The aim of this paper is to offer a formal criterion for physical computation that allows us to objectively distinguish between competing computational interpretations of a physical system. The criterion construes a computational interpretation as an ordered pair of functions mapping (1) states of a physical system to states of an abstract machine, and (2) inputs to this machine to interventions in this physical system. This interpretation must ensure that counterfactuals true of the abstract machine have appropriate counterparts which are (...) true of the physical system. The criterion proposes that rival interpretations be assessed on the basis of simplicity. Simplicity is construed as the Kolmogorov complexity of the interpretation. This approach is closely related to the notion of algorithmic information distance and draws on earlier work on real patterns. (shrink)
This article discusses the role of simplicity and the notion of a best balance of simplicity and strength within the best systems account (BSA) of laws of nature. The article explores whether there is anything in scientific practice that corresponds to the notion of simplicity or to the trade-off between simplicity and strength to which the BSA appeals. Various theoretical rationales for simplicity preferences and their bearing on the identification of laws are also explored. It (...) is concluded that there are a number of issues about the role of simplicity within the BSA and its relation to strength that need to be addressed before the BSA can be regarded as an adequate account of laws. 1 Introduction2 The Best Systems Account3 The Trade-Off between Simplicity and Strength: Preliminary Considerations4 Alternative Conceptions of the Relationship between Simplicity and Strength5 Two Roles for Simplicity6 Simplicity in the Best Systems Account: Curve-Fitting7 Simplicity as a Corrective for Overfitting8 Descriptive Simplicity in the Best Systems Account?9 Simplicity as Due to Human Intellectual Limitations10 Summary11 Concluding Remarks. (shrink)
Metaphysicians frequently appeal to the idea that theoretical simplicity is truth conducive in metaphysics, in the sense that, all other things being equal, simpler metaphysical theories are more likely to be true. In this paper I defend the notion that theoretical simplicity is truth conducive in metaphysics, against several recent objections. I do not give any direct arguments for the thesis that simplicity is truth conducive in metaphysics, since I am aware of no such arguments. I do (...) argue, however, that there is no special problem with the notion that simplicity is truth conducive in metaphysics. More specifically, I argue that if you accept the idea that simplicity is truth conducive in science, then it would be objectionably arbitrary to reject the idea that simplicity is truth conducive in metaphysics. (shrink)
Sometimes metaphysicians appeal to simplicity as a reason to prefer one metaphysical theory to another, especially when a philosophical dispute has otherwise reached a state of equilibrium. In this paper, I show that given a Quinean conception of metaphysics, several initially plausible justifications for simplicity as a metaphysical criterion do not succeed. If philosophers wish to preserve simplicity as a metaphysical criterion, therefore, they must radically reconceive the project of metaphysics.
