1 Introduction
Rudolf Carnapâs first major work, Der logische Aufbau der Welt (The Logical Structure of the World, 1928, hereafter Aufbau),1 is famous for seeking to provide reconstructions of all empirical concepts on a purely phenomenal, âmethodologically solipsistâ basis. Recent decades have seen a successful reinterpretation of what this project was undertaken for and the question of the success or failure of the reconstruction has receded into the background.2 My discussion here addresses the question whether recent re-interpretations of Carnapâs Aufbau make its methodological solipsism any less problematic than it was on the old empiricist perspective. The first reference point here is W.V.O. Quineâs well-known objection that no eliminative definitions of concepts for objects of the perceptual world had been provided, the second is Alan Richardsonâs observation that mathematical physics was simply assumed in the construction of the intersubjective world. Both findings seem to point to the failure to provide a proper phenomenalist reduction and call Carnapâs methodological solipsism into question. I investigate whether these deficits are rendered harmless by the structuralist interpretation of the Aufbau or whether methodological solipsism remains problematic, and I argue for a negative conclusion.
2 The Charge of Reductionism: from Foundationalist to Structuralist Reductionism
Once upon a time, Aufbau-related matters were thought to be simple. The Aufbau was to provide a foundationalist reduction of scientific discourse in its entirety; Carnap thought he had succeeded (one niggle apart), and nearly everybody believed him until Quine argued otherwise and Carnap conceded the point in the second edition ten years later.3 But the foundationalist story no longer holds up and the structuralist interpretation of his reconstructive efforts has to be taken account of.4 Already early in the Aufbau such a different story is told and Carnapâs apparent endorsement of Quineâs reading in later years can be explained away.5 Yet one question appears to have remained unanswered still: how far can the replacement of the foundationalist story help in defending the Aufbau against the criticism of its reductionist failure?
Apart from demonstrating the unity of empirical science by exhibiting that all of its domains are comprehensible in one language, the aim of the Aufbau is demonstrating that âeven though the subjective origin of all knowledge lies in the contents of experiences and their connections, it is still possible [â¦] to advance to an intersubjective, objective world, which can be conceptually comprehended and which is identical for all observersâ (§2). A successful simulation
Yet the Aufbau is not shy also to announce a far-reaching reductive project. Its main business, âconstitutionâ, is defined as the reduction of a concept to more basic concepts: âBecause of the transitivity of reducibility, all objects of the constitution system are thus indirectly constituted from objects of the first levelâ (§2) Therein, of course, lies the motivation for Quineâs reading: why would one want to pursue reductionism if not for foundationalist purposes? The answer is easy, however, once the Aufbauâs radical structuralism is recognized. Reduction to one type of basic element (âelementary experiencesâ, the âobjects at first levelâ) and one basic relation (âremembered similarityâ) would allow the demonstration that âscientific statements speak only of forms without stating what the elements and the relations of these forms areâ (§12), for it would eliminate all terminology as shorthand in favour of the basic relation between basic elements: on analysis, all scientific statements translate into myriad iterations of the basic relation and logical permutations thereof and so are wholly structuralized. All objects of science can be given a âdefinite description through pure structure statementsâ (§15) so that âeach scientific statement can in principle be so transformed that it is nothing but a structure statementâ (§16).
By why should one want such radical structuralism-cum-reductionism? Answer: âthis transformation is not only possible, it is imperative. For science wants to speak about what is objective, and whatever does not belong to the structure but to the material [â¦] is, in the final analysis, subjectiveâ (§16). (Note the radical nature of Carnapâs structuralism: no non-structural elements must remain if objectivity is to be ensured.) So reductionism is in the program even without foundationalism. It is required, for Carnap planned to build his account of objectivity on it (to mark this important difference, letâs call it âstructuralist reductionismâ as opposed to the more common empiricist âfoundationalist reductionismâ which was traditionally ascribed to the Aufbau).
