for a semantic theory, we basically determine semantic contents of particular expressions as well. When applied to semantics, the best semantic theory should be the one which fi ts the data better than others. If more semantic theories fi t the data equally well, then the best semantic theory is the simplest one. Simplicity of theories is then explicated by Williams as a matter of naturalness. Th e theory which has the shortest defi nition in terms of fundamental properties, i.e., which has the lowest syntactic complexity, is the most natural one and so the most simple one. Th e question that needs to be answered is how we can 13 Williams, "Eligibility and Inscrutability," 361–99; Williams, "Lewis on Reference and Eligibility," 367–81. Matej Drobňák 9 state and measure the syntactic complexity of semantic theories in terms of fundamental properties. To achieve this, Williams takes into account semantic theories as presented in Lewis's "General Semantics."14 According to Lewis, semantic theories consist mostly of clauses assigning semantic values to particular expressions. Williams's proposal is that, in the ideal case, the syntactic complexity of a semantic theory could be stated by the syntactic complexity of all the clauses which it consists of. Since these clauses are mostly clauses which assign semantic values to particular expressions, we can in some sense say that the syntactic complexity of a semantic theory is stated by syntactic complexities of the assigned semantic values. To understand the connection between the naturalness of properties and syntactic complexity of clauses assigning semantic values, we need to notice that, according to Lewis, properties can play a role of semantic values for predicates. Th is is a rather unusual position in semantics, but it helps to explain how Lewis's views on properties are interconnected with his views in metasemantics. If we accept that properties can play the role of semantic values, then the syntactic complexity of semantic values can be stated by the defi nitions of properties in terms of fundamental properties. If this is so, then the simplest semantic theory is the one which has the shortest overall defi nition of all the properties that are assigned as semantic values to predicates by the clauses of the theory. Generally speaking, the criterion of simplicity as proposed by Williams says that the best candidate for a theory is the one with the shortest defi nition, if defi ned in terms of fundamental properties. Simplicity of Th eories Before I move to a critical reconsideration of Williams's proposal for a comparison of simplicity of theories, one thing needs to be explicitly stated. Th ere is no indication in Williams's writings that he would intend to apply the criterion of simplicity beyond the comparison of semantic theories. At the same time, however, there is no indication in his writings that his criterion of simplicity should be applied to semantic theories only. It makes sense that Williams focuses on semantic theories, because he tries to provide an expla14 David Lewis, "General Semantics," Synthese 22, no. 1 (1970): 18–67. For a general overview of semantic theories and their assessment see: Lukáš Bielik, "How to Assess Th eories of Meaning? Some Notes on the Methodology of Semantics," Organon F 19, no. 3 (2012): 325–37. Naturalness of Properties 10 nation of how Lewis's view on naturalness could solve sceptical challenges in metasemantics. In other words, he focuses on one particular application of his criterion of simplicity of theories. But the criterion of simplicity of theories, as stated by Williams, should be, in principle, applicable to any two competing theories. If we are be able to state defi nitions of competing theories in terms of fundamental properties, then we should be able to compare their lengths, i.e., to compare their simplicity in accordance with Williams's criterion. However, the sole fact that it is "technically" possible to use the criterion for any two theories does not automatically guarantee that such a use of the criterion can provide reliable results for any two theories. With regard to this, the aim of this paper can be seen as a discussion of possible problems that we might run into if the criterion of simplicity, as stated by Williams, is applied beyond the comparison of candidates for the best semantic theory. Th ere are two reasons that justify a critical assessment of the criterion and its general applicability beyond semantics. Firstly, there is no reason to suppose that semantic theories should be treated diff erently than any other theories with regard to the comparison of their similarity. Th e second reason is that Williams's proposal has a surprisingly wide reach with regard to the topics and problems related to simplicity of theories that are standardly discussed – and so it deserves at least some discussion from the perspective of philosophy of science. Even though the idea of grounding the notion of simplicity of theories in the notion of naturalness has been overlooked so far, I believe that it represents an interesting alternative to more traditional views on simplicity – despite its defi ciencies. Based on which aspects of simplicity of theories are in question, discussions within the philosophy of science can be roughly divided into three thematic areas:15 A) Firstly, philosophers discuss whether simplicity can serve as an indicator of future success of a theory – and so it is a qualitative criterion – or if it is only an aesthetic criterion which says more about a subjective preference of scientists than about empirical plausibility of a theory.16 B) Secondly, philosophers discuss which aspects of theories we should compare with regard to their simplicity. Th is is an important point, because 15 For a general overview see Hugo Keuzenkamp, Michael McAleer, and Arnold Zellner, "Th e Enigma of Simplicity," in Simplicity, Inference and Modelling, eds. Arnold Zellner, Hugo Keuzenkamp, and Michael McAleer (Cambridge: Cambridge University Press, 2001), 1–10. 