Adam Smith was a famous economist and moral philosopher. This book treats Smith also as a systematic philosopher with a distinct epistemology, an original theory of the passions, and a surprising philosophy mind. The book argues that there is a close, moral connection between Smith's systematic thought and his policy recommendations.

In lieu of an abstract, here is a brief excerpt of the content:HUME ON SPACE AND GEOMETRY Hume's discussion of our ideas of space, time and mathematics in Book One of the Treatise is referred to by one recent commentator as 'the least admired part' of this work, while another finds it to be 'one of the least satis2 factory Parts'. Hume himself, it would appear, was not far from endorsing such opinions. The omission of any detailed comment on these (...) subjects from the first Enquiry can be taken as indicating his dissatisfaction with the earlier exposition as well as a felt incompetence to offer a suitable revision. For there was certainly no loss of interest on Hume's part in the philosophical problems of mathematics. In a letter to William Strahan in 1772 he speaks of an essay prepared for publication around 1755 entitled: On the Metaphysical Principles of Geometry, which he withdrew upon the advice of his friend the mathematician Lord Stanhope, who convinced me that either there was some defeat in the argument or in its perspicuity; I forget which... Defects of both kinds are present in the Treatise discussion of geometry and the infinite divisibility of space, which taken together with certain remarks in the Abstract of the Treatise and in the Enquiry, suggest that the problem defying satisfactory solution was the relation between these. Hume was of the opinion that the theory of infinite divisibility constituted an affront to human reason by virtue of the paradoxes it involved. Such paradoxes, he thought, must open the door to scepticism about the certainty of mathematical knowledge, since in the field of abstract reasoning reason is thrown into a kind of amazement and suspence, which, without the suggestions of any sceptic, gives her a diffidence of herself, and of the ground on which she treads. (E157) Hume's attempted solution involved the rejection of those abstract ideas employed in mathematics and most fundamentally, that of infinite divisibility, but he never succeeded in working out a theory of geometry 2. which preserved its desired status as a body of certain knowledge and yet was at the same time consistent with his empiricism. In this paper I set out to examine the relation between Hume's view of space and his theory of geometry. Firstly I take a detailed look at Hume's arguments against infinite divisibility in an attempt to discover why they take the form they do, and to understand what Hume has in mind when he speaks of that 'minimum' idea which is an 'adequate representation" of the most minute possible part of extension. The second section deals with Hume's account of the genesis of our idea of space. I propose, contrary to some commentators, that Hume does not treat the idea of space on an exact parallel with that of time. Although both are said to be abstract ideas they differ in the relation in which they first stand to impressions. My comments on time are confined to drawing attention to this difference since fuller discussion of passages dealing exclusively with time would require a separate paper. In the final section Hume's remarks about geometry are examined. Here I argue that Hume entertains two views of geometry in the Treatise, one of which is abandoned in the Enquiry while the other remains largely unaltered. Hume opens his account of our ideas of space and time with an attack on the thesis of infinite divisibility which he regards as belonging to that body of doctrines which are greedily embrac'd by philosophers, as shewing the superiority of their science, which cou' d discover opinions so remote from vulgar conception. (T26) Two principles, boti taken to be evident, form the basis of his argument. I shal] refer to them hereafter as principles A and B. Principle A: the capacity of the mind is limited, and can never attain a full and adequate conception of infinity. 3. Principle B: whatever is capable of being divided in infinitum, must consist of an infinite number of parts, and ( ) 'tis impossible to set any bounds to the number of parts, without setting bounds at the same time to the division. (T26, 27) From these two principles Hume draws the conclusion that... (shrink)

In this paper I distinguish four methods of empirical inquiry in eighteenth century natural philosophy. In particular, I distinguish among what I call, the mathematical-experimental method; the method of experimental series; the method of inspecting ideas; the method of natural history. While such a list is not exhaustive of the methods of inquiry available, even so, focusing on these four methods will help in diagnosing a set of debates within what has come to be known as ‘empiricism’; throughout the eighteenth (...) century there was a methodological reaction against the hegemonic aspirations of mathematical natural philosophy associated with the authority of Newton.In particular, I argue that the methods of inspecting ideas and natural history remained attractive to ‘empiricist’ thinkers with reservations about aspects of Newtonianism. Moreover, I show that the language of experimentalism meant different things to researchers with different attitudes toward Newton’s legacy. In order to illustrate and make more precise these claims, I embed my taxonomic treatment of the four methods within a narrative in which I primarily focus on Colin Maclaurin, Isaac Newton, David Hume, and Georges-Louis Leclerc de Buffon. (shrink)

Although the mathematization of nature is a distinctive and crucial feature of the emergence of modern science in the seventeenth century, this volume shows that it was a far more complex, contested, and context-dependent phenomenon than the received historiography has indicated.0.

