Frege and Analytical Philosophy

In the course of 1936, Professor Heinrich Scholz of Münster completed the collection of Frege’s unpublished writings, of which he had charge, by obtaining from those, such as Russell and Husserl, whose letters to Frege were included in the collection, the letters Frege had written to them. On 25 March 1945 the US Air Force bombed Münster. I believe that the object was to destroy an important telephone exchange: a large part of the town was destroyed, but the telephone exchange was left intact. Among the things destroyed were all Frege’s manuscripts and the original letters to and from him; there survived typescripts of some of the papers and of part of the correspondence. Even these took a very long time to appear in print: the papers only in 1969, the correspondence not until 1976. An English translation of the former was brought out by Blackwell last year, a decade after the German version. Now we have the correspondence in English, only four years after the German volume, but 44 years after the collection was originally made.

McGuinness has omitted from the English version all those frustrating pages which, in the German one, recorded the dates of letters now lost, together with a certain number of letters with no philosophical or mathematical content. The volume contains much of interest – above all, the famous correspondence between Russell and Frege occasioned by Russell’s discovery of his contradiction, derivable in Frege’s formal system. It is fascinating to watch the emergence, in the course of this long exchange (ten letters from Russell, nine from Frege), of various of Russell’s leading Ideas: fascinating, too, to see the staunchness with which Frege, after the initial shock, defended the fundamental principles of his logic. As is well-known, Russell’s first letter arrived when the second volume of Frege’s Grundgesetze was in press, and necessitated a hasty patching-up of the formal system there used. Even before he has discovered a way of doing this, Frege is writing to Russell in tones of great assurance, rejecting various proposals by Russell to meet the situation. By Frege’s sixth letter, he has discovered the modification to his Axiom V by which, in the Appendix which he added to the Grundgesetze, he hoped, in vain as it was to prove, to avoid contradiction; Russell replies that Frege’s solution is probably correct, though he finds it hard to accept, but by that time he has become too engaged in other lines of thought to give Frege’s proposal the attention he promises. In 1906, Frege was to lose confidence in his own attempted solution, and, therewith, in his principal life’s work, the provision of purely logical foundations for arithmetic and analysts. Russell’s letter of June 1902 had been indeed the turning-point of his career: at once the first tribute from a wholehearted admirer and the announcement of the failure of the task he had set himself to achieve. But, though there is much else in this volume of considerable interest, it is a volume primarily for the specialist; Frege’s published and posthumously published writings are, naturally, of more importance than his correspondence. The translation is, for the most part, accurate and fluent, though Professor Kaal ought to become aware of the difference between ‘forgo’ and ‘forego’; but I deprecate strongly the translation of Satz by ‘proposition’. Frege was obsessively careful to distinguish between a form of words and what it expresses – for instance, taking the trouble, for that purpose, to use both the words Grundsatz and Axiom. A Satz is, for him, always a string of words, and therefore, in his writings, should always be rendered ‘sentence’: ‘proposition’ restores the ambiguity he was at such pains to avoid. Russell’s ambiguous use of Satz does not provide a sufficient reason for this choice; an editorial footnote would have dealt with the difficulty. I think that Kaal has been kind to Husserl in translating the word Sonderling, in the latter’s ludicrously dismissive comment on Frege of 1936, as ‘outsider’: ‘crank’ would surely be more accurate. The volume reproduces the numbering of the letters from the German edition, as well as giving its own; but unfortunately most commentators have cited the German volume by page number, and it will cause great inconvenience to those who have only the English edition that it fails to give the pagination of the German one.

