INTRODUCTION TO THE ARGUMENT AND ITS HISTORY PRIOR TO THE AND CENTURIES In the history of ideas, there is an argument that has been used repeatedly, ...

In previous publications, I have historically traced the prevalence and the influence of an argument—an argument which Kant calls the Achilles, the most powerful, of all rationalist demonstrations in the history of ideas. This proof, which ultimately derives from Plato has been repeatedly used and has had a major influence in shaping philosophic discussions since the Hellenic Age. The form of the argument is fairly straightforward: the essential nature of the soul consists in its power of thinking; thought, being immaterial, (...) is unextended, i.e., simple, having no parts; and what is simple is indestructible; a unity; and an identity. I have attempted to map the incidence and force of this demonstration in the seventeenth and eighteenth centuries—from the Cambridge Platonists to Kant —a time when it becomes crucial in questions concerning the immortality of the soul; the “transcendental” condition necessary for the unity of consciousness ; the necessary and sufficient criteria for the establishment of personal or moral identity; and its use as a sometimes hidden or unconscious premise, but often explicit “principle,” of certain metaphysical and epistemological idealist doctrines. Thus, if thought and soul are essentially unextended, it at once becomes problematic how an immaterial soul can know a material, extended, “external” world. (shrink)

In this paper I will argue that a false assumption drives the attraction of philosophers to a divine command theory of morality. Specifically, I suggest the idea that anything not created by God is independent of God is a misconception. The idea misleads us into thinking that our only choice in offering a theistic ground for morality is between making God bow to a standard independent of his will or God creating morality in revealing his will. Yet what is God (...) is hardly independent of him, and in coupling a perfect being theology with the doctrine of divine simplicity we discover that God’s “reason” is God. Accordingly, obeying the truths of goodness that we humans speak of as contained in the divine wisdom hardly impugns the divine sovereignty. By modifying divine command ethics to give primacy to God’s love or justice, thinkers such as Robert M. Adams, Philip L. Quinn, and Edward J. Wierenga admit the repugnance of this picture in spite of their verbal allegiance to divine command ethics. Accordingly, they implicitly concede that basing morality on God’s sheer power should not be the preferred option for the Christian theist. (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 immense distance between God and creatures is a core statement of Gregory of Nyssa’s thought, which makes it distinctive not only in theology, but also in cosmology, anthropology, and spiritual doctrine. For him, the main distinction between beings that articulates all reality is not that of intelligible and sensible, but the one between infinite God and creatures. This paper, dealing with some selected texts regarding the creation of man, points out the main roots of Gregory’s theism: a high comprehension (...) of God’s transcendence and a proper philosophy of time and creation. From here, Gregory’s understanding of the hierarchy of beings as a non-dialectic unity of creation supported by a transcendent participation in God, and his articulation of Eternity and Time within the unique creative action of God, could be seen as a deep Christian comprehension of reality that is still intriguing for contemporary thinkers. (shrink)

French mathematician Michel Chasles, a staunch defender of pure geometrical methods, is now mostly remembered as the author of the Aperçu historique. In this book, he retraced the history of geometry in order to expound epistemological theses on what constitutes a virtuous practice of geometry. Amongst these stands out the assertion that the values of generality and simplicity in mathematics are intimately connected. In this paper, we flesh out this claim by analysing Chasles’s geometrical solutions to the century-old problem (...) of the attraction of the ellipsoids. We show how these solutions echo Chasles’s evaluation of the relative strengths of geometrical and analytical methods, and how they embody a set of normative rules for the geometer’s practice whose observance Chasles deemed necessary and sufficient for the development of general methods and theories. (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)

There has been a long controversy about the opinions of Aristotle and Maimonides on the best way of life for human beings. They often seem to emphasize a life based on intellectual pursuits as the highest form of existence and to deprecate more social but less rationally demanding forms of existence. This is particularly problematic for Maimonides, for it would imply that the life of a pious person is of little value unless it is combined with intellectual excellence. It is (...) argued that this is not the view of Maimonides, and that he has enough resources in his system to show how a whole gamut of human activities and the lifestyles which go along with them are worthy of respect. (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)

This chapter contains sections titled: The Concept and Difficulties Associated with It The History of the Concept Applications of the Concept to Issues in the Philosophy of Religion Works cited.

