See studies by P. Ricoeur (1967), M. Natanson (1973), J. Kockelmans, ed. (1967, repr. 1978), H. L. Dreyfus and H. Hall, ed. (1982), D. Willard (1984), and E. Levinas (1973, repr. 1985).
Husserl was a pupil of Franz Brentano and Carl Stumpf; his philosophical work influenced, among others, Hans Blumenberg, Ludwig Landgrebe, Eugen Fink, Max Scheler, Martin Heidegger, Jean-Paul Sartre, Emmanuel Levinas, Rudolf Carnap, Hermann Weyl, Maurice Merleau-Ponty, Alfred Schütz, Pierre Bourdieu, Paul Ricœur, Jacques Derrida, Jan Patočka, Roman Ingarden, Edith Stein (St. Teresa Benedicta of the Cross), and Karol Wojtyla. In 1887 Husserl converted to Christianity and joined the Lutheran Church. He taught philosophy at Halle as a tutor (Privatdozent) from 1887, then at Göttingen as professor from 1901, and at Freiburg im Breisgau from 1916 until he retired in 1928. After this, he continued his research and writing by using the library at Freiburg.
He initially studied mathematics at the universities of Leipzig (1876) and Berlin (1878), under Karl Weierstrass and Leopold Kronecker. In 1881 he went to Vienna to study under the supervision of Leo Königsberger (a former student of Weierstrass), obtaining the Ph.D. in 1883 with the work Beiträge zur Variationsrechnung ("Contributions to the Calculus of Variations").
In 1884, he began to attend Franz Brentano's lectures on psychology and philosophy at the University of Vienna. Husserl was so impressed by Brentano that he decided to dedicate his life to philosophy. In 1886 Husserl went to the University of Halle to obtain his Habilitation with Carl Stumpf, a former student of Brentano. Under his supervision he wrote Über den Begriff der Zahl (On the concept of Number; 1887) which would serve later as the base for his first major work, Philosophie der Arithmetik (1891).
In these first works he tries to combine mathematics, psychology and philosophy with a main goal to provide a sound foundation for mathematics. He analyzes the psychological process needed to obtain the concept of number and then tries to build up a systematical theory on this analysis. To achieve this he uses several methods and concepts taken from his teachers. From Weierstrass he derives the idea that we generate the concept of number by counting a certain collection of objects. From Brentano and Stumpf he takes over the distinction between proper and improper presenting. In an example Husserl explains this in the following way: if you are standing in front of a house, you have a proper, direct presentation of that house, but if you are looking for it and ask for directions, then these directions (e.g. the house on the corner of this and that street) are an indirect, improper presentation. In other words, you can have a proper presentation of an object if it is actually present, and an improper (or symbolic as he also calls it) if you only can indicate that object through signs, symbols, etc. Husserl's 1901 Logical Investigations is considered the starting point for the formal theory of wholes and their parts known as mereology.
Another important element that Husserl took over from Brentano is intentionality, the notion that the main characteristic of consciousness is that it is always intentional. While often simplistically summarised as "aboutness" or the relationship between mental acts and the external world, Brentano defined it as the main characteristic of mental phenomena, by which they could be distinguished from physical phenomena. Every mental phenomenon, every psychological act has a content, is directed at an object (the intentional object). Every belief, desire etc. has an object that they are about: the believed, the wanted. Brentano used the expression "intentional inexistence" to indicate the status of the objects of thought in the mind. The property of being intentional, of having an intentional object, was the key feature to distinguish mental phenomena and physical phenomena, because physical phenomena lack intentionality altogether.
From the Ideen onward, Husserl concentrated on the ideal, essential structures of consciousness. The metaphysical problem of establishing the material reality of what we perceive was of little interest to Husserl in spite of his being a transcendental idealist. Husserl proposed that the world of objects and ways in which we direct ourselves toward and perceive those objects is normally conceived of in what he called the "natural standpoint", which is characterized by a belief that objects materially exist and exhibit properties that we see as emanating from them. Husserl proposed a radical new phenomenological way of looking at objects by examining how we, in our many ways of being intentionally directed toward them, actually "constitute" them (to be distinguished from materially creating objects or objects merely being figments of the imagination); in the Phenomenological standpoint, the object ceases to be something simply "external" and ceases to be seen as providing indicators about what it is, and becomes a grouping of perceptual and functional aspects that imply one another under the idea of a particular object or "type". The notion of objects as real is not expelled by phenomenology, but "bracketed" as a way in which we regard objects instead of a feature that inheres in an object's essence founded in the relation between the object and the perceiver. In order to better understand the world of appearances and objects, Phenomenology attempts to identify the invariant features of how objects are perceived and pushes attributions of reality into their role as an attribution about the things we perceive (or an assumption underlying how we perceive objects).