When Geach and Black’s volume of translations first came out in 1952, there existed hardly anything of Frege’s in English save his Foundations of Arithmetic. Moreover, even for readers of German, his other books were almost inaccessible, and his articles available only in ancient German learned journals. The volume, with its selection of articles and excerpts from the other books, therefore did an immense service by making a representative sample of Frege’s writings available to the philosophical public. The situation now is utterly different. The whole of Begriffsschrift is readily accessible, in German and English: the Grundgesetze is in print in German, and there is an English translation of Part I and of the Appendix; almost all the shorter writings are contained in the volume Kleine Schriften edited by Angelelli, and the rest in an earlier volume edited by him: of most of these, English translations have appeared in various places; and the unpublished writings and correspondence are available in German and English. The point of such a volume as that of Geach and Black must now, therefore, be altogether different: it is no longer adequate for the purposes of a serious scholar, even if not a specialist, but serves only as a useful collection of snippets for undergraduates. The contents have remained unaltered, save for the excision of the article on ‘Negation’, on the ground that this is now contained in another volume, Logical Investigations, translated by Geach and Stoothoff. Why, then, not also excise the selection from Begriffsschrift, on the ground that the whole work is translated in a volume by Bynum, or the Appendix to the Grundgesetze and the excerpts from Volume I of that work, on the ground that they are available in Furth’s translation? I am afraid that the answer is that the translations by Bynum and Furth are not published by Blackwell. The omission of ‘Negation’ leaves the volume a no longer representative sample: there is now nothing from after 1904. But the space saved has not been used to repair any of the earlier omissions – for example, by printing the whole of Frege’s review of Husserl instead of extracts from it; nothing has been added save the index. I suppose that the reply would be that the addition of anything more would have pushed the price up. If the purpose is to serve the needs of the undergraduate, however, he would have been catered for better by the inclusion of ‘Thoughts’ than by being pushed into buying another volume or being deprived altogether of the late works. The needs of others are not well served by this volume. What is now needed is, first, a volume of English translations of Frege’s articles which, if not quite as comprehensive as Kleine Schriften, at least contains everything of major importance, and, secondly, a full translation of Part 111(1) (the prose section) of the Grundgesetze. Geach and Black could have provided us with either, or with both: perhaps they still will.

The translation remains the same, save for the rendering of certain of Frege’s technical terms. Of these changes, by far the most important is the substitution of ‘meaning’ for ‘reference’ as the translation of Bedeutung. It is, to my mind, a great pity that this rendering was not adopted in the original edition. Since then, largely through the influence of the Geach/Black translation, the word ‘reference’ has become standard, in English language philosophical writing that discusses or alludes to Frege, and cannot now be dislodged in deference to a change of mind 28 years later, at least without rendering a great deal of commentary unintelligible.

Of the two books about Frege under review. Bell’s is decidedly the better. It is ambitious in scope, but modest in tone, and engages seriously both with Frege’s thought and with the philosophical problems he tried to solve. The title is unpromising. Frege complained of the conventional use of the word ‘judgment’ for the content of a judgment, which, from 1891 onwards, he called a ‘thought’. For him, grasping a thought and judging it to be true are (distinct) mental acts; but he found them mysterious, and, because of their mental character, thought their exact nature irrelevant to logic. On his view, judgment is a mental act directed at a thought that is already a unity; the thought itself is complex, being built up from its component senses, but an account of judgment would not need to take it as a relation to these components, but only to the thought as a whole. Frege had, indeed, a theory of sense, which gives an account of the complexity of thoughts, but he would have regarded a theory of judgment such as that of Russell as quite misguided. Bell remarks on his first page that the theory of judgment no longer has the pre-eminence that it once had. But it had this pre-eminence in the writings of those who failed to make the sharp distinction on which Frege insisted between thoughts and judgments; much of what they took to belong to the theory of judgment he would have regarded as part of the theory of sense. It might thus appear that the content of Bell’s book must be rather thin. That this is not so is due to his reckoning to Frege’s theory of judgment the whole of his theory of sense, which he himself would not have described as part of a theory of judgment.

Frege’s theory of sense is inseparable from his theory of reference. Bell correctly perceives that there were two ingredients in Frege’s notion of reference; indeed, he overstates the case by saying that he had two notions of reference. One of these he characterises, correctly enough, as that of the ‘extra-linguistic entity with which the expression has been correlated or which it picks out’: but he makes a crucial error in characterising the second. He says that it is that property of the expression which renders it capable of being used in a sentence possessing a truth-value, where he should have said that it represents the contribution made by the expression to determining what the truth-value of any sentence containing it is. The theory of reference is a theory of the manner of determination of the truth-value of any sentence in accordance with its composition. This is why Frege thought it obvious that reference must be ascribed to expressions of every genuine logical category: if we understand the notion in this way, we shall see him, not as having had two distinct notions which he improperly conflated, but a single notion, with two ingredients. One ingredient shows what he wanted the notion for, the other how he thought it ought to be applied.