Yet can Carnap achieve what this structuralist program promises? There is not only the niggle that he noted himself but did not manage to dispose of satisfactorily, the foundedness issue to do with whether the Aufbau did, after all, extrude all reference to content even at the very basis of the system, the basic
Put thus blandly, the suspicion is false. The Aufbau does not only employ explicit definitions, but also so-called definitions in use and Carnap stated that âthe ascension to a new constructional level takes place always through a definition in useâ (§40). The latter do not provide a term-for-term replacement but replace sentences (propositional functions) containing the term to be defined with sentences that do not contain it, but which remain extensionally equivalent. As Ka Ho Lam has recently clarified, Quineâs âis atâ objection concerns both types of definition. Carnap himself employed âexplicit definitionâ ambiguously and should have conceded rather that no ââexplicit definition in the wide senseâ (as contra âimplicit definitionâ)â is provided at §126 (this includes both explicit and in-use definitions) (2018, 11). But this does not get Carnap off the hook of Quineâs objection, for it remains crucial that no eliminative translation for âis atâ is offered. All that the canons supplied allow for are âmultiple legitimate but conflicting translationsâ of phenomenal data into the perceptual world: they all balance the various factors to be considered to some extent but need not even preserve extensional equivalence between themselves, as Lam has also pointed out (2018, 14).
So the construction of our empirical concepts that the Aufbau provides for does not provide the required determinacy. This is problematic also in light of
3 Reductionism Redux: Atomistic and Holistic Structuralism
Since the stream of experience is different for each person, how can there be even one statement of science which is objective in this sense (i.e., which holds for every individual, even though he starts from his own individual stream of experience)? The solution to this problem lies in the fact that, even though the material of the individual streams of experience is completely different, or rather altogether incomparable, since a comparison of two sensations or two feelings of different subjects, as far as their immediately given qualities are concerned, is absurd, certain structural properties are analogous for all streams of experience.
§66, orig. emphasis
It was such structural analogies that Carnap set out to build his reconceptualization of objectivity on, but the construction was not a simple matter.
Richardsonâs analysis of the procedure of âintersubjectivizationâ, by which the intersubjective world is constituted, focuses on what Carnap himself stressed, namely that a structural analogy does indeed hold between my autopsychological objects and the autopsychological objects I have reconstructed for another person at lower levels, but that âhigher up the constitutional hierarchyâ, in the constitution of physical objects, these structural analogies break down because the objects constituted by me and by me for
Intersubjective correspondence makes up for the lack of structurally fully analogous constitution formulas by postulating that the objects constituted by âusâ (i.e. by me and others reconstructed by me) are embedded in an identical space-time structure and are therefore brought into congruence. In consequence, objects that are constituted (partly) disanalogously can correspond intersubjectively, for they ârepresent (in realistic language) âthe sameâ object, once as it is recognized by me and the other time as it is (so far as I know) recognized by M [the other]â (§146, insertion added). This holds, Carnap stated, for all types of objects. Richardson summarizes: âUtilizing the mathematical structure and the law-governed nature of the world of physics, mapping from one personâs world of physics onto anotherâs can be done in a univocal way. The class formed from such objects is the intersubjective object that is available to all agents and that grounds the possibility of intersubjective judgmentâ (1998, 86).
Note then what Carnap required and indeed called on for his solution to how the objectivity of science is to be accounted for by means of the constitution of the intersubjective world: mathematical physics. Richardson again: âCarnap clearly indicates that it is the extra, superadded formal structure of mathematically expressed physical concepts that is crucial for the intersubjectivity of knowledgeâ (1998, 89). Note particularly that it was mathematical physics that Carnap here imported, not just mathematics which, given some form of logicism, he counted as presupposed, like logic, by his reconstructive enterprise. Mathematical physics, however, was not constituted from a personâs experience but was invoked deus ex machina, taken off the shelf ready-made. Should the verdict be that Carnapâs Aufbau doubles up on problems, now also failing the demands of structuralist reduction on account of his wholesale importation of mathematical physics into his process of intersubjectivization?
