# Elisabeth Schuhmann (ed.), Review of Edmund Husserl, Alte und Neue Logik: Vorlesungen 1908/09

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DOI: 10.1007/s10743-007-9033-z

- Cite this article as:
- Rosado Haddock, G.E. Husserl Stud (2008) 24: 141. doi:10.1007/s10743-007-9033-z

In recent years several volumes of Husserl’s lecture notes and courses from the years before the publication of his *Ideen zu einer reinen Phänomenologie und einer phänomenologischen Philosophie* (Hua III) in 1913 have been published under the excellent editorship of Elisabeth Schuhmann, who, together with her husband, the late Karl Schuhmann have made invaluable contributions to the better understanding of Husserl’s views. The present book, namely, Husserl’s course on logic of 1908–09 is especially important, since it belongs to the first years of the transcendental phenomenological period, inaugurated by Husserl’s 1907 lectures under the title *Die Idee der Phänomenolgie* (Hua II). Thus, as happens with his already published course of 1907–1908, *Einleitung in die Logik und Erkenntnistheorie* (Hua XXIV), it can serve to assess the impact, if any, of Husserl’s transcendental turn in his views on logic and mathematics. In fact, both books show very clearly, as do his *Logik und allgemeine Wissenschaftstheorie* (Hua XXX), based on later lectures and manuscripts, and his *Formale und transzendentale Logik* of 1929 (Hua XVII) that Husserl’s views on logic and mathematics during the transcendental phenomenological period remain essentially the same as those of the first volume of *Logische Untersuchungen* (Hua XVIII) first published in 1900–1901. There are, of course, a pair of passages that seem to be distinctive of the transcendental phenomenological period, for example, on pp. 175–176, where Husserl distinguishes between a more restricted and a wider notion of sense, which includes, besides the sense in the strict usage of that term, also its mode of apprehension as really existing or as merely given without any postulation of reality. Here both the notion of suspension of judgement and the distinction between the full “noema” and its nucleus are present.

Indeed, Husserl’s logic course of 1908–1909 discusses many of the issues already considered in his *opus magnum*, especially in its first volume and in the first, third and fourth “Logical Investigations” of the second volume (Hua XIX). There is, however, a change of emphasis, as well as some important reflections not paralleled in *Logische Untersuchungen*. The change of emphasis consists basically in the fact that whereas in his *opus magnum* some 250 pages are concerned with the most thorough, well balanced and compelling refutation of psychologism ever made, discussing his views on logic and mathematics mostly in Chapter XI of the *Prolegomena* and introducing his definitions of analytic laws and necessities, and related concepts very briefly in the Third Logical Investigation, in the lecture course the situation is almost exactly the opposite. Most probably, Husserl is presupposing that it is unnecessary to present the refutation of psychologism in a detailed fashion (see, however, for example, pp. 13f., 32 and 277) and opts to concentrate on issues more lightly discussed in his *opus magnum*. However, for readers familiar with *Formale und transzendentale Logik*, *Einleitung in die Logik und Erkenntnistheorie* and *Logik und allgemeine Wissenschaftstheorie* the discussion of his views on logic and mathematics in the book that concerns us does not add much. Another related issue discussed here in more detail than in *Logische Untersuchungen*, and which received its definitive treatment in *Formale und transzendentale Logik* is that of form and matter at the propositional and, especially, subpropositional level (see, for example, the extensive discussion on pp. 66–67 and 72–82). Of course, issues like those of the ideality of meanings (see, for example, pp. 20 and 45–46), the semantic distinction between sense and referent (or meaning and objectuality), obtained almost simultaneously and independently from each other by Husserl and Frege around 1890 (see, for example, pp. 43, 45–46, 49–50, 222–223), meaning categories and laws that govern the formation of statements in contrast to the laws of logic proper, namely, those concerned with derivability and the avoidance of formal contradiction (see, for example, pp. 48–51, 54, 61–63, 224, 243 and 251–253), and the distinction between logic as theory of the proposition, based on the meaning categories, and mathematics as formal ontology (see, for example, pp. 249 and 252–253) are also discussed in the logic lectures. Incidentally, and somewhat ironically, on p. 249 Husserl stresses that he was the first to acknowledge the existence of a proto-logical region of the forms of meanings, the region that is concerned with the distinction between sense and nonsense and forms for Husserl the most basic part of logic. But up to the present date, most logicians ignore the fact that this nowadays generally accepted level of the rules of formation of a logical language originates in Husserl, not in his student Carnap, who took the idea from the former but never acknowledged it.^{1} Of not negligible importance for scholars interested in the relation between Husserl and analytic philosophy is a passage on p. 3 of the logic lectures, in which he states that philosophical logic, as he conceives it, is the first or most basic philosophical discipline, and he goes on to call it “first philosophy in the strictest and most appropriate sense” of the word. Moreover, he conceives his task in a not dissimilar fashion to that of analytic philosophers when he asserts on p. 8 that he will proceed in a purely analytic way, and latter adds on p. 40 that his way of proceeding, being analytic, goes from the composite and nearer to our eyes to the simple.

