Carnap’s Conception of Explication:
From Frege to Husserl?
Michael Beaney

The task of making more exact a vague or not quite exact concept used in everyday life or in an earlier stage of scientific or logical development, or rather of replacing it by a newly constructed, more exact concept, belongs among the most important tasks of logical analysis and logical construction. We call this the task of explicating, or of giving an explication for, the earlier concept ... (Carnap 1947, 8-9.)

1  Introduction
Rudolf Carnap is a key figure in the history of analytic philosophy, for he not only played a central role in the work of the Vienna Circle in the decade from 1925 to 1935, but he also, in his subsequent move to the United States with the rise of Nazi Germany, marked the shift in the centre of gravity of analytic philosophy from a point in the North Sea to the mid-Atlantic. Carnap was influenced by Frege, Russell and Wittgenstein, the three main founders of the analytic tradition, and in turn was a crucial influence on Quine, Goodman and other major thinkers in America. But although in many ways Carnap was the archetypical ‘analytic’ philosopher, he was also influenced by philosophers outside the analytic tradition. In recent years the neo-Kantian roots of his thought have been emphasised; but there are also points of contact between Carnap and Husserl. My aim in this paper is to explore some of these influences and relationships by considering Carnap’s methodology, and in particular, the development of his views on analysis.
	The idea of explication is central to an understanding of Carnap’s methodology; yet the term ‘explication’ itself did not appear in Carnap’s work until 1945 (in ‘The Two Concepts of Probability’), and the idea did not receive a full discussion until 1950 (in the first chapter of the Logical Foundations of Probability). Given that Carnap’s notion of explication bears a striking resemblance to the conception of analysis that Frege articulated in his 1914 lectures on ‘Logic in Mathematics’, which we know Carnap attended, and which Carnap himself mentions in his ‘Intellectual Autobiography’ in discussing Frege’s influence on him, this deserves explanation. Why did it apparently take Carnap over thirty years of active work in philosophy to reflect upon the central methodological conception that, it seems, he took over from Frege? And why did Carnap choose the term ‘explication’ (‘Explikation’)? If his own remarks are to be believed, it was motivated by Kant’s and Husserl’s uses of the term. Yet his own use seems very different from either of theirs. So did Carnap move from a Fregean to a Husserlian conception of analysis? Or should he be seen as offering some kind of synthesis of both? Or does Carnap’s mention of Husserl simply reveal their common neo-Kantian or Fregean heritage? It is these questions that I seek to answer in the present paper.

2  Frege’s Influence on Carnap
Carnap devotes three pages to Frege in the first two sections of his ‘Intellectual Autobiography’ (1963, 4-6, 12-13). In discussing his university education at Jena, Carnap writes that “the most fruitful inspiration I received from university lectures did not come from those in the fields of philosophy proper or mathematics proper, but rather from the lectures of Frege on the borderlands between those fields, namely, symbolic logic and the foundations of mathematics” (1963, 4). After describing Frege as a person, he goes on to mention two courses on Frege’s ‘Begriffsschrift’ that he attended, and Frege’s satirical attack on Hermann Schubert’s account of the foundations of arithmetic, and then writes:

In the summer semester of 1914 I attended Frege’s course, Logik in der Mathematik. Here he examined critically some of the customary conceptions and formulations in mathematics. He deplored the fact that mathematicians did not even seem to aim at the construction of a unified, well-founded system of mathematics, and therefore showed a lack of interest in foundations. He pointed out a certain looseness in the customary formulation of axioms, definitions, and proofs, even in works of the more prominent mathematicians. As an example he quoted Weyerstrass’ definition: “A number is a series of things of the same kind” (“. . . eine Reihe gleichartiger Dinge”). He criticized in particular the lack of attention to certain fundamental distinctions, e.g., the distinction between the symbol and the symbolized, that between a logical concept and a mental image or act, and that between a function and the value of the function. Unfortunately, his admonitions go mostly unheeded even today. (1963, 6.)

Clearly, what takes centre stage here is Frege’s critique of mathematicians’ conceptions of their discipline, and the wider philosophical implications of Frege’s own reconstructive activities were not, at least in Carnap’s eyes, addressed. This is confirmed in the paragraph that immediately precedes the one just quoted:

Although Frege gave quite a number of examples of interesting applications of his symbolism in mathematics, he usually did not discuss general philosophical problems. It is evident from his works that he saw the great philosophical importance of the new instrument which he had created, but he did not convey a clear impression of this to his students. Thus, although I was intensely interested in his system of logic, I was not aware at that time of its great philosophical significance. Only much later, after the first world war, when I read Frege’s and Russell’s books with greater attention, did I recognize the value of Frege’s work not only for the foundations of mathematics, but for philosophy in general. (1963, 6.)

This is reinforced later on in the autobiography, when Carnap writes that “Whereas Frege had the strongest influence on me in the fields of logic and semantics, in my philosophical thinking in general I learned most from Bertrand Russell” (1963, 13). Frege may have provided the logical instrument for Carnap’s own work, then, but it was Russell who was credited more with its philosophical motivation.
	This suggests an obvious answer to our question. The notion of explication that, in effect, is adumbrated in Frege’s ‘Logic in Mathematics’ lectures was simply not appreciated by Carnap at the time; and it took many years of his own reconstructive activities, utilising Fregean logic, before he reached the point at which a conception of explication could be adequately conceptualised. But could we then argue that there was a delayed influence, prompted perhaps by the later (re)reading of Frege’s works that Carnap mentions? Given that the ‘Intellectual Autobiography’ was published in 1963, well after the discussion of explication, the answer might again seem to be largely negative, for Carnap does not mention Frege’s influence in this regard. In any case, Frege’s ‘Logic in Mathematics’ lectures remained unpublished, and although Carnap’s notes on these lectures have survived, there seems to be no evidence that Carnap later reread these ‘with greater attention’. (I return to this in the next section.)
However, whether or not there was any direct influence of Frege’s conception of analysis in ‘Logic in Mathematics’ on Carnap’s later notion of explication, there is still a striking similarity, which suggests that a deeper explanation is required. In §§ 4 and 5 we will examine Carnap’s early notions of ‘rational reconstruction’ and ‘quasi-analysis’, before turning to his account of explication in §6. First, however, we must outline the conception of analysis that Frege articulates in his 1914 lectures.

3  Frege’s Conception of Analysis
One way to approach the conception of analysis that Frege offers in his 1914 lectures on ‘Logic in Mathematics’ is by considering the response he provides there to what is essentially the paradox of analysis. The paradox of analysis is often associated with the work of G.E. Moore, and the name ‘paradox of analysis’ was indeed first used, by C.H. Langford (1942), in discussing Moore’s work. But the problem itself has a much longer history, and really goes back to the paradox of inquiry formulated in Plato’s Meno. But even in its linguistic form, it can be found articulated long before it was named as such, appearing explicitly, for example, in Frege’s own writings. The paradox can be stated as follows. Consider an analysis of the form ‘A is C’, where A is the analysandum (what is analysed) and C the analysans (what is offered as the analysis). Then either ‘A’ and ‘C’ have the same meaning, in which case the analysis expresses a trivial identity; or else they do not, in which case the analysis is incorrect. So no analysis can be both correct and informative.
Now the obvious response to this is to disambiguate the notion of ‘meaning’, so that an analysis can be deemed correct at one level of meaning and informative at another. This is just what Frege did in the first two of the three responses that can be discerned in his work, corresponding to his early, middle and late philosophy. In his early work, taken as including his Begriffsschrift and Grundlagen, Frege distinguished between ‘content’ (‘Inhalt’) and ‘mode of determination’ of content. Consider Frege’s key example in §64 of the Grundlagen:
(Da)	Line a is parallel to line b.
(Db)	The direction of line a is identical with the direction of line b.
According to Frege, (Da) and (Db) have the same ‘content’, but ‘split up’ that content in different ways. This is seen as analogous to the relationship between the following two propositions:
(Na)	The concept F is equinumerous to the concept G. (There are as many objects falling under concept F as under concept G, i.e., there are just as many Fs as Gs.)
(Nb)	The number of Fs is equal to the number of Gs.
The equivalence between these two propositions, asserted in what has come to be known as ‘Hume’s Principle’, underlies Frege’s logicism. Just as (Da) is offered as a way of contextually defining direction terms, through its equivalence to (Db), so (Na) is offered as a way of defining number terms, through its equivalence to (Nb). Although Frege came to reject contextual definitions themselves, Hume’s Principle was retained, being underpinned in his later work by his notorious Axiom V, in which an analogous equivalence was asserted. The equivalences involved here, at the time of the Grundlagen, were understood as involving sameness of ‘content’. On this early view, then, the following response can be given to the paradox of analysis. An analysis of the form ‘A is C’ is correct if ‘A’ and ‘C’ have the same content, and informative if they ‘determine’ or ‘split up’ that content in different ways.
In his Philosophie der Arithmetik, Husserl objected to Frege’s Grundlagen definitions on the grounds that whilst they may be extensionally equivalent, they were not identical in ‘content’ (‘Inhalt’), which Husserl understood intensionally (1891, 122). There is some justification for this view: since (Da) and (Db) involve different concepts, it would seem that they cannot be intensionally equivalent. The ambiguity in the notion of ‘content’ that this suggests, however, had already been recognised by Frege in drawing his distinction between ‘Sinn’ and ‘Bedeutung’. This distinction first appears in ‘Function and Concept’ (FC), which was given as a lecture on 9 January 1891; and in his letter to Husserl of 24 May 1891, he states explicitly that this is a disambiguation of his earlier notion of ‘content’. In his 1894 review of Husserl’s book, he then uses this distinction in responding to Husserl’s criticism. In articulating the criticism, he provides a clear statement of the paradox of analysis itself:

