Structuralism as Transcendental Aesthetic In his early work on the theory of case (La Catégorie d... more Structuralism as Transcendental Aesthetic In his early work on the theory of case (La Catégorie des Cas, Kopenhagen 1935-1937), Hjelmslev's focuses on the general problem of the delimitation of categories; this issue, obviously, has a direct import on the question how categorial form is given and which distinctions in a given substance contribute to schematize the categorial form (constitution of a symbolic domain). With the question of the delimitation of a category, thus, the inquiry manifests a transcendental turn, which is all the more remarkable in view of the predominance of ontology in contemporary European culture. When the author says that the three categories of case, number and genus pose an entanglement (enchevêtrement), he takes issue with two different questions latent in traditional grammar: the relation between formal and material categories (the interpretation of numerus as quantity, of genus as gender); and the problem of the differential definition of a symbolic structure (delimiting the categories one against the other). While these themes prefigure the famous differentiation (form of content/form of expression, substance of content/substance of expression) of the deSassurean scheme in the Prolegomena (1943); the necessity of a mediation (in traditional philosophical terminology: schematism) of categorial form in an expressive medium is stressed throughout Hjelmslev's early work. Also the diacronic considerations point in the same direction, for example when, following the path opened by another great danish linguist, Otto Jespersen, H. says that the shift from a synthetic language (latin), which expresses grammatical roles through desinences, to an analytic language like french with prepositional forms, enacts a relocation (remplacement) of the categorial matter. By 1951, when Merleau-Ponty wrote Sur la Phénoménologie du Langage (published also in Signes, 1960, the author's last published book before his death 1961), this morphological distinction between synthetic and analytic languages must have been a common place; even if we are not in the position to reconstruct Merleau-Ponty's direct source, much in the contest of that essay speaks for Hjelmslev.) Sub-Structure The central idea of Hjelsmlev's reflection on the theory of case, however, is that the articulation of linguistic categories and mathematical (logical) categories are indifferent to one another. The discovery of the symbolic realm is, at the same time, the discovery that what Husserl calls categorial intuition, presupposes a radical disconnectedness between symbolic order and logical form: " the linguistic system is free in relation to the logical realm to which it corresponds " (La Catégorie, op.cit., p. 102). In the early Hjelmslev, the problem of a transcendental schematisme, that is the problem of constructing the relation of possible objects in relation to given rules and a given categorial matter (language), is taken issue with by positing a sublogical system (the claim is that the clarity with which the author develops the problem of a sublogic, remains unattained in his later work, with one exception). Both the associative oppositions (partecipative) of the symbolic system (grammatical forms) and the mathematical oppositions of the logical system, are founded in a sublogical tripartite systems of distinctions (positive, negative and neuter). This dimensionality is foundational in a double sense: it is through operational derivations of a given symbolic order from the sublogical categories, that the formal categories operational in a symbolic and logical domain are apprehended. Secondly, the sublogical operations constitute the relation object-subject, that is reflections concerning the historicity and relativity of a system of categories are motivated by reflections on the contingency of the symbolic order. Structures as semantic-pragmatic interface
After Kant's dictum in the Preface of Metaphysical Foundations of Natural Science&quo... more After Kant's dictum in the Preface of Metaphysical Foundations of Natural Science"in any special doctrine of nature there can be only as much proper science as there is mathematics therein."* (A IX) After introducing the distinction between a philosophy of nature and a pure doctrine of nature (a determination of causality as connectedness of matter), K. states in the same context: "And, since in any doctrine of nature there is only as much proper science as there is a priori knowledge therein, a doctrine of nature will contain only as much proper science as there is mathematics capable of application there."* In trying to spell out the notion "capable of application", recent commentators have failed to exploit the difference between intuition and sensation. Consequently, a focus on but extensive quantity has conditioned the discussion. What is said in Phoronomy about the composition of motions (systems of bodies) as well as in Proposition 8. of the Dynamics, is textual evidence for a conception of mathematical applicability from the point of view of intensive quantity and the second mathematical Grundsatz (KrV B 208).
In Segerberg (2011), a model for metaphoric expressions is constructed, using dynamic doxastic lo... more In Segerberg (2011), a model for metaphoric expressions is constructed, using dynamic doxastic logic as a tool. Metaphors, the author says, are "linguistic means of meaning transmission from one conceptual space to another". While the latter considers metaphors from the specific standpoint of conceptual metaphors; the model fails, so it is claimed in this contribution, to give an account of tropes, specifically of figures of speech, which rely on analogical reasoning.