In a later period, Husserl began to wrestle with the complicated issues of intersubjectivity (specifically, how communication about an object can be assumed to refer to the same ideal entity) and tries new methods of bringing his readers to understand the importance of Phenomenology to scientific inquiry (and specifically to Psychology) and what it means to "bracket" the natural attitude. The Crisis of the European Sciences is Husserl's unfinished work that deals most directly with these issues. In it, Husserl for the first time attempts a historical overview of the development of Western philosophy and science, emphasizing the challenges presented by their increasingly (one-sidedly) empirical and naturalistic orientation. Husserl declares that mental and spiritual reality possess their own reality independent of any physical basis, and that a science of the mind ('Geisteswissenschaft') must be established on as scientific a foundation as the natural sciences have managed:
After his death, Husserl's manuscripts, amounting to approximately 40,000 pages of "Gabelsberger" stenography and his complete research library, were smuggled to Belgium by Herman Van Breda in 1939 and deposited at Leuven to form the Husserl-Archives of the Higher Institute of Philosophy. Much of the material in his research manuscripts has been published in the Husserliana critical edition series.
Husserl also identifies a series of "formal words" which are necessary to form sentences and have no sensible correlates. Examples of formal words are "a", "the", "more than", "over", "under", "two", "group", and so on. Every sentence must contain formal words to designate what Husserl calls "formal categories". There are two kinds of categories: meaning categories and formal-ontological categories. Meaning categories relate judgments; they include forms of conjunction, disjunction, forms of plural, among others. Formal-ontological categories relate objects and include notions such as set, cardinal number, ordinal number, part and whole, relation, and so on. The way we know these categories is through a faculty of understanding called "categorial intuition".
Through sensible intuition our consciousness constitutes what Husserl calls a "situation of affairs" (Sachlage). It is a passive constitution where objects themselves are presented to us. To this situation of affairs, through categorial intuition, we are able to constitute a "state of affairs" (Sachverhalt). One situation of affairs through objective acts of consciousness (acts of constituting categorially) can serve as the basis for constituting multiple states of affairs. For example, suppose a and b are two sensible objects in a certain situation of affairs. We can use it as basis to say, "a<b" and "b>a", two judgments which designate different states of affairs. For Husserl a sentence has a proposition or judgment as its meaning, and refers to a state of affairs which has a situation of affairs as a reference base.
Thanks to "eidetic intuition" (or "essential intuition"), we are able to grasp the possibility, impossibility, necessity and contingency among concepts or among formal categories. Categorial intuition, along with categorial abstraction and eidetic intuition, are the basis for logical and mathematical knowledge.
Husserl criticized logicians of his time for not focusing on the relation between subjective processes that give us objective knowledge of pure logic. All subjective activities of consciousness need an ideal correlate, and objective logic (constituted noematically) as it is constituted by consciousness needs a noetic correlate (the subjective activities of consciousness).
He stated that logic has three strata, each further away from consciousness, and further away from psychology.
Logic's first stratum is what Husserl called a "morphology of meanings" concerning a priori ways to relate judgments to make them meaningful. In this stratum we elaborate a "pure grammar" or a logical syntax, and he would call its rules "laws to prevent non-sense", which would be similar to what logic calls today " formation rules". Mathematics, as logic's ontological correlate, also has a similar stratum, a "morphology of formal-ontological categories".
Logic's second stratum would be called by Husserl "logic of consequence" or the "logic of non-contradiction" which explores all possible forms of true judgments. He includes here syllogistic classic logic, propositional logic and that of predicates. This is a semantic stratum, and the rules of this stratum would be the "laws to avoid counter-sense" or "laws to prevent contradiction". They are very similar to today's logic " transformation rules". Mathematics also has a similar stratum which is based among others on pure theory of pluralities, and a pure theory of numbers. They provide a science of the conditions of possibility of any theory whatsoever.
He also talked about what he called "logic of truth" which consists of formal laws of possible truth and its modalities, and is previous to the third logical third stratum.
