T HE ANALYSIS OF GEOMETRY AND CONGRUENCE IN “P HILOSOPHIE DER R AUM- Z EIT- L EHRE”

4. T HE ANALYSIS OF GEOMETRY AND CONGRUENCE IN “P HILOSOPHIE DER R AUM- Z EIT- L EHRE”

I think that the disagreement between Schlick and Reichenbach was not of an ex- clusively terminological nature. It was more related to the question of whether it is possible to understand the cognitive process by taking recourse to only two components, experience and linguistic conventions (including coordinative con-

ventions), or whether besides these two we also have to admit some presupposi- tions of a synthetic nature constitutive not only of science’s language (such as the more strictly linguistic ones) but also of the objects of knowledge.

Disregarding our judgement on this matter from the theoretical point of view, from a historical point of view we have to underline that in the years following 1922, Reichenbach changed his original position and ended up embracing the

one defended by Schlick. Even in his 1924 work Axiomatik der relativistischen Raum-Zeit-Lehre, Reichenbach adopts Schlick’s perspective and terminology: he refers to implicit and explicit definitions (impliziten and expliziten Definitionen), but instead of speaking of constitutive principles or coordination principles he

speaks of coordinative definitions [Zuordnungsdefinitionen], seen in contraposi- tion with conceptual definitions [Begriffsdefinitionen] 10 .

Moreover, he already sees the problem of the choice of the best set of defi- nitions as having “nothing to do with the truth of a theory”. He presents it in connection with “descriptive simplicity”, viewed in contrast to “inductive sim- plicity” as “a principle of probability” containing “an important assertion about

the physical world” 11 . In Axiomatik der relativistischen Raum-Zeit-Lehre he still considers the distinction between the different components (conventional and empirical) of scientific theories as one of the main tasks of epistemological analysis: some of these components, though, are no longer seen as constitutive

principles, but simply as conventions that have the value of coordinative defini- tions.

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A similar position is expressed in Philosophie der Raum-Zeit-Lehre (1928). While discussing the problem of the empirical determination of geometry, Reichenbach underlines the existence of a subjective arbitrary component in the scientific cognitive process without which – he explicitly states – objectivity cannot be attained. Now, though, he speaks of Zuordnungsdefinitionen, and these coordinative definitions are described in semantic-linguistic terms. If we change the coordinative definitions, we no longer constitute a different object. We simply give empirically equivalent descriptions – for example, different geo- metrical descriptions of the physical world – that differ only for the language in

which they are formulated 12 .

What can we say about Reichenbach’s relevant change of perspective? What prompted him to move closer and closer to Schlick’s position according to which we only have either hypotheses or conventions? Until now, I have found no in-

dicative references in either Reichenbach’s works or in the archive material 13 . So, even allowing that future studies might bring to light new documents, it

seems to me that the only possible conclusion here is that neither Schlick, Rei- chenbach or Carnap felt the need to say even a few words about Reichenbach’s change of perspective.

Personally, I don’t know how to interpret this silence. Is it a meaningful event or simply a twist of fate not worth any further consideration? An analysis of Reichenbach’s text, though, allows us, I think, to advance a hypothesis and

here we come to the main point of my paper: the re-evaluation of the role played by Russell’s and Wittgenstein’s ideas in the formation of what was considered the standard doctrine of Logical Empiricism, the way in which Logical Empiricism was viewed for a number of decades, and Quine’s criticism thereof

in his famous “Two Dogmas of Empiricism”. This possible answer can be explained on the basis of the fact that Reichen- bach’s argumentation about the problem of empirical determination of physical geometry, and the necessity to take recourse to a coordinative definition of con- gruence, are perfectly in tune with the ideas elaborated by the Logical Empiri- cists of the Vienna and Berlin Circles on the nature of logic and meaning. I am referring here to the ideas that more or less freely, and more or less legitimately, referred back to Russell’s philosophy of logical atomism and Wittgenstein’s