Bell, conceiving of reference in his unduly restricted way, as that which guarantees some truth-value for sentences containing the expression, spends much time arguing against Frege’s requirements that in order for predicates and functional expressions to have a reference they should be sharp and everywhere defined – and has no trouble scoring some points against them. But he misjudges how grave is the damage done to Frege’s theory if these requirements are shown to be wrong: in particular, he mistakenly concludes that Frege had no basis to ascribe reference to predicates and other incomplete expressions. This mistake inevitably leads to error in his discussion of Frege’s notion of sense. Sense is very tightly connected with reference in Frege’s theory by the principle that the sense of an expression is the way in which its reference is given to us. Bell, however, is forced to reject this, as a general account, in view of his denial that the notion of reference is generally applicable. This leads him to complain that the reference of a sentence is overdetermined on Frege’s account – namely, both by the references of its parts and by its own sense, which in turn depends on the senses of the parts. There is, however, no overdetermination when sense is construed as Frege intended – namely, as that component in meaning which determines reference.

Anyone who engages to write about Frege’s theory of meaning must treat of his notion of incompleteness or unsaturatedness. Bell makes a big point of this in his Introduction: as he rightly remarks, the notion represents Frege’s solution to the problem of the unity of the proposition. Denying, as he does, that incomplete expressions have reference, he naturally cannot defend the doctrine at the level of reference. He quite correctly observes, however, that Frege applied the complete/incomplete distinction also to the senses of expressions, and wishes to defend it at this level. He does not make the mistake that many have made, of holding that the sense of a predicate is incomplete in the same way that its reference is supposed to be – i.e. that its sense is itself a function; but, because of his opinions concerning reference, he cannot give what seems to me the simple, and true, explanation, that its sense is incomplete in that we understand it as standing for a function (from objects to truth-values).

Bell’s final account of the matter is to be found in his last chapter, by far the most interesting and valuable of the four. The matter is delicate, because it is one Frege never fully thought through. In his Begriffsschrift and other early writings, he emphasised that a concept or function is extracted from a complete content of judgment by a process of omitting the content of one or more occurrences of some term. If, however, this thesis were taken as yielding the full content of the doctrine of the incompleteness of the senses of predicates and functional expressions, it would not provide us with an explanation of the unity of the proposition. The thought that the Earth spins has, as components, the sense of the name ‘the Earth’ and that of the predicate ‘spins’. We cannot plausibly say, however, that the sense of the predicate has been extracted from a thought antecedently grasped as a whole, since we can form no conception of a grasp of that thought that involves no apprehension of its complexity. Frege showed some awareness of the difficulty, but he did not fully resolve it, even implicitly. Roughly, I know what ‘That tree is green’ means by knowing, among other things, what ‘is green’ means; but my knowledge of what ‘is green’ means consists in my knowing what it means to say, of any specific object, that it is green. It does not seem that either a grasp of the thought or a grasp of the sense of the predicate can precede the other; Bell very aptly quotes, in this connection, Wittgenstein’s Tractatus 3.263. The difficulty arises for a predicate that is both simple and primitive. If it is complex, it can be regarded as extracted from the thought, and hence as subsequent to it; if it was introduced by definition, then it could be understood in advance of being used to express any thought.

Bell considers the picture theory of the Tractatus, according to which every ‘elementary proposition consists entirely of names’, all propositions proving, on analysis, to be compounds of elementary ones. In such a theory, there is still room for a notion corresponding to that of a complex predicate, regarded as extracted in a Fregean manner from a proposition: but it eliminates anything like simple primitive predicates, and hence the problem of explaining in what their incompleteness consists. Perhaps Bell is not to be understood as actually advocating the picture theory; if not, it is unclear to me how consideration of it yields a solution of the problem. In any case, we are still left with the problem of the relative priority of a proposition and its components, which still arises when the components are all names. In some very compressed pages. Bell argues that the problem can be solved if we adopt Wittgenstein’s later account of fundamental rules as embodied solely in a practice for which no justification can be given or required, saying that this compels us to abandon Frege’s realism for ‘an anti-realist account of human thought and language’.