Husserl recognized a logical third stratum, a meta-logical level, what he called a "theory of all possible forms of theories". It explores all possible theories in a priori fashion, rather than the possibility of theory in general. We could establish theories of possible relations between pure forms of theories, investigate these logical relations and the deductions from such general connection. The logician is free to see the extension of this deductive, theoretical sphere of pure logic. Husserl finds as ontological correlate to this the "theory of manifolds" It is, in formal ontology, a free investigation where a mathematician can assign several meanings to several symbols, and all their possible valid deductions in a general and indeterminate manner. It is, properly speaking, the most universal mathematics of all. Through the posit of certain indeterminate objects (formal-ontological categories) as well as any combination of mathematical axioms, mathematicians can explore the apodeictic connections between them just as long as consistency is preserved.
This view of logic and mathematics accounted, according to him, for the objectivity of a series of mathematical development of his time, such as n-dimensional manifolds, whether Euclidean or non-Euclidean, Hermann Grassmann's theory of extensions, William Rowan Hamilton's Hamiltonians, Sophus Lie's theory of transformation groups, and Cantor's set theory.
Likewise, the opinion that Husserl's notion of noema and object is due to Frege's conception of sense and reference is anachronistic, for in Husserl's review of Schröder, a clear distinction is made between sense and reference. Likewise, in his criticism of Frege in the Philosophy of Arithmetic, Husserl remarks on the distinction between the content and the extension of a concept. Moreover, the distinction between the subjective mental act, namely the content of a concept, and the (external) object, was developed independently in the School of Brentano, and may have surfaced as early as Brentano's 1870's lectures on logic.
Philosophers and scholars such as J. N. Mohanty, Claire Ortiz Hill and Guillermo E. Rosado Haddock, among others, have argued that Husserl's so-called change from psychologism to platonism was effected independently of Frege's review. For example, the review falsely accuses Husserl of subjectivizing everything, so that no objectivity is possible, and falsely attributes to him a notion of abstraction whereby objects disappear until we are left with numbers as mere ghosts. Contrary to what Frege states, already in Husserl's Philosophy of Arithmetic we find two different kinds of representations: A subjective representation and an objective representation. Objectivity is clearly defined in that work. Frege's attack seems to be directed at certain doctrines pertaining to the foundations of mathematics current in the Berlin School of Weierstrass, of which Husserl and Cantor cannot be said to be orthodox representatives.
Furthermore, various sources indicate that Husserl changed his mind about psychologism as early as 1890, a year before the Philosophy of Arithmetic was published: He states that when it was published, he had already changed his mind,--that he had doubts about psychologism from the very beginning. He attributes this change of mind to Leibniz, Bolzano, Lotze, and David Hume. Husserl makes no mention of Frege as a decisive factor in this change. In his Logical Investigations, Husserl mentions Frege only twice, once in a footnote to point out that he had retracted three pages of criticism of Frege's The Foundations of Arithmetic, and again to question Frege's use of the word Bedeutung in the designation of reference rather than meaning (sense).
Frege thanked Husserl in a letter dated May 24, 1891 for sending him a copy of the Philosophy of Arithmetic and Husserl's review of E. Schröder's Vorlesungen über die Algebra der Logik. In the same letter, Frege used the review of Schröder's book to analyze Husserl's notion of the sense of reference of concept words. Frege recognized, as early as 1891, that Husserl distinguished between sense and reference. Consequently both Gottlob Frege and Edmund Husserl, before 1891, independently elaborated a theory of sense and reference.
Commentators argue that Husserl's notion of noema has nothing to do with Frege's notion of sense, because noemata are necessarily fused with noeses which are the conscious activities of consciousness. Noemata have three different levels: The substratum, which is never presented to consciousness, and is the support of all the properties of the object; the noematic senses, which are the different ways the objects are presented to us; and modalities of being (possible, doubtful, existent, non-existent, absurd, and so on). Consequently, in intentional activities, even non-existent objects can be constituted, and form part of the whole noema. Frege, however, did not conceive of objects as forming parts of senses: If a proper name denotes a non-existent object, it does not have a reference, hence concepts with no objects have no truth value in arguments. Moreover, Husserl did not maintain that predicates of sentences designate concepts. According to Frege the reference of a sentence is a truth value, while for Husserl it is a state of affairs. Frege's notion of sense is unrelated to Husserl's noema, while the latter's notion of meaning and object is different from that of Frege.
In fine, Husserl's conception of logic and mathematics differs from that of Frege, who held that arithmetic could be derived from logic. For Husserl this is not the case: Mathematics (with the exception of geometry) is the ontological correlate of logic, and while both fields are related, neither one is strictly reducible to the other.
