„My sole purpose in this paper is to try and correct what I take to be a common misinterpretation of Hume’s opinions on mathematics. I shall not enquire whether he was right or wrong in holding these opinions. Nor shall I offer opinions of my own.“.

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In lieu of an abstract, here is a brief excerpt of the content:HUME'S IDEAS In the eighteenth century, there was widespread acceptance of a physiological basis for cognition. Some writers even argued for a rather detailed correlation between awareness and physiological changes, suggesting that (a) the former could be adequately explained in terms of the latter or, in some few instances, (b) that the former are the latter. David Hartley may come to mind as fitting one or the other of (...) these alternatives, but Robert Hooke had earlier argued for ideas as brain impressions, as of course did Descartes in his early scientific treatises. There was also one medical doctor in the eighteenth century, Dr. Astruc, who seems (on the basis of what Chambers reports) to have attempted a very specific correlation between specific forms of awareness and specific states and changes in physiology. There were also writers in this century who warned against the dangers of using physical-object vocabulary when talking about the mind and acts of awareness. Berkeley is one such writer,- Thomas Reid at the end of the century traced, to the use of this vocabulary, what he took to be the indirect realism of the way of ideas. Hume is writing in both these traditions: the tradition of using physical language for characterizing mental operations and the tradition of physiological explanations and correlations. The phrase used by Alexander Pope and Hume, 'the anatomy of the mind', seems to be a mixed metaphor, but it is a phrase which I take as an indication that Hume is doing what we would call 'cognitive psychology'. Another phrase used by Hume (this time in the Enquiry), 'mental geography', may capture his enterprise better: 'geography' still sounds physical, but it is modified by 'mental'. Hume is engaged in mental mapping. I want to take a look at the use of the term 'idea' in Hume's writing (mainly in the Treatise) in order to see 2. whether Hume's text enables us to say anything about the nature of his ideas, to discover what role they play in his mental geography. As far as I can determine, there are three possible candidates for the nature of ideas in Hume: images, brain impressions, and cognitive contents. The first of these is, I think, the standard reading of Hume's ideas. Professor Anderson has presented strong argument and evidence to support the second. I will be suggesting that the third is the best candidate, given the full range of the text of the Treatise. Of course, the correct answer 4 may be all three of these. The Treatise opens by dividing all perceptions of the human mind into two kinds. Impressions and ideas differ in the degree of force and liveliness with which they strike upon the mind. Even though the language of 'force' and 'liveliness' may be borrowed from physical talk, it is the mind, not the brain, on which perceptions strike. The examples of impressions are sensations, passions, and emotions. Ideas are said to be the faint images of these impressions in thinking and reasoning. The term 'image' throughout the eighteenth century never receives any clear explication. Its inheritance from optical treatises always hangs about it. We should look to the examples cited by Hume, in order to see whether we can construct a meaning for that term when used in these psychological contexts. Let us look first at his very first example of 'ideas': all the perceptions excited by the present discourse. (Tl) He explicitly excludes from these perceptions those which arise from the sight and touch, as well as the immediate pleasure or uneasiness his discourse may excite in us. The perceptions which are thus excluded are sensations and emotions, the impressions he has just distinguished. The only candidate left for ideas would seem to be what this discourse says, our thoughts about it, my understanding of what it says. The distinction is not one Hume thinks is difficult to follow: Every one of himself will readily perceive the difference betwixt feeling and thinking. (Tl-2) Last week I was sad, today I recall that feeling of sadness/ the difference between being sad and remembering that I was sad. Hume gives a different example: the perceptions formed when... (shrink)

Introduction A brief look at the competing present-day interpretations of Hume's philosophy will leave the uninitiated reader completely baffled. On the one hand , Hume is seen as a philosopher who attempted to analyse concepts with ...

In lieu of an abstract, here is a brief excerpt of the content:149. RELATIVE IDEAS REJECTED Hume's claim that ideas copy impressions seems to provide prima facie evidence for the interpretation that he also believed that all thought is restricted to images. Clearly such a view would be fatal to Hume's epistemological framework for at least two reasons. The first reason is quite simply that images are not a necessary element for thought, since we rarely think in images or pictures. (...) The second reason is that the imagistic interpretation prevents the possibility of universal a priori knowledge; since images only represent particulars they can never permit the inference from knowledge of particular instances to knowledge of universal cases. Yolton's paper, "Hume's Ideas", is a valiant effort to save Hume from the crippling imagistic interpretation. Although Yolton presents a reading of the Treatise that might avoid this interpretation, he fails to provide a sufficiently detailed account of any one counter-example to the imagistic view of Hume. However, such a counter-example has been worked out in Flage's 2 recent paper "Hume's Relative Ideas". Although the search for non-picturable ideas in Hume's system, and subsequent destruction of the imagistic interpretation is an admirable path for investigation, I intend to show that Flage's attempt to produce a Humean theory of non3 picturable "relative" ideas is entirely misguided. I shall argue that Flage has produced a theory without application in Hume's framework, a theory actually based on a distinction between relative ideas and relations of ideas, that Hume never intends. Flage argues that Hume has a theory of relative ideas, and that the application of this theory can produce intelligible concepts of essentially imperceptible 150. objects. A relative idea is obtained by an inference, of sorts, from the relations of ideas obtained from impressions; or in Flage' s words, a relative idea "singles out an unperceived entity on the basis of its relations to a perceived entity, i.e. a positive [picturable] idea" (HS 56). Flage admits that "Hume often regarded epistemic claims based upon relative ideas with at least a modicum of scepticism" (HS 55). He also realizes that no such theory of relative ideas can be used to justify ontological claims of the unperceivable objects (HS 63), but that "the doctrine of relative ideas at least accounts for the intelligibility of various concepts" (HS 59). Flage applies the theory of relative ideas to three concepts that Hume discusses in an effort to demonstrate how this theory can make these concepts intelligible. The three concepts are substratum, the missing shade of blue, and the idea of a thousandth part of a grain of sand; however, Flage fails to realize that Hume successfully argues against the intelligibility of these concepts. I shall present the arguments that Hume gives to show that Flage' s theory of relative ideas does not apply in the cases he argues for. Hopefully this will show that Flage has created a theory that lacks application; however, this is not Flage' s only failing. "Relative" ideas are obtained from relations of ideas (HS 56), and by this description Flage has implicitly distinguished between Hume's use of "relative" and the philosophical "relations of ideas!', a distinction that Hume never intends. In the latter part of this paper I shall show that Hume uses "relative" to refer to the relations of ideas, and that Flage has simply located and produced a theory on the basis of a distinction that has no real difference. In the discussion of substance, Flage correctly points out that Hume distinguishes three definitions of substance in the fourth part of book I of the Treatise (HS 63-4). 151. Flage also correctly points out that at least two of these definitions are unintelligible (HS 64). The definition of substance, as an autonomous object that is distinct from dependent qualities, fails to properly 4 distinguish substance from qualities (T 233), and substance defined as the "subject of inhesion" fails because there is no empirical evidence to justify the claim that qualities inhere in a substance J(T 234). However, Flage incorrectly argues that Hume asserts that the idea of substance as "the entity that is simple and identical through time... (shrink)

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)

(I) MATHEMATICAL LECTURES. LECTURE I. Of the Name and general Division of the Mathematical Sciences. BEING about to treat upon the Mathematical Sciences, ...

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