In opposing Frege’s realism, he appeals also to Kant. He maintains that we should no more speak of an object of judgment (that which is judged to be true) than of an object of leaping: but he fails to indicate how he proposes to dispense with objects of thought. He rightly stresses that, for Frege, a thought is not a content of consciousness, but he does not see the force of this contention, which Wittgenstein carried further when he said that understanding is not a mental process, and dismisses it as a misguided way of safeguarding the objectivity of sense. Frege was, however, right to hold that no coherent account of thought can be given if it is taken to be an inner process; and it is just such an account we should have to give if we understood ‘think’ as an intransitive verb like ‘leap’.

For Frege, sense usually figures as the principal ingredient in linguistic meaning: but he insists that the thought expressed by an utterance is true or false absolutely, not relatively to a person or a time. Bell is convinced that no one notion of sense can satisfy both requirements; but his discussion is hasty. He distinguishes ‘input sense’ (linguistic meaning) from ‘output sense’ (the thought expressed), citing others (but, oddly, not Strawson) as having made a like distinction. The linguistic meanings of the component words go to compose the input sense: but Bell simply declares, what is very far from obvious, that nothing short of a sentence can have output sense. This discussion illustrates a major defect of the book: it is too ambitious for its length, or too short for its ambition. It simply is not feasible to do justice to these difficult questions in the compass of 140 pages which Bell allows for the body of the book; when he fails to make his thesis clear or his argument cogent, the fault may often lie, not in his thinking, but in the compression of his exposition. The current economics of publishing indeed create a crisis for scholarship. Perhaps, obsessed with present book prices, Bell has striven to pare his writing to the briefest possible: but it is surely not a correct response to the crisis to publish lecture notes in place of books.

Sluga makes some large, even grandiose, claims. Analytical philosophy misinterprets its own history in general, and Frege, the first analytical philosopher, in particular. There are two reasons for this. First, being realists, analytical philosophers misread Frege as a realist. (I had better explain that I am cited as the chief offender, with Carnap running me close.) That philosophers of a given school misinterpret a founder of the school by assimilating his ideas too closely to their own is a familiar, and plausible, type of charge: but the second reason cited by Sluga is more surprising – namely, that they adhere to just the kind of anti-historical and ‘logically oriented philosophy of language that originated with Frege’. Paradoxically, then, being too faithful to Frege’s ideas makes it impossible to understand him aright. ‘Frege thought he had banished radical empiricism,’ but analytical philosophy has since been forced to make ever greater concessions to the claims of empiricism. It has not yet, however, come to terms with the radical empiricism implicit in the thought of Wittgenstein, whose work demands that ‘the abstract theory of meaning must give way ... to the examination of actual historical discourse.’ ‘No meaning analysis of the kind offered by analytic philosophers from Frege through Tarski and Carnap to Dummett can recover the actual historical meaning’ of a philosophical statement: ‘that requires historical analysis of the kind provided in this study ... Only then can the limits of the “objective” unhistorical kind of meaning analysis conducted by analytic philosophers be overcome.’ We are thus evidently meant to see this book as the first Wittgensteinian examination of Frege’s thought; Fregean approaches to it, as intrinsically unhistorical, cannot but get it wrong.