It is widely recognized that Frege's systematic conception of science has a major impact on his work. I argue that central to this conception and its impact is Frege's Simplicity Requirement that a scientific system must have as few primitive truths as possible. Frege states this requirement often, justifies it in several ways, and appeals to it to motivate important aspects of his broader views. Acknowledging its central role illuminates several aspects of his work in new ways, including his (...) treatment of truth values, logical concepts, and the dependence relations that induce a ‘natural order’ of truths. (shrink)

It is often said that the best system account of laws needs supplementing with a theory of perfectly natural properties. The ‘strength’ and ‘simplicity’ of a system is language-relative and without a fixed vocabulary it is impossible to compare rival systems. Recently a number of philosophers have attempted to reformulate the BSA in an effort to avoid commitment to natural properties. I assess these proposals and argue that they are problematic as they stand. Nonetheless, I agree with their aim, (...) and show that if simplicity is interpreted as ‘compression’, algorithmic information theory provides a framework for system comparison without the need for natural properties. (shrink)

One of the primary concerns of the Consolatio is to draw out many of the paradoxical conclusions concerning the relation between creation and God that stem from the premises of classical creationist metaphysics, and attempt to solve them. Once one accepts that God does exist, is omnipotent, omniscient, and simple, it becomes viciously difficult to explain: (1) how anything contrary to God’s will—evil—can exist; (2) how any cause can act independently of God’s will—human freedom; and (3) how “independent causes” can (...) relate to God through their own agency—human prayer. This naturally begs the question: why should we accept the premises of classical creationist metaphysics? This paper addresses this question by analyzing and defending two of the central premises of Boethius’s version of classical creationist metaphysics as they are addressed in Consolatio III,10: (a) that God exists, and (b) that God is simple. (shrink)

Socrates contradicts himself when he claims that a good doctor must have the experience of having an unsound body and when he claims that a good judge must have a sound soul, for the unsound of body will not be treated and how a judge decides the case of a good person is a matter of indifference. These pages are really about the meaning of simplicity of soul, and arguing against Glaucon's claim, 'to be moved by self-advantage is the (...) end which it is natural to pursue as good, until forcibly turned aside by law and custom to respect equality'. (shrink)

Contrary to many interpreters, I argue that Thomas Aquinas’s account of divine simplicity is compatible with the accounts of divine simplicity given by John Duns Scotus and Gregory Palamas. I synthesize their accounts of divine simplicity in a way that can answer the standard objections to the doctrine of divine simplicity more effectively than any of their individual accounts can. The three objections that I consider here are these: the doctrine of divine simplicity is inconsistent (...) with distinguishing divine attributes, with the doctrine of the Trinity, and with the doctrine of divine freedom. (shrink)

DOES the sun travel around the earth or does the earth travel around the sun? Our limited objective in this article is to see how one seventeenth century thinker of note, thinking on the topic previous to the publication of Newton’s Principia, answered this question and why he gave the answer that he did. Our procedure will be to set out the views of Copernicus’ important predecessors, the view of Copernicus, the view of Hooke, and then to place these views (...) in their wider historical context. (shrink)

This paper presents a broad-ranging critique of the traditional strong doctrine of divine simplicity which is attributed to Augustine and Aquinas. After showing two important arguments in favor of the doctrine to be unsuccessful, it argues that the doctrine itself, in this strong version, is problematic in three main ways. First, the doctrine involves extensive category mistakes. Second, it is difficult to reconcile with truths about God that are universally acknowledged, such as that God knows contingent truths and performs (...) actions which he is not necessitated by his nature to perform. Finally, it is difficult to reconcile with personal attributes of God which are important both for the Bible and for religious practice, such as the claims that God is responsive to human beings and that he loves them. This article contends that while there is a sense in which it is true that God is simple, the traditional strong doctrine of divine simplicity, attributed to Augustine and Aquinas, is a mistake from which theology needs to be liberated. (shrink)

