ISBN:
9789401011112
Language:
English
Pages:
Online-Ressource (364p)
,
online resource
Edition:
Springer eBook Collection. Humanities, Social Sciences and Law
Parallel Title:
Erscheint auch als
Parallel Title:
Erscheint auch als
Keywords:
Philosophy (General)
;
Logic
;
Phenomenology
Abstract:
Preparatory Considerations -- § 1. Outset from the significations of the word logos: speaking, thinking, what is thought -- § 2. The ideality of language. Exclusion of the problems pertaining to it -- § 3. Language as an expression of “thinking.” Thinking in the broadest sense, as the sense-constituting mental process -- § 4. The problem of ascertaining the essential limits of the “thinking” capable of the significational Function -- § 5. Provisional delimination of logic as apriori theory of science -- § 6. The formal character of logic. The formal Apriori and the contingent Apriori -- § 7. The normative and practical functions of logic -- § 8. The two-sidedness of logic; the subjective and the Objective direction of its thematizing activity -- § 9. The straightforward thematizing activity of the “Objective” or “positive” sciences. The idea of two-sided sciences -- § 10. Historically existing psychology and scientific thematizing activity directed to the subjective -- §11. The thematizing tendencies of traditional logic -- a.Logic directed originally to the Objective theoretical formations produced by thinking -- b.Logic’s interest in truth and the resultant reflection on subjective insight -- c. Result: the hybridism of historically existing logic as a theoretical and normative-practical discipline -- I / The structures and the sphere of objective formal logic -- The way from the tradition to the full idea of formal logic -- 1. Formal logic as apophantic analytics -- § 12. Discovery of the idea of the pure judgment-form -- § 13. The theory of the pure forms of judgments as the first discipline of formal logic -- a.The idea of theory of forms -- b.Universality of the judgment-form; the fundamental forms and their variants -- c.Operation as the guiding concept in the investigation of forms -- § 14. Consequence-logic (logic of non-contradiction) as the second level of formal logic -- § 15. Truth-logic and consequence-logic -- § 16. The differences in evidence that substantiate the separating of levels within apophantics. Clear evidence and distinct evidence -- a.Modes of performing the judgment. Distinctness and confusion -- b.Distinctness and clarity -- c.Clarity in the having of something itself and clarity of anticipation -- § 17. The essential genus, “distinct judgment,” as the theme of “pure analytics” -- § 18. The fundamental question of pure analytics -- § 19. Pure analytics as fundamental to the formal logic of truth. Non-contradiction as a condition for possible truth -- § 20. The principles of logic and their analogues in pure analytics -- § 21. The evidence in the coinciding of “the same” confused and distinct judgment. The broadest concept of the judgment -- § 22. The concept defining the province belonging to the theory of apophantic forms, as the grammar of pure logic, is the judgment in the broadest sense -- 2. Formal apophantics, formal mathematics -- § 23. The internal unity of traditional logic and the problem of its position relative to formal mathematics -- a.The conceptual self-containedness of traditional logic as apophantic analytics -- b.The emerging of the idea of an enlarged analytics, Leibniz’s “mathesis universalis,” and the methodico-technical unification of traditional syllogistics and formal mathematics -- § 24. The new problem of a formal ontology. Characterization of traditional formal mathematics as formal ontology -- § 25. Formal apophantics and formal ontology as belonging together materially, notwithstanding the diversity of their respective themes -- § 26. The historical reasons why the problem of the unity of formal apophantics and formal mathematics was masked -- a.Lack of the concept of the pure empty form -- b.Lack of knowledge that apophantic formations are ideal -- c.Further reasons, particularly the lack of genuine scientific inquiries into origins -- d.Comment on Bolzano’s position regarding the idea of formal ontology -- § 27. The introduction of the idea of formal ontology in the Logische Untersuchungen -- a.The first constitutional investigations of categorial objectivities, in the Philosophie der Arithmetik -- b.The way of the “Prolegomena” from formal apophantics to formal ontology -- 3. Theory of deductive systems and theory of multiplicities -- § 28. The highest level of formal logic: the theory of deductive systems; correlatively, the