If words and combinations of words refer to [bedeuten] ideas, then for any two of them there are only two possibilities: either they designate the same idea or they designate different ideas. In the former case it is pointless to equate them by means of a definition: this is ‘an obvious circle’; in the latter case it is wrong. These are also the objections the author raises, one of them regularly. A definition is also incapable of analysing the sense, for the analysed sense just is not the original one. In using the word to be explained, I either think clearly everything I think when I use the defining expression: we then have the ‘obvious circle’; or the defining expression has a more richly articulated sense, in which case I do not think the same thing in using it as I do in using the word to be explained: the definition is then wrong. (RH, 319/ FR, 225.)

In reply, Frege argues that for the mathematician – as opposed to the ‘psychological logician’ – it is only Bedeutung, i.e., ‘the thing itself’, that matters. So ‘coincidence in extension’ is all that a definition need capture: neither the senses of the relevant expressions nor the ideas evoked by them are relevant (RH, 319-20/ FR, 225-6). Frege’s second response to the paradox of analysis can thus be stated as follows. An analysis of the form ‘A is C’ is correct if ‘A’ and ‘C’ have the same Bedeutung, and informative if ‘C’ has a ‘more richly articulated sense’ than ‘A’ (something that is not, strictly speaking, of concern to the mathematician).
In essence, however, Frege’s second response is the same as his first: a distinction is drawn between two notions of meaning. ‘Content’ has become ‘Bedeutung’, and ‘mode of determination of content’ has become ‘sense’. So is Frege’s second response better? The answer is ‘No’, for analyses and definitions must capture more than just sameness of Bedeutung. Consider the following two examples:
(CH)	A cordate is a creature with a heart.
(CK)	A cordate is a creature with a kidney [i.e., a renate].
In both cases we have extensional equivalence, but only (CH) would count as a good definition. (CH) involves sameness of sense – on some conception of ‘sense’ – and not just sameness of Bedeutung. So too in the case of Frege’s own definitions and axioms, sameness of sense and not just sameness of Bedeutung is required. In some places, Frege seems to acknowledge this. In ‘Function and Concept’, for example, he remarks that what, in effect, are instances of the two sides of Axiom V ‘express the same sense, but in a different way’ (FC, 11/ FR, 136). This sounds more like the ‘content’/‘mode of determination of content’ distinction, with ‘content’ now being understood as ‘sense’. In the Grundgesetze itself, Frege talks of the two sides of Axiom V being ‘gleichbedeutend’ (GG, I, §3/ FR, 213-4), but what he means in this case is sameness of Bedeutung and sense, as his later use of the term ‘gleichbedeutend’ shows (GG, I, §27/ FR, 220). Even Frege, then, was aware that analyses and definitions require sameness of sense and not just sameness of Bedeutung. But if this is so, then the response to the paradox of analysis that is suggested in his reply to Husserl is inadequate.
In his 1914 lectures on ‘Logic in Mathematics’, Frege makes his most sustained attempt to resolve the issues involved here; and we can regard these lectures as offering his third and final response to the paradox of analysis. He begins by distinguishing between ‘constructive’ (‘aufbauende’) and ‘analytic’ (‘zerlegende’) definitions. Constructive definitions simply stipulate, for abbreviatory purposes, that a new sign is to have the same sense as well as the same Bedeutung as a more complex sign. Analytic definitions analyse the sense of a sign ‘with a long established use’; and it is here that the problems arise. If we take an analytic definition of the form ‘A is C’, then there are two cases to consider. In the first case, ‘A’ and ‘C’ obviously have the same sense, but here, Frege notes, we should really talk of axioms, encapsulating what “can only be recognized by an immediate insight” (LM, 227/ FR, 316). In the second case, ‘A’ and ‘C’ do not obviously have the same sense. But what we do here, Frege argues, is introduce a new term ‘B’ to replace ‘A’, where ‘B’ is defined in the way we want, by means of ‘C’. Since ‘B is C’ is a constructive definition, we in effect bypass the question as to whether ‘A’ and ‘C’ have the same sense. Having done this, we can then reintroduce the sign ‘A’ if we wish, as long as we understand that it is to be treated “ as an entirely new sign which had no sense prior to the definition”. (LM, 227-8/ FR, 317.)
This strategy looks attractive as a response to the paradox of analysis. For if the original sense drops out of consideration in our constructive activities, then there is no longer an issue about capturing it. Consider, for example, Frege’s definition of ‘0’:
(E0)	The number 0 is the extension of the concept ‘equinumerous to the concept not identical with itself’. (Cf. FR, 118.)
It is clearly absurd to suggest that the ordinary person knows this definition. But given the amount of confusion that there has been about our concept of zero, it would seem equally absurd to expect an analysis to capture our ordinary understanding. All that is necessary for such definitions to count as both correct and informative is that they allow us to derive “the well-known properties of numbers”, as Frege put it in the Grundlagen (§70).
However, this strategy merely avoids rather than solves the paradox. Even if our ordinary understanding is deficient, it still acts as a constraint on our constructive activities: there remains something to which our analyses are answerable. At the very least, the paradox of analysis simply re-emerges at the level of the system as a whole, as Frege’s appeal to the ‘well-known properties of numbers’ indicates. Frege admits to a residual worry here, but according to him, what constraints there may be operate purely at the pre-theoretical level. Our grasp of the senses of simple terms is often confused, as if seen “through a mist”, and the aim of logical analysis is to articulate those senses clearly, in preparing the building stones for the subsequent work of construction (cf. LM, 228/ FR, 317-8). But again, this merely seems to displace rather than resolve the paradox of analysis.
It should be clear just how close Frege’s conception of analysis is to Carnap’s later conception of explication. Given that Carnap attended the lectures in which Frege elaborated it, the obvious suggestion is that Carnap simply took over his conception from Frege. However, although Carnap’s notes on Frege’s lectures have survived, there are not, unfortunately, any interpolations or marginalia to indicate that Carnap was inspired by Frege’s conception. But even if there were, it would be to miss the real point here. For what is important is the tension that underlies any reconstructive project. On the one hand, the work of analysis is to elicit and clarify what we already know, and we cannot depart too radically from our ordinary understanding, on pain of clarifying nothing at all. On the other hand, there must be a certain amount of reconstruction and revision, since our ordinary understanding is frequently confused and unreliable. Given that Carnap follows Frege in using logic in a programme of philosophical reconstruction, it is not surprising that the tension underlies his thought too, and that it should eventually prompt him to reflect systematically on his methodology in just the way that Frege did in his own later work.