There is a traditional theistic doctrine, known as the doctrine of divine simplicity, according to which God is an absolutely simple being, completely devoid of any metaphysical complexity. On the standard understanding of this doctrine—as epitomized in the work of philosophers such as Augustine, Anselm, and Aquinas—there are no distinctions to be drawn between God and his nature, goodness, power, or wisdom. On the contrary, God is identical with each of these things, along with anything else that can be (...) predicated of him intrinsically. (shrink)
In this paper I compare parametric and nonparametric regression models with the help of a simulated data set. Doing so, I have two main objectives. The first one is to differentiate five concepts of simplicity and assess their respective importance. The second one is to show that the scope of the existing philosophical literature on simplicity and model selection is too narrow because it does not take the nonparametric approach into account, S112–S123, 2002; Forster and Sober in The (...) British Journal for the Philosophy of Science 45, 1–35, 1994; Forster, 2001, in Philosophy of Science 74, 588–600, 2007; Hitchcock and Sober in The British Journal for the Philosophy of Science 55, 1–34, 2004; Mikkelson in Philosophy of Science 73, 440–447, 2006; Baker 2013). More precisely, I point out that a measure of simplicity in terms of the number of adjustable parameters is inadequate to characterise nonparametric models and to compare them with parametric models. This allows me to weed out false claims about what makes a model simpler than another. Furthermore, I show that the importance of simplicity in model selection cannot be captured by the notion of parametric simplicity. ‘Simplicity’ is an umbrella term. While parametric simplicity can be ignored, there are other notions of simplicity that need to be taken into consideration when we choose a model. Such notions are not discussed in the previously mentioned literature. The latter therefore portrays an incomplete picture of why simplicity matters when we choose a model. Overall I support a pluralist view according to which we cannot give a general and interesting justification for the importance of simplicity in science. (shrink)
The fact that simplicity has been linked with induction by many philosophers of science, some of whom have proposed or supported criteria of “inductive simplicity,” means that the problem must be given some serious attention. I take “inductive simplicity” as a title, however, only by way of concession to these historical treatments, since it is precisely the burden of my paper to show that there is no such thing. So much for the conclusion. I shall spend the (...) remainder of my time arguing for it. (shrink)
The idea that simplicity matters in science is as old as science itself, with the much cited example of Ockham's Razor, 'entia non sunt multiplicanda praeter necessitatem': entities are not to be multiplied beyond necessity. A problem with Ockham's razor is that nearly everybody seems to accept it, but few are able to define its exact meaning and to make it operational in a non-arbitrary way. Using a multidisciplinary perspective including philosophers, mathematicians, econometricians and economists, this 2002 monograph examines (...)simplicity by asking six questions: what is meant by simplicity? How is simplicity measured? Is there an optimum trade-off between simplicity and goodness-of-fit? What is the relation between simplicity and empirical modelling? What is the relation between simplicity and prediction? What is the connection between simplicity and convenience? The book concludes with reflections on simplicity by Nobel Laureates in Economics. (shrink)
The doctrine of divine simplicity has recently been ably defended, but very little work has been done considering reasons to believe God is simple. This paper begins to address this lack. I consider whether divine aseity or the related notion of divine sovereignty provide us with good reason to affirm divine simplicity. Divine complexity has sometimes been thought to imply that God would possess an efficient cause; or, alternatively, that God would be grounded by God’s constituents. I argue (...) that divine complexity implies neither of these, and so that a complex God could also exist a se. Similarly, a complex God might be thought less sovereign than a simple God, due to lacking control over the divine constituents. I argue in reply that a complex God either has just as much control as a simple God, or that a complex God’s relative lack of control should cause no theological problems. The upshot is that neither the doctrines of divine aseity or of divine sovereignty give theists good reason to endorse divine simplicity. (shrink)
This chapter is a work in applied metaphysics. Recent discussions of monism and metaphysical dependence are deployed to develop a view—the doctrine of divine priority (DDP)—that is a viable alternative to the doctrine of divine simplicity (DDS). DDS and the traditional motivation for it are introduced using an analogy involving Jonathan Schaffer’s distinction between two forms of monism. It is argued that DDP is an alternative to DDS by showing that it is consistent with the traditional motivation for the (...) latter view, and argued that DDP is a viable alternative by showing that objections to its peculiar implications rest on assumptions that can reasonably be rejected. In the concluding section, the findings of the main discussion are summarized and DDP’s potential theological import is illustrated by briefly discussing a possible solution to the Problem of the Trinity it suggests. (shrink)
We continue , developing simplicity in the framework of compact abstract theories. Due to the generality of the context we need to introduce definitions which differ somewhat from the ones use in first order theories. With these modified tools we obtain more or less classical behaviour: simplicity is characterized by the existence of a certain notion of independence, stability is characterized by simplicity and bounded multiplicity, and hyperimaginary canonical bases exist.