16 A wider discussion of qualitative and aesthetic understanding of simplicity see James McAllister, "Th e Simplicity of Th eories: Its Degree and Form," Journal for General Philosophy of Science 22, no. 1 (1991): 1–14. Matej Drobňák 11 our decision infl uences the result of comparison. How simple a theory is depends on which aspects of theories we assess. For example, we can focus, e.g., on ontological parsimony or syntactical complexity. Th eory A can end up simpler when compared with theory B according to one aspect (e.g., number of types of objects postulated), or more complicated according to another aspect (e.g., number of expressions needed to state a theory). C) Th irdly, answering which aspects we should focus on does not automatically answer how simplicity of a theory should be measured. Let us say that we decide that syntactic complexity is a relevant parameter for the comparison of simplicity. Even if this is so, the fi nal result of measuring of syntactic complexity depends on how we decide to state a theory; which theoretical tools (what kind of terminology) we decide to employ in our linguistic representation of a theory and which syntactic features of the linguistic representation of a theory we decide to count.17 Williams's proposal could be used to resolve all three issues mentioned above. First of all, Williams's proposal presents simplicity as a qualitative criterion. On the basis of Lewis's views on naturalness of properties, a theory which scores better in the comparison of simplicity is also metaphysically privileged and so the comparison should grant better prospects of a theory.18 With regard to the second thematic area, naturalness of properties can also be used to settle which aspects of theories should be compared – namely the length of defi nitions of the clauses that a theory consists of.19 And it also answers how simplicity should be measured – by counting the number of fundamental properties that takes part in those defi nitions. Th e most interesting part of Williams's proposal is that it is able to maintain a syntactical character of measuring simplicity and, at the same time, it is able to explain why the criterion of simplicity is a qualitative criterion. All those features make the Williams's proposal for measuring simplicity of theories to be a rather interesting outline of a theory that might be generalized and further developed. However, as I will try to show in the rest of the paper, this 17 In the same vein, in the discussions of evaluation of theories on the basis of Bayesian statistics and probability, Jeff ryes suggested that the number of adjustable parameters should be among relevant criteria for comparing simplicity. However, the number of adjustable parameters depends on how we decide to state a theory (what kind of equations we decide to use etc.). For a pioneering work on this topic see Harold Jeff reys, Th eory of Probability (Oxford: Clarendon Press, 1961). 18 For a wider discussion of metaphysical privilege of natural properties see Sider, Writing the Book. 19 And so it is a syntactical criterion. Naturalness of Properties 12 proposal for measuring simplicity of theories has also several constraints that might make it less appealing than it may seem at fi rst glance. General Applicability Th e fi rst constraint is related to the role that fundamental properties play in the criterion of simplicity. Simply put, the criterion of simplicity, as stated by Williams, cannot be used to decide the best candidate for the "fundamental" theory (i.e., the theory that specifi es fundamental properties). For William's criterion of simplicity to work, it is necessary to specify fundamental properties fi rst. And the decision about the fundamental properties is the decision about the best "fundamental" theory. Th e fundamental theory is a metaphysical theory that we adopt in order to specify which properties will be considered as fundamental.20 As in the case of all other theories, it is possible that there will be more candidates and some criterion for deciding between them must be adopted. If the criterion of simplicity is used to decide the best candidate for the "fundamental" theory and the fundamental properties are defi ned by up-to-date physics, then the criterion will always affi rm the position of an up-to-date physical theory when compared to other candidates. For example, suppose that someone proposes that mass, charge, and spin are not fundamental properties and she shows that the physical reality can be described in terms of some esoteric properties such as energetic vibrations. Th is esoteric theory is in no way a continuation of physics – it does not show that there is another layer of fundamental properties under the layer of mass, charge and spin, but it claims that physical reality needs to be studied from a completely diff erent perspective. Suppose also that both theories fi t the data equally well and there is no diff erence in their predictive power. In the spirit of the criterion of simplicity, as proposed by Williams, we should compare the lengths of defi nitions of both candidates for the best fundamental theory (an up-to-date physical theory and the esoteric theory) when defi ned in terms of fundamental properties. We have two options how to proceed. Firstly, we can state both defi nitions in terms of fundamental properties as proposed by up-to-date physics. Th is practically means that the defi nition of an up-to-date physical theory will be most probably the shortest one of all possible candidates because it is stated in terms of fundamental properties. Such a comparison would always confi rm the superior position of an up-to20 I am grateful to an anonymous reviewer for pointing this out. Matej Drobňák 13 date physical theory, because no other theory can warrantedly score better than the one that is stated in terms of fundamental properties. Secondly, we could compare