4  Carnap’s Early Work: Rational Reconstruction
Carnap may not have introduced the term ‘explication’ until 1945, but the central idea that that term gave expression to was present in some form from Carnap’s very earliest work, and in particular, was encapsulated in his conception of ‘rational reconstruction’ (‘rationale Nachkonstruktion’), which formed the underlying motivation of his first major book, Der logische Aufbau der Welt, which was published in 1928. The connection between explication and rational reconstruction was made very clear in Carnap’s preface to the second edition of the Aufbau, which appeared in 1962. After noting that he would no longer put things in quite the way he had earlier, he goes on to endorse the philosophical orientation of the book:

This holds especially for the problems that are posed, and for the essential features of the method which was employed. The main problem concerns the possibility of the rational reconstruction of the concepts of all fields of knowledge on the basis of concepts that refer to the immediately given. By rational reconstruction is here meant the searching out of new definitions for old concepts. The old concepts did not ordinarily originate by way of deliberate formulation, but in more or less unreflected and spontaneous development. The new definitions should be superior to the old in clarity and exactness, and, above all, should fit into a systematic structure of concepts. Such a clarification of concepts, nowadays frequently called “explication”, still seems to me one of the most important tasks of philosophy, especially if it is concerned with the main categories of human thought. (1961, v.)

Carnap’s call for new definitions of old concepts echoes Frege’s famous passage in the Grundlagen (vi-viii) where he rejects the ‘historical’ approach to understanding our concepts and advocates precisely that conceptual systematisation that is here called ‘rational reconstruction’.
	The Aufbau opens with a quote from Russell: “The supreme maxim in scientific philosophising is this: Wherever possible, logical constructions are to be substituted for inferred entities.” But Russell’s maxim is notoriously ambiguous. Does it entail a programme of ontological eliminativism, or just of epistemological reductionism? Russell’s theory of descriptions lies at the root of the maxim, but even if we agree that Russell’s theory shows how definite descriptions may form part of a meaningful sentence whilst lacking meaning in themselves, this does not imply that the definite descriptions ‘analysed away’ do not have a referent. But it is clear that Carnap himself interpreted Russell’s maxim epistemologically rather than ontologically, as permitting rational reconstruction rather than ontological deconstruction. Carnap was famously dismissive of ontological endeavours, and it was the project of conceptual clarification with the help of modern logic that Carnap saw as important.
	The fact, however, that Carnap attempts to reduce our knowledge to a ‘given’ that is understood phenomenalistically has often led to Carnap being interpreted as more Russellian than he was. But Carnap also offers the possibility of a reduction to a physicalistic base; and the possibility of alternative ‘reductions’ shows that rational reconstruction is not regarded as part of an ontological enterprise – to see what kinds of things are ‘really’ or ‘ultimately’ there (cf. 1963, 18). One of its aims was to show the futility of ontological disputes. This goes back to Carnap’s first work, his doctoral dissertation, Der Raum (1921), which had attempted to reconcile the different conceptions of space of mathematicians, philosophers and physicists, by distinguishing between formal space (understood as an abstract logical system), intuitive space (interpreted in a Kantian way but restricted to topological properties) and physical space (which was empirical). (Cf. 1963, 11-12.) The purpose of clarifying the various conceptions of space was to resolve the disagreements between rival philosophical conceptions – not by endorsing one as opposed to the others, but by showing how all three contained elements of the truth. The aim, in other words, was to clarify the ‘logic’ of our spatial concepts, and it was this project that Carnap generalised to encompass the whole of our scientific concepts.
	What this suggests is a deeper motivation that is more Kantian or neo-Kantian than Russellian. Carnap was more concerned with the form and structure of our scientific knowledge than with its foundations. He was less interested in the logical atomist project of uncovering ‘ultimate constituents’ than in elucidating the intersubjective conceptual structures that underlie the objectivity of our scientific practices. Although the ‘linguistic turn’ that was prompted by the writings of Frege, Russell and Wittgenstein can be seen as being played out through the work of Carnap, the rational reconstructions that this involved were all aimed at the clarification of our scientific concepts.
	This neo-Kantian reading of Carnap’s philosophy has gained considerable ground over the last decade, and it certainly provides an antidote to the more traditional, Russellian reading. The key theme of the reading concerns the notion of the a priori. As Reichenbach explained in 1920, in The Theory of Relativity and A Priori Knowledge, there are two aspects of Kant’s own notion which need to be separated – the a priori as what is necessary or universally valid, and the a priori as what is constitutive; and it was the latter only that came to be endorsed. The importance of the role of constitution in Carnap’s philosophy is encapsulated in the avowed central aim of the Aufbau – to develop what he calls a ‘constitution system’ (‘Konstitutionssystem’), which shows how all our concepts can be organized into a structured system based on a few fundamental concepts (§§ 1-2). Indeed, Carnap originally wanted to call his book ‘Konstitutionstheorie’, or more fully, ‘Prolegomena zu einer Konstitutionstheorie der Wirklichkeit’, but in the end settled reluctantly on the title that Schlick had suggested. ‘Der logische Aufbau der Welt’ certainly carries Russellian connotations of ‘construction’, whereas ‘constitution’ is more in keeping with the neo-Kantian aspirations of the book. Of course, ‘constitution’ too can be interpreted as ‘construction’, but whilst – arguably – the latter is used more for ‘combination’ in a physical sense, the former allows more for ‘composition’ in a conceptual sense. At any rate, it is worth separating the two notions, reserving the first for the epistemic or semantic realm and the latter for the metaphysical or ontological realm.
	Rational reconstruction, then, might be better named ‘rational reconstitution’, although the term ‘rational’ certainly suggests an epistemological rather than metaphysical motivation. The point was not to ‘reconstruct’ the world but to ‘reconstitute’ our knowledge of it, and the aim of this was to elucidate the structure of our knowledge to demonstrate its objectivity. The importance of structure can be brought out if we ask what the relationship is between ‘ordinary’ and ‘reconstituted’ knowledge. What, more specifically, justifies a rational reconstruction? Carnap’s later principle of tolerance might suggest that anything goes, but there must clearly be some constraints on the adequacy of a reconstruction. In describing his Aufbau project in his ‘Intellectual Autobiography’, Carnap writes: “Although I was guided in my procedure by the psychological facts concerning the formation of concepts of material things out of perceptions, my real aim was not the description of this genetic process, but rather its rational reconstruction – i.e., a schematized description of an imaginary procedure, consisting of rationally prescribed steps, which would lead to essentially the same results as the actual psychological process” (1963, 15; italics added). But what does Carnap mean by ‘the same results’? The only example he gives is that of material things, “usually immediately perceived as three-dimensional bodies”, but to be “constructed out of a temporal sequence of continually changing forms in the two-dimensional visual field” (ibid.). The way that film and television work illustrates very well what Carnap has in mind here, but it is unclear how to generalise from this case, and ‘the same results’ still needs further specification. However, if we focus on the role of structure, then an answer can be given. For if it is structure that we are primarily concerned to reveal, then preservation of structure must operate as the essential criterion of correctness for rational reconstruction.
	Of course, ‘preservation of structure’ itself still needs further specification, but at the time of the Aufbau, Carnap did not suppose that there could be alternative logical structures, and it is logical structure that is essentially at issue here. If we recognise once again the Kantian dimension to Carnap’s thought, and distinguish, in particular, between form and content, then we can say that not only must rational reconstructions preserve form or structure, but also that their value precisely lies in abstracting from content. Given that the actual content (the intuitive ‘Inhalt’) of human experience may vary from person to person, or indeed from one time to another within the life of a single individual, then it is shared form or structure to which we must appeal in elucidating the intersubjectivity that underlies the objectivity of our conceptual practices.
	To the extent that Carnap’s early conception of logical analysis, then, can be characterised as involving rational reconstruction, we can extract from his early thought a relatively clear answer to the paradox of analysis. Carnap may not have explicitly addressed the issue in the way that Frege did in his 1914 lectures, but his work suggests how Frege’s response might be refined. Rational reconstructions can be regarded as correct in so far as they preserve structure, and informative to the extent that, by abstracting from content, the structure they reveal elucidates the objectivity of our scientific practices.