In a recent work, Popper claims to have solved the problem of induction. In this paper I argue that Popper fails both to solve the problem, and to formulate the problem properly. I argue, however, that there are aspects of Popper's approach which, when strengthened and developed, do provide a solution to at least an important part of the problem of induction, along somewhat Popperian lines. This proposed solution requires, and leads to, a new theory of the role of (...) class='Hi'>simplicity in science, which may have helpful implications for science itself, thus actually stimulating scientific progress. (shrink)
The doctrine of divine simplicity, according to which God is devoid of physical or metaphysical complexity, is widely believed to be incoherent. I argue that although two prominent recent attempts to defend it fail, it can be defended against the charge of obvious incoherence. The defense rests on the isolation and rejection of a crucial assumption, namely, that no property is an individual. I argue that there is nothing in our ordinary concepts of property and individual to warrant the (...) assumption, and that once the assumption is rejected, the way is clear to viewing the divine attributes as self-exemplifying properties whose self-exemplification entails their identity with an individual. (shrink)
I explain the doctrine of divine simplicity, and reject what is now the standard way to explicate it in analytic philosophy. I show that divine simplicity imperils the claim that God is free, and argue against a popular proposal for dealing with the problem.
The doctrine of God’s absolute simplicity denies the possibility of real distinctions in God. It is, e.g., impossible that God have any kind of parts or any intrinsic accidental properties, or that there be real distinctions among God’s essential properties or between any of them and God himself. After showing that some of the counter-intuitive implications of the doctrine can readily be made sense of, the authors identify the apparent incompatibility of God’s simplicity and God’s free choice as (...) a special difficulty and associate it with two others: the apparent incompatibilities between essential omnipotence and essential goodness, and between perfect goodness and moral goodness. Since all three of these difficulties are associated with a certain understanding of the nature of God’s will, the authors base their resolution of them on an account of will in general and of God’s will in particular, drawing on Aquinas’s theory of will.Taking creation as their paradigm of divine free choice, the authors develop a solution of the principal incompatibility based on three claims: God’s acts of choice are both free and conditionally necessitated; the difference between absolutely and conditionallynecessitated acts of will is not a real distinction in God; and the conditional necessity of God’s acts of will is compatible with contingency in the objects of those acts. The heart of their solution consists in their attempt to make sense of and support those claims.The authors extend their solution to cover the two associated apparent incompatibilities as well.The article concludes with observations on the importance of the doctrine of God’s absolute simplicity for resolving problems in religious morality and in the cosmological argument. (shrink)
My project is to examine and critically discuss the role of simplicity in Swinburne’s probabilistic natural theology. After describing that role and the details of his theory of simplicity, I challenge Swinburne’s view that the criterion of simplicity is a fundamental criterion for evaluating causal explanations, proposing instead that what is right about that criterion can be derived from a more fundamental criterion of “coherence.” I close by exploring the implications of my proposal for Swinburne’s natural theology.
This paper examines a variety of approaches in order to make sense of the doctrine of divine simplicity. Discussing the implications of traditional and contemporary philosophical concepts of divine simplicity, the author argues for taking the divine nature as a stupendous substance to serve as the one and only truthmaker of statements regarding God, while we can resolve the predication problem which is caused by the idea that, as implied by divine simplicity, God is identical to his (...) attributes if we conceive of the divine nature as an equivalent to Platonic forms. (shrink)
According to Timothy Williamson, we should accept the simplest and most powerful second-order modal logic, and as a result accept an ontology of "bare possibilia". This general method for extracting ontology from logic is salutary, but its application in this case depends on a questionable assumption: that modality is a fundamental feature of the world.
Simplicity provides a new logic with which to approach intellectual situations. Using the simplicity way of thinking as a tool helps clarify intellectual standpoints and conceptually problematic situations in philosophy, mathematics and physics.