Since "truth-in-itself" has "being-in-itself" as ontological correlate, and psychologists reduce truth (and hence logic) to empirical psychology, the inevitable consequence is scepticism. Besides, also psychologists have not been so successful in trying to see how from induction or psychological processes we can justify the absolute certainty of logical principles, such as the principles of identity and non-contradiction. It is therefore futile to base certain logical laws and principles on uncertain processes of the mind.
This confusion made by psychologism (and related disciplines such as biologism and anthropologism) can be due to three specific prejudices:
1. The first prejudice is the supposition that logic is somehow normative in nature. Husserl argues that logic is theoretical, i.e., that logic itself proposes a priori laws which are themselves the basis of the normative side of logic. Since mathematics is related to logic, he cites an example from mathematics: If we have a formula like (a+b)(a-b)=a²-b² it does not tell us how to think mathematically. It just expresses a truth. A proposition that says: "The product of the sum and the difference of a and b should give us the difference of the squares of a and b" does express a normative proposition, but this normative statement is based on the theoretical statement "(a+b)(a-b)=a²-b²".
2. For psychologists, the acts of judging, reasoning, deriving, and so on, are all psychological processes. Therefore, it is the role of psychology to provide the foundation of these processes. Husserl states that this effort made by psychologists are a "μετάβασις εἰς ἄλλο γένος" (a transgression to another field). It is a μετάβασις because psychology cannot possibly provide any foundations for a priori laws which themselves are the basis for all the ways we should think correctly. Psychologists have the problem of confusing intentional activities with the object of these activities. It is important to distinguish between the act of judging and the judgment itself, the act of counting and the number itself, and so on. Counting five objects is undeniably a psychological process, but the number 5 is not.
3. Judgments can be true or not true. Psychologists argue that judgments are true because they become "evidently" true to us. This evidence, a psychological process that "guarantees" truth, is indeed a psychological process. Husserl responds to it saying that truth itself as well as logical laws remain valid always regardless of psychological "evidence" that they are true. No psychological process can explain the a priori objectivity of these logical truths.
From this criticism to psychologism, the distinction between psychological acts from their intentional objects, and the difference between the normative side of logic from the theoretical side, derives from a platonist conception of logic. This means that we should regard logical and mathematical laws as being independent of the human mind, and also as an autonomy of meanings. It is essentially the difference between the real (everything subject to time) and the ideal or irreal (everything that is atemporal), such as logical truths, mathematical entities, mathematical truths and meanings in general.
Rudolf Carnap was also influenced by Husserl, not only concerning Husserl's notion of essential insight that Carnap used in his Der Raum, but also his notion of "formation rules" and "transformation rules" is founded on Husserl's philosophy of logic.
Ludwig Landgrebe became assistant to Husserl in 1923. From 1939 he collaborated with Eugen Fink at the Husserl-Archives in Leuven, authorized by Husserl. In 1954 he became leader of the Husserl-Archives. Landgrebe is known as one of Husserl's closest associates, but also for his independent views relating to history, religion and politics as seen from the viewpoints of existentialist philosophy and metaphysics..
Max Scheler met Husserl in Halle and found in his phenomenology a methodological breakthrough for his own philosophical endeavors. Even though Scheler later criticised Husserl's idealistic logical approach and proposed instead a "phenomenology of love", he states that he remained "deeply indebted" to Husserl throughout his work. Husserl also had some influence on Pope John-Paul II, which appears strongly in a work by the latter, The Acting Person, or Person and Act. It was originally published in Polish in 1969 under his pre-papal name Karol Wojtyla (in collaboration with the polish phenomenologist: Anna-Teresa Tymieniecka) and combined phenomenological work with Thomistic Ethics.
Wilfrid Sellars, an influential figure in the so-called "Pittsburgh school" (Robert Brandom, John McDowell) had been a student of Marvin Farber, a pupil of Husserl, and was influenced by phenomenology through him:
Husserl also influenced Martin Heidegger, who was Husserl's assistant, and who Husserl himself considered best suited as his successor until Heidegger started supporting the Nazi ideology. Heidegger's magnum opus Being and Time is dedicated to Husserl.
Kurt Gödel expressed very strong appreciation for Husserl's work, especially with regard to "bracketing" or epoche.
Jean-Paul Sartre was also largely influenced by Husserl, although he didn't agree with every aspect of his analyses.
The influence of the Husserlian phenomenological tradition in the 21st century is extending beyond the confines of the European and North American legacies. It has already started to impact (indirectly) scholarship in Eastern and Oriental thought, including research on the impetus of philosophical thinking in the history of ideas in Islam.