5  Carnap’s Conception of Quasi-Analysis
In what way does rational reconstruction ‘abstract from content’? Given that in his main (phenomenalistic) sketch of a ‘Konstitutionssystem’, Carnap bases his construction on what he calls ‘Elementarerlebnisse’ (‘elementary experiences’), it might be thought that his aim is precisely to reveal the (phenomenal) ‘content’ that underlies our conceptual system – just as Russell sought to reduce our knowledge to ‘sense-data’ or ‘sensibilia’. But once again, the suggested comparison with Russell here is misleading; and the difference between their two projects comes out most strikingly in what is perhaps the most intriguing conception in Carnap’s Aufbau – that of quasi-analysis.
	Citing the work of both neo-Kantians and Gestalt psychologists, Carnap held that the fundamental units of experience were not the qualities (the colours, shapes, etc.) involved in individual experiences (such as seeing a physical object), but those experiences themselves, taken as indivisible wholes. These were his ‘Elementarerlebnisse’, which formed the basis of the phenomenalistic version of his ‘Konstitutionssystem’ (§67). But if these were indeed ‘indivisible’, then how was it possible to determine the qualities involved in the elementary experiences? ‘Analysis’ – understood in the decompositional sense – could not yield these qualities, precisely because they were not seen as constituents of the elementary experiences (§68). Carnap’s answer was that they are ‘constructed’ (in the sense of ‘constituted’) by what he called ‘quasi-analysis’, a method that mimics analysis in yielding ‘quasi-constituents’, but which proceeds ‘synthetically’ rather than ‘analytically’ (§§ 69, 74).
	In essence, Carnap’s method of quasi-analysis is just that method of contextual definition or logical abstraction that Frege had introduced in the Grundlagen. This was the example that Frege had given to motivate his logicist ‘constructions’ (see §3 above):
(Da)	Line a is parallel to line b.
(Db)	The direction of line a is identical with the direction of line b.
A line, we might suggest, is also an ‘indivisible’ unit (at least in so far as it is intuited, i.e., where it is not seen as ‘composed’ of an infinity of points, or smaller lines). Yet it too has properties that can be ascribed to it on the basis of the relations it has to other geometrical figures. In particular, we can talk of its ‘direction’, which, whilst not literally a ‘constituent’ of it arrived at by (decompositional) ‘analysis’, can nevertheless be introduced contextually, by means of the relation of parallelism. So too in the case of Hume’s Principle, we have an equivalence relation holding between things of one kind (concepts) being used to define – or ‘construct’, as Carnap would put it – things of another kind (numbers):
(Na)	The concept F is equinumerous to the concept G.
(Nb)	The number of F’s is identical with the number of G’s.
Numbers too are not constituents of the concepts to which they are ascribed, but are ‘constructed’ from the appropriate equivalence relation.
	How, then, does Carnap apply the method of abstraction? Although he distinguishes between analysis and quasi-analysis, what he actually gives to explain the operation of quasi-analysis is an example of analysis, involving colours, which at least normally are thought of as properties rather than ‘quasi-properties’ of objects (§70). The simplest case can be seen as based on the following (seemingly trivial) contextual definition, the term ‘is equicoloured to’ abbreviating ‘has the same colour as’, to bring out its connection with the examples just given (the term ‘equicoloured’ is my own):
(Fa)	Object X is equicoloured to object Y.
(Fb)	The colour of X is identical with the colour of Y.
Accepting such a definition as unproblematic, and given that being ‘equicoloured’ is an equivalence relation, we can immediately proceed to form the equivalence classes, within the relevant domain, from which to (structurally) define the constituent colours.
	Carnap’s method gives rise to a number of difficulties, however, and Carnap himself admits that his method only works if certain ‘unfavourable circumstances’ are ruled out (§70). One such difficulty is what Goodman calls the ‘companionship difficulty’ (1977, 117), which arises whenever one of the colours to be defined is always accompanied by another colour. In response to this difficulty, Carnap suggests that the more objects there are and the smaller the average number of colours that an object possesses, the less likely this difficulty will arise (§70). But as he himself also recognises, this presupposes that there are no systematic connections between colours, and as Goodman remarks (ibid.), this threatens to make the ruling out of ‘unfavourable circumstances’ circular – Carnap’s method is to be restricted to those cases where it works. However, in defence of Carnap, Richardson has argued that the companionship difficulty is only a problem if the method of abstraction is used in analysis rather than quasi-analysis (1998, 59-64). In quasi-analysis, where there are no actual constituents to pick out, there is no independent reality against which to judge the resulting constructions. If it is only structural properties with which we are concerned, then these are indeed only answerable to the relations on which the constructions are based.
	This defence is clearly in keeping with the neo-Kantian rather than Russellian interpretation of the Aufbau: the aim is to reveal the structure of our conceptual judgements rather than to uncover the ‘ultimate’ constituents of our experiences. The problem, though, is that Carnap is by no means as clear about the difference between analysis and quasi-analysis as this defence suggests, for in §81 Carnap talks of ‘unfavourable circumstances’ not obtaining – as a condition of ‘irregularities’ in the constructions not arising – even in the case of quasi-analysis. However, almost as an afterthought, he concludes this section as follows:

a more detailed investigation, which we have to omit for lack of space, shows that these interferences in the concept formation through quasi analysis can occur only if circumstances are present under which the real process of cognition, namely, the intuitive quasi analysis which is carried out in real life, would also not lead to normal results. (§81.)

What Carnap seems to be suggesting here is that similar ‘interferences’ occur in actual psychological processes, so that it is to the credit of his account of quasi-analysis that room is made for them. The difficulties, in other words, can be turned to his own advantage. Furthermore, this only reinforces the neo-Kantian reading. If the aim is to reveal the structure of our actual conceptual experience, then whatever ‘hidden’ properties may underlie our experiences are irrelevant. If in our experience two particular shades of colour do indeed always go together, and their distinguishability is nowhere apparent in our experience, then there is no need to respect this in our rational reconstruction – indeed, this fact should precisely be reflected.
	However, what the above passage also reveals is the appeal to ‘how things really are’ that frequently surfaces in Carnap’s pre-systematic or extra-systematic remarks. He does not explicitly take the neo-Kantian line in arguing that there simply is no ‘fact of the matter’ as to what the world is like independently of our cognitive processes. The tension between his Russellian and neo-Kantian motivations is perhaps nowhere so clear as in the very distinction he draws between analysis and quasi-analysis. For if analysis is understood as uncovering ‘constituents’, and quasi-analysis is understood as merely constructing ‘quasi-constituents’, then that makes the distinction an ontological one. But this is in clear conflict with Carnap’s professed ontological neutrality. Carnap suggests that analysis and quasi-analysis are formally analogous – to the extent that both make use of the method of abstraction (§69). But if we wanted to capture the distinction more formally, we might suggest that we distinguish between the following two results, (Fb) and (F), of the method of abstraction applied to our initial proposition (Fa):
(Fa)	Object X is equicoloured to object Y.
(Fb)	The colour of X is identical with the colour of Y.
(F)	The colour (constituent) of X is equal to the colour (constituent) of Y.
For if analysis yields constituents rather than quasi-constituents, and the wholes of which the constituents are parts are themselves distinct (i.e., the objects X and Y in this case), then the two colour constituents of X and Y cannot, strictly speaking, be identical but only equal, in the relevant respect. So whilst quasi-analysis can be seen as yielding (Fb), analysis should be thought of as yielding (F).
	However, if this account of analysis is right, then an infinite regress threatens. For if two constituents are uncovered, then there will be some similarity relation holding between them, in which case the method of abstraction (contextual definition) can be applied again to uncover further constituents. So either we need some different account of constituent, which Carnap does not supply, or we no longer have a clear distinction between analysis and quasi-analysis. All we really have is quasi-analysis; and this in any case might seem to be all we have in (‘pure’ uses of) the method of abstraction, which, after all, is seen more as a ‘constructive’ process.
	Of course, if there is no viable distinction between analysis and quasi-analysis, where both are seen as involving the method of abstraction, then this might seem to support the neo-Kantian rather than Russellian interpretation – or better, ‘rational reconstruction’ – of Carnap’s Aufbau project. But the truth seems to be that Carnap, at the time of the Aufbau, was in a transitional stage. His position was inherently unstable: he was in the process of freeing himself from the Russellian programme that had to some extent inspired him, whilst allowing his more neo-Kantian instincts, which one might suggest were more deeply embedded in his philosophical outlook, to guide his development, a development that was to lead to the conception of logical analysis characteristic of his later philosophy. This conception surfaces even in the Aufbau. Here is one characteristic passage, in which Carnap summarises his view of quasi-analysis:

the analysis or, more precisely, quasi-analysis of an entity that is essentially an indivisible unit into several quasi-constituents means placing the entity in several kinship contexts on the basis of a kinship relation, where the unit remains undivided. (§71.)

