Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens / von Dr. Gottlob Frege,...Date de l'edition originale : 1879Ce livre est la reproduction fidele d'une oeuvre publiee avant 1920 et fait partie d'une collection de livres reimprimes a la demande editee par Hachette Livre, dans le cadre d'un partenariat avec la Bibliotheque nationale de France, offrant l'opportunite d'acceder a des ouvrages anciens et souvent rares issus des fonds patrimoniaux de la BnF.Les oeuvres faisant partie de cette collection ont ete (...) numerisees par la BnF et sont presentes sur Gallica, sa bibliotheque numerique.En entreprenant de redonner vie a ces ouvrages au travers d'une collection de livres reimprimes a la demande, nous leur donnons la possibilite de rencontrer un public elargi et participons a la transmission de connaissances et de savoirs parfois difficilement accessibles.Nous avons cherche a concilier la reproduction fidele d'un livre ancien a partir de sa version numerisee avec le souci d'un confort de lecture optimal. Nous esperons que les ouvrages de cette nouvelle collection vous apporteront entiere satisfaction.Pour plus d'informations, rendez-vous sur www.hachettebnf.frhttp://gallica.bnf.fr/ark:/12148/bpt6k65658c. (shrink)

Dieser Band enthält die vier Arbeiten Freges: Begriffsschrift, eine der arithmetischen nachgebildeten Formelsprache, 1879; Anwendungen der Begriffsschrift, 1879; Über den Briefwechsel Leibnizens und Huggens mit Papin, 1881; Über den Zweck der Begriffsschrift, 1883; Über die wissenschaftliche Berechtigung einer Begriffsschrift, 1882. Frege's research work in the field of mathematical logic is of great importance for the present-day analytic philosophy. We actually owe to Frege a great amount of basical insight and exemplary research, which set up a new (...) standard also in other fields of knowledge. As the founder of mathematical logic he severely examindes the syllogisms on which arithmetic is built up. In doing so, Frege recognized that our colloquial language is inadequate to define logic structures. His notional language corresponded to the artaivicial logical language demandes by Leibniz. Frege's achievement in the field of logic were so important, that they radiated into the domain of philosophy and influenced the development of mathematical logic decisively. (shrink)

In Begriffsschrift, Frege presented a formal system and used it to formulate logical definitions of arithmetical notions and to deduce some noteworthy theorems by means of logical axioms and inference rules. From a contemporary perspective, Begriffsschrift’s deductions are, in general, straightforward; it is assumed that all of them can be reproduced in a second-order formal system. Some deductions in this work present—according to this perspective—oddities that have led many scholars to consider it to be Frege’s inaccuracies which should (...) be amended. In this paper, we continue with the analysis of Begriffsschrift’s logic undertaken in an earlier work and argue that its deductive system must not be reconstructed as a second-order calculus. This leads us to argue that Begriffsschrift’s deductions do not need any correction but, on the contrary, can be explained in coherence with a global reading of this work and, in particular, with its fundamental distinction between function and argument. (shrink)

Well over a century after its introduction, Frege's two-dimensional Begriffsschrift notation is still considered mainly a curiosity that stands out more for its clumsiness than anything else. This paper focuses mainly on the propositional fragment of the Begriffsschrift, because it embodies the characteristic features that distinguish it from other expressively equivalent notations. In the first part, I argue for the perspicuity and readability of the Begriffsschrift by discussing several idiosyncrasies of the notation, which allow an easy conversion (...) of logically equivalent formulas, and presenting the notation's close connection to syntax trees. In the second part, Frege's considerations regarding the design principles underlying the Begriffsschrift are presented. Frege was quite explicit about these in his replies to early criticisms and unfavorable comparisons with Boole's notation for propositional logic. This discussion reveals that the Begriffsschrift is in fact a well thought-out and carefully crafted notation that intentionally exploits the possibilities afforded by the two-dimensional medium of writing like none other. (shrink)

