Plato used mathematics extensively in his account of the cosmos in the Timaeus, but as he did not use equations, but did use geometry, harmony and according to some, numerology, it has not been clear how or to what effect he used mathematics. This paper argues that the relationship between mathematics and cosmology is not atemporally evident and that Plato’s use of mathematics was an open and rational possibility in his context, though that sort of use of mathematics has subsequently (...) been superseded as science has progressed. I argue that there is a philosophically and historically meaningful space between ‘primitive’ or unreflective uses of mathematics and the modern conception of how mathematics relates to cosmology. Plato’s use of mathematics in the Timaeus enabled the cosmos to be as good as it could be, allowed the demiurge a rational choice and allowed Timaeus to give an account of the cosmos. I also argue that within this space it is both meaningful and important to differentiate between Pythagorean and Platonic uses of number and that we need to reject the idea of ‘Pythagorean/platonic number mysticism’. Plato’s use of number in the Timaeus was not mystical even though it does not match modern usage. (shrink)

Seeking to reassess Plato's views on how we might investigate and explain the natural world, this book argues that many of the common charges against Plato (disinterest, ignorance, dismissal of observation) are unfounded, and that Plato had a series of important and cogent criticisms of the early atomists and other physiologoi. His views on science, and on astronomy and cosmology in particular, develop in interesting ways. It also argues that Plato can best be seen as someone who is struggling with (...) the foundations of scientific realism, and that he has interesting epistemological, cosmological and nomological reasons for his teleological approach. (shrink)

Anaximander, the sixth-century BCE philosopher of Miletus, is often credited as being the instigator of both science and philosophy. The first recorded philosopher to posit the idea of the boundless cosmos, he was also the first to attempt to explain the origins of the world and humankind in rational terms. Anaximander's philosophy encompasses theories of justice, cosmogony, geometry, cosmology, zoology and meteorology. Anaximander: A Re-assessment draws together these wide-ranging threads into a single, coherent picture of the man, his worldview and (...) his legacy to the history of thought. Arguing that Anaximander's statements are both apodeictic and based on observation of the world around him, Andrew Gregory examines how Anaximander's theories can all be construed in such a way that they are consistent with and supportive of each other. This includes the tenet that the philosophical elements of Anaximander's thought (his account of the apeiron, the extant fragment) can be harmonised to support his views on the natural world. The work further explores how these theories relate to early Greek thought and in particular conceptions of theogony and meterology in Hesiod and Homer. (shrink)

Journal Name: Apeiron Issue: Ahead of print.

It is well known that Harvey was influenced by Aristotle. This paper seeks to show that Harvey's quantitative argument for the circulation and his analogy of the heart with a pump do not go beyond Aristotle and may even have been inspired by passages in Aristotle. It also considers the fact that Harvey gives much greater prominence to a macrocosm/microcosm analogy between the weather cycle and the circulation of the blood than he does to the pump analogy. This analogy is (...) prominent in both the preface to the king and pivotal chapter eight of De Motu Cordis, and may indicate a significant influence from the Renaissance natural magic tradition. The full implications of this analogy are critical for Harvey's conception of the nature of the circulation, especially the constant interconversion of venous and arterial blood and the passage of blood through the lungs. The tendency to assume that Harvey had a superior method since he made such an important discovery may have led not only to overestimation of the influence from the new science of the seventeenth century, but also to underestimation of influence from the magical tradition. (shrink)

What ought we to make of Aristotle's apparently disparate comments on bodies in motion? I argue that Aristotle is concerned with a higher level project than dynamics and that is the establishment of a coherent theory of change in general. This theory is designed to avoid the paradoxes and infinities that Aristotle finds in Eleatic, Heraclitean and atomist accounts, notably in relation to comparatives such as 'quicker' and 'slower'. This theory relies on a broad application of proportionality to all types (...) of change, not merely those we would label 'dynamics'. To support this I argue that Aristotle denied the existence of the void and the possibility of instantaneous change, and that he could accommodate 'threshold' changes within his scheme. If this is so, then the aims of Aristotle's comments on motion become more comprehensible, and it will be understandable why Aristotle was more concerned with the application of proportionality in general rather with the investigation of specific cases in dynamics. (shrink)

In this paper I argue that William Harvey believed in a form of astrology. It has long been known that Harvey employed a macrocosm–microcosm analogy and used alchemical terminology in describing how the two types of blood change into one another. This paper then seeks to examine a further aspect of Harvey in relation to the magical tradition. There is an important corollary to this line of thought, however. This is that while Harvey does have a belief in astrology, it (...) is strongly related to Aristotle's views in this area and is quite restricted and attenuated relative to some contemporary beliefs in astrology. This suggests a more general thesis. While Harvey was amenable to ideas which we associate with the natural magic tradition, those ideas had a very broad range of formulation and there was a limit to how far he would accept them. This limit was largely determined by Harvey's adherence to Aristotle's natural philosophy and his Christian beliefs. I argue that this is also the case in relation to Harvey's use of the macrocosm–microcosm analogy and of alchemical terminology, and, as far as we can rely on the evidence, this informs his attitudes towards witches as well. Understanding Harvey's influences and motives here is important in placing him properly in the context of early seventeenth-century thought. (shrink)