Compare this with Carnap’s characterisation of logical analysis in his 1934 paper, ‘Die Methode der logischen Analyse’:

The logical analysis of a particular expression consists in the setting-up of a linguistic system and the placing of that expression in this system. (1936, 143.)

After the publication of the Aufbau, Carnap never talks of ‘quasi-analysis’ again, except in referring to the ideas of the Aufbau itself, and we can see why. For in the contrast it suggests with ‘analysis’, there were realist undertones of an ontological kind that Carnap was later keen to purge. It would be tempting to conclude by saying that Carnap’s distinction between analysis and quasi-analysis turned out to be only a quasi-distinction; but it would be more accurate to say – as far as Carnap was concerned – that it was only a pseudo-distinction, a residue of unreconstructed metaphysical thinking.

6  Carnap’s Later Work: Explication
Between the Aufbau and the introduction of the term ‘explication’, Carnap’s ideas developed in important ways. In ‘The Elimination of Metaphysics through Logical Analysis of Language’, which appeared in 1932, Carnap outlined a conception of logical analysis in which metaphysical thinking was not merely abandoned but explicitly repudiated. The aim of logical analysis was, on the positive side, to clarify the concepts of empirical science, and, on the negative side, to show that metaphysical statements were meaningless ‘pseudo-statements’. Logic was seen as the only method of philosophy, and as Carnap argued in his second major work, The Logical Syntax of Language (1934), this entailed the identification of philosophy with the logic of science:

The aim of logical syntax is to provide a system of concepts, a language, by the help of which the results of logical analysis will be exactly formulable. Philosophy is to be replaced by the logic of science – that is to say, by the logical analysis of the concepts and sentences of the sciences, for the logic of science is nothing other than the logical syntax of the language of science. (1937, xiii.)

In his subsequent work, Carnap came to recognise that logical syntax needed to be supplemented by semantics, and it was the aim of the two volumes of his Studies in Semantics (1942, 1943) to provide this supplementation. There is a great deal to say about these developments, and their relationship to the work of other philosophers and logicians, most notably, Wittgenstein, Gödel and Tarski. But there remained an underlying methodological unity in these developments, and for the purposes of the present paper, we can concentrate on the more systematic account of methodology that Carnap later provided.
The term ‘explication’ first appears in Carnap’s work, in print, in June 1945, in a paper entitled ‘The Two Concepts of Probability’. Carnap makes clear in the opening paragraph that his main goal is to offer explications of our pre-scientific conceptions of probability, although he concentrates in this paper on providing ‘clarifications’ of the two explicanda that he claims to find in ordinary language. (The detailed explications were to be published in 1950.) Carnap also published another paper on a related topic in April 1945, ‘On Inductive Logic’, which, though it refers to his forthcoming June paper in a footnote, makes no mention of explication. This may not in itself signify that Carnap did not have the concept of explication in mind when he wrote the paper, except that, in the final section of this paper, he does indeed offer some methodological reflections, in terms not of ‘explication’ but of ‘rational reconstruction’, which, as we have seen, was his original term for his philosophical method. So we can conclude that at some point between the writing of ‘On Inductive Logic’ and ‘The Two Concepts of Probability’, which were published in April 1945 and June 1945, respectively, though obviously written earlier, Carnap introduced the term ‘explication’.
	Given that the underlying idea of rational reconstruction was already in place at this time, what can have stimulated talk of ‘explication’? Two particular publications are relevant here: firstly, the appearance in 1942 of the volume on Moore in ‘The Library of the Living Philosophers’ series, edited by Paul Schilpp, in which C. H. Langford has a paper on the paradox of analysis; and secondly, the publication also in 1942 of the Dictionary of Philosophy edited by Dagobert Runes, in which Carnap himself makes a number of contributions. Let us consider their possible influences by turning to the two main publications that presented Carnap’s work in the period from 1942, Meaning and Necessity (1947) and Logical Foundations of Probability (1950).
	The notion of explication is introduced very early in Meaning and Necessity. In §2 Carnap writes:

The task of making more exact a vague or not quite exact concept used in everyday life or in an earlier stage of scientific or logical development, or rather of replacing it by a newly constructed, more exact concept, belongs among the most important tasks of logical analysis and logical construction. We call this the task of explicating, or of giving an explication for, the earlier concept; this earlier concept, or sometimes the term used for it, is called the explicandum; and the new concept, or its term, is called an explicatum of the old one. (1947, 8-9.)

At this point there is then the following footnote: “What is meant here by ‘explicandum’ and ‘explicatum’ seems similar to what Langford means by ‘analysandum’ and ‘analysans’; see below, n. 42, p. 63.” (1947, 8, fn. 7.)  Following up this further footnote, we find a reference to Langford’s paper on Moore and the paradox of analysis, at the point in Carnap’s own book where he offers his conception of intensional structure as a solution to the paradox of analysis. As we have noted, Langford’s paper was published in 1942; and the obvious suggestion is that it was this paper that prompted not only Carnap’s own response to the paradox of analysis, as illustrating his conception of intensional structure, but also his conception of explication, as modelled on Langford’s conception of analysis.
	In illustrating his conception of explication in §2 of Meaning and Necessity, Carnap takes the example of Frege’s and Russell’s logicist ‘explication’ of number terms such as ‘two’ – “the term ‘two’ in the not quite exact meaning in which it is used in everyday life and in applied mathematics”, and their different explications of phrases of the form ‘the so-and-so’. But Carnap’s introduction of the idea of explication precedes his discussion of ‘L-truth’, which is offered “as an explicatum for what philosophers call logical or necessary or analytic truth” (1947, 7), and other such ‘L‑concepts’. However, Carnap says little about what constraints there may be on the adequacy of an explication. He does indeed say that explication “consists in laying down rules for the use of corresponding expressions in language systems to be constructed” (1947, 8), but on the relation between the explicandum and the explicatum, all he says is this: “Generally speaking, it is not required that an explicatum have, as nearly as possible, the same meaning as the explicandum; it should, however, correspond to the explicandum in such a way that it can be used instead of the latter.” (Ibid.)
	Carnap provides a much fuller discussion of explication in the first chapter of Logical Foundations of Probability. One of Carnap’s main aims in this book is to clarify our various conceptions of probability. Since these conceptions have only a vague articulation in everyday life, Carnap sees his task as that of making these conceptions more precise, that is, of providing an explication for them (cf. 1950, 1‑2). He thus first offers some general methodological remarks concerning explication. Since these also develop, to a considerable extent, the brief remarks he makes about explication in ‘The Two Concepts of Probability’, which, revised, formed the second chapter of Logical Foundations of Probability, I shall concentrate on the fuller discussion here.
	§2 of Carnap’s first chapter is entitled ‘On the Clarification of an Explicandum’, and after offering a characterisation of explication similar to that provided in Meaning and Necessity (quoted above), Carnap goes on:

The term ‘explicatum’ has been suggested by the following two usages. Kant calls a judgement explicative if the predicate is obtained by analysis of the subject. Husserl, in speaking about the synthesis of identification between a confused, nonarticulated sense and a subsequently intended distinct, articulated sense, calls the latter the ‘Explikat’ of the former. (For both uses see Dictionary of philosophy [1942], ed. D. Runes, p. 105). What I mean by ‘explicandum’ and ‘explicatum’ is to some extent similar to what C.H. Langford calls ‘analysandum’ and ‘analysans’: “the analysis then states an appropriate relation of equivalence between the analysandum and the analysans” [1942, 323]; he says that the motive of an analysis “is usually that of supplanting a relatively vague idea by a more precise one” [1942, 329].
	(Perhaps the form ‘explicans’ might be considered instead of ‘explicatum’; however, I think that the analogy with the terms ‘definiendum’ and ‘definiens’ would not be useful because, if the explication consists in giving an explicit definition, then both the definiens and the definiendum in this definition express the explicatum, while the explicandum does not occur.) The procedure of explication is here understood in a wider sense than the procedures of analysis and clarification which Kant, Husserl, and Langford have in mind. The explicatum (in my sense) is in many cases the result of analysis of the explicandum (and this has motivated my choice of the terms); in other cases, however, it deviates deliberately from the explicandum but still takes its place in some way; this will become clear by the subsequent examples.