theory of multiplicities -- § 29. The theory of multiplicities and the formalizing reduction of the nomological sciences -- § 30. Multiplicity-theory as developed by Riemann and his successors -- §31. The pregnant concept of a multiplicity-correlatively, that of a “deductive” or “nomological” system-clarified by the concept of “definiteness” -- § 32. The highest idea of a theory of multiplicities: a universal nomological science of the forms of multiplicities -- § 33. Actual formal mathematics and mathematics of the rules of the game -- § 34. Complete formal mathematics identical with complete logical analytics -- § 35. Why only deductive theory-forms can become thematic within the domain of mathesis universalis as universal analytics -- a.Only deductive theory has a purely analytic system-form -- b.The problem of when a system of propositions has a system-form characterizable as analytic -- § 36. Retrospect and preliminary indication of our further tasks -- b. Phenomenological clarification of the two-sidedness of formal logic as formal apophantics and formal ontology -- 4. Focusing on objects and focusing on judgments -- § 37. The inquiry concerning the relationship between formal apophantics and formal ontology; insufficiency of our clarifications up to now -- § 38. Judgment-objects as such and syntactical formations -- § 39. The concept of the judgment broadened to cover all formations produced by syntactical actions -- § 40. Formal analytics as a playing with thoughts, and logical analytics. The relation to possible application is part of the logical sense of formal mathesis -- §41. The difference between an apophantic and an ontological focusing and the problem of clarifying that difference -- § 42. Solution of this problem -- a.Judging directed, not to the judgment, but to the thematic objectivity -- b.Identity of the thematic object throughout changes in the syntactical operations -- c.The types of syntactical object-forms as the typical modes of Something -- d.The dual function of syntactical operations -- e.Coherence of the judging by virtue of the unity of the substrate-object that is being determined. Constitution of the “concept” determining the substrate-object -- f. The categorial formations, which accrue in the determining, as habitual and inter subjective possessions -- g. The objectivity given beforehand to thinking contrasted with the categorial objectivity produced by thinking — Nature as an illustration -- § 43. Analytics, as formal theory of science, is formal ontology and, as ontology, is directed to objects 119 -- § 44. The shift from analytics as formal ontology to analytics as formal apophantics -- a.The change of thematizing focus from object- provinces to judgments as logic intends them -- b.Phenomenological clarification of this change of focus -- ?. The attitude of someone who is judging naïvely-straightforwardly -- ?. In the critical attitude of someone who intends to cognize, supposed objectivities as supposed are distinguished from actual objectivities -- ?. The scientist’s attitude: the supposed, as supposed, the object of his criticism of cognition -- § 45. The judgment in the sense proper to apophantic logic -- § 46. Truth and falsity as results of criticism. The double sense of truth and evidence -- 5. Apophantics, as theory of sense, and truth-logic -- § 47. The adjustment of traditional logic to the critical attitude of science leads to its focusing on the apophansis -- § 48. Judgments, as mere suppositions, belong to the region of senses. Phenomenological characterization of the focusing on senses -- § 49. The double sense of judgment (positum, proposition) -- § 50. The broadening of the concept of sense to cover the whole positional sphere, and the broadening of formal logic to include a formal axiology and a formal theory of practice -- §51. Pure consequence-logic as a pure theory of senses. The division into consequence-logic and truth- logic is valid also for the theory of multiplicities, as the highest level of logic -- § 52. “Mathesis pura” as properly logical and as extralogical. The “mathematics of mathematicians” -- § 53. Elucidations by the example of the Euclidean multiplicity -- § 54. Concluding ascertainment of the relationship be-tween formal logic and formal ontology -- ?.The problem -- b.The two correlative senses of formal logic -- c. The idea of formal ontology can be separated from the idea of theory of science -- II / From Formal to Transcendental Logic -- 1. Psychologism and the laying of a transcendental foundation for logic -- § 55. Is the development of logic as Objective-formal enou...