the length of defi nitions of both theories when defi ned in terms of their own fundamental properties (in terms of up-to-date physical properties and esoteric properties respectively). Th is strategy may sound reasonable. Aft er all, Lewis accepted physical properties as fundamental because those were properties proposed by the best theory. If there is another candidate for the fundamental theory, then maybe we should reassess in terms of which properties we state defi nitions as well. However, the question of how we can compare two theories if they are defi ned in terms of diff erent fundamental properties now arises. Th e biggest advantage of Lewis's proposal is that it states an objective criterion for measuring and comparing naturalness of properties because it settles a measure unit – all the defi nitions/theories eligible for comparison of naturalness/simplicity must be stated in terms of the same fundamental properties (mass, charge, and spin). Th e number of these fundamental properties in defi nitions is then what we count. If two theories are defi ned in terms of diff erent fundamental properties, then we need some rule for "unit conversion" to be able to reasonably compare the two theories. As far as I know, there is no such rule for fundamental properties and I do not believe that it is possible to fi nd such a rule at all. Any "unit conversion" for fundamental properties can be settled only with respect to the results of their mutual comparison, but this is exactly what we try to fi nd out. In other words, to fi nd out and compare the values of diff erent fundamental properties in defi nitions requires knowing how theories defi ned in diff erent fundamental properties score in comparison of simplicity and this is something we do not know until we settle the value of diff erent fundamental properties. Simply said, we end up in a vicious circle. Because of that, it is not possible to use the criterion of simplicity, as proposed by Williams, to determine the best candidate for the fundamental theory. Th e decision about the best candidate for the fundamental theory, i.e., the decision about which properties will be considered to be fundamental must be made without relying on the criterion of simplicity – at least, if stated as it is discussed here. Naturalness and Social Sciences Th e fi rst constraint stated in the previous section aims at the possibility to use the criterion of simplicity, as stated by Williams, for a comparison of Naturalness of Properties 14 theories which aspire to settle fundamental properties. As I tried to show, the comparison is obstructed if fundamental properties are in question. Th e second constraint has even wider scope – I believe that it is doubtful whether the criterion of simplicity, as stated by Williams, can play any signifi cant role in the case of social sciences. As far as I can see, there are at least two reasons that might problematize the applicability of the criterion in social sciences. Firstly, the applicability of Williams's criterion of simplicity in social sciences depends on the success of reductionism. Basically, all the social sciences are interested in phenomena which are (more or less) dependent on behaviour of people. For example, results of an economic research in purchasing power (very roughly) depend on willingness and ability of individuals to work (and pay for the work) and subsequently to spend money. Results of linguistic research depend on linguistic behaviour of some community of speakers, and so on. Th e criterion of simplicity can be used for a comparison of theories in social sciences only if someone shows how to state theories standardly engaged with phenomena related to human behaviour and cooperation in terms of fundamental properties. Th is is possible only if someone can show how social sciences can be "translated" into the language of physics without any loss. Despite many attempts, the future prospect of concluding debates between reductionism and anti-reductionism looks poor. Debates on reductionism in social sciences are ongoing since seventies and each attempt to vindicate reductionism has been followed by a rival proposal that tried to undermine it. Such discussions can be found, e.g., in philosophy of mind. Any attempt to reduce mental states to neurological states of brain, e.g., Churchlands' eliminativism,21 is counterbalanced with an attempt to show its defi ciencies22 and to vindicate anti-reductionism (see, e.g., Fodor's23 and Putnam's24 argument from multiple realization). 21 Patricia Churchland, Neurophilosophy (Cambridge, MA: MIT Press, 1989); Paul Churchland, Matter and Consciousness (Cambridge, MA: MIT Press, 1988). 22 Th e most common arguments against eliminativism include self-refutation and the problem of qualia. 23 Jerry Fodor, "Special Sciences, or the Disunity of Science as a Working Hypothesis," Synthese 28, no. 2 (1974): 97–115; Jerry Fodor, "Special Sciences: Still Autonomous Aft er All Th ese Years," Philosophical Perspectives 11 (1977): 149–63. 24 Hilary Putnam, "Th e Nature of Mental States," in Mind Language and Reality: Philosophical Papers, Vol. 2, ed. Hilary Putnam (Cambridge: Cambridge University Press, 1975), 429–40. Matej Drobňák 15 Similar discussions can be found in sociology. Wilson's25 attempt to build sociology on biological grounds has been immediately questioned by Sahlins26 and Lenski27 for omitting cultural infl uences and mechanisms as driving forces in shaping social aspects of our behaviour and in shaping the organization of human societies in general. Wilson's idea that all aspects of human conduct can be explained in terms of biological determination was criticized especially with respect to explanations of particular sociological phenomena. Motivations and decisions of a person in various social situations were sometimes rather forcibly explained as a result of deep evolutionary (or otherwise biological) mechanisms instead of relying on intuitive psychological