What we have here is a reference both to Langford’s paper on the paradox of analysis, and also to Kant’s and Husserl’s notions of explication as Carnap found them described in a dictionary of philosophy published in 1942. Kant’s and Husserl’s conceptions, however, are quite different. For Kant, ‘explicative’ is opposed to ‘ampliative’, as one way to characterise his analytic/synthetic distinction. ‘Explication’ in Kant’s sense simply means to ‘extract’ the constituent concepts of a complex concept (to find the predicates ‘contained’ in the subject concept) – ‘analysis’ in the sense of ‘decomposition’. But Husserl’s notion is much closer to Carnap’s, as involving a precisification of an everyday concept. Indeed, Carnap recognises in the second paragraph that there is an important difference here, in distinguishing between ‘analysis’ in what is clearly the Kantian sense and ‘explication’ in his sense. Although it may be that the results of ‘analysis’ and ‘explication’ coincide in specific cases, i.e., where there is a precise concept that is simply being clarified (‘decomposed’), they may diverge in other cases, where ‘analysis’ perhaps can only go so far and explication has to take over.
	This distinction is in effect put to work in what Carnap goes on to say. For if the explicandum is not itself exact, then there cannot be an exact answer as to whether the explicatum correctly explicates the explicandum (as was recognised by Frege in his ‘Logic in Mathematics’ lectures). But we clearly need to say something about the explicandum if the explication is to be understood at all, and it is here that ‘analysis’ in the sense of ‘clarification’ takes place. Even though the terms to be explicated may be imprecise, Carnap writes, “there are means for reaching a relatively good mutual understanding as to their intended meaning. An indication of the meaning with the help of some examples for its intended use and other examples for uses not now intended can help the understanding.” (1950, 4.) What is required is ‘elucidation’ (‘Erläuterung’) rather than explication proper, which requires a theoretical system in which rules for the use of the corresponding expressions are laid down (cf. 1950, 3, 5).
	Accepting, then, that an everyday concept has been ‘elucidated’ sufficiently to engage in explication, what are the criteria of adequacy for explication? In §3, Carnap lays down four requirements for a concept to be an adequate explicatum for a given explicandum:
(1)	similarity to the explicandum;
(2)	exactness;
(3)	fruitfulness;
(4)	simplicity.
As far as the first is concerned, Carnap writes: “The explicatum is to be similar to the explicandum in such a way that, in most cases in which the explicandum has so far been used, the explicatum can be used; however, close similarity is not required, and considerable differences are permitted” (1950, 7). As an example, Carnap takes the case of a biologist explicating our pre-scientific concept of a fish, replacing it by the biologically defined concept, which Carnap suggests we call ‘piscis’ to avoid confusion. Most of what we used to call ‘fishes’ still come out as ‘pisces’, but whales are obviously one exception. There is enough similarity, even though there are important divergences.
	So what justifies the divergences from ordinary language? The answer, of course, lies in the advantages of the scientific system in which the explicatum is located, and this is what is brought out by the other three requirements that Carnap formulates. As far as the second is concerned, Carnap writes: “The characterization of the explicatum, that is, the rules of its use (for instance, in the form of a definition), is to be given in an exact form, so as to introduce the explicatum into a well-connected system of scientific concepts” (ibid.). The requirement of exactness lay at the core of the idea of rational reconstruction, and talk of ‘well-connectedness’ here highlights once again the importance of a clearly revealed structure in the system that is constructed.
	Well-connectedness also lies at the basis of the third requirement. “The explicatum is to be a fruitful concept, that is, useful for the formulation of many universal statements (empirical laws in the case of a nonlogical concept, logical theorems in the case of a logical concept).” (Ibid.) And in explaining this, Carnap writes: “A scientific concept is the more fruitful the more it can be brought into connection with other concepts on the basis of observed facts; in other words, the more it can be used for the formulation of laws” (1950, 6). Taking Carnap’s example once again, fishes as scientifically defined (pisces) have more properties in common – have more connections with one another – than fishes as pre-scientifically understood (animals living in water), allowing more general statements to be formulated (ibid.).
	The requirement of fruitfulness that Carnap formulates here is a clear echo of the emphasis that Frege placed on the fruitfulness of definitions in his early work, and in the Grundlagen, in particular. According to Frege, the definitions of number that he offers are fruitful precisely to the extent that they allow him to derive ‘the well-known properties of numbers’ (see §3 above); and here too, we might say, the value of the reconstructed system lies in the connections that it exhibits between the concepts defined and the statements formulated.
	Carnap’s final requirement is simplicity: “The explicatum should be as simple as possible; this means as simple as the more important requirements (1), (2), and (3) permit” (1950, 7). The simplicity of a concept is to be measured, Carnap states, according to the form of its definition and the forms of the laws connecting it with other concepts, but he rightly emphasises that any simplicity considerations are subordinate to the other three considerations (ibid.).
	The central example that Carnap discusses to elucidate his account of explication is the concept of temperature, which Carnap offers as an explicatum for the concept of warmth. Carnap first distinguishes between classificatory, comparative and quantitative concepts. To concentrate on the simplest cases (monadic properties and dyadic relations), classificatory concepts, such as warm, classify things into two mutually exclusive kinds (warm and not-warm); comparative concepts, such as warmer, express a relation between two things based on a comparison, given in the form of a ‘more (in a certain respect)’ statement; whilst quantitative concepts, such as that of temperature, describe things by the ascription of numerical values (cf. 1950, 8-9). Carnap writes: “Classificatory concepts are the simplest and least effective kind of concept. Comparative concepts are more powerful, and quantitative concepts still more; that is to say, they enable us to give a more precise description of a concrete situation and, more important, to formulate more comprehensive general laws.” (1950, 12.) The concept of temperature, Carnap then argues, may be regarded as an explicatum for the comparative concept warmer, in that it makes more precise what the latter expresses. Things may indeed be ordered by means of the relation warmer than, and thereby assigned a number representing their position in the series, but assigning them a number representing their temperature grants them some more ‘absolute’ value.
	How then does the explication of ‘warmth’ by means of ‘temperature’ satisfy Carnap’s four requirements? We may readily grant that the explicatum is exact: there are clear rules governing the use of the concept of temperature, and a thermometer, for example, can be easily used to measure temperature. The explicatum is fruitful, as there is indeed a well-connected scientific system in which the concept of temperature plays a central role in the formulation of laws and general statements. The explicatum is also relatively simple: it is both easily defined (or at least permits straightforward measurement) and readily incorporated into scientific laws. All three requirements concern the nature and role of the explicatum within the scientific theory. The interesting – and problematic – philosophical question concerns the relation between the explicatum and the explicandum, precisely the question raised by the paradox of analysis. If ‘considerable differences are permitted’ (cf. 1950, 7), then what constraint at all does the requirement of similarity impose?
	In the present example, Carnap interprets the requirement of similarity as follows: “The concept Temperature is to be such that, in most cases, if x is warmer than y (in the prescientific sense, based on the heat sensations of the skin), then the temperature of x is higher than that of y” (1950, 12). To see the connection with Frege’s examples of ‘fruitful’ definitions, particularly as given as contextual definitions in the Grundlagen (and Axiom V of the Grundgesetze has the same form), and Carnap’s own use of the method of abstraction in the Aufbau, let us set this out as follows:
(Ta)	x is warmer than y.
(Tb)	The temperature of x is higher than the temperature of y.
(Tc)	There are numerical values n and d, where d > 0, such that x has a temperature of (n+d)° and y has a temperature of n°.
Just as in Frege’s examples, an equivalence relation holding between objects of one kind is offered as a way of defining an identity statement concerning objects of a more abstract kind, so too here a comparative relation holding between two objects, expressed in (Ta), is used as the starting-point for an explication that involves a more theoretical concept, captured in (Tb). (Tc) just makes explicit the quantitative measurement that the appeal to temperature allows. In each case, there is at least a hope that the definiens and the definiendum, or the explicandum and the explicatum, are ‘equivalent’ in some appropriate sense; but in so far as one relies on ordinary language and the other uses concepts precisely defined within a scientific system, there may be cases where discrepancies arise. Carnap himself describes a case in which a discrepancy occurs:

Suppose I enter a moderately heated room twice, first coming from an overheated room and at a later time coming from the cold outside. Then it may happen that I declare the room, on the basis of my sensations, to be warmer the second time than the first, while the thermometer shows at the second time the same temperature as at the first (or even a slightly lower one). Experiences of this kind do not at all lead us to the conclusion that the concept Temperature defined with reference to the thermometer is inadequate as an explicatum for the concept Warmer. On the contrary, we have become accustomed to let the scientific concept overrule the prescientific one in all cases of disagreement. In other words, the term ‘warmer’ has undergone a change of meaning. Its meaning was originally based directly on a comparison of heat sensations, but, after the acceptance of the scientific concept Temperature into our everyday language, the word ‘warmer’ is used in the sense of ‘having a higher temperature’. (1950, 12-13.)