The correspondence in 1680 and 1681 between John Flamsteed and Isaac Newton on Flamsteed’s theory of the comet of 1680 tells half the story. Related manuscripts reveal Newton was pursuing his own comprehensive line of inquiry based on principles that were the antithesis of Flamsteed’s procedures. Following generally accepted views in England, Newton’s work was marked by critical evaluation of data but marred by uncritical use of simple calculating techniques based on what might be termed Platonic archetypes of straightness. Flamsteed’s (...) intervention provided useful data and allowed Newton to seek additional information. Although Newton supposedly briefly considered a solution that vaguely resembled his parabolic approximation of the path of the comet determined 5 years later, the evidence Newton provided (based on simple hypotheses) did not support such a highly curved path or one in which the sun apart from the solar vortex exerted influence. Newton’s work, including an alleged harmonic law of tails, was quietly abandoned in favor of other work. With new insight, Newton revived work on comets as fully gravitational objects immediately following Halley’s visit in 1684. This little known side of the episode provides a fresh opportunity to examine Newton’s sources and actual practice in developing a new line of inquiry. An appendix dating sections of Newton’s Waste Book entries on comets is included. (shrink)

The idea of elegance in science is not necessarily a familiar one, but it is an important one. The use of the term is perhaps most clear-cut in mathematics - the elegant proof - and this is where Ian Glynn begins his exploration. Scientists often share a sense of admiration and excitement on hearing of an elegant solution to a problem, an elegant theory, or an elegant experiment. The idea of elegance may seem strange in a field of endeavour that (...) prides itself in its objectivity, but only if science is regarded as a dull, dry activity of counting and measuring. It is, of course, far more than that, and elegance is a fundamental aspect of the beauty and imagination involved in scientific activity. Ian Glynn, a distinguished scientist, selects historical examples from a range of sciences to draw out the principles of science, including Kepler's Laws, the experiments that demonstrated the nature of heat, and the action of nerves, and of course the several extraordinary episodes that led to Watson and Crick's discovery of the structure of DNA. With a highly readable selection of inspiring episodes highlighting the role of beauty and simplicity in the sciences, the book also relates to important philosophical issues of inference, and Glynn ends by warning us not to rely on beauty and simplicity alone - even the most elegant explanation can be wrong. (shrink)

Classical Trinitarian dogma affirms that God is simple—a teaching also advanced by major proponents of classical monotheism. Nevertheless, as each one knows, this notion is controversial in modern analytic philosophy, where it is commonly contested. It is also largely ignored in contemporary continental dogmatic theology. Nevertheless, the teaching that God is simple is requisite for any authentic interpretation of the Trinitarian dogma of Nicaea. It is also eminently defensible from a rational, philosophical point of view. In what follows I will (...) begin with (I) a theological consideration of the notion of Trinitarian simplicity before considering (II) the metaphysics of the simplicity of the divine essence. (III) I will then consider briefly two special problems that are associated with the metaphysics of divine simplicity: divine knowledge and divine freedom. (IV) Finally, I will consider briefly the significant Christological consequences of the acceptance (or non-acceptance) of the traditional affirmation of divine simplicity. (shrink)

Aquinas maintains that, although God created the universe, he could have created another or simply refrained from creating altogether. That Aquinas believesin divine free choice is uncontroversial. Yet doubts have been raised as to whether Thomas is entitled to this belief, given his claims concerning divine simplicity.According to simplicity, there is no potentiality in God, nor is there a distinction in God between God’s willing, His essence, and His necessary being. On the surface, it appears that these claims (...) leave no room for divine free choice. I argue that attempts by Aquinas and a pair of his contemporary defenders to reconcile God’s freedom with God’s simplicity fail to resolve the problem. Nevertheless, I maintain that Aquinas provides the key to a resolution in his claim that while creatures are really related to God, God is not really related to creatures. (shrink)

This paper takes an integrated history and philosophy of science approach to the topic of "simplicity out of complexity". The reflex theory was a framework within early twentieth century psychology and neuroscience which aimed to decompose complex behaviours and neural responses into simple reflexes. It was controversial in its time, and did not live up to its own theoretical and empirical ambitions. Examination of this episode poses important questions about the limitations of simplifying strategies, and the relationship between simplification (...) and the engineering approach to biology. (shrink)

