In a passage (§56) from his 1929 Formal and Transcendental Logic, Husserl expresses frustration at a particular group of interpreters of his Logical Investigations. Fearing the specter of the historical-empiricist move that denies the objectivity of the ideal, these interpreters reject the phenomenological investigations in Volume II of the LI. This rejection is based on the critiques of psychologism that Husserl provides in Volume I. Presumably, what the interpreters found to celebrate in the LI was its insistence that logical formations—e.g. judgments, proofs, theories—are not mental events, which secured the possibility of a purely formal logic. Their disappointment with the foray into the constitutive acts correlative to the logical formations in Volume II likely persisted in light of Husserl’s subsequent publications. Around the time of the publication of Ideas I (1913), Husserl admits to having cooled to formal logical investigation, preferring instead the examination of transcendental subjectivity.
For this reason, Claire Ortiz Hill’s 2019 translation of Volume 30 of the Husserliana Series entitled Logik und Allgemeine Wissenschaftstheorie may come as a surprise to an English-speaking readership. The volume, with the English title Logic and General Theory of Science, consists of the final version of a series of lectures given by Husserl on the topic of formal logic, its bounds, fundamental formations, and its relation to the Idea of science in general. The lectures date from the Winter Semester of 1910/11 through Winter 1917/18, the same decade that saw the publication of his Ideas I and Ideas II. Given those dates, it would seem that, whatever his interest in the constitutive acts of logical formations, his interest in those objective formations themselves did continue.
The volume is divided into three sections with a series of appendices added to the main text. In Section I, Husserl is concerned with setting the bounds for formal logic. This is a preparatory step for the formal logical investigations in Section II that seek to develop systematically a theory of the forms of meaning. Section III deals with the Idea of Science, which for Husserl includes formal logic but, as he outlines, encompasses more than just formal logic. The appendices are Husserl’s notes and additions to the lectures. In what follows, I give a brief overview of each of the three sections.
Setting the Bounds of Formal Logic (Section I)
The first section is entitled “Fundamental Considerations for the Demarcation and Characterization of Formal Logic.” Husserl begins the section with a series of reflections on the understanding, which, as the activity that sets norms for both the sciences and extra-theoretical life, serves as a leading clue for the scope of logic. Rather than reflecting on the acts of understanding, those “mental activities and achievements” (§1) at work in the norm-setting, we can inquire into the norms themselves, or the forms that the various acts of understanding imprint on their content. The work of logic, Husserl suggests, is to fix these forms conceptually and systematically.
However, before that work can get underway, it is necessary to distinguish understanding as norm-setting from understanding as a mental event. Interpreting the norm-setting activity of understanding as a mental event would result in subsuming logic under psychology, the science that deals with the “inner sphere.” Note that, just as in the earlier Logical Investigations and the later Formal and Transcendental Logic, Husserl is again careful at the outset to disentangle logical investigation from psychological investigation. The major difference between psychology and logic is that, while the latter is normative, the former is not. In other words, logic strives after normative laws by which to measure if purported knowledge is actually knowledge. The origin of the norms of logic lies in, in Husserl’s own words, “the ideal essence of acts of understanding and their contents” (§4), whereas the understanding figures in psychology only as a mental event to be explained according to natural, i.e., causal laws. One of the major consequences of this distinction is that the logical norms are unconditionally binding and discoverable regardless of any reference to factual, or empirical, existence.
Anticipating the controversy of his position (he predicts that he will be pejoratively dubbed a “Scholastic” or “mystic” (§4)), Husserl retorts that the psychologizing interpretation of logic falls prey to the prevalent naturalistic prejudice in the sciences. By naturalism, Husserl understands the rejection of any sort of any non-natural, i.e., non-empirical, non-spatiotemporal, objectivity. Thus, any ideal objectivity, be it logical norms, cardinal numbers, or self-evident statements is reinterpreted psychologically. In contrast, Husserl insists on the admission that Ideas are genuine objects that merely give themselves differently (“as eternal, selfsame, as non-temporal and non-spatial, as unmoved, as unchangeable” (§8)) than spatiotemporal objects.