Tractatus logico-philosophicus, in other words to that type of philosophy that traditional interpretations have considered, along with Mach’s thought, to be one of the main origins of Logical Empiricism as it appeared on the philosophical

scene between the late 1920s and the early 1930s. These philosophical ideas are the following: (i) the subdivision of statements in simple (elementary, atomic) and complex, and the dependency of the value of truth of the former on specific experiences associated to them; (ii) the tauto- logical nature of some complex statements, in other words, the fact that they are devoid of any empirical-factual content; (iii) the argument expressed by proposi- tion 4.024 of the Tractatus (“To understand a sentence means to know what the case is when it is true”), understood by Logical Empiricists as stating (contrary

O N THE F ORMATION OF L OGICAL E MPIRICISM 15

to what Wittgenstein wanted to say) that understanding a statement means under- standing the conditions of its empirical verification. This formulation amounts to the verification principle, according to which the meaning of a statement is its means of empirical verification and implying that all those statements that cannot

be verified empirically have to be considered as devoid of meaning. As I have already shown 14 , both Reichenbach’s final position and its under- lying argumentation are far closer to Poincaré’s geometric conventionalism than what Reichenbach admitted himself. What is relevant for the purposes of my paper, though, is that Reichenbach’s argumentation (like that already presented by Poincaré) is explicitly posited in terms of meaning and lends itself to recon- struction taking into consideration the above-mentioned typically neo-empirical ideas. Reichenbach mentions neither Russell’s nor Wittgenstein’s names; he does not even quote the verification principle or the thesis of the tautological character – and thus empirical and factual vacuity – of certain statements.

Nevertheless, when explaining why a certain assumption (the coordinative defi- nition of congruence expressed through the elimination of universal forces) has to be seen as a definition without justifying his change of perspective with respect to the years when he considered similar assumptions as being constitutive principles analogous to Kant’s synthetic a priori principles, he uses the concept of meaning and expresses his arguments by means of verificational terms and ideas.

In Philosophie der Raum-Zeit-Lehre, in fact, the argument of the linguistic conventionality of the assumption regarding congruence is characterized by the following three fundamental aspects: (i) first of all, Reichenbach offers an analy- sis that aims at proving the absence of empirico-cognitive content (of a ‘direct’ type, as I will elaborate later) in the questions regarding the geometric descrip- tion of physical space or, alternatively, of the relation of congruence; (ii) sec- ondly, he states that these questions are devoid of any sense or meaning because they are devoid of any empirical-factual content; (iii) finally, he concludes that it is only by taking recourse to suitable conventions (the coordinative ones) that we can give them meaning. In other words, it is only by means of the implicit adop- tion of a verificational-reductionist theory of meaning that we can qualify as de-

void of any meaning a statement such as the one concerning the self-congruence or rigidity during transportation of the differentially corrected rod. Consequently,

we can consider as a stipulation concerning the fixation of meaning the conven- tion asserting the rigidity of this rod in the course of its transportation (that is the

assertion of the non-existence of universal deforming forces) 15 .

To put it briefly, in order to justify the necessity of a convention concerning congruence and to assimilate it to a definitional or semantic-linguistic stipula- tion, Reichenbach first points out the lack of empirico-cognitive content of the assertion of congruence, then qualifies this assertion as devoid of meaning and, finally, states that we can talk about it in terms of truth or falsity only relative to

a conventional assumption regarding linguistic rules. This argumentation seems to agree perfectly with a reductionist interpretation (which was establishing itself

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in those years) of the two most characteristic doctrines of Logical Empiricism: the verification principle and the linguistic theory of the a priori.

Reichenbach is in line with a reductionist formulation of the verificational theory for two reasons. First of all, because – as was to become clear after Quine’s criticism of empiricism’s two dogmas – he implicitly takes as a unit of

empirical meaning a single assertion, individually considered. In other words, Reichenbach states that the assertion of the rigidity of the differentially corrected solid rod statement is devoid of meaning on the basis of the fact that, if con- sidered individually, it does not have any specifiable empirico-factual content.

Secondly, because he implicitly considers the absence of direct empirico-factual content tantamount to the absence of any empirico-factual content.