It is no excuse that already in the earlier step of the constitution of the world of physics from the perceptual world, Carnap introduced wholesale the system of mathematical physics (§136) and it was this move that his intersubjectivization
Consider now again the indeterminacy left by the non-reductive constitution of the perceptual world at §126 which allowed for different and extensionally non-equivalent ways of satisfying general principles concerning potentially conflicting desiderata. This indeterminacy was gradually reduced by integrating the data of other sense modalities and revising and completing assignments of sense data to world points so as to arrive at the constitution of perceptual things (§134). It was overcome still further at the level of the constitution of the physical world with its mathematically expressed laws, though even here a choice between âdifferent systems of physicsâ with incompatible physical magnitudes was ultimately required though the world points of the
Yet Carnapâs appeals to physical theory at §§136 and 146 violate the program of structuralist reductionism. Now on what grounds can we take Carnapâs commitment to such a program for granted? As weâve seen, Carnap was aware of the reductive shortcomings of the constructions he provided. Should we perhaps think of the process of constitution in §§136 and 146 as involving something like conventional postulation â as Carnap later darkly suggested had been his procedure in the Aufbau without âclearly realizing itâ? The procedure he employed was, he wrote, ârelated to the method of introducing concepts through postulatesâ (1961/1967, viii) which he employed in (1956). However, even though Carnapâs retrospective remark referred to his procedure at §126, not to §§136 and 146, it misapplies across the board: if âthe method of introducing concepts through postulatesâ means the introduction of theoretical concepts either by correspondence rules or implicit definition, then Carnap misidentified the procedure used at §§126, 136 and 146 â or at least left utterly unclear how the method applies.7
Yet in any case, what are the prospects for a radical rethink? Rather than think of Carnapâs moves as violating his own program, how about expanding horizons and thinking of them as bringing into play a second, different mode of constitution? (To be sure, this would need far more explanation than readers of the Aufbau have been given). So far our interpretation of the Aufbau moved from foundationalism to reductive structuralism, affording a reinterpretation of the reductionism so prominent in play. Should we perhaps move towards dropping any reference to reductionism as a primary characteristic feature, focus solely on structuralism and allow Carnap both reductive and holistic versions of it to pursue his reconstructive goal?
4 An Aufbau for All Seasons? Post-Reductionism Considered
Clearly then, structuralist reductionism is not the only game in Carnapâs Aufbau: there is also the nonreductive constitution of the world of perceptual things and the holism of mathematical structures. Both structuralist reductionism and the holism of mathematical-physical structures play essential roles in accounting for the objectivity of science. This invites an alternative interpretation of Carnapâs undertaking as seeking to overcome the opposition of reduction and systemic holism. Letâs consider whether one such interpretation can resolve the Aufbau problems which exclusively reductionist structuralism still left us with.
Suppose that the Aufbau project was as described above, to provide a logico-linguistic exemplification of the unity of science thesis and to provide an account of objectivity â albeit, and thatâs the difference, in a two-part process of reconstruction. The objectivity of scientific knowledge is owed to the structural nature of its medium, but âstructureâ does its constitutive work differently at different levels of the constitution system: once by reduction, once by systemic holism.8
The first part, the constitution of objects at the lower levels proceeds wholly according to the official plan by explicit definitions and definitions in use. At this still subjective level of pure experience, it was a reductive analysis that was employed to cut through phenomenological vagueness and instability to fix the determinacy of content types to establish constancy across temporal periods.
