After the complete collection of the published works of Rudolf Carnap (1891-1970) was accepted to be published by Oxford University Press in 2016, the long-awaited first volume of the 14-volume edition of the Collected Writings of Rudolf Carnap has been finally published. This volume represents the first ever English translation of Carnap’s early writings published from 1918 through 1926, before Carnap moved to Vienna becoming one of the leading figures of the Vienna Circle. Carnap is rightly considered one of the most influential philosophers of the twentieth century. He made contributions in many areas, from the philosophy of science to the philosophy of logic, always stressing the need for a critical assessment of the role logic, mathematics and philosophy should play in scientific knowledge. His works played a key role in the development of Logical Empiricism; one of the main sources of what would become analytic philosophy. Although in the present day a fruitful dialogue between analytic philosophy and other philosophical traditions is not always easily achievable, at that time rather different philosophical perspectives were coexisting. The perspectives shared a common cultural framework and, most importantly, they were used to profitably interact with each other in a way that has since become increasingly difficult and Carnap’s early writings are a perfect example of this. Carnap was an eclectic intellectual whose interests embraced different philosophical ways of thinking to such an extent that his multifaceted interests appeared to some as objectionable or even inconsistent, as he recalls in his autobiography. However, he was proud to claim that he acquired valuable insights from philosophers and scientists of ‘a great variety of philosophical creeds’. Carnap’s early writings indeed shows a clear influence of the main philosophers usually regarded as belonging to the analytic tradition, such as Frege and Russell, but Husserl’s phenomenology and many neo-Kantian thinkers such as Natorp and Cassirer play an important role as well. These essays represent a fundamental resource for both Carnap scholars and historians of analytic philosophy. Firstly, these writings make possible a better understanding of Carnap’s thought and its development since the early years and, secondly, they shed some light on the origins of analytic philosophy and the multi-faceted nature of the cultural framework around that time.
I wish now to make a few general considerations on the editorial work. First of all, let’s say the present volume represents an outstanding work in Carnap scholarship both for its great attention to detail and for its richness in several in-depth analyses that furnish all the historical and mathematical background needed to understand Carnap’s writings. The volume is the final outcome of the work of many people and the editors present an overall picture of all those who have contributed to the project. The volume begins with a brief chronology of Carnap’s life followed by an Introduction edited by Carus and Friedman which presents an exhaustive overview of the essays that follow. The editors show the original German alongside the English translation and at the end of volume they accurately report any minimal changes they have made with respect to the original text. Each essay is followed by a section giving further information that carefully helps the reader to contextualize and understand the text, and in places, the editorial notes are impressively accurate. The editors indeed make extensive use of Carnap’s Nachlass to furnish us with a clear representation of Carnap’s view. Although, reference to an English translation of much of the literature quoted in the final bibliography would have been useful to the reader. The editors accurately report the corrected bibliographic information for all items cited in Carnap’s texts, but they do not indicate whether an English translation of each item is available . As the present volume is mainly addressed to an English audience, this would have been useful even though it would have resulted in a longer bibliographical list. Finally, I would report a misprint at page 189: towards the end of the page the editors refers to note mm (twice), but it should be note ll. In the following I will briefly show the content of the different essays and give a few remarks on the editorial work on these texts whenever appropriate.
The first essay is entitled Völkerbund – Staatenbund and depicts a young Carnap in his twenties engaged in the social-political life of his country towards the end of World War I. At that time Carnap was actively engaged with the German Youth Movement, particularly the parts of the movement politically engaged against the war, and this text represents his contribution to the first issue of the left-wing political newsletter Politische Rundbriefe, published by Karl Bittel in October 1918. This brief text should have been followed by another text where a few critical considerations on the German’s defeat in the war were addressed; however, this second text was never published. However, in the Introduction the editors sketch the content of both texts and we can then see how they present an overview of Carnap’s political world view at that time. According to Carnap, politics is not to be understood in a narrow sense, rather it refers to everything that has ‘some connection with the public social life of people’. As the editors suggest, this view of politics underlies Carnap’s philosophical work for most of his life, especially with respect to the role that reason, and more specifically ‘scientific’ reasoning should play in a society or a community where all the activities should be regulated and so removed ‘from the realm of chaotic whim’ and subordinated ‘to goal-oriented reason’. On the contrary, an excessive contemplative, quietist, or even mystical approach of mental life, not properly balanced by a politically active life is instead suggested to be one of the main reasons for Germany’s guilt for causing the war. This text represents an important resource in order to understand the interconnection between the political and philosophical reflections that were co-existing in Carnap’s philosophy and more generally, in the ambitious and multi-faced cultural phenomenon represented by the Vienna Circle.