explanations. While we can say that we have some ways how to reduce social sciences to biological theories (and subsequently to physics), it is not so clear that we will be able to provide a full reduction without misrepresenting important aspects of social phenomena. In any case, even aft er fi ft y years of discussions, reductionism is far from providing conclusive evidence and reaching a general consensus. Secondly, it is questionable whether the criterion of simplicity, as stated by Williams, should have any decisive role in social sciences. Th e idea that simpler theory is the one which is metaphysically more homogeneous is in the heart of Williams's proposal. Th is is granted by the units of comparison – microphysical fundamental properties. More complicated theories "consist of" a bigger number of fundamental properties and because of that we can assume that they are also metaphysically less homogenous. Th e idea that the simplest theory must be also the most metaphysically homogenous one sounds quite reasonable when applied on sciences such as chemistry, astronomy or geology.28 At the heart, objects of research of all those disciplines can be easily explained in terms of physical processes and so we can assume that more complicated candidate theories require also more complicated 25 Edward O. Wilson, Sociobiology: Th e New Synthesis (Cambridge, MA: Harvard University Press, 1975). 26 Marshall Sahlins, Th e Use and Abuse of Biology: An Anthropological Critique of Sociobiology (Ann Arbor: University of Michigan Press, 1977). See also Winch's book for a more theoretical attempt to vindicate anti-reductionism and recent incarnations of his ideas: Peter Winch, Th e Idea of a Social Science and its Relation to Philosophy (London: Routledge, 1958); Phil Hutchinson, Rupert Read, and Wes Sharrock, Th ere is No Such Th ing as a Social Science: In Defence of Peter Winch (Aldershot: Ashgate, 2008). 27 Gerhard Lenski, "Reviewed Work: Sociobiology: Th e New Synthesis. by Edward O. Wilson," Social Forces 55, no. 2 (1976): 530–31. 28 With some provisos we could probably talk about natural sciences in general. Naturalness of Properties 16 explanations in terms of physics and therefore their defi nitions in terms of microphysical fundamental properties are also longer. However, even if there is some way how to state theories within social sciences in terms of microphysical fundamental properties, the question why microphysical (metaphysical) homogeneity of those theories should have any impact on their soundness and subsequent acceptance needs further reasoning. Th is is not only the question of feasibility of Williams's criterion of simplicity, but, even more importantly, it is the question of its legitimacy. Th e biggest advantage of Williams's criterion is that is off ers an objective procedure for measuring simplicity – in the sense that conditions under which we compare candidates are the same for all of them. But why should we expect that an economic theory which focuses on a development of the real estate market must be also simpler with regard to microphysical properties such as mass, charge, and spin? In other words, why should we expect that Williams's criterion sets the right conditions for measuring simplicity of theories in social sciences? Decisions of investors in real estate market are standardly resulting from a rational reconsideration of several aspects – including their income, the price of a real estate and (very oft en) an interest rate on mortgage. In order to provide a working theory that would be able to track and predict a development of the real estate market, psychological and economical explanations might be of a very good use. With respect to such explanations, the metaphysical homogeneity of a theory does not seem to be a reasonable decisive criterion. Th e fact that the expression "an interest rate on mortgage" can be defi ned in terms of xn microphysical fundamental properties does not provide any substantial information related to a possible successfulness of a theory. Measuring simplicity of theories in social sciences in terms of metaphysical homogeneity means that we are applying measures that are not eff ectively engaged in determining the future prospect of those theories. With regard to this, the applicability of the criterion of simplicity, as proposed by Williams, beyond natural sciences seems to be questionable. Th is is not to say that simplicity should not play any role in social sciences at all. However, it might be more useful to look for criteria that may better fi t their object of study – similarly to natural sciences.29 Th e reason why microphysical properties are well-suited for natural sciences is that they provide a ground that is common for all of them. In a similar way, social sciences 29 I am grateful to an anonymous reviewer for pointing this out. Matej Drobňák 17 might look for something that they have in common – psychological or behavioural terminology could be a good fi rst guess. Conclusion Th e aim of this paper is twofold. My partial aim was to show the connection between Lewis's views on naturalness and the criterion of simplicity of theories, as proposed by Williams. Th e main aim of this paper was to show that the criterion of simplicity, if based on the notion of fundamental properties, has a limited applicability. As far as I can see, there are at least two constraints that prevent its general applicability to a comparison of simplicity of theories. Th e fi rst constraint is that the criterion of simplicity is not able to determine the best candidate for a "fundamental" theory (i.e., the theory that determines fundamental properties). Th e second constraint is that while the acceptance of the criterion of simplicity based on the notion of fundamental properties sounds reasonable in the case of natural sciences, it is doubtful whether it is legitimately applicable in the case of social sciences. 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