This difference in position on the status of Ideas proves consequential for formal-logical investigation. On the one hand, Husserl identifies the failure to recognize Ideas as the basis of a series of errors propagated by traditional logic, a point substantiated more in Section II of the volume. On the other, acknowledging the genuineness of Ideas at the outset opens up an avenue of inquiry in formal logic, namely investigating according to ideal meaning forms rather than empirical contents. To that end, Husserl notes that in these lectures he is foregoing a noetic orientation, i.e., one that takes up the cognitive and related acts constitutive of logical objectivities, for a noematic one. To clarify what he means by a noematic orientation, he points us to a series of distinctions, beginning with that between knowing and known. The former is a cognitive act while the latter leads us towards the ideal. A parallel distinction between judging and judgment (§7) and another between naive judgment as directed at the state-of-affairs and judgment as proposition and Idea (§9-10) help to clarify. Judgments as ideal objects are importantly not determinate, therfore not empirical, and yet they have ideal properties (e.g., all judgments with the form of a contradiction are false). When the idea is made into an object of reflection, it becomes the basis of norms sought in logical investigation.
As far as the demarcation of formal logic goes, the introduction of the Idea of judgment places us in the terrain of apophantics, or the logic of affirmative statements. This harkens back to Aristotle’s original demarcation of pure logic, which he called analytics. Husserl sometimes adopts this term. It is worth noting that he employs several related terms synonymously throughout the lecture, namely analytics, along with pure logic, formal logic, and the mathesis universalis (more accurately, he uses these terms to emphasize different aspects of the same science). In contrast to Aristotle, Husserl’s own demarcation of analytics is not limited to affirmative statements. It includes an underlying level of investigation into more basic forms of meaning. This level both serves as a foundation for a second level of logic and also provides some crucial conceptual distinctions that allows for its expansion. It could be said that one of the ubiquitous features of Husserl’s thinking on formal logic is its effort at expansive unity. The second level of logic, for instance, is not only concerned with the logic affirmative statement (“A is b”), but also with its modifications (e.g. “It is possible that A is b”). Further, in a series of complexifications that occur at the second-level, Husserl further expands the notion of logic to include cardinal and ordinal numbers, sets, and eventually a third level. This third level, the highest of analytics, is the formal theory of manifolds, or the theory of theories (§47).
For Husserl, then, formal logic is a three-tiered science, connecting disciplines and Ideas that were once thought to belong to disparate sciences. Importantly, Husserl’s insistence on the genuineness of Ideas makes this possible. As ideal, the basic meaning forms that constitute the first-level of logical investigation and are the basis of the other two exhibit an ideal structure and conformity to law. These basic meaning structures can then combine in indefinitely many ways in accordance with their conformity to laws, allowing an ideal building up and out of formal logic that itself occurs with lawful regularity. Husserl compares this structure to crystals in that each form exhibits its own structure that is also taken up in the crystal system (§27 B).
The Systematic Investigation into Forms of Meanings (Section II)
If Section I concerns the demarcation of formal logic, Section II jumps into the discipline itself. Husserl’s strategy is to start with the most basic forms of meaning and, insofar as it is possible in a lecture-series, to obtain a systematic overview of the possible kinds. From there, he gradually builds his way up to propositionally simple judgments and beyond to more complex judgments, to inferences, and to theories. My own synopsis of the section is divided into two parts. First, following Husserl, I give a very general outline of the development from the most basic meaning components up to the highest tier of formal logic. Second, I indicate a handful of the concrete ways in which, as I stated above, Husserl imagines that traditional logic’s rejection of Ideas leads it astray.