In Wer erzwingt die Geltung des Naturgesetzes? Carnap reviews Hugo Dingler’s Physik und Hypothese where the author defends a conventionalist account of the primary laws of nature. Carnap acknowledges Dingler’s philosophical view as one of the most important influences on his own thought. In 1920 Carnap even considered writing a doctoral dissertation under Dingler’s direction at the physics department in Munich, and a joint publication was also planned till September 1921. Despite several disagreements, Dingler remained an important influence Carnap’s writings in the early 1920s. At the very beginning Carnap asked himself a question: what if someone comes along and claims that laws of nature are matter of free decision? That’s exactly the kind of question that Dingler’s book seeks to address. Dingler holds that nature can neither impose a particular choice, nor ever contradict our stipulations, but we are free to choose the primary laws of nature; the spatial and causal laws. Carnap admits that a view of this sort appears odd, and he is reluctant to agree with Dingler, (especially with respect to Dingler’s rejection of Einstein’s general theory of relativity), but he proudly claims that this book ‘clears the ground on which an examination of the foundations of physics, and in particular the theory of relativity, could rest’. The present essay is an important resource in order to better understand the genesis of very distinctive Carnapian notion, i.e. Carnap’s conventionalism. This notion is clearly influenced by Dingler’s view on the conventional nature of the laws of nature that Carnap identifies as critical conventionalism, thereby distinguishing it from Poincaré’s notion of conventionalism. According to Carnap, Poincaré’s conventionalism relies on a free choice that is completely arbitrary, whereas Dingler’s view holds that our choices can be uniquely determined by a certain principle of maximal simplicity. Carnap favours Dingler’s conventionalism over Poincaré’s account and will reformulate Dingler’s criteria of simplicity in later years. Carnap’s early conventionalism then seems to find its roots in a critical reformulation of Dingler’s conventionalism. Moreover, this essay shows us the extent to which Carnap’s philosophical considerations rely on an in-depth knowledge of physics and scientific practice. This is evident from his remarks on stipulations that rely on a critical analysis of physical knowledge, conceived not simply as a study of empirical data, but as a stratified and articulated measurement practice of empirical phenomena.
Der Raum is definitely a fundamental text for Carnap scholars. It is a lengthy and substantial book, it was largely written in late 1920, then submitted in 1921 to the philosophy department as a doctoral dissertation, and eventually published in Kant-Studien in 1922. The book aims to make things clear on the debate taking place at the time regarding the source of our knowledge of space and, especially, to what extent an objective knowledge of space could depend on experience. Carnap argues that the many different perspectives advocated by philosophers, mathematicians and physicists are contradictory as their differences rely on confusion over the different meanings of space. Der Raum then aims to show that a proper conceptual clarification of the different meanings of space and their interconnections can shed light on this debate and finally dissolve the controversy.