Indeed, in this review I will concentrate on a few issues that need to be emphasized in order to better understand Husserl’s relation to so-called analytic philosophy. First of all, it should be pointed out that in the logic lectures of 1908–09 Husserl is not content with general considerations on logical issues, but discusses specific forms of propositions, namely, conjunctions, disjunctions and conditionals, as well as rules of inference, for example, *Modus Ponens* and *Modus Tollens*—see p. 29–, as well as conjunction elimination—see p. 254—and three other rules of inference on pp. 255–257, the distinction between material and formal implication—see, for example, pp. 207 and 215–, formalization—see, for example, pp. 30–31, 88 and 213–, and the relation between logical laws and rules of inference—see, for example, p. 253, where he stresses that not all logical laws correspond to a rule of inference. Moreover, Husserl not only mentions, as he already did in *Logische Untersuchungen*, that logic should be extended to include an objective theory of probability—see p. 230–, but also stresses that it should be extended to include the concepts of possibility and necessity, that is, that it should be extended to a modal logic—see pp. 230–232. Indeed, on the issue of the relevance of modal notions for logic—as occurs with the relation between logic and mathematics—Husserl’s views seem more in touch than Frege’s with more recent developments. Furthermore, the problem of mathematical existence is also touched—see, for example, p. 231–, as is the problem of axiomatisation—see p. 276. Finally, the extremely important semantic distinction between state of affairs (Sachverhalt) and situation of affairs (Sachlage), barely made in the Sixth Logical Investigation, is clearly made—see p. 273.

The last point brings us to one of the two issues that I would like to discuss here in more detail. In 1906 Husserl and Frege interchanged letters for the second time, having already done it in 1891.^{2} Regrettably, almost none of Husserl’s letters to Frege—and certainly none of 1906—survived the Second World War. Frege’s letters to Husserl survived and, thus, up to now scholars have had access only to one of the two parties involved in the discussion. Now, in Frege’s letters to Husserl of 1906 he argued that sameness of sense should be identified with logical equivalence. Fregean scholars—with the exception of the present author—seem not to have noticed the incongruity between such a thesis of Frege and his assertions on sense both in “Über Sinn und Bedeutung”^{3} and in *Grundgesetze der Arithmetik*.^{4} In this last work he asserts that the expressions “2 + 2” and “2^{2}” express different senses and, thus, “2 + 2 = 4” and “2^{2} = 4” also have different senses, that is, express different thoughts. Nonetheless, they are mathematically equivalent and, in virtue of Frege’s logicist thesis, also logically equivalent. That conclusion clearly contradicts Frege’s assertion in the letters to Husserl that logical equivalence coincides with sameness of sense. In fact, as I have argued more than once,^{5} Frege’s assertion in the letters to Husserl is the result of a confusion of Frege between his official notion of sense and his old notion of conceptual content of *Begriffsschrift*.^{6} In the logic lectures of 1908–09 Husserl answers Frege—or most surely simply elaborates what he replied to Frege in the missing letters. Let us now see what Husserl answered.

*Begriffsschrift*, while at the same time stressing that logical equivalence does not coincide with sameness of sense. Husserl says p. 272):

In English the above passage reads:Also mit Beziehung auf denselben Inbegriff von Grundwahrheiten und dieselben Termini soll M aus N und N aus M folgen bzw. beweisbar sein. Natürlich brauchen dabei M und N nicht dieselben Termini zu haben.

In symbols, Husserl’s characterization can be rendered:Thus, with respect to the same collection of fundamental truths [axioms: GERH] and the same terms M ought to follow, that is, be demonstrable, from N and N from M. Of course, M and N do not need to have the same terms.