Simplicity has long been recognized as an apparent mark of truth in science, but it is difficult to explain why simplicity should be accorded such weight. This chapter examines some standard, statistical explanations of the role of simplicity in scientific method and argues that none of them explains, without circularity, how a reliance on simplicity could be conducive to finding true models or theories. The discussion then turns to a less familiar approach that does explain, in (...) a sense, the elusive connection between simplicity and truth. The idea is that simplicity does not point at or reliably indicate the truth but, rather, keeps inquiry on the cognitively most direct path to the truth. (shrink)
A well-known objection to divine simplicity holds that the doctrine is incompatible with God’s contingent knowledge. I set out the objection and reject two problematic solutions. I then argue that the objection is best answered by adopting an “extrinsic model of divine knowing” according to which God’s contingent knowledge, which varies across worlds, does not involve any intrinsic variation in God. Solutions along these lines have been suggested by others. This paper advances the discussion by developing and offering partial (...) defenses of three such models. (shrink)
This paper is devoted to Bolzano’s theory of grounding (Abfolge) in his Wissenschaftslehre. Bolzanian grounding is an explanatory consequence relation that is frequently considered an ancestor of the notion of metaphysical grounding. The paper focuses on two principles that concern grounding in the realm of conceptual sciences and relate to traditionally widespread ideas on explanations: the principles, namely, that grounding orders conceptual truths from simple to more complex ones (Simplicity), and that it comes along with a certain theoretical economy (...) among them (Economy). Being spelled out on the basis of Bolzano’s notion of deducibility (Ableitbarkeit), these principles are revealing for the question to what extent grounding can be considered a formal relation. (shrink)
According to many philosophical theologians, God is metaphysically simple: there is no real distinction among His attributes or even between attribute and existence itself. Here, I consider only one argument against the simplicity thesis. Its proponents claim that simplicity is incompatible with God’s having created another world, since simplicity entails that God is unchanging across possible worlds. For, they argue, different acts of creation involve different willings, which are distinct intrinsic states. I show that this is mistaken, (...) by sketching an adequate account of reasons-guided activity that does not require distinct intrinsic states of willing corresponding to each possible act of creation. (shrink)
Paleobiologists often provide simple narratives to explain complex, contingent episodes. These narratives are sometimes ‘one-shot hypotheses’ which are treated as being mutually exclusive with other possible explanations of the target episode, and are thus extended to accommodate as much about the episode as possible. I argue that a provisional preference for such hypotheses provides two kinds of productive scaffolding. First, they generate ‘hypothetical difference-makers’: one-shot hypotheses highlight and isolate empirically tractable dependencies between variables. Second, investigations of hypothetical difference-makers provision explanatory (...) resources, the ‘raw materials’ for constructing more complex—and likely more adequate—explanations. Provisional preferences for simple, one-shot hypotheses in historical science, then, is defeasibly justified on indirect—strategic—grounds. My argument is made in reference to recent developments regarding the K–Pg extinction. (shrink)
In The City of God, XI, 10, St Augustine claims that the divine nature is simple because ‘it is what it has’ (quod habet hoc est). We may take this as a slogan for the Doctrine of Divine Simplicity (DDS), a doctrine which finds its way into orthodox medieval Christian theological speculation. Like the doctrine of God's timeless eternality, the DDS has seemed obvious and pious to many, and incoherent, misguided, and repugnant to others. Unlike the doctrine of God's (...) timeless eternality, the DDS has received very little critical attention. The DDS did not originate with Augustine, but I am not primarily concerned with its pedigree. Nor am I concerned to ask how the doctrine interacts with trinitarian speculation. I will have my hands full as it is. In Section I of this paper I shall provide a rough characterization of the DDS, indicate its complexity, and focus on a particular aspect of the doctrine which will exercise us in the remainder of the paper, namely, the thesis that the divine attributes are all identical with each other and with God. In section n I shall discuss Alvin Plantinga's recent objections to Aquinas' version of the DDS. I shall then offer a more detailed presentation of what I take to be Aquinas' version (section III), and recast it in terms of a theory of attributes which is significantly different from Plantinga's (section IV). Although the recasting of the doctrine will enable me to rebut Plantinga's objections (section v), it by no means solves all the problems of the DDS. In section vi I shall discuss the chief lingering problem facing a defender of the DDS. (shrink)
According to Richard Swinburne, the principle of simplicity is of great importance to theory choice scenarios and theoretical changes in the sciences. In particular, he holds that the theory choice criterion of fit with background evidence can be reduced to the criteria of simplicity and of yielding the data. We will, however, rebut this reduction thesis and show that three central aspects of theoretical change (confirming power of empirical data, reliability of experimental methods, and truth of new theoretical (...) proposals) cannot be adequately reconstructed if simplicity is regarded as a key criterion of theory choice. (shrink)
An up-to-date account of the current techniques and results in Simplicity Theory, which has been a focus of research in model theory for the last decade. Suitable for logicians, mathematicians and graduate students working on model theory.