The first three chapters deal respectively with three different meanings of space; formal, intuitive and physical space, whereas the last two chapters focus on their interconnections and how each space is related to experience. The notion of formal space (formale Raum) is defined in terms of ‘relational or structural system’, i.e. a system fully determined by a set of formal axioms whose objects and relations (holding among them) are indeterminate and not related to any specific intuitive meaning. From this formal system we can obtain the spatial system once we substitute spatial elements (point, line, …) for their indeterminate correlation. Carnap refers to this formal system also in terms of “pure theory of relations” (reine Beziehungslehre). He further claims that the construction of formal space can be undertaken in a different way, which is the only path that ‘makes the complete construction of formal space possible, comprising all the special cases’. Starting from formal logic, i.e. the general theory of classes and relations, Carnap then briefly sketches this construction. He introduces the basic notions of ‘judgment’, ‘proposition’, ‘concept’, ‘relation’, and so on, until he defines the notion of ‘(ordered) series’ (natural numbers, real numbers, etc) and finally he arrives at the most general notion of formal space, called n-dimensional topological space and designated by Rnt. By imposing specific conditions on this structure, Carnap obtains the n-dimensional projective space Rnp and the n-dimensional metrical space Rnm. Starting from these formal structures we can obtain the three different intuitive spaces (topological, projective, metrical) by substituting their indeterminate elements with spatial elements. Carnap explicitly claims that ‘a relation of substitution (Einsetzung) holds between the theory of formal and that of intuitive space’, even though the connection between formal space and intuitive space is not so straightforward since postulates and generalizations also play a role in the construction of the order-structure of intuitive space (for any dimension). However, this kind of connection resembles Husserl’s distinction between formal ontology and regional ontology and Carnap is well aware of this and he explicitly refers to it in order to clarify his perspective. Moreover, Husserl’s Wesenserschauung is mentioned to specify the kind of intuitive knowledge involved, making clear that it is not to be confused with ‘intuition (Anschauung) in the narrower sense, focused on the fact itself’ as it pertains to the essential features that can be grasped within phenomena. In agreement with Husserl’s remarks on Kant’s conception of a priori, Carnap claims that the essential features of intuitive space turn out be ‘the synthetic a priori propositions claimed by Kant’. Therefore, the principles governing the formal space are analytic a priori, whereas the ones governing the topological space are synthetic a priori. These two kinds of space, however, are not enough to give a comprehensive picture of scientific knowledge of space. We need to introduce the physical space that represents the domain of synthetic a posteriori knowledge. The knowledge of physical space, however, other than being based on the empirical results of experiments, necessarily relies on conventions that are based on the choice of metric stipulation we decide to adopt. Carnap further claims that, if we wish, we could impose a different metric geometry and still obtain a physical space that is compatible with all our everyday and scientific observations, even though the final outcome might be far from straightforward. Physical space, therefore, relies on conventions but the choice of metric stipulation should be evaluated in terms of some criteria of simplicity that consider the overall description of nature.
Carnap’s Der Raum shows an impressive richness both from a philosophical and mathematical point of view. Carnap’s appendix ‘Pointers to the Literature’ contains substantial resources to historically contextualize many of the issues raised in the book. Starting from his adherence to the logistic approach of Frege and Russell, then going through the neo-Kantian perspectives of Natorp and Cassirer, on to Husserl’s phenomenology and Dingler’s conventionalism, Carnap’s Der Raum turns out to be a very interesting re-elaboration and combination of different philosophical perspectives. Moreover, the most important mathematical and physical literature of the time is seriously taken into account and the major works of Hilbert, Poincaré, Weyl, Riemann, and many others, are discussed and their results are assimilated into Carnap’s view. Several issues in Der Raum, therefore, should be enlightened by reference to the rich cultural framework that underlies this book. For instance, further investigation into the interconnections between Der Raum and Weyl’s Raum-Zeit-Materie would prove very interesting and fruitful. Carnap explicitly makes reference to Weyl’s writings several times, and a comparison between Carnap’s and Weyl’s studies on space – the latter being clearly influenced by Husserl’s phenomenology – might shed light on the nature of Husserl’s influence on Der Raum. Similarly, further investigation into Carnap’s re-elaboration of Russell’s and Husserl’s perspectives on logic to construct formal space could be useful in order to clarify several aspects of Carnap’s later notion of rational reconstruction. Carnap’s notion of metrical stipulation is another example. A detailed analysis of Carnap’s account on stipulations could shed light on the development of his later conventionalism. The editorial work on Der Raum (edited by Michael Friedman) successfully achieves a great deal of this task. It is extremely accurate and several in-depth analyses furnish the historical and mathematical background that a reader needs to properly understand the many issues contained in this book. The editor further includes Carnap’s marginalia (contained in Carnap’s own copy of Der Raum) in the editorial notes at the corresponding points which gives the reader a clearer picture of Carnap’s view on this specific issue.