So rather than fail the Aufbau for its frustrated reductionist ambition, this proposal considers its reconstructive project, to be structuralist in approach but having two components: an atomistc and a holistic one. The former provides a reductive constitutional analysis of the experiential given to regiment pure subjectivity and the latter integrates the objects so constituted ultimately in mathematical structures whose adoption is guided by holistic considerations. Reductively regimented and linked up by postulation to certain nodes in an abstract structure, the subjective thus becomes a cornerstone of objectivity.9
A radical reinterpretation of the Aufbau project that promises to iron out the tensions, which we saw afflicting it, emerges here. It pre-empts the antireductionist criticism by foreswearing reductionist ambitions precisely where they are problematic. On it no foundationalist agenda could possibly make sense: not only is the Aufbauâs remaining reductionism differently motivated, but foundationalismâs whole raison dâêtre is contradicted by the holistic postulation manoeuvres needed to constitute the external worlds. Moreover, the holistic considerations involved in ascribing colours to space-time points in
Yet before we can celebrate the new proposal, we must consider its plausibility as an interpretation of the Aufbau. Is it the case that with a two-track structuralist reconstruction in place the Aufbau better withstands standard criticisms and also can weather new ones? The first thing to note here is that while advocates of the proposal would presumably start by noting again that, according to it, Carnap did not attempt what critics like Quine hold to be impossible, namely reduce external world discourse, ordinary or scientific, to talk of private sense data or unanalysed whole phenomenal experiences, they would have to give this line of defence an unusual, perhaps unexpected twist. So far it may have sounded as if the new defence against the charge that no reductions of physical object to phenomenal discourse were achieved conceded that such a reduction is not after all possible and must be replaced with conventionalist strategems akin to those in physical science. If that were the case, however, the methodological solipsism that informed the way the constitution system of the Aufbau was developed would be compromised. For this reason, the defence of the two-track structuralist reading of the Aufbau cannot take its talk of âperceptual worldâ and âworld of physicsâ at face value â on pain of failing to offer a reading of what makes Carnapâs Aufbau distinctive. To have neither effected nor attempted a phenomenalist reduction would mean the abandonment of methodological solipsism professed there â unless a radical correction of our ordinary understanding of words âperceptual worldâ and âworld of physicsâ in the Aufbau were offered. Indeed, it is precisely this latter path that advocates of the two-track structuralist reading must take, since there is, apart from the alleged failures, no indication in the Aufbau that Carnap was not fully committed to the application of methodological solipsism as reflecting not only the epistemic order of objects but also as encompassing the entire domain of empirical discourse.10
In consequence the proposed reading of the Aufbau faces a new challenge. The telling objection is not that his Aufbau refers to unreduced physical objects â it does not, for the reasons just rehearsed â but that on this two-track structuralist reading the Aufbau makes substantive use of an empirical theory that presupposes the existence of objects which, as noted, it cannot reconstruct on its own terms. So even though the nomological framework of mathematical physics into which the autopsychological objects are projected was only used for purposes of simulating cognition of the physical and intersubjective worlds, it remains the case that such simulations proceed with illegitimate means. To see this, we must stress that the reliance on physical theory here is of an entirely different order from Carnapâs procedure elsewhere in the Aufbau of letting mature science guide oneâs choice between constitutive formulae for autopsychological objects (§122): here the reliance of the framework of mathematical physics is itself (partly) constitutive of the domain being reconstructed. What makes this reliance troublesome is that the methodologically solipsist project of rational reconstruction must reject the categorical assumptions made by the physical theory which it relies on because it is unable to constitute their equivalents by its own resources. The very idea of object transcendence that the methodologically solipsist rational reconstruction must discount is essential to the physical theories the descriptive and explanatory capacity of which the reconstruction claims to simulate.
Might it be countered here that this objection is void because the methodologically solipsist subject need not know the truth or empirical adequacy of the physical theory relied upon, that all that is required is that it be true or empirically adequate? I donât think so. There is no need to bring subjects and their knowledge into the discussion at all â âThe given does not have a subjectâ (§65) â and without it talk of merely externalist conditions having to be justified seems redundant. Moreover, the ambition was to reconstruct all scientific concepts on the exclusive basis of autopsychological, phenomenal objects and relations obtaining between them. So even if the reconstruction were to be psychologised, an appeal to an externalist condition requiring conceptual resources not reconstructable in terms of phenomenal objects and relations obtaining between them would be illegitimate in light of the reconstructionâs own methodological demands.