In this paper I suggest an answer to the question of what Frege means when he says that his logical system, the Begrijfsschrift, is like the language Leibniz sketched, a lingua characteristica, and not merely a logical calculus. According to the nineteenth century studies, Leibniz's lingua characteristica was supposed to be a language with which the truths of science and the constitution of its concepts could be accurately expressed. I argue that this is exactly what the Begriffsschrift is: it (...) is a language, since, unlike calculi, its sentential expressions express truths, and it is a characteristic language, since the meaning of its complex expressions depend only on the meanings of their constituents and on the way they are put together. In fact it is in itself already a science composed in accordance with the Classical Model of Science. What makes the Begrijfsschrift so special is that Frege is able to accomplish these goals with using only grammatical or syncategorematic terms and so has a medium with which he can try to show analyticity of the theorems of arithmetic. (shrink)

Dieser Band enthält die vier Arbeiten Freges: Begriffsschrift, eine der arithmetischen nachgebildeten Formelsprache, 1879; Anwendungen der Begriffsschrift, 1879; Über den Briefwechsel Leibnizens und Huggens mit Papin, 1881; Über den Zweck der Begriffsschrift, 1883; Über die wissenschaftliche Berechtigung einer Begriffsschrift, 1882. Frege's research work in the field of mathematical logic is of great importance for the present-day analytic philosophy. We actually owe to Frege a great amount of basical insight and exemplary research, which set up a new (...) standard also in other fields of knowledge. As the founder of mathematical logic he severely examindes the syllogisms on which arithmetic is built up. In doing so, Frege recognized that our colloquial language is inadequate to define logic structures. His notional language corresponded to the artaivicial logical language demandes by Leibniz. Frege's achievement in the field of logic were so important, that they radiated into the domain of philosophy and influenced the development of mathematical logic decisively. (shrink)

It is widely taken that the first-order part of Frege's Begriffsschrift is complete. However, there does not seem to have been a formal verification of this received claim. The general concern is that Frege's system is one axiom short in the first-order predicate calculus comparing to, by now, the standard first-order theory. Yet Frege has one extra inference rule in his system. Then the question is whether Frege's first-order calculus is still deductively sufficient as far as the first-order completeness (...) is concerned. In this short note we confirm that the missing axiom is derivable from his stated axioms and inference rules, and hence the logic system in the Begriffsschrift is indeed first-order complete. (shrink)

ABSTRACT Frege presents the eponymous distinction of "Über Sinn und Bedeutung" as a correction to the theory of identity he held in the Begriffsschrift.1 His retrospective assessment has prompted different reactions from commentators. Many have simply taken him at his word.2 Others, who have lingered over the relevant texts, have encountered a difficulty: in the Begriffsschrift Frege appears to raise the same problem with which he begins USB and to respond to it in words that are strikingly similar (...) to those found in the later work.3 Thus, a number of important scholars have been led to argue that Frege misrepresents his earlier view: contrary to what he says in USB, the Begriffsschrift already contains the distinction between Sinn and Bedeutung.4 Despite their obvious differences, the logic of both interpretations requires that the two works be responsive to the same problem. In this paper I challenge that fundamental premise.5 If I might be allowed to express my thesis tersely but suggestively: the problem of the Begriffsschrift is epistemological; that of USB, ontological.6 The two problems and Frege's solutions to them shall be explained in what follows. (shrink)

It is a familiar fact that different systems of notation can function in radically different ways. Consider, to take a very simple example, the difference between the sign-designs ‘twenty-three’, ‘XXIII’, and ‘23’. The first is an expression of English tracing the sounds a speaker makes in uttering the words ‘twenty’ and ‘three’. The second is a Roman numeral that uses signs for collections of things—‘X’ for ten things and ‘I’ for one thing—to present by addition the idea of ten and (...) ten and one and one and one, that is, twenty-three, things. Instead of tracing the sounds a speaker makes in speaking in some natural language, the Roman numeral ‘XXIII’ directly represents a collection of things. The Arabic numeral ‘23’ is different again. Like the Roman numeral ‘XXIII’ it in some way represents a number directly; unlike the Roman numeral it is not immediately additive. The numeral ‘23’ is not to be read as designating two and three things. The Arabic numeration system functions as a notational system in a way that is different both from the notational system of a written natural language such as English and from that of the Roman numeration system. (shrink)

If the begriffsschrift from Frege does represent the logical form of natural language it either lacks a logical form itself, or its logical form is different to that of natural language. But Frege insists that his notation has a logical form. So the second disjunct holds. This suggests that Frege's notation will generate consequences different to those that can be derived with natural language, with its different logical form. For anyone looking for "a means of avoiding misunderstandings", as Frege (...) does, this would be unpalatable, to say the least. (shrink)