However, a few critical remarks can be put forward. Friedman does not seem to capture the exact nature of the Husserlian framework underlying Carnap’s view nor how it relates to the neo-Kantian framework that – as Friedman rightly suggests – underlies Der Raum. In the Introduction (edited also by Carus), for instance, the editors charge Carnap with confusion in respect to his conception of intuitive topological space, which ‘somewhat confusingly’ shares the status of conditions for the possibility of experience with formal topological space. This remark seems to underlie a misconception of Husserl’s philosophy. The introduction of phenomenology is definitely one major difference between the previous Masters dissertation of 1920 and the published version of Der Raum. The published edition of 1922, indeed, is a revisited version of the previous Masters dissertation that Carnap had written for the philosophy department in 1920. In the revisited version Carnap substitutes his previous conception of ‘pure geometry’ with ‘intuitive space’ and this very change marks a shift from a neo-Kantian notion of ‘condition for the possibility of experience’ to a Husserlian reinterpretation thereof. I do not mean that Carnap adheres completely to Husserl’s perspective, but his major interest in phenomenology relies exactly on the Husserlian reformulation of Kant’s synthetic a priori propositions in terms of regional axioms that belong to a certain regional ontology. It is precisely this notion of regional ontology that shapes Carnap’s notion of intuitive topological space, and more generally it is precisely the Husserlian distinction between regional ontology and formal ontology that shapes the overall Carnapian distinction between intuitive and formal space. Husserl’s transcendental phenomenology is a philosophical account that – by the introduction of the notion of categorial intuition (that later develops into the notion Wesenserschauung) – enables Husserl to speak in terms of essential structures intuitively given in a phenomenal domain and playing the role of regional axioms, i.e. conditions for the possibility of experience of this very domain. These regional axioms, moreover, are connected to their correlated abstract structures – free from any intuitive elements and belonging to the domain of formal ontology – by means of relations of formalization and de-formalization (categorical intuitions come into play again). These abstract structures, moreover, share the status of experience-constituting validity since they represent the categorical form of the essential structures governing the given phenomenal domain. Carnap’s intuitive topological space – shaping Husserl’s notion of regional ontology – does not share ‘confusingly’ the status of conditions for the possibility of experience with formal topological space, rather they both have this experience-constituting validity – even though in a different way – in agreement with Husserl’s perspective. Further remarks can be found in the editorial notes that do not seem to capture adequately the nature of the Husserlian framework underlying Der Raum. The editors rightly point out that Husserl’s phenomenology is essentially a descriptive science based on essential insight (Wesenserschauung), but they do not seem to ascribe the role of essences – grasped by Wesenserschauung – directly to the axioms of intuitive space. They designate these axioms as ‘describing the Wesenserschauung’ of our perceptual experience of objects in space, or as ‘codifying certain attributes of intuition’. These remarks seem to underlie that firstly, they keep distinct essences grasped by Wesenserschauung and the axioms describing them, and secondly, they do not ascribe to the axioms any intuitiveness by essential insight. Although the relation between a phenomenological description of a given phenomenal domain and the regional ontology characterizing the domain itself is a complex, multi-faced, and problematic field of phenomenological research, Husserl clearly states that they both have to investigated by Wesenserschauung. Therefore, the axioms themselves are intuitively given and they do not ‘describe’ or ‘codify’ an intuitive knowledge but, at most, we could say that in-depth phenomenological analysis can clarify their meaning-constitution.
It seems to me that this misconception of Husserl’s philosophy undermines their evaluation of Husserl’s contribution to Der Raum in several instances. However, the editors are right not to over-estimate Husserl’s influence on Der Raum over Carnap’s adherence to Kant’s philosophy or neo-Kantian thinkers. Der Raum is arguably a personal re-elaboration of several philosophical perspectives rather than a complete adherence to one specific account. It is not clearto what extent Carnap is fully accepting Husserl’s phenomenology in Der Raum, especially, with respect to the possibility to explore exhaustively a given phenomenal domain by Wesenserschauung in all its essential and stratified connections. Instead he seems interested in Husserl’s perspective only so far as it represents a philosophical account (with a Kantian flavor) within which it is possible – starting from the domain of empirical reality – to avoid the restrictions imposed by a neo-Kantian approach. This would enable him to freely explore the ‘characteristic structures’ belonging to this domain as without it implies a contingent knowledge and laying the foundations for a structural objective analysis of experience.
Über die Aufgabe der Physik addresses the question of what should be regarded as a criterion for maximal simplicity within a physical theory. Two different possibilities are examined with the aim of clarifying the relevant aspects that should rule the choice between them, even though no decision between these two possibilities is suggested in the paper. This text is an important resource to better understand Carnap’s view on simplicity and stipulations within a physical theory and how they both are related to Carnap’s conception of scientific rationality.