It is difficult then to escape the conclusion that appeal to mathematical physics is incompatible with the aim of upholding methodological solipsism. The envisaged procedure amounts to the abandonment of the Aufbauâs claim that a methodologically solipsist base is sufficient for the reconstruction of
5 Hope against Reason? The Reductionist Ambition Excused
A defender of Carnapâs Aufbau project may at this juncture drop the demand for a radical anti-reductionist reinterpretation. This defender will take Carnap at his word and heed his admission âthat our kind of construction of physical points and of the physical space is by no means a fully satisfactory solutionâ (§124). In defence of the Aufbau project as a structuralist reductive one â which, we just saw, is required for the methodologically solipsist case to carry â it will now be argued that Carnap was merely âmaking do,â and that his menu of principles for assigning colours to world points was merely a placeholder, that it was not meant to replace forever the provision of definitions allowing the elimination of terms for our sentences about physical entities in favour of terms for our sentences about methodologically constructed objects. What briefly looked like a bold overcoming of reductionism is but a temporary fix, a holding operation until the real constitutional definition comes along. This Aufbau is, as it were, self-consciously incomplete.
The validity of this defence appears to me to be as questionable as that of the two-step structuralist reinterpretation. Of course, there is no denying that Carnap saw himself as engaged in a holding operation in §126. Yet this fact cannot do more than save his reputation as earnest investigator, it cannot save his project. To consider §§126, 136, and 146 holding operations, one must hold out hope for a successful or at least more satisfactory outcome than what the Aufbau achieved. What could have Carnap been reasonably hoping for as a solution to the reductive failures so far and why was he mistaken?
§95, insertion added
In the following outline we shall give only the construction of the lower levels in [the symbolic language of logistics]. The reason for this does not lie in the fact that the objects of higher type offer particular difficulties of expression for this language, but in the fact that the problem of constructing the higher objects has itself not been solved with precision and that these constructions therefore can be given only in bold outline. As soon as the content of the construction of any object is precisely known, there are no difficulties in the way of a logistical formulation.
This is naturally read as indicating that Carnap âremained hopefulâ that the formulation of constitutional definitions of the objects of higher type âcan eventually be accomplishedâ (Lam 2018, 17). Yet on closer inspection Carnap here claims only that he is confident that the language of symbolic logic can deal with any type of content one might wish to formulate â once we know what we want to say. But the problem is precisely that we have no idea how such a constitutional definition of physical objects on a methodologically solipsist basis would go. So it is difficult to see reasons for Carnapâs undeniable hope in this remark. Elsewhere the suggestion is that the difficulties were due to the demand that his project be fully consistent with the results of science. âThese shortcomings were not so much due to difficulties which arise from some of the unsolved logical problems; rather, they arose from the difficulties and as yet unresolved problems in the individual empirical sciencesâ (§156). But this also does not offer an adequate response to the question at issue in §126. What empirical theory might provide us with a phenomenalist reduction formula for physical objects?
At the time Carnap believed that while he had as yet been unable to provide precise definitions of physical objects in phenomenal terms, he had good reason to believe that their in-principle definability in these terms was established on logical grounds. To be sure, Carnap himself was less than fully explicit about this in the Aufbau and even the critical discussion has only caught up with the facts of the case relatively recently. Help is at hand from Thomas Rickettsâ investigation of Carnapâs âconfidenceâ that âthe concepts which figure in our knowledge of the perceptual and physical worlds are explicitly definable by the application of logic to sensory conceptsâ (2010, p. 312). Carnapâs underlying idea appears to have been that of treating physical concepts as theoretical in relation to phenomenal ones and conceiving of the former as definable
Until Gödel showed otherwise, Carnap believed that, not only in first- but also in second-order logic, the categoricity of an axiom system (having only models that are isomorphic) entailed the decidability of all of its theorems (see Awodey and Carus 2001). Since a consistent set of axioms determines a second-order concept (namely the property of satisfying the conditions laid down by the axioms) and since decidability entails definability, Carnap concluded that definitions of this second-order concept in the first-order terms employed in the axioms became available in principle. It was on these supposedly purely logical grounds that Carnapâs confidence was based that the perceptual world and the world of physics can in principle be defined in phenomenal terms (given that the empirical and mathematical conditions imposed on the constitution of the perceptual and physical worlds are consistent).16 Yet this definability in principle comes to nought once it is realized that categoricity does not entail decidability for second-order concepts. Discovery
Rickettsâ analysis explains both why at the time Carnap held out hope for the definability of physical concepts by phenomenal ones and why that hope is forlorn after all. It further builds the case against taking the Aufbau as actually developed as a reasonable holding operation. The inadequacy of the reduction effected was no news to Carnap, we saw, but now we know better than to share his hope for a better solution. While Rickettsâ analysis does not prove in full generality that a phenomenalist reduction is logically impossible, it grounds inductive confidence that none will be found. For we may glean from it also that Carnap himself had no idea just how such a reduction would go in concrete terms: he tied his reductionist flag to very general abstract reasoning that turned out to be deeply flawed. Note also that Carnap never brought the reductive program closer to completion, nor has anybody else.