According to the linguistic theory of the a priori, all a priori assertions, beginning with the logico-mathemathical ones, have to be considered as analyti- cal assertions, in other words as assertions whose truth value is based only on

their logical structure and the meaning of the terms used. Analytical assertions, thus, are true in all conceivable circumstances and their truth is independent of the contingent facts of the world. This is why they tell us nothing about the world and have no factual content. In the neo-positivistic interpretation, there-

fore, there is a link between the analyticity of an assertion and the fact that it is devoid of empirico-factual content.

It seems evident to me, though, that even admitting such a link, the step from the absence of empirico-factual content of the assertion of congruence, viewed by itself, to the assertion that the corresponding conventional assumption is of a semantic-linguistic sort – and so to the assertion of the analiticity or tautological nature of such an assertion once that the convention has been established – is possible only by implicitly taking for granted the non-validity of the thesis from which reductionism springs. In other words, in order to pass from one assertion to the other, we need to assume that an assertion devoid of direct empirico-

factual content cannot even have an indirect content deriving from the network of relationships that connect it to the other assertions belonging to the theoretical system of which it is a part. As we know, the very recognition of this fact would lead Hempel and Quine, in the 1950s, to recover Duhem’s holism. They put

aside any form of reductionism and defended the impossibility of formulating an empirical criterion of cognitive meaningfulness capable of making a clear distinction between a cognitively meaningful or meaningless discourse.

The fact remains that, in 1928, Reichenbach discussed the problem of geometry using the verificational and reductionist terms typical of the classical neo-empiricist conception current during the active period of the Vienna and Berlin Circles. And these very terms allow him to justify the attribution to the coordination conventions of that linguistic-semantic value Schlick had defended since the early 1920s without having a fully developed philosophical justification of his position. Therefore, it is not surprising that at a certain point Reichenbach himself gave a classical formulation of neo-empiricist criticism of Kant’s theory of synthetic a priori judgements. During the first International Conference on

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Scientific Philosophy held in Paris in 1935, he presented a paper on the problem of the a priori in which we find again his criticism of Kant, but where there is no mention of the constitutive principles and all assertions are seen as either synthetic assertions deriving from experience or analytical assertions (“Tout ce que nous savons du monde est tiré de 1’expérience, et les transformations des données empiriques son purement tautologiques, analytiques” l6 ).

5. I NTERPRETATIVE C ONSEQUENCES The path followed by Reichenbach between 1920 and 1928 (when certain ideas

matured fully) and his change of perspective can help us – I think – to charac- terize the formation process of Logical Empiricism, its development and its crisis as a result of alternative theoretical perspectives. To illustrate this better, I will refer to Howard’s, Oberdan’s and Uebel’s interpretations mentioned at the be- ginning.

Uebel seems to be perfectly right in saying that one of the essential character- istics of Schlick’s Allgemeine Erkenntnislehre was the anti-Kantian use of French Conventionalism, and that such a use was in line with the desiderata of

the most representative exponents of the first Vienna Circle (Frank, Neurath and Hahn). Here, though, we need to be more specific about two points.

First, when using the term “French Conventionalism”, we must refer mainly to Poincaré’s linguistic conventionalism. This regards both Schlick’s position

and, partly, the more clear-cut direction that prevailed within the first Vienna Circle. In Allgemeine Erkenntnislehre Schlick does not mention the names of other important French epistemologists of the same period and, more particu-

larly, he does not seem to know Duhem’s holistic conception. Frank, in his pages on the origins of Logical Empiricism and the first Vienna Circle, explicitly says that they looked at Poincaré’s conception in order to account for the subjective and abstract tracts of the scientific cognitive process in order to avoid both an old form of Kantism and a form of Machian sensism. It is certainly true that among the epistemologists mentioned there, Frank also included Duhem, but – with the exception of Neurath – Duhem, at least initially, does not seem have had as great

an influence on the development of Logical Empiricism as Poincaré 17 . Secondly, the ideas formulated by Schlick in the first edition (1918) of Allge-

meine Erkenntnislehre, if considered separately, were not such that they excluded an interpretation of the philosophical meaning of the theory of relativ-

ity that did not ascribe to Kant any merits beyond the negation of a naively empiricistic or radically sensistic conception of knowledge. As I said before,