In this paper I suggest an answer to the question of what Frege means when he says that his logical system, the Begriffsschrift, is like the language Leibniz sketched, a lingua characteristica, and not merely a logical calculus. According to the nineteenth century studies, Leibniz’s lingua characteristica was supposed to be a language with which the truths of science and the constitution of its concepts could be accurately expressed. I argue that this is exactly what the Begriffsschrift is: (...) it is a language, since, unlike calculi, its sentential expressions express truths, and it is a characteristic language, since the meaning of its complex expressions depend only on the meanings of their constituents and on the way they are put together. In fact it is in itself already a science composed in accordance with the Classical Model of Science. What makes the Begriffsschrift so special is that Frege is able to accomplish these goals with using only grammatical or syncategorematic terms and so has a medium with which he can try to show analyticity of the theorems of arithmetic. (shrink)

In this paper I suggest an answer to the question of what Frege means when he says that his logical system, the Begriffsschrift, is like the language Leibniz sketched, a lingua characteristica, and not merely a logical calculus. According to the nineteenth century studies, Leibniz’s lingua characteristica was supposed to be a language with which the truths of science and the constitution of its concepts could be accurately expressed. I argue that this is exactly what the Begriffsschrift is: (...) it is a language, since, unlike calculi, its sentential expressions express truths, and it is a characteristic language, since the meaning of its complex expressions depend only on the meanings of their constituents and on the way they are put together. In fact it is in itself already a science composed in accordance with the Classical Model of Science. What makes the Begriffsschrift so special is that Frege is able to accomplish these goals with using only grammatical or syncategorematic terms and so has a medium with which he can try to show analyticity of the theorems of arithmetic. (shrink)

Before Frege, the term Begriffsschrift'was used to indicate a language the expressions of which adequately represent the structure of the judgements or concepts which they signify, and a language the written signs of which designate ideas rather than sounds. In 1879 Frege follows . Later he adopts —and with it the Aristotelian theory of language in which it is embedded.

Before Frege, the term Begriffsschrift'was used to indicate a language the expressions of which adequately represent the structure of the judgements or concepts which they signify, and a language the written signs of which designate ideas rather than sounds. In 1879 Frege follows. Later he adopts —and with it the Aristotelian theory of language in which it is embedded.

Translation of Frege's 'Über die Begriffsschrift des Herrn Peano und meine eigene' (1896). Translated by V.H. Dudman.

Frege’s views on identity continue to provoke scholars, and rightly so. In particular his view in Begriffsschrift of 1879, and its relation to his view in ‘Über Sinn und Bedeutung’ of 1892 deserve careful attention. The issues involved have a wider significance than Frege’s specific views on identity in different periods, though these are important enough. They concern also the move from what I call below ‘thin’ semantics, which is exhausted in signs being assigned content, to a ‘thick’ semantics, (...) in which ‘modes of determining their content’, or Sinne are also concerned. (shrink)

It is well known that the formal system developed by Frege in Begriffsschrift is based upon the distinction between function and argument—as opposed to the traditional distinction between subject and predicate. Almost all of the modern commentaries on Frege's work suggest a semantic interpretation of this distinction, and identify it with the ontological structure of function and object, upon which Grundgesetze is based. Those commentaries agree that the system proposed by Frege in Begriffsschrift has some gaps, but it (...) is taken as an essentially correct formal system for second-order logic: the first one in the history of logic. However, there is strong textual evidence that such an interpretation should be rejected. This evidence shows that the nature of the distinction between function and argument is stated by Frege in a significantly different way: it applies only to expressions and not to entities. The formal system based on this distinction is tremendously flexible and is suitable for making explicit the logical structure of contents as well as of deductive chains. We put forward a new reconstruction of the function-argument scheme and the quantification theory in Begriffsschrift. After that, we discuss the usual semantic interpretation of Begriffsschrift and show its inconsistencies with a rigorous reading of the text. (shrink)

Frege’s views on identity continue to provoke scholars, and rightly so. In particular his view in Begriffsschrift of 1879, and its relation to his view in ‘Über Sinn und Bedeutung’ of 1892 deserve careful attention. The issues involved have a wider significance than Frege’s specific views on identity in different periods, though these are important enough. They concern also the move from what I call below ‘thin’ semantics, which is exhausted in signs being assigned content, to a ‘thick’ semantics, (...) in which ‘modes of determining their content’, or Sinne are also concerned. (shrink)