Part 1. Lecture 1. What is big history? ; Lecture 2. Moving across multiple scales ; Lecture 3. Simplicity and complexity ; Lecture 4. Evidence and the nature of science ; Lecture 5. Threshold 1, Origins of Big Bang cosmology ; Lecture 6. How did everything begin? ; Lecture 7. Threshold 2, The first stars and galaxies ; Lecture 8. Threshold 3, Making chemical elements ; Lecture 9. Threshold 4, The earth and the solar system ; Lecture 10. The (...) early earth, a short history ; Lecture 11. Plate tectonics and the earth's geography ; Lecture 12. Threshold 5, Life -- Part 2. Lecture 13. Darwin and natural selection ; Lecture 14. The evidence for natural selection ; Lecture 15. The origins of life ; Lecture 16. Life on earth, single-celled organisms ; Lecture 17. Life on earth, multi-celled organisms ; Lecture 18. Hominines ; Lecture 19. Evidence on hominine evolution ; Lecture 20. Threshold 6, What makes humans different? ; Lecture 21. Homo sapiens, the first humans ; Lecture 22. Paleolithic lifeways ; Lecture 23. Change in the Paleolithic Era ; Lecture 24. Threshold 7, agriculture -- Part 3. Lecture 25. The origins of agriculture ; Lecture 26. The first agrarian societies ; Lecture 27. Power and its origins ; Lecture 28. Early power structures ; Lecture 29. From villages to cities ; Lecture 30. Sumer, the first agrarian civilization ; Lecture 31. Agrarian civilizations in other regions ; Lecture 32. The world that agrarian civilizations made ; Lecture 33. Long trends, expansion and state power ; Lecture 34. Long trends, rates of innovation ; Lecture 35. Long trends, disease and Malthusian cycles ; Lecture 36. Comparing the world zones -- Part 4. Lecture 37. The Americas in the later Agrarian Era ; Lecture 38. Threshold 8, the modern revolution ; Lecture 39. The Medieval Malthusian Cycle, 500-1350 ; Lecture 40. The Early Modern Cycle, 1350-1700 ; Lecture 41. Breakthrough, the Industrial Revolution ; Lecture 42. Spread of the Industrial Revolution to 1900 ; Lecture 43. The 20th century ; Lecture 44. The world that the modern revolution made ; Lecture 45. Human history and the biosphere ; Lecture 46. The next 100 years ; Lecture 47. The next millennium and the remote future ; Lecture 48. Big history, humans in the cosmos. (shrink)

The first sophisticated wargames were developed between 1770 and 1830 and are models of military conflict. Designers of these early games experimented fruitfully with different concepts that were formulated in interaction with the external dynamics of the military systems that they tried to represent and the internal dynamics of the design process itself. The designers of early wargames were confronted with a problem that affects all models: the trade-off between realism and simplicity, which in the case of wargames amounts (...) to the trade-off between realism and playability. I try to show how different game concepts were developed as an answer to this problem, and how these seemingly arcane concepts form a relevant topic of investigation in the history of ideas. Moreover, a direct offshoot of this conceptual experimentation between 1770 and 1830 was the ‘free’ German wargame, which became an integral part of German operational planning in the nineteenth and twentieth centuries, thus adding another chapter to the story of the influence of ideas on human history. (shrink)

Copernicus claimed that his system was preferable in part on the grounds of its superior harmony and simplicity, but left very few hints as to what was meant by these terms. Copernicus’s pupil, Rheticus, was more forthcoming. Kepler, influenced by Rheticus, articulated further the nature of the virtues of harmony and simplicity. I argue that these terms are metaphors for the structural features of the Copernican system that make it more able to effectively exploit the available data. So (...) it is a mistake to conclude that early Copernicans could only offer aesthetic or pragmatic arguments; they could and did offer evidential ones as well. Moreover, the evidential arguments they offered parallel current arguments in the philosophical literature.Keywords: Nicolaus Copernicus; Georg Joachim Rheticus; Johannes Kepler; Simplicity; Bayesianism; Hirotsugu Akaike. (shrink)

In his recent article “Against Divine Truthmaker Simplicity,” Noël Saenz has provided two careful arguments for the falsity of a theory of divine simplicity which he dubs “Divine Truthmaker Simplicity.” In this brief response, I criticize his two arguments, arguing that neither is sound.