In his System of Transcendental Idealism, Schelling suggests, while dealing with the systematic p... more In his System of Transcendental Idealism, Schelling suggests, while dealing with the systematic part of the System of Practical Philosophy (section iv), that the facticity of the empirical will (the necessity for the will to be directed toward an external object) is systematically connected to Kant's conception of Radical Evil (Religion within the limits of Reason alone). The proposition which poses a conative directedness, has among its corollaries, the claim that an " original negation of self-determination " constitutively belong to individuality and to the possibility of a plurality of minds in reciprocation (Wechselwirkung). Schelling, though, does not fully develop this implication in the System. Radical Evil (original evil, in the System) marks, thus, a systematic jointure of Practical Philosophy, as well as a unaccomplished task. Later, in his Investigations (1809), Schelling explicates the connection of evil and the will, by restating the fundamental propositions of section iv of the System, in the following terms: " […] the question also falls by the wayside: Why is exactly this individual destined to act in an evil and base manner while, in contrast, another is destined to act piously and justly? For the question presupposes that man is not initially action and act and that he as a spiritual being has a Being which is prior to, and independent of, his will, which […] is impossible ". The Philosophical Investigations into the Essence of Human Freedom and Matters connected herewith are the first post-Kantian full account of Evil within Absolute Idealism. In fact, in the Phenomenology (1807), Hegel's treatment of Kant's Radical Evil quite one-sidedly focuses upon the question of moral worth (to act according to and from a sense of duty): for Hegel, the consciousness of natural individuality is taken to be evil (" Hypocrisy to be unmasked ") by the consciousness which " stands by the fact of duty ". But if evil is but a corollary of moral worth, then Goethe's objection to Kant (alleged reintroduction of the doctrine of the original sin) seems more than justified, Evil being the stain of the irrational in the mantle of critical philosophy. What is more, in Hegelian terms, Evil as original sin is a pictorial representation which falls short of transcending the " bare form " of revealed religion, in order to attain absolute knowledge.
In the Subjective Logic (1816) Hegel claims that cognition is the concept's self-comprehension an... more In the Subjective Logic (1816) Hegel claims that cognition is the concept's self-comprehension and opposes " logical life " to the externality of existence and to spirit. In the latter, life obtains its articulations (determinateness) from its externality (presuppositions and purposes): " the objectivity which stands indifferent against it ". Life as a living individual, on the other hand, can be understood as the stage of intuitionistic mathematics: the constructional mental activity of the living individual; both the living individual and spirit rely on " logical life " for the " transition into cognition ". We ask whether the " Idea of Life by itself " , as emancipated from externalities (institutions and conditionings), is compatible with a representation of human reasoning (default reasoning), or does it entail an ideal rational reasoner (omniscience). I. In Legal Hermeneutics, there is no conflict at all between analogue interpretations (interpretatio extensiva) on the one hand, and the reconstruction of a text by its own standards on the other hand. While the latter (technically called intensio) aims at a deep understanding of the mens legis, the sense of a norm; the former intends to develop the logical consequences of the ratio legis, so as to adapt a supposedly complete system of norms to different contexts of application (convenientia rationi). The present essay offers a tentative analogical reading of Hegel's Logic in the context of Knowledge Representation. The attempts at reconstructing Hegel's Dialectical Methods (or, which amounts to the same kind of delusion) at refuting the accountability of Hegel's cognitive enterprise by the means of today's formal techniques are legions. The reasons for their failure to reconstruct the significance of Hegel's insights are: 1. Hegel's critique of logical form, though programmatic and often formulated with an ideological impetus which dismisses his adversaries without appeal to charity (Leibniz and Wolff), presupposes Kant's formal logic: that is, a radically intensional term logic. 2. The attempt to spell out a basis for a formalization of Kantian Logic is idle: if the goal of formalization ought to be the clarification of (formal) categories, then the Kantian project of developing formal logic from a subjective point of view and starting from the logic of concepts (as cognition) cannot be translated in the formalisms of classical propositional calculus or modal logics. 3. Hegel fosters the Kantian undertaking, though he has to dismiss Kant's construction of transcendental logic (which presupposes the confinement of the absolute to the realm of postulates and regulative ideas); but the reference frame of both Kant and Hegel's (transcendental) logic is the absolute (the unconditioned).