This paper challenges a standard interpretation according to which Frege’s conception of logic (early and late) is at odds with the contemporary one, because on the latter’s view logic is formal, while on Frege’s view it is not, given that logic’s subject matter is reality’s most general features. I argue that Frege – in Begriffsschrift – retained the idea that logic is formal; Frege sees logic as providing the ‘logical cement’ that ties up together the contentful concepts of specific (...) sciences, not the most general truths. Finally, I discuss how Frege conceives of the application of Begriffsschrift, and of its status as a ‘lingua characteristica’. (shrink)

This paper addresses an issue with the sign ‘⊢’ in Frege’s mature version of Begriffsschrift, i.e., the version in ‘Function and Concept’ and Grundgesetze. The sign is a performative for asserting in that writing down ‘⊢p’ is equivalent to asserting that p. Frege further says that writing ‘ p’ is also equivalent to identifying the reference of ‘p’ with the truth-value True. It looks as if he holds that asserting that p consists in identifying the True with the reference (...) of ‘p’. Frege’s commitment to it, however, seems to encounter a number of tensions. This paper aims to show that these tensions can be avoided by endorsing a non-assertive conception of identification under which making an identification is not making an identity assertion. The suggested reading leads to an entirely di erent understanding of the compositionality of the sign ‘⊢’ as well as Frege’s conception of assertion and judgment. (shrink)

In diesem Buch wird ein zweihundert Jahre altes Problem gelost: Wie beweist Kant in der Kritik der reinen Vernunft die Vollstandigkeit seiner Urteilstafel? Da diese Tafel, zusammen mit der Kategorientafel (die von ihr abhangt) das Herzstuck von Kants Hauptwerk ausmacht, gilt das Problem von jeher als Kernproblem der Kantinterpretation. Uberraschenderweise kann es durch sorgfaltige immanente Textauslegung gelost werden: Nachweisbar ist, dass das Leitfadenkapitel, also der unmittelbare Kontext der Urteilstafel innerhalb der Kritik, eine dicht geschriebene Argumentationsskizze zu einem strengen Vollstandigkeitsbeweis enthalt, (...) dessen Uberzeugungskraft nichts zu wunschen ubriglasst. Fur die Rekonstruktion dieses Beweises kommt es zunachst auf eine genaue Analyse der Behauptungen an, die Kant mit der Urteilstafel aufstellt. Diese Analyse prasentiert das erste Kapitel. Das zweite bietet dann einen ausfuhrlichen Satz-fur-Satz-Kommentar zu der fur den Vollstandigkeitsbeweis einschlagigen Textpassage und rekonstruiert ihn in allen Details. Das dritte Kapitel schliesslich untersucht den Begriff von 'formaler Logik', den Kant voraussetzt und von dem seine Behauptung abhangt, die in der Urteilstafel vorgenommene Aufzahlung logischer Formen sei vollstandig. Der im Anhang abgedruckte Essay behandelt die bis heute kaum beachtete Auseinandersetzung, die Gottlob Frege in seiner Begriffsschrift von 1879 mit der kantischen Urteilstafel Punkt fur Punkt gefuhrt hat. Freges Kritik an ihr wird im ersten Teil des Anhangs dargestellt und erlautert. Im zweiten Teil wird dann gezeigt, dass diese Kritik in allen Punkten auf grundlegenden Irrtumern und Missverstandnissen beruht. Als besonders schwerwiegender und folgenreicher Irrtum stellt sich Freges Ansicht heraus, die Regeln dessen, was Kant als formale Logik ansah, seien aus dem Axiomensystem der Begriffsschrift ableitbar. (shrink)