Reichenbach’s position in Relativitätstheorie und Erkenntnis Apriori shows that Schlick’s conception of knowledge as coordination could be used to negate Kant’s theory of synthetic a priori judgements while still according a certain value to the idea of synthetic principles that, even though deprived of their apo- deictic quality, still maintained a certain degree of constitutive value. If I inter-

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pret Philosophie der Raum-Zeit-Lehre correctly, then we have to say that, in or- der to abandon this idea completely, it was necessary to adopt a general philoso- phical conception centered around two doctrines typical of Logical Empiricism

in its classic Vienna and Berlin version: the verification principle and the lin- guistic theory of the a priori.

This interpretation allows us to consider as still valid the traditional view of Logical Empiricism that has always ascribed great degree of anticipation to the ideas developed by Schlick in the first edition of Allgemeine Erkenntnislehre, without forcing us to say, as Oberdan feared, that virtually all the essential con- ceptions of Vienna and Berlin Logical Empiricism were contained in that work.

Actually, in order to arrive to these conceptions it was necessary to adopt the verification principle and the linguistic theory of logical truths neither of which had been clearly formulated in Allgemeine Erkenntnislehre.

All this is confirmed by two letters written by Schlick in 1926 and 1927 when

he was presenting the second edition of Allgemeine Erkenntnislehre. In the first one (7 March 1926) addressed to Rudolf Carnap, Schlick moves closer to the position that Carnap was elaborating and that was fully expressed in Der logische Aufbau der Welt. When communicating this evolution of his thought, he says that Carnap and himself agreed more than one might imagine on the basis of the revisions contained in the second edition (1925) of Allgemeine Erkenntnislehre: an adequate formulation of his new ideas – Schlick says – would have required him to revise his work much more exstensively. In fact, after the impact of Russell’s, Wittgenstein’s and Carnap’s ideas (Aufbau and Scheinprobleme),

he changed his position and came to the conclusions expressed in the 1932 works “Positivismus und Realismus” and Form and Content. The second letter was addressed to Cassirer and was written one year later (30 March 1927) after the publication of “Erkenntnistheorie nebst den Grenz- fragen der Logik und Denkpsychologie”, an essay where Cassirer also discusses

the main theses of the Allgemeine Erkenntnislehre 18 . Schlick responds to some of the criticism put to him by Cassirer, who in a letter dated 4 March 1927 l9 had

admitted he had overlooked the changes made in the second edition of Allgemei- ne Erkenntnislehre. In this sense, Schlick’s letter shows well the philosophical path that led him from the positions defended in that work to the ones formulated in the London lectures Form and Content (1932) where, following Russell and using the verification principle, he rejected as senseless the distinction between reality in itself and phenomenic appearence. So this letter shows very clearly the role played by Wittgenstein’s and Russell’s ideas on the development of Schlick’s thought towards the classic formulations of the Vienna Circle that he had anticipated in the essay-manifesto “Die Wende der Philosophie” (1930).

When his ‘turn’ was complete, Schlick indicated as the starting points of his new philosophy the attention given to the problems of language, the argument regarding the tautological nature of logic and the linguistic foundation of the a priori, the representative conception of language and, finally, the verification

principle which he described as “the fundamental principle of philosophizing” 20 .

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It is only in light of the importance given to these ideas that we can under- stand the process that led to the most typical formulations of neo-empiricism. In Reichenbach’s 1928 work on the philosophy of space and time, these arguments are never mentioned explicitly nor do we find any mention of their connections with the problem of geometry. Even so, the argumentation in favour of the necessity of a coordinative assumption of congruence and its linguistic-semantic value seem to indicate clearly enough that it was only by means of an implicit reference to the verification principle and the tautological nature of the a priori that it was possible to abandon the idea of the constitutive a priori, as formulated in his 1920 work on the theory of relativity.

Whether this was a theoretically valid move or not, whether this involved the emergence of a tension with Einstein’s perspective and, finally, whether this in some ways concealed a vision of the relationship between theory and experience

less defensible than Cassirer’s, is a completely different story 21 .