6 Conclusion
The success of Carnapâs Aufbau project demands a methodologically solipsist, phenomenalist reduction whether it is given a foundationalist or a structuralist interpretation. Yet such a reduction was not forthcoming, neither in the case of the constitution of the perceptual world nor in that of the case of the intersubjective world: ordinary physical object concepts are left unreduced by the former and the latter relies on mathematical physics. Carnap was aware of the insufficiency of his provision (at least in the former case), but held out hope that the reduction could be completed, wrongly believing himself to be in possession of an in-principle metalogical proof of its possibility. Since his methodological solipsism blocks all non-reductionist strategies and since the Aufbau also cannot be regarded as a successful holding operation, its reductive failure remains unredeemed.
Note again that it is Carnapâs Aufbau I am concerned with â and the very version of a constitution system of concepts elaborated there (not the versions he could have but did not elaborate). That recent attempts to revive something like Carnapâs project broaden his base considerably in order to retain a chance of success would seem to prove my point. Hannes Leitgebâs Aufbau in (2011), which comes closest to Carnapâs own while claiming success by contemporary standards, employs experiential tropes (property instances) in place of whole experiences as elements of the system, employs two basic non-formal relations between them in place of the one basic relation of remembered similarity
Carnapâs Aufbau has many virtues, but its strategy of methodologically solipsist simulation of human cognition does not appear to be one of them. The Aufbauâs value lies in having asked what allows for objective knowledge, given a subjective starting point in subjective experience, and in the logical ingenuity displayed in developing a structuralist answer â but not in so far as that answer built on his assumption about the epistemic order of the objects of human cognition. Still, some failures in philosophy are far more instructive than most successes: that of the Aufbauâs methodological solipsism would appear to be one of the most spectacular and deep ones.
References to the Aufbau are by paragraph; all references solely by paragraph number are to this work.
This is not to deny that alternative attempts at broadly Aufbau-style reconstructions have been undertaken that seek to avoid standard criticisms. My concern here lies with Carnapâs original. For some pertinent comparative remarks see section 6 below.
For the locus classicus of both the criticism and the traditional reading, see Quine (1951) and (1969). For Carnapâs concession see his (1961). I neglect Goodmanâs criticism (1951) which does not engage methodological solipsism and the phenomenalist reduction as such (but only the constitution of phenomenal objects) and refer readers to the discussion in Richardson (1998, Ch. 2); for repairs to Goodman-type problems see also Mormann (1994) and (2009) and Leitgeb (2011, §§4 and 6â7).
For authoritative statements of the new structuralist reading see Friedman (1987) and (1992) and Richardson (1998). It is endorsed with qualifications also in Pincock (2005) and Uebel (2007, Ch. 2).
In the mid '50s Carnap referred to the Aufbau in foundationalist terms (1963, p. 50). Friedman (1992/1999, Pt. iv) suggests that these puzzling passages be read as reporting how the Aufbau was (initially) understood in the Vienna Circle, especially by members with a Machian background. Another interpretation has it that Carnap himself did come to see the Aufbau that way ca. 1929/30, influenced by the psychologistic interpretation of the Tractatus then shared in the Circle and seemingly encouraged by its author. But this discrepancy need not be decided now: what matters is the agreement that foundationalism cannot be held to have been the mover of the Aufbau itself.