A Mathematical Review by John Corcoran, SUNY/Buffalo -/- Macbeth, Danielle Diagrammatic reasoning in Frege's Begriffsschrift. Synthese 186 (2012), no. 1, 289–314. ABSTRACT This review begins with two quotations from the paper: its abstract and the first paragraph of the conclusion. The point of the quotations is to make clear by the “give-them-enough-rope” strategy how murky, incompetent, and badly written the paper is. I know I am asking a lot, but I have to ask you to read the quoted passages—aloud (...) if possible. Don’t miss the silly attempt to recycle Kant’s quip “Concepts without intuitions are empty; intuitions without concepts are blind”. What the paper was aiming at includes the absurdity: “Proofs without definitions are empty; definitions without proofs are, if not blind, then dumb.” But the author even bollixed this. The editor didn’t even notice. The copy-editor missed it. And the author’s proof-reading did not catch it. In order not to torment you I will quote the sentence as it appears: “In a slogan: proofs without definitions are empty, merely the aimless manipulation of signs according to rules; and definitions without proofs are, if no blind, then dumb.”[sic] The rest of my review discusses the paper’s astounding misattribution to contemporary logicians of the information-theoretic approach. This approach was cruelly trashed by Quine in his 1970 Philosophy of Logic, and thereafter ignored by every text I know of. The paper under review attributes generally to modern philosophers and logicians views that were never espoused by any of the prominent logicians—such as Hilbert, Gödel, Tarski, Church, and Quine—apparently in an attempt to distance them from Frege: the focus of the article. On page 310 we find the following paragraph. “In our logics it is assumed that inference potential is given by truth-conditions. Hence, we think, deduction can be nothing more than a matter of making explicit information that is already contained in one’s premises. If the deduction is valid then the information contained in the conclusion must be contained already in the premises; if that information is not contained already in the premises […], then the argument cannot be valid.” Although the paper is meticulous in citing supporting literature for less questionable points, no references are given for this. In fact, the view that deduction is the making explicit of information that is only implicit in premises has not been espoused by any standard symbolic logic books. It has only recently been articulated by a small number of philosophical logicians from a younger generation, for example, in the prize-winning essay by J. Sagüillo, Methodological practice and complementary concepts of logical consequence: Tarski’s model-theoretic consequence and Corcoran’s information-theoretic consequence, History and Philosophy of Logic, 30 (2009), pp. 21–48. The paper omits definitions of key terms including ‘ampliative’, ‘explicatory’, ‘inference potential’, ‘truth-condition’, and ‘information’. The definition of prime number on page 292 is as follows: “To say that a number is prime is to say that it is not divisible without remainder by another number”. This would make one be the only prime number. The paper being reviewed had the benefit of two anonymous referees who contributed “very helpful comments on an earlier draft”. Could these anonymous referees have read the paper? -/- J. Corcoran, U of Buffalo, SUNY -/- PS By the way, if anyone has a paper that has been turned down by other journals, any journal that would publish something like this might be worth trying. (shrink)

In the explanations of logical laws and inference rules of the mature version of Begriffsschrift in Grundgesetze, Frege uses the predicate “… is the True.” Scholars like Greimann maintain that this predicate is a metalinguistic truth-predicate for Frege. This paper examines an argument for this claim that is based on the “nominal reading” of Frege’s conception of sentences—the claim that for Frege a sentence “p” is equivalent to a nonsentential phrase like “the truth-value of the thought that p.” In (...) particular, this paper attempts to establish two points concerning this argument based on the nominal reading. First, the argument implies a claim about the nature of assertion which Frege repeatedly denies in his mature works. Secondly, the nominal reading on which the argument depends is false. A sentence “p” is not equivalent to a nonsentential phrase like “the truth-value of the thought that p” for Frege. Our discussion will lead to an important lesson about Frege’s conception of sentences and of assertion. (shrink)

Frege uses Greek letters in two different ways in his Begriffsschrift. One way is the familiar use of bound variables, in conjunction with variable-binding operators, to mark and close argument-places. The other, which is quite unfamiliar, employs letters to mark places for operators to reach into, without thereby closing these places. Frege thereby invents a powerful and compact notation for functional operations which can be recommended even today. His regrettable double use of Greek letters obscured his invention, and this, (...) together with the fact that in the Grundgesetze he no longer has need of function-valued functions, explains why the device was overlooked and has not passed into general use. (shrink)