The point of departure for the investigation of meaning forms is the ideal distinction between independent and dependent meaning (§20). Independent meanings are those which are capable of standing alone, i.e., complete propositions. Dependent meanings, on the other hand, are those that, although they may express something, intrinsically belong to an independent unit as a component. These dependent meanings cannot be put together in any half hazard way, but fall under fixed types governed by laws (e.g., in the proposition S is p, grammatically speaking, p cannot have any kind of meaning (§22)). Any basic component also admits of a conceptual distinction between syntactical form, which refers to its role within the proposition (e.g., the subject-form, object-form, predicate-form), and syntagma, or the “stuff” (§24), the content of the component. The phrase “ethical human beings,” for instance, can function as the subject-form in one case, the antecedent in a hypothetical in another, but in any case retains the same content, namely “ethical human beings.” A further, parallel distinction in the syntagmas between the nucleus-form (e.g. nominal-forms, or adjectival-forms) and the nucleus-stuff gives us the most basic components in our investigation of the meaning of forms. This last distinction is especially important because the nucleus need not contain any definite content and could instead be “an empty something.” For one thing, it allows for the entrance of generality, or universality and particularity. For another, formal logic, says Husserl, is characterized by this emptiness (§26 B), as this emptiness signifies its being ideal rather than empirical.
Equipped with the most basic meaning components, namely the syntagma, Husserl moves on to the basic forms of simple judgments. He arrives at that basic form by considering in what way the fewest syntagmata might unite to form a judgment. Similarly to Aristotle, he decides that the most basic form involves one nominal and one adjectival syntagma (S is p) (§28). This simple judgment-form is then the basis for another series of variations and complexifications. Of note, here, is his discussion of the effect of empty syntagma (§32), of plural judgments (S is p and/or n) as the origin of the Ideas cardinal numbers, arithmetic, and sets (§34—37), and existential and impersonal judgments (§40). After the simple judgment-forms, Husserl turns to the propositionally complex judgment-forms (conjunction and disjunction) (§41—42), following which is his introduction of modifications (e.g., possibility and probability). This latter topic is of particular note in that it is accompanied by an extended treatment of the Ideas of law, apodicticity, and analyticity (§44—45). Husserl insists not only that analytic (apodictic) laws have been crucial in the investigations up to this point in apophantics, but that a proper conception of analyticity allows for the connection between formal logic, formal ontology, and mathematics to emerge (§46). Finally, Husserl turns to inference, whose ideal laws allow for the introduction of the third-level of formal logic, i.e., the theory of manifolds, or the theory of theories (§47, §54), a discussion which spills over into Section III (§46—59).
That suffices for a general outline of Husserl’s thinking in Section II. Because he is insistent on the unity of what might seem, from the perspective of the history of logic, like disparate disciplines, it might already be visible in broad strokes how Husserl’s own account differs. Additionally, there are several, concrete, and persistent logical problems dealt with in the course of Section II. In general, if Husserl disagrees with logicians, it is on the grounds of their mistakingly rejecting Ideas, and so of not sufficiently recognizing the ideal as the guide in formal logical investigations. For instance, Husserl accuses logicians of conflating equivalence and identity (§29, §39, §48). Two judgments might be equivalent in their relation to a state-of-affairs, but not identical with regard to their ideal meaning form. Among the errors that Husserl identifies in this regard are:
- Traditionally, affirmative and negative judgments (S is p; S is not p) are thought to be coeval. But if analyzed according to their meaning-form, it seems that the negative is a modification of the affirmative, which must then be prior.
- Instead of recognizing the difference in meaning-form between determinative judgments and functional judgments (universal and particular judgments), traditional logic takes all judgments to be either universal, particular, or individual.
These are far from the only topics of interest that Husserl treats in Section II, but it suffices to give the examples mentioned above as an indication.
Reflections on the Idea of Science (Section III)
In Section III, the final section of the lecture, Husserl concludes the thorough, systematic investigation of the forms of meaning and begins to consider the relationship of the science of analytics to other theoretical sciences. By theoretical science, he means those that are not normative and practical and whose primary interest is explanatory. Theoretical sciences, insofar as they are applicable to any particular science without that particular science’s forfeiting its unique domain, comprise the general Idea of science. Analytics has priority because, insofar as it deals with those activities present in every science, it is operative in every science. But there are other sciences that can be included in the Idea of science as well, and even those that deal with a particular region of being can be included insofar as they deal with it in an a priori manner. Among these sciences are pure natural science, which deals with objectivity and spatiotemporal being in general (§61), the science of consciousness, both individually and communally (§63-64), and formal axiology (§61). The final chapter in the Section offers some reflections on noetics, which, as mentioned above, Husserl has set aside in these lectures in favor of a noematic analysis. Central in this chapter is the question of justification of knowledge and the relevant concepts of Evidenz and givenness.