This article suggests that scientific philosophy, especially mathematical philosophy, might be one important way of doing philosophy in the future. Along the way, the article distinguishes between different types of scientific philosophy; it mentions some of the scientific methods that can serve philosophers; it aims to undermine some worries about mathematical philosophy; and it tries to make clear why in certain cases the application of mathematical methods is necessary for philosophical progress.

I identify a set of interlocking views that became (and still are) very influential within philosophy in the wake of Newton’s success. These views use the authority of natural philosophy/mechanics to settle debates within philosophy. I label these “Newton’s Challenge.”.

In lieu of an abstract, here is a brief excerpt of the content:66. ' HUME ON SPACE AND GEOMETRY * : A REJOINDER TO FLEW ' S 'ONE RESERVATION '.? Flew' s reservation about my assertion that the Enquiry contains no significant revision of the Treatise conception of geometry as a body of necessary and synthetic knowledge, appears to involve two charges. Firstly, he alleges that I dismiss but offer no substantial argument against his own view that the Enquiry restores (...) pure geometry "to its place alongside the other two elements of the trinity ". Secondly, he thinks that I have committed a serious sin of omission in failing to take into consideration a certain passage in the Enquiry (page 31, section 27) which, in his opinion, constitutes "a quite decisive reason" for supposing that Hume abandoned the Treatise position, in that it contains an account of applied mathematics, a subject on which the Treatise is silent. To the charge of omission I plead guilty, and I shall presently seek to remedy this defect and to state why I do not share Flew' s view of the significance of the said passage. To the former charge I am not so ready to plead guilty, and I shall counter-charge that Flew has failed not only to do justice to my proposed reading of Enquiry page 25, section 20, but also to provide clear and convincing support for his own. One difficulty encountered in answering Flew lies in understanding whether or not his claim about the status of geometry as a pure science in the Enquiry is put forward independently of his interpretation of E31. As originally presented in Hume's Philosophy of Belief this appears to be the case, and if so, on what evidence does it rest? 2 In his book, Flew' s statement about Hume replacing pure geometry alongside arithmetic and algebra follows directly upon a paragraph in which he comments that Hume's references to geometrical propositions at E25 signify "an important advance from the position of the Treatise". For whereas the status of perfect precision and certainty was 67. there withheld from geometry (T71), Hume now speaks of the certainty and evidence of the propositions of Euclidean geometry, and declares such propositions to be discoverable by the mere operation of thought, without dependence on what is anywhere existent in the universe. (E25) Now, I argued at some length in my paper (pp. 21-24) that Hume is prepared to grant scientific status to geometry in the Enquiry because he has come to regard its certainty as that proper to a mathematics of space. He has abandoned the Treatise contrast between an ideal or theoretical standard of equality, viewed therein as necessary to geometry considered as a science proper, and the merely sensible standard of equality upon which geometry as practised depends. It should not be forgotten that Hume recognises two kinds of certainty where "Relations of Ideas" are concerned, intuitive and demonstrative. Since he fails to provide any detail of the place of each of these in mathematics, the door is left open for speculation along the lines followed in pp. 28-29 of my paper. For there is nothing in?25 which implies that the certainty of all geometrical propositions is of the same kind, or that the process of geometrical demonstration is of the same logical nature as demonstrative reasoning in arithmetic and algebra. In his comment on my position Flew makes no reference to my proposed reason why Hume classes geometry as a science in the Enquiry.· Yet, even if this reclassification does mark an advance of a kind, the fact remains that E25 does not furnish incontrovertible evidence for that advance which Flew thinks he finds there. Nor, therefore, is it conclusive against my assertion that Hume in both works regards the propositions of geometry as necessary and synthetic truths. Given that Flew does not wish to deny the inclusion of a synthetic element even in the Enquiry account of mathematics (see H. P. B. pp. 64-66), I find it difficult to see why he supposes that the logical status of the propositions of geometry is different in the Enquiry from that in the Treatise, since in the latter too they are held 68. to be truths which depend... (shrink)