What critics consider the biggest problem of the Aufbau tends to reflect the interpretation of they prefer. Given his structuralist reading, Friedman (1987) drew attention to the foundedness problem at §§154â156, replacing Quineâs exclusive focus in (1951, 1969) on the problem of the constitution of the perceptual world at §126. For an important new take on the foundedness problem see MacBride (2021).
Did Carnap think of the lists of desiderata as approximating implicit definitions informally? Both Richardson (2016, p. 7) and Lam (2018, p. 21) find it difficult to make sense of Carnapâs retrospective remark. Ricketts notes that it âdoes not fit the text of the Aufbauâ (2010, p. 324), but rather relates to the longer-term development of Carnapâs views of theoretical terms. Leitgeb suggests that the issue at §126 could be solved by Ramseyfication and points out (2011, p. 296) that already in the Aufbau Carnap toyed with the idea â albeit, it must be noted, only with regard to the foundedness problem at §155.
It may be noted that, put in such broad two-step terms, the rescue effort envisaged here parallels Leitgebâs ânewâ Aufbau (2011) which also switches to a non-reductive strategy for the constitution of perceptual world and higher, but the similarity stops at this broad outline.
Carnap here followed Ernst Cassirerâs lead who conceived of mathematical physics as purely structural already in Substance and Function (1910), which is referred to repeatedly in the Aufbau (unlike Russellâs Analysis of Matter [1927] which was added to its bibliography but not yet âtaken account ofâ in the text [1928/1967, 347]).
Lest my talk of âcommitmentâ here and in similar contexts later be misunderstood, let me state that it refers to the reconstructive methodology professed in the Aufbau and is not to be understood as suggesting that Carnap believed the autopsychological language to be the correct one ontologically. Carnap chose the autopsychological basis for his construction system precisely because he took it to reflect the rational epistemic order of human cognition (§§54 and 64) and even considered the autopsychological domain âthe natural starting point in the epistemic order of objectsâ (§66).
It may be wondered how it is possible for me both to speak of the Aufbau providing a thought-experimental simulation of human cognition and to take Carnap as characterising âtheâ epistemic order of cognition. The answer is that Carnap distinguished âthe actual order of cognitionâ (§54) from the rational logical structure that underlies knowledge claims actually made and that the Aufbau reconstructed. The simulation the Aufbau offered was precisely that of reconstructing knowledge claims in a methodologically solipsist manner.
This was no stray comment. Concerning the domain of the heteropsychological as a whole, he noted that âthe entire experience sequence of the other person consists of nothing but a rearrangement of my own experiences and their constituentsâ (§140, orig. emphasis; cf. §§145, 147 and 160).
Ricketts reminds us with reference to Physikalische Begriffsbildung (1926, p. 51â52) that Carnap thought of the physical world so reconstructed as âa class of 14-tuplesâ consisting of the space-time coordinates and ten further types of physical magnitude (2010, p. 318).
With this Carnap may be seen to have taken a leaf out of Frege and Russellâs book who defined a natural number n as the collection of sets with n numbers.
To be sure, Carnap at the time had not yet recognized it as a âmetalogicalâ argument as he had not yet recognized the language/metalanguage distinction. The, at the time unpublished, work is Carnap (2000).
As Ricketts puts it: Carnap âassumes the consistency of the mathematical and empirical conditions that extant knowledge imposes on the constitution of the physical world, and so assumes the existence of a class of 14-tuples satisfying these conditions. This existence claim is expressible by a higher-order existential generalization inside the constitution system. Moreover, I maintain that Carnap believes that any true existential generalization has true instances expressible in the constitution system. A definition of a class of 14-tuples satisfying all the conditions on the physical world can be extracted from any such instance. Of course, we may not on the basis of the existential generalization actually formulate a definition that constitutes the physical world; but the definability of the class is all that Carnap claims in the Aufbau. The constitution of the perceptual world, the assignment of colours to locations, can be treated similarlyâ (2010, pp. 322â323, orig. emphasis).
Acknowledgments
I wish to thank André Carus, Fraser MacBride, Paul Roth and the editors of the present volume for helpful warnings and critical comments on earlier drafts that were not always heeded.
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