In Dreidimensionalität des Raumes und Kausalität Carnap explores how we construct reality starting from a world of sense impressions. Carnap draws an important distinction between experience that exhibits only necessary formation – or first-order experience – and experience that is processed further – or second-order experience. This distinction echoes the previous one in Der Raum between the necessary topological form and the various metrical conventions that could be imposed on it. In the paper Carnap explores this specific issue in a wider perspective where his conventional view is elaborated in the light of Vaihinger’s pragmatic view. It is no coincidence that the paper was published in Annalen der Philosophie, regarded as the house journal of Vaihinger and his followers. Vaihinger argues that we are able to access only the ‘chaos’ of our world of sense impressions whereas the reality we construct is not genuine knowledge but is rather based on useful fictions that allow us to get things done and live in the world. Carnap agrees with Vaihinger as far as it concerns the role of fictions in constructing the reality, but he argues that such a construction is not completely arbitrary. Firstly, we face a first-order experience that exhibits a basic form of ordering, and secondly, certain kinds of logical connections can be established among fictions shaping second-order experience. The paper aims to show that the fiction of three-dimensionality of space and the fiction of physical causality ‘stand in a relation of logical dependence with each other’, and the former is conditioned by the latter. This text is especially important because it helps us to shed light on the development of Aufbau. The first draft of Aufbau dates back to early 1922 and it was completed in 1925. During these years we can observe an important shift: in the early phase (1922-24) Carnap distinguishes a fixed ‘primary world’ of immediate experience – in accordance with the text we are discussing – from a ‘secondary world’ (or ‘realities’) that could be constructed by quasi-analysis on this intuitive basis. However, sometime during 1924 the distinction between primary and secondary world was dropped. Further investigation of Carnap’s intellectual encounters during these years is required , but the present text is clearly an important resource to better understand the development of his thought from Der Raum to Aufbau, especially with respect to his changing perspective on the epistemic value of intuitive knowledge.
In Über die Abhängigkeit der Eigenschaften des Raumes von denen der Zeit Carnap argues that statements about the topological structure of physical space can be reduced to statements about temporal or causal order. The paper needs a proper mathematical and physical background to be properly understood and Malament’s appendix satisfies this requirement. Malament gives a detailed reconstruction of Carnap’s account and he further discusses a number of mathematical problems suggesting how they could be fixed. This text is clearly an important resource for understanding Carnap’s efforts during these years not only in logic and philosophy of science, but also in physical and mathematical research of the time.
The last paper, entitled Physikalische Begriffsbildung, is an important paper written shortly before Carnap moved to Vienna in 1926. In the Introduction Carnap outlines what is science: an activity of collecting and organizing items of knowledge with the aim of subjecting the reality ‘to an ever higher degree of control’”. According to this pragmatic view of science, the task of physics is ‘to order perceptions systematically and to draw inferences from perceptions at hand to perceptions to be expected’. Carnap then explores thoroughly the hierarchical structure of physical concept formation, subdividing its formation into three main stages: qualitative stage, quantitative stage, and abstract stage. The present paper gives us an interesting overall picture of Carnap’s conception of rational reconstruction at the very moment when Carnap was on his way to the final version of the Aufbau. The editorial work (edited by Creath and Richardson) is again very accurate and detailed, although a few remarks on the comparison between Carnap’s Begriffsbildung and Weyl’s Begriffsbildung (as well as Weyl’s Konstitution) might have been useful, especially with respect to Carnap’s later conception of Konstitution.
But aside from these last considerations, the editors have done an excellent job firstly, in making all these texts available to English readers for the first time, and secondly, in making them more understandable thanks to their very rich in-depth analysis. This volume enhances the increasing English literature on the early young Carnap, which in turn provides a clearer picture of the development of logical empiricism and early analytic philosophy. The essays provide a fundamental resource to explore the multi-faceted cultural framework of the time where different philosophical movements were used to profitably interact with each other in a way that has become increasingly difficult in the later years. For all these reasons, the present volume is of considerable merit and should be of interest to Carnap scholars, historians of analytic philosophy and to Husserl scholars and researchers working at the intersection between the philosophy of science, logic and phenomenology.
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.