Augustine, Aquinas and many other medievals held the doctrine of divine simplicity (DDS) -that God has no parts of any sort. Augustine took this to imply that for any non-relational attribute F, if God is F, God = Fness. This can seem to create three problems. I set them out. Having done so, I show that Augustine's DDS is set within a view of attributes now unfamiliar to us. When we bring this into the picture, it turns out that (...) two of the problems do not really arise and the third is not really problematic. I then suggest that my rescue of Augustine may rescue other prominent friends of DDS as well. (shrink)
In this paper, I argue that a natural selection-based perspective gives reasons for thinking that the core of the ability to mindread cognitively complex mental states is subserved by a simulationist process—that is, that it relies on nonspecialised mechanisms in the attributer's cognitive architecture whose primary function is the generation of her own decisions and inferences. In more detail, I try to establish three conclusions. First, I try to make clearer what the dispute between simulationist and non-simulationist theories of mindreading (...) fundamentally is about. Second, I try to make more precise an argument that is sometimes hinted at in support of the former: this 'argument from simplicity' suggests that, since natural selection disfavours building extra cognitive systems where this can be avoided, simulationist theories of mindreading are more in line with natural selection than their competitors. As stated, though, this argument overlooks the fact that building extra cognitive systems can also yield benefits: in particular, it can allow for the parallel processing of multiple problems and it makes for the existence of backups for important elements of the organism's mind. I therefore try to make this argument more precise by investigating whether these benefits also apply to the present case—and conclude negatively. My third aim in this paper is to use this discussion of mindreading as a means for exploring the promises and difficulties of evolutionary arguments in philosophy and psychology more generally. (shrink)
In this paper we explore material simplicity, defined as the virtue disposing us to act appropriately within the sphere of our consumer decisions. Simplicity is a conscientious and restrained attitude toward material goods that typically includes (1) decreased consumption and (2) a more conscious consumption; hence (3) greater deliberation regarding our consumer decisions; (4) a more focused life in general; and (5) a greater and more nuanced appreciation for other things besides material goods, and also for (6) material (...) goods themselves. It is to be distinguished from simple-mindedness, a return to nature, or poverty. Simplicity overlaps with traditional virtues such as temperance, frugality, and wisdom, and sustains and enables traditional virtues such as justice and generosity. Simplicity is a virtue because it furthers human flourishing, both individual and social, and sustains nature’s ecological flourishing. For analytic purposes, we consider six areas in which simplicity can make important contributions: (1) basic individual flourishing, (2) basic societal flourishing, (3) individual freedom or autonomy, (4) the acquisition of knowledge, (5) living meaningfully, and (6) preserving and protecting nonhuman beings. The proven failure of materialism to secure subjective happiness or objective flourishing argues for the practice of voluntary simplicity and for the radical reform of modern consumer societies. (shrink)
Theoretical simplicity is difficult to characterize, and evidently can depend upon a number of distinct factors. One such desirable characteristic is that the laws of a theory have relatively few "counterinstances" whose accommodation requires the invocation of a ceteris paribus condition and ancillary explanation. It is argued that, when one theory is reduced to another, such that the laws of the second govern the behavior of the parts of the entities in the domain of the first, there is a (...) characteristic gain in simplicity of the sort mentioned: while I see no way of quantitatively measuring the "amount" of defeasibility of the laws of a theory, microreduction can be shown to decrease that "amount.". (shrink)