These claims introduce the book and conclude it; if what came between formed an impressive piece of exegesis, they might have acquired some substance. Unfortunately, the book is inadequate as the merest introduction to the thought of Frege. Consider, for instance, the most celebrated of Frege’s ideas in philosophical logic, the distinction between sense and reference. An excellent book might be written on Frege by someone who thought the distinction to be incoherent: but it would have to explain just what the theory was, and how it was supposed to work, and to demonstrate in detail why it does not work. Sluga makes no serious attempt to do any of these things. He connects the sense/reference distinction almost exclusively with the explanation of identity-statements, the condition for whose truth is that the references of the two sides coincide, and the condition for whose informativeness is that their senses differ. He deprecates the substitution of this account of identity-statements for that earlier given by Frege, which he thinks ‘appears more plausible’; he admits certain difficulties in that earlier account, but assures us that it could have been modified to meet them, without explaining how. He nevertheless assigns the distinction between sense and reference a vital role as a basis for Frege’s introduction of value-ranges as logical objects. His argument here is extremely hard to follow. At first, it appears that the reason is that Axiom V, which governs value-ranges, takes the form of a generalised identity-statement. It then emerges, however, that Sluga believes Frege to have held the two sides of Axiom V to coincide in sense, which would indeed make it, not merely true, but self-evident, as an axiom ought to be. If this were so, it would be one of the identity-statements which can be explained without appeal to the sense/reference distinction. Sluga cites in his support a passage from ‘Function and Concept’, but fails to explain why Frege did not repeat the claim in the Grundgesetze, in which much space is devoted to justifying the introduction of value-ranges. ‘Function and Concept’ was in fact the earliest publication in which the sense/reference distinction is made. The passage in question echoes a parallel claim made in the Foundations, before Frege had drawn that distinction. I believe it to be a residue from the earlier style of thought: when he had reflected further on his new distinction, he realised that he could not sustain the claim, which in any case is difficult to reconcile with all else that he says concerning sense. Sluga does not try to give any account of sense on the basis of which such a claim would be plausible.

It is, in fact, a mistake to link the notion or sense as tightly as Sluga does with that of identity, as Frege’s manifold other uses of it show. One might try, on such a basis, to justify the extension of the distinction between sense and reference to incomplete expressions as needed to explain generalised identity-statements: but Sluga does not so much as discuss this extension. He does repudiate an interpretation according to which Frege began by distinguishing sense and reference for singular terms, and then moved on to do the same for sentences, on the ground that Frege counted sentences as a kind of singular term. But Sluga does not mean that Frege’s initial explanation of sense already clearly applied to sentences. The initial explanation was that the sense is the mode of presentation of the reference, and, for that to apply unproblematically to sentences, the notion of reference would have to apply unequivocally to them; whereas Sluga says that Frege failed to give a compelling reason for regarding thoughts as the senses of sentences and truth-values as their references. All that Sluga had meant, it seems, was that Frege had intended from the start to apply the sense/reference distinction to sentences, which I do not think anyone has denied. Sluga seems unaware that the question what the sense and the reference of a sentence are has no clear content unless we have some general characterisation of sense and of reference. He provides no account of what, in general, sense and reference are, or how they are related, or for what purpose, save that of explaining identity-statements, they are needed.

A feature of Frege’s philosophy on which Sluga lays great stress is the thesis that judgments are prior to concepts, which he equates with the context principle, that a word has meaning only in the context of a sentence. In fact, this is for him the prime example of a doctrine which analytical philosophers have failed, with their unhistorical meaning analysis, to understand: so his account of it should provide the crucial test for the superiority of his own approach. His conflation of the priority thesis with the context principle is a bad start, since those are in fact two quite separate doctrines. The former relates only to incomplete expressions, and is concerned with how we arrive at them (or their contents); the latter holds good of all words, is applied by Frege in the Foundations particularly to abstract singular terms, and is concerned with what it is for a word to have a meaning. When he comes to discuss the doctrine at length, Sluga runs together yet more distinct theses. He says, indeed, that the priority thesis ‘implies at least four different things’: in fact, only one (listed second by Sluga, and explained very vaguely by him) is to be identified as the priority thesis, the rest being quite distinct. The third, which Sluga says that Frege derived from Kant, is the predicative nature of concepts: this can be ascribed to Kant, and was emphatically held by Frege, but could well be believed by someone who denied the priority thesis. The fourth ingredient has to do exclusively with natural language, and is based by Sluga on two passages, from 1879 and 1896 respectively, which in fact themselves make distinct points.