Abstract:
2 called in question, then naturally no fact, science, could be presupposed. Thus Plato was set on the path to the pure idea. Not gathered from the de facto sciences but formative of pure norms, his dialectic of pure ideas - as we say, his logic or his theory of science - was called on to make genuine 1 science possible now for the first time, to guide its practice. And precisely in fulfilling this vocation the Platonic dialectic actually helped create sciences in the pregnant sense, sciences that were consciously sustained by the idea of logical science and sought to actualize it so far as possible. Such were the strict mathematics and natural science whose further developments at higher stages are our modern sciences. But the original relationship between logic and science has undergone a remarkable reversal in modern times. The sciences made themselves independent. Without being able to satisfy completely the spirit of critical self-justification, they fashioned extremely differentiated methods, whose fruitfulness, it is true, was practically certain, but whose productivity was not clarified by ultimate insight. They fashioned these methods, not indeed with the everyday man's naivete, but still with a naivete of a higher level, which abandoned the appeal to the pure idea, the justifying of method by pure principles, according to ultimate apriori possibilities and necessities.
Description / Table of Contents:
Preparatory Considerations§ 1. Outset from the significations of the word logos: speaking, thinking, what is thought -- § 2. The ideality of language. Exclusion of the problems pertaining to it -- § 3. Language as an expression of “thinking.” Thinking in the broadest sense, as the sense-constituting mental process -- § 4. The problem of ascertaining the essential limits of the “thinking” capable of the significational Function -- § 5. Provisional delimination of logic as apriori theory of science -- § 6. The formal character of logic. The formal Apriori and the contingent Apriori -- § 7. The normative and practical functions of logic -- § 8. The two-sidedness of logic; the subjective and the Objective direction of its thematizing activity -- § 9. The straightforward thematizing activity of the “Objective” or “positive” sciences. The idea of two-sided sciences -- § 10. Historically existing psychology and scientific thematizing activity directed to the subjective -- §11. The thematizing tendencies of traditional logic -- a.Logic directed originally to the Objective theoretical formations produced by thinking -- b.Logic’s interest in truth and the resultant reflection on subjective insight -- c. Result: the hybridism of historically existing logic as a theoretical and normative-practical discipline -- I / The structures and the sphere of objective formal logic -- The way from the tradition to the full idea of formal logic -- 1. Formal logic as apophantic analytics -- § 12. Discovery of the idea of the pure judgment-form -- § 13. The theory of the pure forms of judgments as the first discipline of formal logic -- a.The idea of theory of forms -- b.Universality of the judgment-form; the fundamental forms and their variants -- c.Operation as the guiding concept in the investigation of forms -- § 14. Consequence-logic (logic of non-contradiction) as the second level of formal logic -- § 15. Truth-logic and consequence-logic -- § 16. The differences in evidence that substantiate the separating of levels within apophantics. Clear evidence and distinct evidence -- a.Modes of performing the judgment. Distinctness and confusion -- b.Distinctness and clarity -- c.Clarity in the having of something itself and clarity of anticipation -- § 17. The essential genus, “distinct judgment,” as the theme of “pure analytics” -- § 18. The fundamental question of pure analytics -- § 19. Pure analytics as fundamental to the formal logic of truth. Non-contradiction as a condition for possible truth -- § 20. The principles of logic and their analogues in pure analytics -- § 21. The evidence in the coinciding of “the same” confused and distinct judgment. The broadest concept of the judgment -- § 22. The concept defining the province belonging to the theory of apophantic forms, as the grammar of pure logic, is the judgment in the broadest sense -- 2. Formal apophantics, formal mathematics -- § 23. The internal unity of traditional logic and the problem of its position relative to formal mathematics -- a.The conceptual self-containedness of traditional logic as apophantic analytics -- b.The emerging of the idea of an enlarged analytics, Leibniz’s “mathesis universalis,” and the methodico-technical unification of traditional syllogistics and formal mathematics -- § 24. The new problem of a formal ontology. Characterization of traditional formal mathematics as formal ontology -- § 25. Formal apophantics and formal ontology as belonging together materially, notwithstanding the diversity of their respective themes -- § 26. The historical reasons why the problem of the unity of formal apophantics and formal mathematics was masked -- a.Lack of the concept of the pure empty form -- b.Lack of knowledge that apophantic formations are ideal -- c.Further reasons, particularly the lack of genuine