Nach Herrmann Broch ist jeder säkulare Intellektuelle ein Häretiker, wie auch jeder Held ein Rebe... more Nach Herrmann Broch ist jeder säkulare Intellektuelle ein Häretiker, wie auch jeder Held ein Rebell gegen die Platonische Ordnung ist. Es ist demnach ironisch genug, dass Kurt Gödel auf dem Gebiet der mathematischen Logik Entdeckungen machte, deren Tragweite voll zu durchmessen (philosophisch wie fachspezifisch) der Arbeit von kommenden Jahrzehnten vorbehalten bleibt 1 , während er zeitlebens an einem (zugegeben sehr differenzierten) Platonismus 2 festhielt. In den Jahren 1928-1939 legte Gödel einige der wichtigsten Ergebnisse für die Formale Logik seit Aristoteles vor: Die Vollständigkeit der Logik erster Stufe; die Unvollständigkeit axiomatischer Systeme, welche die elementare Zahlentheorie enthalten; die Konsistenz des Auswahlaxioms und der Kontinuum-Hypothese mit den übrigen Axiomen der Zermelo-Fränkel'schen Mengenlehre. In den selben Jahren, in denen er sich mit dem Entscheidungsproblem und dem Begriff der Berechenbarkeit befasste (beide stellen Grundlagen der Künstlichen Intelligenz dar), oder eine zukunftsweisende Interpretation der intuitionistischen Logik erarbeitete, reifte in dem evangelisch getauften (tatsächlich aber nie einer Kirche angehörenden) Mathematiker ein rationalistischer Theismus heran, der sich gut in die Tradition des Böhmischen Reform-Katholizismus einfügt (wie dieser z.B. von Bernard Bolzano verkörpert wird). Gödels wohl bekannteste Ergebnisse, die Unvollständigkeitssätze, grenzen die Leistung der Axiomatischen Kalkülisierung (David Hilberts formalistischer Ansatz) auf die Ermöglichung eines unscharfen kartographischen Blicks ein, während eine durch die Axiomatisierung vorgeblich zu leistende apodiktische Evidenz für das Ganze der Mathematik prinzipiell in Zweifel gezogen wird. Ein ausreichend starkes formales System enthält nach dem ersten Gödel'schen Unvollständigkeitssatz wahre, im selben System jedoch formal unbeweisbare Sätze 3 , wobei dieses Ergebnis auch für die Eigenschaft der Widerspruchsfreiheit des fraglichen Systems selbst gilt (so dass ein ausreichend starkes formales System nicht vollständig und widerspruchsfrei sein
Structuralism as Transcendental Aesthetic In his early work on the theory of case (La Catégorie d... more Structuralism as Transcendental Aesthetic In his early work on the theory of case (La Catégorie des Cas, Kopenhagen 1935-1937), Hjelmslev's focuses on the general problem of the delimitation of categories; this issue, obviously, has a direct import on the question how categorial form is given and which distinctions in a given substance contribute to schematize the categorial form (constitution of a symbolic domain). With the question of the delimitation of a category, thus, the inquiry manifests a transcendental turn, which is all the more remarkable in view of the predominance of ontology in contemporary European culture. When the author says that the three categories of case, number and genus pose an entanglement (enchevêtrement), he takes issue with two different questions latent in traditional grammar: the relation between formal and material categories (the interpretation of numerus as quantity, of genus as gender); and the problem of the differential definition of a symbolic structure (delimiting the categories one against the other). While these themes prefigure the famous differentiation (form of content/form of expression, substance of content/substance of expression) of the deSassurean scheme in the Prolegomena (1943); the necessity of a mediation (in traditional philosophical terminology: schematism) of categorial form in an expressive medium is stressed throughout Hjelmslev's early work. Also the diacronic considerations point in the same direction, for example when, following the path opened by another great danish linguist, Otto Jespersen, H. says that the shift from a synthetic language (latin), which expresses grammatical roles through desinences, to an analytic language like french with prepositional forms, enacts a relocation (remplacement) of the categorial matter. By 1951, when Merleau-Ponty wrote Sur la Phénoménologie du Langage (published also in Signes, 1960, the author's last published book before his death 1961), this morphological distinction between synthetic and analytic languages must have been a common place; even if we are not in the position to reconstruct Merleau-Ponty's direct source, much in the contest of that essay speaks for Hjelmslev.) Sub-Structure The central idea of Hjelsmlev's reflection on the theory of case, however, is that the articulation of linguistic categories and mathematical (logical) categories are indifferent to one another. The discovery of the symbolic realm is, at the same time, the discovery that what Husserl calls categorial intuition, presupposes a radical disconnectedness between symbolic order and logical form: " the linguistic system is free in relation to the logical realm to which it corresponds " (La Catégorie, op.cit., p. 102). In the early Hjelmslev, the problem of a transcendental schematisme, that is the problem of constructing the relation of possible objects in relation to given rules and a given categorial matter (language), is taken issue with by positing a sublogical system (the claim is that