Ethics in Thucydides uses the historian's account of the resolution at Corcyra as the basis for determining a moral or ethical perspective in Thucydides'History. Various scenes, speeches, and narrative descriptions are analyzed in relation to ethical vocabulary, their conformity to an ethical perspective, and the way in which they promote an ethical outcome. Ethics in Thucydides is ground-breaking because up to this point, scholars have not persuasively argued that ethics played a role in History. Williams' work is an extensive analysis (...) which also considers Thucydides in relation to his predecessors and contemporaries. (shrink)

I discuss Hume's views about whether simplicity and generality are positive features of explanations. In criticizing Hobbes and others who base their systems of morality on self interest, Hume diagnoses their errors as resulting from a "love of simplicity". These worries about whether simplicity is a positive feature of explanations emerge in Hume's thinking over time. But Hume does not completely reject the idea that it's good to seek simple explanations. What Hume thinks we need is good (...) judgment about when we are going too far in our search for simple explanations. These worries about simplicity are not unique to Hume. We can see versions of them in the work of Hutcheson, Smith, and Reid. (shrink)

Einstein proclaimed that we could discover true laws of nature by seeking those with the simplest mathematical formulation. He came to this viewpoint later in his life. In his early years and work he was quite hostile to this idea. Einstein did not develop his later Platonism from a priori reasoning or aesthetic considerations. He learned the canon of mathematical simplicity from his own experiences in the discovery of new theories, most importantly, his discovery of general relativity. Through his (...) neglect of the canon, he realised that he delayed the completion of general relativity by three years and nearly lost priority in discovery of its gravitational field equations. (shrink)

This text, touching on the problem of the ontology of the image from a political-theological perspective, focuses on Reiner Schürmann’s philosophical reading of the pictorial art of Louis Comtois. While placing it in the context of post-World War II modernism, he nevertheless underlines its special spiritual quality that, far from any theorization of messianic abstractionism or any affirmation of artistic sovereignty, shows all the anarchic simplicity of painting. It is a form of modernity still to be imagined but one (...) that is already in some way active in the unpredictable meeting of matter and light, which Comtois’s pictorial act and Schürmann’s thought contemplate in the inseparable connection between history and immortality. (shrink)

Einstein proclaimed that we could discover true laws of nature by seeking those with the simplest mathematical formulation. He came to this viewpoint later in his life. In his early years and work he was quite hostile to this idea. Einstein did not develop his later Platonism from a priori reasoning or aesthetic considerations. He learned the canon of mathematical simplicity from his own experiences in the discovery of new theories, most importantly, his discovery of general relativity. Through his (...) neglect of the canon, he realised that he delayed the completion of general relativity by three years and nearly lost priority in discovery of its gravitational field equations. (shrink)

This chapter contains sections titled: * An Overview of Historical Approaches * Simplicity, Complexity, Modesty * Historical Developments * Recent Developments * Contemporary Proposals * Notes * Bibliography.

A frequent criticism of the neuroscientific approach to consciousness is that its theories describe only 'correlates' or 'analogues' of consciousness, and so fail to address the nature of consciousness itself. Despite its apparent logical simplicity, this criticism in fact relies on some substantive assumptions about the nature and evolution of scientific explanations. In particular, it is usually assumed that, in expressing correlations, neural correlate of consciousness (NCC) theories must fail to capture the causal structure relating brain and mind. Drawing (...) on work in the history and philosophy of science, I argue that this assumption - along with the related claim that even a correct NCC theory would fail to explain consciousness - is grounded in an inadequate conception of the way in which scientific explanations develop. Examination of parallel developments in 20th century biology reveals that, under the right circumstances, seemingly crude correspondences can play an essential role in scientific discovery and can sometimes become central to our everyday understanding of the phenomena in question. A proper understanding of this process clarifies the value of NCC theories and sheds light on the standards by which they should be evaluated. In closing, I describe two specific criteria for evaluating NCC proposals: intertheoretic bridge potential and detailed mapping. (shrink)