Divine Simplicity has it that God is absolutely simple. God exhibits no metaphysical complexity; he has neither proper parts nor distinct intrinsic properties. Recently, Jeffrey Brower has put forward an account of divine simplicity that has it that God is the truthmaker for all intrinsic essential predications about him. This allows Brower to preserve the intuitive thought that God is not a property but a concrete being. In this paper, I provide two objections to Brower’s account that are (...) meant to show that whatever merits this account of divine simplicity has, plausibility is not one of them. (shrink)
Descartes famously endorsed the view that (CD) God freely created the eternal truths, such that He could have done otherwise than He did. This controversial doctrine is much discussed in recent secondary literature, yet Descartes’s actual arguments for CD have received very little attention. In this paper I focus on what many take to be a key Cartesian argument for CD: that divine simplicity entails the dependence of the eternal truths on the divine will. What makes this argument both (...) important and interesting is that Descartes’s scholastic predecessors share the premise of divine simplicity but reject the CD conclusion. To properly understand Descartes, then, we must determine precisely where he diverges from his predecessors on the path from simplicity to CD. And when we do so we obtain a very surprising result: that despite many dramatic prima facie differences, there is no substantive difference between the relevant doctrines of Descartes and the scholastics . Or so I argue. (shrink)
I provide a simple solution to the problem of determining the characterising feature(s) of the simple approach to personal identity, sometimes also called the simple view: instead of focusing on claims regarding the analysability, reducibility, or triviality of the concepts used in simple theories of personal identity, I propose instead a metaphysical criterion to define this approach. In particular, I claim that the simple approach is (best seen as) that family of theories according to which personal identity is a relation (...) that essentially depends on a mereologically simple (or impartite) entity the existence and features of which may be known directly (e.g., by introspection) or indirectly (e.g., by deduction from a series of other premises). (shrink)
Almost all commentators acknowledge that among the grounds on which scientists perform theory-choices are criteria of simplicity. In general, simplicity is regarded either as only a logico-empirical quality of a theory, diagnostic of the theory's future predictive success, or as a purely aesthetic or otherwise extra-empirical property of it. This paper attempts to demonstrate that the simplicity-criteria applied in scientific practice include both a logico-empirical and a quasi-aesthetic criterion: to conflate these in an account of scientists' theory-choice (...) is to court confusion. (shrink)
In a short 1997 book entitled Simplicity as Evidence of Truth, the Oxford philosopher Richard Swinburne has put forward the following thesis summarily: ‘… for theories rendering equally probable our observational data, fitting equally well with background knowledge, the simplest is most probably true’.
What do mathematicians mean when they use terms such as ‘deep’, ‘elegant’, and ‘beautiful’? By applying empirical methods developed by social psychologists, we demonstrate that mathematicians' appraisals of proofs vary on four dimensions: aesthetics, intricacy, utility, and precision. We pay particular attention to mathematical beauty and show that, contrary to the classical view, beauty and simplicity are almost entirely unrelated in mathematics.
Firstly, in this paper, we prove that the equivalence of simplicity and the symmetry of forking. Secondly, we attempt to recover definability part of stability theory to simplicity theory. In particular, using elimination of hyperimaginaries we prove that for any supersimple T, canonical base of an amalgamation class P is the union of names of ψ-definitions of P, ψ ranging over stationary L-formulas in P. Also, we prove that the same is true with stable formulas for an 1-based (...) theory having elimination of hyperimaginaries. For such a theory, the stable forking property holds, too. (shrink)