the clarity with which the author develops the problem of a sublogic, remains unattained in his later work, with one exception). Both the associative oppositions (partecipative) of the symbolic system (grammatical forms) and the mathematical oppositions of the logical system, are founded in a sublogical tripartite systems of distinctions (positive, negative and neuter). This dimensionality is foundational in a double sense: it is through operational derivations of a given symbolic order from the sublogical categories, that the formal categories operational in a symbolic and logical domain are apprehended. Secondly, the sublogical operations constitute the relation object-subject, that is reflections concerning the historicity and relativity of a system of categories are motivated by reflections on the contingency of the symbolic order. Structures as semantic-pragmatic interface
Action failure is tied to different types of incompleteness. The conjecture is advanced that a pr... more Action failure is tied to different types of incompleteness. The conjecture is advanced that a proposition defining the type sensitiveness of action tokens should be taken as a starting point for structuring the syntax of a modal logic of action, if the multifaceted phenomenon of action incompleteness is to be accounted for. In the following, the focus on actions which " consume " their type features is functional to the interest in acting on / within institutions: the design of minimal institutions must take a completeness criterion into account, unless unplayable games are to be cast upon agents. Since an agent's performance involves reference to a composite frame (resource spaces, e.g. varying availabilities; epistemic spaces, i.e. changing preferences; time points, paths, histories), it seems to make sense to assume that the notion of action incompleteness allows for different general interpretations. As a matter of fact, action incompleteness is part of the very fabric of agency in at least three respects: 1. Learning (reiteration as a device for designing and planning): given a training routine, for learners it is crucial to distinguish between weak and strong default (to use the jargon of programmers), with the former involving reference to an object which is not being retained for retrieval in subsequent implementations of the program, whereas the latter typically defines conditions for an object to be retrieved if a policy requests such revision or update. Learning by doing is systematically linked to a specific iteration pattern performed, while this same feature ties learning (belief update) to a radical contingency: if the choice to deliberate and change the agent's intentions is designed as functional to running routines, then reconsidering and updating are modeled as mechanisms triggered by some intervening collapse or breakdown or unavailability (an agent might go on indefinitely on the basis of unrealistic assumptions); whereas an agent constantly reconsidering and updating its delete list would run out of time for the realization of any proposed task. 2. Linguistic representation: since the seminal distinction by Vendler (Vendler, 1957) between achievements and accomplishments has been under some criticism of late1, a finer grained modeling and formalization of agency default is likely to help in discriminating between purely lexical meaning and grammatical structure of natural language expressions relating to 1 See the summary of the discussion in Hagit Borer, The Normal Course of Events. OUP 2005 (vol. II of Structuring Sense); p. 326. States and Activities are the other two categories of events which Vendler distinguishes. In the context of this paper, I decide to focus on achievements and accomplishments, for the sake of the peculiar relation they entertain to planning. Furthermore, by studying the design (Pollock) of accomplishments and achievements one may better understand the role of operations in the performance of specific action chains. See on this aspect Pollock (1995), ch. 6, The Logical Structures of Plans.
After Kant's dictum in the Preface of Metaphysical Foundations of Natural Science"in any special ... more After Kant's dictum in the Preface of Metaphysical Foundations of Natural Science"in any special doctrine of nature there can be only as much proper science as there is mathematics therein."* (A IX) After introducing the distinction between a philosophy of nature and a pure doctrine of nature (a determination of causality as connectedness of matter), K. states in the same context: "And, since in any doctrine of nature there is only as much proper science as there is a priori knowledge therein, a doctrine of nature will contain only as much proper science as there is mathematics capable of application there."* In trying to spell out the notion "capable of application", recent commentators have failed to exploit the difference between intuition and sensation. Consequently, a focus on but extensive quantity has conditioned the discussion. What is said in Phoronomy about the composition of motions (systems of bodies) as well as in Proposition 8. of the Dynamics, is textual evidence for a conception of mathematical applicability from the point of view of intensive quantity and the second mathematical Grundsatz (KrV B 208).