How should we treat the cosmogonies of the early ancient Greek philosophers? Much work has been done in showing how these cosmogonies differ from creation myths and how they relate to philosophical issues such as change, persistence through change and matter theory. Here, using Leucippus and Democritus as examples, Gregory tries to show that interesting light can be shed on these cosmogonies by looking at them in relation to perennial problems in cosmogony and perennial types of solutions to these problems. (...) Ancients and moderns have formulated both in different ways, but there are significant structural similarities. To understand ancient cosmogonies, we need to understand how these perennial problems were perceived, and what types of solutions were available. We then need to analyse how the basic ontological and aetiological principles of their systems lead them to choose certain types of solution over others. (shrink)

Plato's comments on astronomy and the education of the guardians at Republic 528e ff have been hotly disputed, and have provoked much criticism from those who have interpreted them as a rejection or denigration of observational astronomy. Here I argue that the key to interpreting these comments lies in the relationship between the conception of enquiry that is implicit in the epistemological allegories, and the programme for the education of the guardians that Plato subsequently proposes. We have, I suggest, been (...) too eager to stress the similarities here, when recognition of the differences may supply us with the tools required for a better understanding of 528e ff, one that to a large extent disarms the anti-empirical critique. My discussion proceeds in three stages. Firstly, Plato takes great care to place his comments on astronomy in the context of the preceding epistemological allegories. Is there any evidence here, where Plato might be thought to discuss enquiry in general, that he rejected or denigrated observation? I argue that even if Plato advocated a 'Two Worlds' (TW) ontology, he still envisaged a dynamic process of enquiry, interrelating sensibles and intelligibles, the investigation of each being necessary but not sufficient to achieve the overall aim. Secondly, Plato appears to be deriving how we ought to go about educating the guardians from how we ought to conduct our enquiries. While the two are intimately related there are important differences, recognition of which turns the supposed rejection of observation into an affirmation of the need for an initial empirical approach. I contend that this makes good sense of the internal structure of 528e ff, and of its relations to other parts of the Republic. Thirdly, I discuss the Republic in relation to the evidence offered by later works on the question of astronomy and observation, and raise the question of whether Plato's views on the imperfection of the sensible world necessarily lead to the denigration of careful and prolonged empirical work. (shrink)

This book examines the philosophies of nature of the early Greek thinkers and argues that a significant and thoroughgoing shift is required in our understanding of them. In contrast with the natural world of the earliest Greek literature, often the result of arbitrary divine causation, in the work of early Ionian philosophers we see the idea of a cosmos: ordered worlds where there is complete regularity. How was this order generated and maintained and what underpinned those regularities? What analogies or (...) models were used for the order of the cosmos? What did they think about causation and explanatory structure? How did they frame natural laws? Andrew Gregory draws on recent work on mechanistic philosophy and its history, on the historiography of the relation of science to art, religion and magic, and on the fragments and doxography of the early Greek thinkers to argue that there has been a tendency to overestimate the extent to which these early Greek philosophies of nature can be described as 'mechanistic'. We have underestimated how far they were committed to other modes of explanation and ontologies, and we have underestimated, underappreciated and indeed underexplored how plausible and good these philosophies would have been in context. (shrink)

This paper introduces the idea that if theories of history generate different taxonomies of history they too are incommensurable. I argue this is unavoidable for Kuhn given what he says about incommensurability and I investigate the consequences in relation to reflexivity, justification, and paradox for Kuhn’s account of science. I want to do this on two levels, firstly looking at different possibilities for characterising individual paradigms. I will look at some examples from ancient and early modern astronomy as here it (...) is clearest that paradigms can be characterised in different ways and that this has important consequences. I will argue in particular that Kuhn’s characterisation of the paradigm for astronomy which emerges from antiquity is favourable to his general account of the history of science, but that there is a very plausible and extremely damaging alternative. I argue that these differing characterisations generate differing, incommensurable taxonomies of the history of astronomy, with attendant “local holism,” untranslatability of key terms and issues of theory choice. If so, Kuhn then has problems with generating an adequate decision making protocol for choosing between the two paradigm characterisations. That is problematic in itself, but I also argue this problem is systemic and affects the evidence needed for Kuhn to justify his general account of the history of science. I also want to investigate the implications of differing taxonomies of the history of science at a more abstract level. Kuhn’s general theory of the history of science generates a taxonomy of the history of science, as do other theories such as those of Popper and of gradualism. If so, the incommensurability involved here, again with attendant “local holism,” untranslatability of key terms and issues of theory choice, leads to issues of paradox and justification for Kuhn’s general account of the history of science. With this broader understanding of taxonomic issues, some important Kuhn statements about scientific theories become self-referential, again generating problems of paradox and justification. (shrink)