Sluga associates these passages with the Other doctrines because of a verbal resemblance with the context principle, which, he has claimed, can be shown to have been held by Frege throughout his career. In fact, since their contents are quite different from the context principle, they are good evidence that, at those two dates, Frege either did not hold that principle or at least would not have expressed it in the same way. The 1896 passage, for example, lays it down that every word ought to have a sense and a reference independently of a context, and reproaches natural language for failing to satisfy this demand. In fact, Frege is not here demanding just what the context principle denies to obtain, but something compatible with the principle: but he would hardly have expressed himself in this way if he still adhered to the context principle as originally stated in the Foundations. Sluga goes on to speak of the context principle, in that work, as ‘meant ... primarily as a methodological principle for the analysis of sentences of ordinary language’. This is obviously an attempt to reconcile it with the 1896 passage, and, at that, quite unsuccessful, since the latter passage does not propose a means of analysing natural language, but roundly condemns it as too unsystematic to allow of analysis. In much of Frege’s writing a sharp contrast is drawn between natural language, with all its defects, and the perfected instrument for expressing thought which his logical symbolism aspired to be: but in the Foundations this contrast is hardly alluded to. There the context principle is stated as a general doctrine, in terms of which Frege’s own procedure is to be justified, not, as in the 1896 passage, as an instance of the uselessness of natural language for purposes of exact reasoning. Sluga partly realises this, because he goes on to say that ‘the implication seems to be that there is a priority of sentence meaning over word meaning for every language, including a logically perfect one’: but his only explanation of the gnomic saying is that ‘in this ... sense the principle would amount to the reaffirmation of the Kantian doctrine of the priority of judgments over concepts.’ This is quite wrong: as already noted, in the Foundations the principle is not confined to concepts or predicates, but applied particularly to abstract terms as standing for abstract objects.

Sluga’s discussion of the priority thesis and the context principle is thus a mélange of disparate ideas, inadequately explained, whose relations and exact content ought to be carefully explored in any competent study of Frege’s thought. Even at that, I have omitted the first of Sluga’s four ingredients, ‘the implication ... that the contents of judgments are epistemically primary.’ This is explained no further than by the citation of two passages in which Frege states the priority thesis: but since that thesis is the second of Sluga’s different ingredients, something else must be meant. This is important for the charge that analytical philosophers have misunderstood the context principle, since, while Carnap is said to have ignored it, I am accused of ‘rejecting its supposed epistemic implications’. (I cannot account for this occurrence of the word ‘supposed’.) Sluga gives us no help in understanding what he intends by speaking of judgments as ‘epistemically primary’. I have some conjectures, which I will not here go into: but it is altogether characteristic of this book that he should thus content himself with merely labelling an important thesis instead of stating it. He repeatedly does this, for theses he wants to defend, or to attack, or to ascribe to Frege or some other philosopher, usually by means of adjectives like ‘ontological’: for instance, Frege’s thesis that numbers are objective is said to have been ‘intended as an epistemological thesis’, without its being explained any further what the content of the thesis, so interpreted, would be. The result is that the reader remains, for most of the time, in a kind of mental blur; the writing frequently resembles art history, with its talk of tendencies and influences, more than philosophy.

Sluga’s first two chapters are devoted to a sketch of the general philosophical scene in 19th-century Germany. The accounts of some little remembered philosophers such as Czolbe are interesting and agreeably written, but I believe that the general picture is misleading. Even if it is not, it does not greatly affect the argument concerning Frege. At the end of my own book on Frege, I spoke of him as having possibly played some part in the overthrow of Hegelianism. Sluga has convinced me that this was a mistake, and that the philosophy of Hegel retained little influence in Frege’s day. But he goes further, saying that idealism as such ‘had ceased to be a real power in German thought by 1830’, whereas, on his own showing, this is quite untrue: for he represents the neo-Kantian movement as dominant from about 1870 on, and this was another form of idealism. All this historical discussion is, in fact, directed towards showing that Frege was not a realist but a transcendental idealist. As regards physical objects, the case rests on an assimilation of Frege to Kant: Sluga thinks that Frege ‘held a Kantian view of space and hence a transcendentally subjective view of the objects that occupy it’. Frege was at pains in the Foundations to make his stance towards Kant’s thought quite clear. I need therefore say little about this matter, save to point out, first, that, in the footnote on page 37, Frege deprecated the idealist tinge of Kant’s doctrine, and that, in Section 26, he argued that the axioms of geometry are objective and therefore independent of intuition.