Husserl, of course, says much more than I am able to relay here, but the above should suffice as direction for further inquiry. Those who do delve into the volume further will find it readable, and well-edited and translated. As Ortiz Hill mentions in her introduction, that these are lectures make them clearer and more transparent than some of the writings published during Husserl’s lifetime. For any given point, Husserl offers a variety of examples, and approaches it from several directions. Further, Ortiz Hill provides a lucid translation of an already well-edited volume. There are a handful of pesky German terms that are difficult to translate, which she either alerts readers to or leaves untranslated. She decides on “presentation” for Vorstellung, but points to its ambiguity in Husserl’s writing (xliv-xlv)—Husserl himself also notes the difficult ambiguity of the term. I should also note that, in the case of terms like “nucleus-stuff,” the “stuff” is presumably translating Stoff, which more generally means material in German (der Stoff des Mantels—the material of the coat). Given that terms like “nucleus-stuff” are often contrasted with something formal, it might seem more appropriate to translate Stoff as material. However, Husserl does use the latinized Materie sometimes making it seem worthwhile to translate Stoff differently. Only in the case of the terms Geist and Gemüt do I hesitate with the translation. The former, she translates as “mind” (l), which might seem strange in the context of the discussion of community and culture in Section III. For Gemüt and its variations, Ortiz Hill employs adjectival expression with the word “inner.” Although I think this doesn’t quite capture the emotive connotation that translations like “heart” do, this term plays almost no role in the volume. The few passages in which it could cause some confusion, such as its being contrasted with will and understanding at the beginning of Section I (§1), do not interfere with the trajectory of Husserl’s thought. Beyond these terms, there are a handful that Ortiz Hill leaves untranslated, e.g. Unsinn, Widersinn, and Evidenz. In each case, I appreciate the choice to leave the terms in their original German. In the case of the first two, no English equivalents readily suggest themselves that capture their contrast. In the case of Evidenz, the English cognate “evidence” suggests something like external proof, which is different than the “consciousness of fulfillment” that Husserl has in mind.
In closing, I offer a few words on the significance of the volume. For those primarily interested in Husserl or more broadly in phenomenology, the edition offers an interesting link between different periods of Husserl’s thought. Many of the topics that he addresses in Section II, for instance, harken backward to his Logical Investigations (which he himself notes on occasion) and also point forward to the concerns of Formal and Transcendental Logic (such as the preoccupation with the unity of disciplines thought to be disparate under the banner of formal logic). This is especially significant for those who, as I suggest above, accuse Husserl of abandoning formal analyses in favor of transcendental ones. For those primarily interested in formal logic, or in topics predominately discussed in analytic philosophy, the volume represents a significant overlap of concerns. In both the translator’s introduction and a review of the German edition, Ortiz Hill does a remarkable job at indicating the overlap and ultimate differences between Husserl and the school of thought that emerges from Frege and runs through Russell, Carnap, Hilbert, and Gödel. At any rate, readers of all kinds may be surprised to find Husserl undertaking a systematic survey of formal logic in the decade of the 1910’s, and that makes the volume a welcome contribution to the scholarship.
 See Ursula Panzer’s “Einleitung” in the original German volume, quoted in Ortiz Hill’s “Introduction.”
 Ortiz Hill, Claire. “Review of E. Husserl, Logik Und Allgemeine Wissenschaftstheorie. Vorlesungen 1917/18, Mit Ergänzenden Texten Aus Der Ersten Fassung 1910/11.” History and Philosophy of Logic, 1998.