Husserl goes on (pp. 273–274) to distinguish a narrower and a broader concept of equivalence. The first one—see p. 273–, which he calls ‘specifically logical equivalence’ concerns statements with different sense but referring to the same state of affairs, and, thus, excludes the pair of inequalities ‘a > b’ and ‘b < a’. The second one, which he calls ‘content equivalence’, includes such inequalities, which are rendered—as usual in Husserl’s writings on logic—as sameness of the situation of affairs, though they have different categorial objectual content, briefly, they refer to different states of affairs.

In English the above reads:... der ganze Satz, dem sie [die gegenständliche Beziehung: GERH] angehört, erwächst als ein Bedeutungsganzes, das einen einheitlichen Sachverhalt bedeutet. Es ist aber klar, dass diese Sachbezüglichkeit der Formen eine sekundäre ist, nämlich eine solche, welche schon die Sachbezüglichkeit der Glieder voraussetzt.

This is a clear rejection of the notorious context principle with respect to the referents.... the whole sentence, to which it [the objectual reference: GERH] belongs, forms a totality of meaning, that refers to a unique state of affairs. But it is clear that this objectual reference of the forms is a secondary one, namely, one that already presupposes the objectual reference of the constituent parts.

The remaining issue that I want to comment on in this review pervades the whole lectures, though it obtains prominence in the second half. It is the problem of the analytic–synthetic distinction and the corresponding definitions. This issue was already discussed in the Third Logical Investigation, though more briefly. Nowadays that both Carnap’s definition of analyticity and that of Frege are, for different reasons, in almost complete philosophical disgrace, it seems pertinent to consider a very different sort of notion of analyticity, namely, that of Husserl, which does not have its roots in Kant, like those very different, nonetheless, of Carnap and Frege, but in Bolzano. It is impossible, however, to take into account in this review all passages of Husserl’s 1908–09 lectures on logic, in which Husserl discusses the notions of analyticity and syntheticity a priori, and the reader is simply referred to the book for a more thorough treatment.

Interestingly, Husserl does not proceed directly to a characterization of the notions of analyticity and syntheticity a priori, but considers first presumed synthetic a priori inferences and contrasts them with logical or analytic inferences. Thus, on p. 30 and elsewhere—see pp. 33, 261–262– Husserl considers presumed synthetic a priori inferences. His examples are, on the one hand, arguments based on the relation of congruence in geometry, as well as some arguments about tonalities, like the transitivity of the relation of being a lower (or deeper) tone. Those presumed arguments are, according to Husserl, not capable of complete formalization and are, thus, contrasted by Husserl on pp. 30–32 with what he calls ‘analytic–logical’ or ‘formal–logical’ arguments, which are valid in virtue only of their forms and, thus, are capable of complete formalization. Indeed, as Husserl makes it perfectly clear on pp. 244–245, for him the notions of ‘analytic’ and ‘formal’ are extensionally equivalent. In concordance with this extensional identification of the formal and the analytic, he characterizes pure concepts already on p. 233 as free from any relation to individual objectualities. Mathematical—see p. 233– and, of course, logical concepts are for Husserl pure concepts. Moreover, Husserl characterizes purely conceptual truths as apodictic laws, whereas the particularizations of those apodictic laws are apodictic necessities. This runs parallel to Husserl’s definition of analytic laws and analytic necessities in the Third Logical Investigation, but does not coincide with it. Such apodictic laws and necessities are contrasted by Husserl on p. 234 with natural laws, which contrary to the first are not true in any possible world and do not intend to be so, but just true in our physical world. Moreover, as Husserl asserts on the same page, pure geometrical laws that do not refer to the actual or physical space are also apodictically valid. Husserl stresses on p. 236 that the unrestricted generality of laws excludes any sort of existential postulation of individual objects. This, of course, brings to the fore, as Husserl stresses on p. 237, the fundamental difference between conceptual (rational) truths and factual truths, and, thus—see p. 238–, between a priori truths and a posteriori truths. As Husserl observes on p. 238, the last distinction is not logical but epistemological, since it concerns the different grounds on which truths are ultimately founded. Thus, a priori truths are for Husserl—see p., 230– ultimately founded on what he calls in his logic lectures “conceptual intuition”, a term he probably meant to include both material essential and categorial intuition. Finally, on pp. 242ff. Husserl arrives at the characterizations of analytic law and analytic necessity, as well as to their distinction. He first observes on p. 242 that analytic laws and necessities are only a (proper) part of the conceptual laws and necessities, and on p. 243 he offers examples of both analytic and presumably synthetic a priori truths. Analytic laws are laws founded exclusively on their form and are also called by Husserl ‘categorial laws’—see p. 245–, whereas analytic necessities are particularizations or individualisations of analytic laws, and could be transformed in analytic laws by replacement of their determined terms by undetermined terms (or variables). Husserl also contrasts analytic laws with synthetic a priori laws and analytic necessities with synthetic a priori necessities. In particular, the transposition of geometrical truths to particular objects, like crystals—see p. 246– are, for Husserl, synthetic a priori necessities. The same distinction is made on p. 248, whereas on pp. 246–247, Husserl sums up his distinction between analytic and synthetic truths. It is not possible to expound here those passages in more detail.