The example is instructive. For it is not just that we can allow the odd discrepancy without invalidating the explication, but that the explication may actually have value to the extent that it opens up and explains discrepancies – and indeed, not only discrepancies between our ordinary language and the scientific language, but also within ordinary language. Two people may disagree over whether the room, say, is warmer or colder than it was a few minutes ago, and an appeal to the thermometer reading may settle the question. And furthermore, as Carnap points out, our ordinary use of language may change as a result, and become more refined in its own application. At the very least we will become more sensitive to possible discrepancies, and all these advantages may be seen as contributing to the value of the explication. Explications, we might say – and we might see this as revealing a further Kantian dimension to Carnap’s thought – come to play a regulative role in ordinary life.
	All of this opens up a whole range of issues that Carnap himself did not say a great deal about, but that we should indeed appreciate in accounting for the value of an explication. From his earliest work, it seems, Carnap was more interested in the ‘explicatum’ or the ‘rationally reconstructed’ side of things; and we can see this as reflected in the requirements for an adequate explication that Carnap lays down. Three of the four requirements concern solely the properties of the explicatum, and even the first requirement only talks vaguely of a ‘similarity’ relation. Yet we ought, perhaps, to heed Brentano’s insight into the structure of intentionality, and emphasise that an explication is always an explication of something, and we cannot simply judge the value of an explication solely in terms of the scientific system in which it plays a part. Appreciation of the context in which the explication arises, and the way in which it refines, or resolves discrepancies within, our ordinary understanding, is essential. This was something to which Husserl was highly sensitive.

7  Husserl’s Conception of Explication
As we saw in the last section, according to Carnap himself, his introduction of the term ‘explication’ was partly motivated by Husserl’s talk of ‘explication’ as “the synthesis of identification between a confused, nonarticulated sense and a subsequently intended distinct, articulated sense” (Carnap, 1950, §2). Although it seems that Carnap’s knowledge of Husserl’s conception was derived solely from Dorion Cairns’ definition in Runes’ Dictionary of Philosophy (1942), and no genuine influence can be detected, it is instructive to compare Carnap’s conception with Husserl’s.
	Husserl’s most substantial discussion of explication occurs in chapter 2 of Part I of Experience and Judgement, a work that was edited (with Husserl’s authority) by Ludwig Landgrebe and published in 1939, the year after Husserl died. Husserl here distinguishes between ‘simple’ or ‘immediate’ apprehension (‘schlichte Erfassung’) and ‘explication’ (‘Explikation’), and does indeed talk of a ‘synthesis of identification’ (§22). His concern is with the different levels of reflective perception of an object. ‘Simple apprehension’ is the lowest level, when all we are aware of is the object ‘as a whole’ (ibid.). But as Husserl had explained earlier in the book (§8), every experience of a thing has its ‘internal horizon’, delimiting an area of possible knowledge beyond that core that constitutes our immediate apprehension. Experience has a ‘retentional’ and ‘protentional’ structure: in observing an object, our experience is informed by our existing knowledge and expectations. We may recall previous perceptions or already have in mind a type that the object instantiates, for example, and we may imagine what the object would look like from a different angle or anticipate how it might change. At the second level, then, our knowledge is enriched as we elucidate further aspects of the object. This is explication.

Explication is penetration of the internal horizon of the object by the direction of perceptual interest. In the case of the unobstructed realization of this interest, the protentional expectations fulfill themselves in the same way; the object reveals itself in its properties as that which it was anticipated to be, except that what was anticipated now attains original givenness. A more precise determination results, eventually perhaps partial corrections, or – in the case of obstruction – disappointment of the expectations, and partial modalization. (EJ, §22.)

In so far as this process reveals aspects of the object that are there to be revealed, talk of ‘explication’ seems appropriate – appropriate, that is, if something like the Kantian conception of explication, as the mental dissection of a complex into its constituents, is the model. But this is not Husserl’s conception, as he makes clear in §26. For him, explication is the clarification (Verdeutlichung) of what is anticipated within the inner horizon of the object, and what is anticipated is typically vague and confused. Instead of a ‘completely determined sense’, which simply requires unpacking, there is what Husserl calls a ‘frame of empty sense’, which is gradually filled in as explication proceeds. But to talk of this ‘frame of empty sense’ is not to say, on the other hand, that there is nothing from which we start. Husserl distinguishes explication as he understands it from ‘analytic clarification’ (‘analytische Verdeutlichung’), which is indeed an ‘explication in empty consciousness’, where the object of explication need not be ‘intuitively given’ (§26). ‘Brother’ can be analysed as ‘male sibling’, for example, without any brother being present; but it is not conceptual analysis that Husserl has in mind. Explication is an enrichment of sense operating throughout within the domain of intuition. Nevertheless, Husserl does allow that our expectations may be disappointed, and that partial corrections may occur, and this brings him closer to Carnap. Carnap may conceive of rational reconstruction or explication as abstracting from intuitive content, but both Husserl and Carnap see explication as a process of precisification, by means of which our ordinary understanding is refined, and if necessary, transformed.
As we have seen, however, Carnap is not particularly concerned with the relationship between the explicandum and explicatum, requiring merely that they be ‘similar’. For Husserl, on the other hand, it is the movement of explication itself that is of central concern, and he describes its essential structure in §24. Taking an object S, with internal properties or ‘determinations’ (‘Bestimmungen’) α, β, etc., Husserl characterises explication as a process in which the determinations are referred to a ‘substrate’ which serves as the locus for the ‘synthesis of identification’.

The process of explication in its originality is that in which an object given at first hand is brought to explicit intuition. The analysis of its structure must bring to light how a twofold constitution of sense [Sinngebung] is realized in it: “object as substrate” and “determination α …”; it must show how this constitution of sense is realized in the form of a process which goes forward in separate steps, through which, however, extends continuously a unity of coincidence – a unity of coincidence of a special kind, belonging exclusively to these sense-forms. (EJ, §24a.)