The case, in respect of abstract (logical) objects and of thoughts, hangs on a comparison of Frege’s twin notions of the objective and the wirklich with those expressed, by the same two terms, in Lotze’s Logik. The influence of Lotze upon Frege is asserted in the strongest terms by Sluga: in this, he is swimming against the tide, since Frege never once mentioned Lotze, although, according to Sluga, he derived many of his leading doctrines from him. It is sad that Sluga misses the fact that a post-humously published fragment by Frege, consisting of 17 numbered aphorisms, is in reality a set of comments on the Introduction to Lotze’s Logik, as a comparison will reveal; some are in agreement, but more are critical. I should not like to vouch, however, that Frege read any further than the Introduction; most of the derivations claimed by Sluga rest on misinterpretations by him of Lotze’s text. In the crucial case, however, both Lotze and Frege are distorted to make them appear similar. Lotze uses wirklich much as Frege uses ‘objective’; objectivity, for Lotze, does not imply independence of our thought and experience, as it does for Frege. Sluga further misunderstands Lotze’s distinction between validity and existence, which he equates with that between the objective and the real (wirklich), whereas in fact it is a distinction within reality. Frege explains what he means by wirklich quite clearly when he says, in the Preface to Grundgesetze, ‘... to be wirklich, i.e. to be capable of acting directly or indirectly on the senses’; numbers cannot act on our senses, even indirectly, and so are not wirktich: but he does not mean to say that they are not real in the sense that there are not really any such objects. Sluga quotes, in support of his supposedly Lotzean interpretation of Frege, a sentence from ‘Thoughts’: ‘what I hold in my hand can ... be regarded as the content of my hand, but is the content of my hand in quite a different way from the bones and muscles of which it consists, ... and is far more alien to it than they.’ ‘If we take this analogy seriously,’ Sluga comments, ‘it seems to imply that Frege does not hold that thoughts are in the mind as the bird is in the hand, but rather as the muscles and bones are in the hand.’ He has got it exactly the wrong way round. Frege always denied that a thought is a mental content; he is here allowing that the word ‘content’ is ambiguous. If, when I grasp a cricket ball, the ball were called the content of my hand, then a thought might, in a comparable sense, be called the content of my mind: for what is grasped exists independently of its being grasped. The sense in which a thought cannot be called a content of my mind is that analogous to my hand’s being said to contain bones and muscles: the thought does not go to constitute the mind, nor does the mind constitute it.

I have contested some of Bell’s interpretations, but someone unfamiliar with Frege would gain, from Bell’s book, a reasonably sound general impression of Frege’s ideas and of their general flavour, and would know what it was to engage with them and the kind of problem Frege was trying to solve. From reading Sluga’s book, he would gain only the haziest impression of Frege’s thought, and would miss entirely any feel for what it is like to try to grapple with those problems with the rigour and exactitude for which Frege is celebrated but for which Sluga appears to have little sympathy. Above all, he would find it hard to see why Frege was a great philosopher or what he did that was new. Sluga tells us that he was the first analytical philosopher, but he is so keen to discover sources for his ideas, and so imprecise at distinguishing one idea from another, that he omits to explain what distinguishes analytical philosophy from that of other schools, or what it was that Frege said that made him the originator of a new movement in philosophy. If one undertakes a historical study, these are the questions which, above all, one ought to answer. In interpreting a philosopher, there can be no substitute for thinking through, in detail, what his argument is, what answers could be given to objections, what relation one thesis has to another – in short, for subjecting his work to logical analysis. Historical comparisons do not provide an alternative, or preferable, path to the same goal: they are useless unless informed by analysis. Sluga has convinced himself that he has found a means to bypass such analysis: he has accordingly fallen very short of understanding Frege. It is not just that he so often misrepresents him, but that, in Sluga’s exposition, the thought of this least obscure, though among the most profound, of all philosophers seldom comes into sharp focus at all.