Neste artigo daremos principal atenção aos dois critérios de identidade de conteúdo conceitual que estão presentes nos §§ 3 e 8 da Conceitografia de Gottlob Frege. Nosso propósito é analisar as características destes critérios da notação conceitual de Frege porque pretendemos delimitar a discussão em torno dos problemas relacionados às noções de identidade intensional e extensional. Dessa forma, pretendemos: analisar os critérios de identidade de conteúdo conceitual presentes nos §§ 3 e 8 da Conceitografia com o objetivo de mostrar que (...) Frege apresentou uma caracterização híbrida da noção de conteúdo conceitual e fazer considerações a respeito de relações que podemos estabelecer entre os critérios intensionais e extensionais de Frege e Richard Kirkham presentes no livro Teorias da Verdade: Uma Introdução Crítica. Com tais comparações pretendemos averiguar: se o critério de identidade do § 8 da Conceitografia é idêntico ao critério extensional de equivalência material de Kirkham e se o critério de identidade do § 3 da Conceitografia é mais forte, mais fraco ou idêntico aos critérios intensionais de equivalência essencial e de equivalência de sinonímia de Kirkham.: In this paper we will give primary attention to two identity criteria of conceptual content that are present in §§ 3 and 8 of Gottlob Frege's Begriffsschrift. Our purpose is to analyze the characteristics of these criteria of conceptual notation of Frege because we want to delimit the discussion around problems related to the notions of intensional and extensional identity. Thus, we intend to: analyze the identity criteria of conceptual content present in §§ 3 and 8 of Begriffsschrift aiming to show that Frege introduced a hybrid characterization of the notion of conceptual content and make considerations about the relationships that we establish between intensional and extensional criteria of Frege and Richard Kirkham present in the book Theories of Truth: A Critical Introduction. With such comparisons we intend to investigate: if the identity criterion of § 8 of Begriffsschrift is identical to the extensional criterion of material equivalence in Kirkham and if the identity criterion of § 3 of Begriffsschrift is stronger, weaker or identical to intensional criteria of essential equivalence and of synonyms equivalence of Kirkham. Key words: Identity, Intensional Criterion, Extensional Criterion. (shrink)

Beginning with a research review, the present paper shows that Hans Slugaʼs and esp. Robert Brandomʼs thesis, according to which Frege has adopted the context-principle and the priority of propositional from Kant, can solve problems in current Frege scholarship, on the one hand, but is itself fraught with further problems, on the other hand. In contrast, this paper maintains that the context-principle and the priority of the propositional are implicitly present in Fregeʼs Begriffsschrift since both have not been taken (...) over from Kant, but rather from neo-Aristotelianism: The context-principle and the priority of the propositional were first drawn up in 1834 by O. F. Gruppe. As a consequence, A. F. Trendelenburg has published a re-arranged edition of Aristotleʼs Organon in 1836 which became one of the most influential schoolbooks on logic in the 19th century and of which Frege ought to have been aware. In the beginning of this schoolbook, using the original ancient Greek sentences of Aristotle, the priority of the propositional (De int. I 1) is deduced from the context-principle (De anima III 6). (shrink)

The goal of the paper is to offer an explanation why Frege has changed his Begriffsschrift account of identity to the one presented in Über Sinn und Bedeutung.The main claim of the paper is that in order to better understand Frege’s motivation for the introduction of his distinction between sense and reference, which marks his change of views, one should place this change in its original setting, namely the broader framework of Frege’s fundamental preoccupations with the foundations of arithmetic (...) and logic. The Fregean thesis that mathematics is contentful, and its defense against formalism and psychologism, provides us an valuable interpretative key. Thus, Fregean senses are not just the mere outcome of some profound reflections on language, rather they play an important role in the articulation of Frege’s program in the foundations of arithmetic. (shrink)

Translation of Frege's 'Über den Zweck der Begriffsschrift' (1882).

Der Autor analysiert die methodologische Grundlegung der Transzendentalphilosophie durch Fichte. Als entscheidenden Punkt arbeitet er den durch Fichte vollzogenen Paradigmenwechsel heraus Danach kommt der Systembegründung nicht mehr ein vorwissenschaftlicher Status zu, sondern diese wird Moment der Systemkonstitution und Systemkonstruktion. Das erlaubt Fichte, die philosophische Methode in ihrer Strenge von der Methode der Mathematik abzuheben. The author analyzes the methodological basis of Fichte's transcendental philosophy. As a decisive point, he works out the paradigm shift that Fichte carried out. According to this, (...) the justification of the system no longer has a pre-scientific status, but becomes a moment of the system constitution and system construction. This allows Fichte to distinguish the philosophical method in its rigor from the method of mathematics. (shrink)