Explication not only reveals properties of an object, but also opens up the very distinction between ‘substrate’ and ‘determination’ on which the integrity of the process depends (§24b). As Husserl writes, “After the explication of the α, the S becomes Sα; after the emergence of the β, (Sα)β, and so on” (§24c). The movement of explication consists in “a continuous internal transformation”, whereby the properties of the object that are precipitated out are rooted in “a permanent synthesis of coincidence” (ibid.).
Husserl goes on to discuss various complications, in further explication of the process itself, but the essential conception is clear. Although Husserl focuses on reflective perception of an object, the account can be readily extended to other cases such as the mathematical and scientific ones that occupied Frege and Carnap. Here explication involves opening up not just logical distinctions such as that between subject and predicate but also function-argument forms, causal structures, and so on. Indeed, we can regard the whole panoply of science as a tool in opening up the structures of experience in just that enrichment of our understanding that Husserl was so concerned to conceptualise.
Developing this Husserlian account offers a way of supplementing and partially correcting the Fregean-Carnapian conception of reconstructive explication. To see this, let us return to the paradox of analysis, and consider how it might be resolved by bringing together elements from Frege’s, Carnap’s and Husserl’s thought. If we begin with Frege’s first two responses, then we can agree that a good analysis must ‘split up content’ in a ‘more richly articulated’ way, but there is no single bifurcation of meaning that provides a general answer. Explication may open up more than just one distinction; the full resources of a broader conceptual framework or more powerful theoretical system may be required. We can agree with all three that an analysis should not be regarded as simply trying to capture our pre-existing conceptions, confused as they often are, although our ordinary understanding does act as a constraint, at the level of structure. The aim of analysis is to elucidate this structure, and to refine rather than replace our ordinary conceptions, which does not rule out revising them wherever necessary.
	This can be illustrated by taking a simple example from chemistry, involving the analysis of a process rather than an object:
(SW)		Salt dissolves in water.
(NH)		2H2O  +  NaCl      H3O+  +  Cl  +  Na+  +  OH.
(SW) represents a familiar process (an everyday phenomenon of our ‘life-world’), and (NH), we could say, provides its ‘chemical analysis’ (a translation into the language of science). There is also a sense in which, for the purposes of chemistry, (NH) does replace (SW), in that it is this equation that represents the reaction and that plays its part in more complex analyses of chemical processes. Nevertheless, in no sense does a chemist discard its informal characterisation, as captured in (SW). Whatever manipulation of chemical formulae a chemist may perform, the informal characterisations remain in the background, presupposed in our scientific activity. In offering (NH) as the analysis of (SW), then, the chemist is refining rather than replacing ordinary language, for certain scientific purposes.
	There is an extent to which correct and informative analyses do involve ‘splitting up content’ differently. What makes (NH) a correct analysis of (SW), for example, is that they both refer to the same ‘content’ – in this case, the same chemical process. However, even this requires qualification. For ‘water’ as we ordinarily understand it – the water that we drink and wash in – is not just H2O, but also contains ‘impurities’; and ‘salt’ too can refer to more than just NaCl. So the ‘content’ of (NH) is itself an idealised refinement of the ‘content’ of (SW). But what tends to happen in such cases is adjustment of our ordinary notions to reinforce the analysis. (NH) makes us interpret (SW) as “Sodium chloride dissolves in ‘pure’ water”; and once the adjustment is made, then we do have sameness of ‘content’. Sameness of ‘content’ is indeed a constraint on the adequacy of an analysis, but this is not to say that the ‘real’ content of the sentence of ordinary language is properly grasped prior to understanding the theory in which the analysis is offered. Husserl talks of the results of explication as ‘precipitates’ (‘Niederschläge’), and the metaphor is apt. For contents or senses too should be seen as crystallised out in analysis: the material is already there in the fluid of our everyday life, but it needs the seed of a theoretical concern to precipitate them out. In the end, what makes an analysis a good one is its success, as part of some overall theory, in convincing us that our ordinary discourse is indeed imprecise, and requires refinement for scientific purposes.
	 How informative an analysis is will depend on what we learn in this process. Ultimately, there is no ahistorically positioned answer as to whether an analysis is both correct and informative. Before the theory is developed in which the analysis is offered, the analysis, if it is understood at all, will seem incorrect; and after it is developed, with the necessary transformation in our understanding effected, it will be correct but uninformative. To talk of ‘correctness’ is to make a move within a system; yet informativeness arises in the process of developing, learning and using a system. An analysis is ‘informative’, in other words, by being transformative. Frege and Carnap may have developed systems in which ‘correctness’ was located, but it was Husserl who recognised the transformative aspect of explication.

8  Conclusion: Carnap and the Paradox of Analysis
As we saw in §3, the conception of analysis that Frege articulated in his 1914 lectures, which Carnap attended, was essentially a response to the paradox of analysis (although it was not known as such at the time). As we saw in §6, according to Carnap himself, his introduction of the term ‘explication’ was partly prompted by Langford’s discussion of the paradox of analysis in 1942. So it might seem surprising that Carnap does not offer his conception of explication, which bears a striking similarity to Frege’s later conception of analysis, as his own response to the paradox of analysis. In Meaning and Necessity (1947), where his conception of explication is first discussed, Carnap also offers a solution to the paradox, but here he appeals to the notion of intensional structure. Consider the example that Carnap takes from Moore:
(B1)	The concept brother is identical with the concept male sibling.
(B2)	The concept brother is identical with the concept brother.
The first, Carnap writes, “is a sentence conveying fruitful information, although of a logical, not a factual, nature”, whilst the second is “quite trivial” (1947, 63). But if the two concepts are identical, how can this be? Carnap’s answer is to distinguish two notions of meaning, which is precisely the response that Frege gave to the paradox in his early and middle periods. (B1) and (B2) are ‘L-equivalent’, in Carnap’s terms, but differ in intensional structure, i.e., are not ‘intensionally isomorphic’. (B1) L-implies (B2), and vice versa, but (B1) and (B2) are built up in different ways out of their constituent ‘designators’. Langford, in his original discussion of the paradox, had suggested that the two expressions representing the analysandum and analysans in a correct and informative analysis were “cognitively equivalent in some appropriate sense” but not “synonymous” (1942, 326). According to Carnap, the notion of L-equivalence explicates cognitive or logical equivalence, and the notion of intensional isomorphism explicates synonymy (1947, 64).
	In a short critique of this account, Leonard Linsky (1949) argued that Carnap’s solution was not in general adequate. His objection can be seen by comparing (B2) with the following variant:
(B3)	The concept brother is identical with the concept Bruder.
(B2) and (B3) are intensionally isomorphic, but (B3) is arguably not as trivial as (B2). Admittedly, using terms from two different languages introduces complications, but the essential point remains. It would be perfectly possible to define a new English word, say, ‘mibling’, as an abbreviation for ‘male sibling’, and then the following would equally seem not as trivial as (B2):
(B4)	The concept brother is identical with the concept mibling.
As Linsky remarks, “one can produce intensional isomorphism at will (or destroy it) by definitional abbreviation” (1949, 347).
In reply to Linsky, Carnap (1949) admits that his account does not resolve the paradox in this particular kind of case, but he defends his general strategy. A distinction must always be drawn between two notions of meaning, such that the relevant expressions have the same ‘meaning’ in one sense but different ‘meanings’ in a another sense; but what these senses are will depend on the case. Carnap goes on to offer seven different explicata for the ordinary notion of ‘synonymy’ (and notes that there may be many more besides), of varying degrees of strength, and suggests that a different pair of explicata is required in Linsky’s case.
	Carnap’s reply is deeply revealing of his philosophical methodology, illustrating both its value and limitations. For given that a distinction seems called for, it is certainly useful to have a series of possible explicata to choose from. But the real work is to be done in showing how one pair of explicata clears up the problem. Carnap’s response to the paradox of analysis is to offer explications rather than explication itself. Ironically, the solution is there in Carnap’s very practice, but it lies in the process, not the results. For if we simply offer the results, then the paradox of analysis will re-emerge with respect to them. The distinction that needs to be drawn is not so much between different senses of ‘sense’, but between our understanding before and after the analysis. The relevant expressions do not have a range of timeless ‘meanings’, two of which simply require specification to solve the paradox. If ‘sense’ encapsulates what we understand, then this changes in the process of analysis, and it is the process that needs clarification. Carnap’s distinctions may help us think about the process, but they are not the solution to the paradox itself.
If someone has only a vague idea of what ‘brother’ means, then being told that a brother is a male sibling may be informative (though ‘sibling’ may require even more explanation), but it is informative by crystallising the sense of ‘brother’. It may also be informative by making clear the logical relations between the concepts brother, male and sibling, but this too helps crystallise the relevant senses for us (so that we can use the terms more accurately or spontaneously, for example). Once the senses are crystallised, then the sentence is no longer informative. If we still regard it as so, then it is because we imagine a process by which someone comes to learn something; and it is this process that underlies the informativeness. Similarly, for someone who is fluent in both English and German, (B3) will be uninformative, and if we regard it as informative, it is because we imagine an English-speaker, say, learning German.
	Of course, examples such as (B3) and (B4) would not normally count as analyses. We do in general demand, as Frege, Husserl, Langford and Carnap all recognised, that the analysans be more ‘articulate’. Carnap provides useful conceptual tools to understand such articulation, and often illustrates their use in philosophical work himself. But when he does so, he tends to overlook the constraints imposed by our ordinary understanding, even when they implicitly operate in his own thought, as his employment of quasi-analysis in the Aufbau shows. What is philosophically important is the process of explication rather than simply its end-products. Nietzsche wrote that “All concepts in which an entire process is semiotically telescoped elude definition” (1887, 80). This is certainly true of the concept of explication. But even where definitions and analyses can helpfully be offered, they themselves should be understood as telescoping a whole process.

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Michael Beaney
Department of Philosophy, Open University, Milton Keynes, MK7 6AA, England
m.a.beaney@open.ac.uk