I will finish this review with some brief remarks concerning some issues related to Husserl’s assertions on the synthetic a priori. As already mentioned, in his logic lectures, Husserl not only argues for the existence of synthetic a priori laws, but also of synthetic a priori inferences. Independently of the correctness or incorrectness of that thesis and of the adequacy or inadequacy of his examples, such a thesis reminds the reader of Poincaré’s similar thesis about mathematical induction. In the case of Husserl, however, his examples are not arithmetical, since for him arithmetic was purely analytic. Indeed, the most interesting of Husserl’s examples of presumed synthetic a priori inference concerns the geometric congruence relation. My main interest here, however, is not in presumed synthetic a priori inferences, or even in the synthetic a priori per se, but in Husserl’s views on geometry. At first sight, on the basis of what has already being said, it would seem that geometrical statements not presupposing real physical space are simply synthetic a priori. However, Husserl’s views on geometry are more nuanced. Thus, under the influence of Riemann and others, Husserl stated very clearly in *Logische Untersuchungen*,^{7} that n-dimensional multiplicities, of which Euclidean and non-Euclidean spaces are singularizations, are not only a priori but also analytic. Hence, those properties of Euclidean spaces had only in virtue of being singularizations of an n-dimensional multiplicity are analytic. On the other hand, as can be seen from a letter of Husserl to Brentano of 1892 and one to Natorp of 1901—see his *Briefwechsel*—,^{8} both the Euclidean or non-Euclidean nature of physical space and the number of dimensions are for him—once again following Riemann—empirical, thus, neither analytic nor synthetic a priori. More succinctly, the particular metric of real physical space is not given a priori, but empirically. Nonetheless, when Husserl considers arguments concerning congruence as examples of synthetic a priori arguments, he is presupposing the synthetic a priori nature of the notion of congruence. Thus, Husserl’s views on space are, like those of Carnap in *Der Raum*,^{9} three-headed. There is a purely formal, analytic treatment of space, directly influenced in the case of Husserl by Riemann’s theory of manifolds. There is also the study of such properties of space, like congruence, which is non-analytic, but still a priori, thus, synthetic a priori. Finally, as soon as we consider the metric of real physical space, we enter the realm of experience. The similarity with Carnap’s trichotomy between formal space, intuitive space and physical space is, however, not complete, since for Husserl the synthetic a priori components of physical space extend far beyond the topological ones, since congruence is not a general topological notion, not even an affine notion, but already presupposes the notion of isometry, that is, of an affine transformation that preserves distance. Thus, not only affine (and projective) features, but also some general features of the metric seem to be synthetic a priori for Husserl, though the particular metric of real physical space is not.^{10}

It is pertinent to end this review with a brief comparison of Husserl’s views with those of Kant^{11} and Frege.^{12} Firstly, it is clear that not only Husserl’s notion of a mathematical synthetic a priori is much more restricted than Kant’s—since for Husserl non-geometrical mathematics was analytic—, but also his very notion of the geometrical synthetic *a priori*—though, of course, the distinction between topological, affine and metric features of space was not known to Kant. Moreover, Husserl’s geometrical synthetic a priori was more restricted than Frege’s, for whom the Euclidean structure of physical space was synthetic a priori. On the other hand, it is clear that Husserl’s notion of a synthetic (also called by him ‘material’) a priori was much wider than Kant’s or Frege’s in another important aspect, since for Husserl there were synthetic a priori statements in the foundations of any regional ontology. But that issue transcends by far the boundaries of this review.