scientific inquiries into origins -- d.Comment on Bolzano’s position regarding the idea of formal ontology -- § 27. The introduction of the idea of formal ontology in the Logische Untersuchungen -- a.The first constitutional investigations of categorial objectivities, in the Philosophie der Arithmetik -- b.The way of the “Prolegomena” from formal apophantics to formal ontology -- 3. Theory of deductive systems and theory of multiplicities -- § 28. The highest level of formal logic: the theory of deductive systems; correlatively, the theory of multiplicities -- § 29. The theory of multiplicities and the formalizing reduction of the nomological sciences -- § 30. Multiplicity-theory as developed by Riemann and his successors -- §31. The pregnant concept of a multiplicity-correlatively, that of a “deductive” or “nomological” system-clarified by the concept of “definiteness” -- § 32. The highest idea of a theory of multiplicities: a universal nomological science of the forms of multiplicities -- § 33. Actual formal mathematics and mathematics of the rules of the game -- § 34. Complete formal mathematics identical with complete logical analytics -- § 35. Why only deductive theory-forms can become thematic within the domain of mathesis universalis as universal analytics -- a.Only deductive theory has a purely analytic system-form -- b.The problem of when a system of propositions has a system-form characterizable as analytic -- § 36. Retrospect and preliminary indication of our further tasks -- b. Phenomenological clarification of the two-sidedness of formal logic as formal apophantics and formal ontology -- 4. Focusing on objects and focusing on judgments -- § 37. The inquiry concerning the relationship between formal apophantics and formal ontology; insufficiency of our clarifications up to now -- § 38. Judgment-objects as such and syntactical formations -- § 39. The concept of the judgment broadened to cover all formations produced by syntactical actions -- § 40. Formal analytics as a playing with thoughts, and logical analytics. The relation to possible application is part of the logical sense of formal mathesis -- §41. The difference between an apophantic and an ontological focusing and the problem of clarifying that difference -- § 42. Solution of this problem -- a.Judging directed, not to the judgment, but to the thematic objectivity -- b.Identity of the thematic object throughout changes in the syntactical operations -- c.The types of syntactical object-forms as the typical modes of Something -- d.The dual function of syntactical operations -- e.Coherence of the judging by virtue of the unity of the substrate-object that is being determined. Constitution of the “concept” determining the substrate-object -- f. The categorial formations, which accrue in the determining, as habitual and inter subjective possessions -- g. The objectivity given beforehand to thinking contrasted with the categorial objectivity produced by thinking - Nature as an illustration -- § 43. Analytics, as formal theory of science, is formal ontology and, as ontology, is directed to objects 119 -- § 44. The shift from analytics as formal ontology to analytics as formal apophantics -- a.The change of thematizing focus from object- provinces to judgments as logic intends them -- b.Phenomenological clarification of this change of focus -- ?. The attitude of someone who is judging naïvely-straightforwardly -- ?. In the critical attitude of someone who intends to cognize, supposed objectivities as supposed are distinguished from actual objectivities -- ?. The scientist’s attitude: the supposed, as supposed, the object of his criticism of cognition -- § 45. The judgment in the sense proper to apophantic logic -- § 46. Truth and falsity as results of criticism. The double sense of truth and evidence -- 5. Apophantics, as theory of sense, and truth-logic -- § 47. The adjustment of traditional logic to the critical attitude of science leads to its focusing on the apophansis -- § 48. Judgments, as mere suppositions, belong to the region of senses. Phenomenological characterization of the focusing on senses -- § 49. The double sense of judgment (positum, proposition) -- § 50. The broadening of the concept of sense to cover the whole positional sphere, and the broadening of formal logic to include a formal axiology and a formal theory of practice -- §51. Pure consequence-logic as a pure theory of senses. The division into consequence-logic and truth- logic is valid also for the theory of multiplicities, as the highest level of logic -- § 52. “Mathesis pura” as properly logical and as extralogical. The “mathematics of mathematicians” -- § 53. Elucidations by the example of the Euclidean multiplicity -- § 54. Concluding ascertainment of the relationship be-tween formal logic and formal ontology -- ?.The problem -- b.The two correlative senses of formal logic -- c. The idea of formal ontology can be separated from the idea of theory of science -- II / From Formal to Transcendental Logic -- 1. Psychologism and the laying of a transcendental foundation for logic -- § 55. Is the development of logic as Objective-formal enough t...
DOI:
10.1007/978-94-010-1111-2
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