Structuralism as Transcendental Aesthetic In his early work on the theory of case (La Catégorie d... more Structuralism as Transcendental Aesthetic In his early work on the theory of case (La Catégorie des Cas, Kopenhagen 1935-1937), Hjelmslev's focuses on the general problem of the delimitation of categories; this issue, obviously, has a direct import on the question how categorial form is given and which distinctions in a given substance contribute to schematize the categorial form (constitution of a symbolic domain). With the question of the delimitation of a category, thus, the inquiry manifests a transcendental turn, which is all the more remarkable in view of the predominance of ontology in contemporary European culture. When the author says that the three categories of case, number and genus pose an entanglement (enchevêtrement), he takes issue with two different questions latent in traditional grammar: the relation between formal and material categories (the interpretation of numerus as quantity, of genus as gender); and the problem of the differential definition of a symbolic structure (delimiting the categories one against the other). While these themes prefigure the famous differentiation (form of content/form of expression, substance of content/substance of expression) of the deSassurean scheme in the Prolegomena (1943); the necessity of a mediation (in traditional philosophical terminology: schematism) of categorial form in an expressive medium is stressed throughout Hjelmslev's early work. Also the diacronic considerations point in the same direction, for example when, following the path opened by another great danish linguist, Otto Jespersen, H. says that the shift from a synthetic language (latin), which expresses grammatical roles through desinences, to an analytic language like french with prepositional forms, enacts a relocation (remplacement) of the categorial matter. By 1951, when Merleau-Ponty wrote Sur la Phénoménologie du Langage (published also in Signes, 1960, the author's last published book before his death 1961), this morphological distinction between synthetic and analytic languages must have been a common place; even if we are not in the position to reconstruct Merleau-Ponty's direct source, much in the contest of that essay speaks for Hjelmslev.) Sub-Structure The central idea of Hjelsmlev's reflection on the theory of case, however, is that the articulation of linguistic categories and mathematical (logical) categories are indifferent to one another. The discovery of the symbolic realm is, at the same time, the discovery that what Husserl calls categorial intuition, presupposes a radical disconnectedness between symbolic order and logical form: " the linguistic system is free in relation to the logical realm to which it corresponds " (La Catégorie, op.cit., p. 102). In the early Hjelmslev, the problem of a transcendental schematisme, that is the problem of constructing the relation of possible objects in relation to given rules and a given categorial matter (language), is taken issue with by positing a sublogical system (the claim is that the clarity with which the author develops the problem of a sublogic, remains unattained in his later work, with one exception). Both the associative oppositions (partecipative) of the symbolic system (grammatical forms) and the mathematical oppositions of the logical system, are founded in a sublogical tripartite systems of distinctions (positive, negative and neuter). This dimensionality is foundational in a double sense: it is through operational derivations of a given symbolic order from the sublogical categories, that the formal categories operational in a symbolic and logical domain are apprehended. Secondly, the sublogical operations constitute the relation object-subject, that is reflections concerning the historicity and relativity of a system of categories are motivated by reflections on the contingency of the symbolic order. Structures as semantic-pragmatic interface
After Kant's dictum in the Preface of Metaphysical Foundations of Natural Science&quo... more After Kant's dictum in the Preface of Metaphysical Foundations of Natural Science"in any special doctrine of nature there can be only as much proper science as there is mathematics therein."* (A IX) After introducing the distinction between a philosophy of nature and a pure doctrine of nature (a determination of causality as connectedness of matter), K. states in the same context: "And, since in any doctrine of nature there is only as much proper science as there is a priori knowledge therein, a doctrine of nature will contain only as much proper science as there is mathematics capable of application there."* In trying to spell out the notion "capable of application", recent commentators have failed to exploit the difference between intuition and sensation. Consequently, a focus on but extensive quantity has conditioned the discussion. What is said in Phoronomy about the composition of motions (systems of bodies) as well as in Proposition 8. of the Dynamics, is textual evidence for a conception of mathematical applicability from the point of view of intensive quantity and the second mathematical Grundsatz (KrV B 208).
In Segerberg (2011), a model for metaphoric expressions is constructed, using dynamic doxastic lo... more In Segerberg (2011), a model for metaphoric expressions is constructed, using dynamic doxastic logic as a tool. Metaphors, the author says, are "linguistic means of meaning transmission from one conceptual space to another". While the latter considers metaphors from the specific standpoint of conceptual metaphors; the model fails, so it is claimed in this contribution, to give an account of tropes, specifically of figures of speech, which rely on analogical reasoning.
In his System of Transcendental Idealism, Schelling suggests, while dealing with the systematic p... more In his System of Transcendental Idealism, Schelling suggests, while dealing with the systematic part of the System of Practical Philosophy (section iv), that the facticity of the empirical will (the necessity for the will to be directed toward an external object) is systematically connected to Kant's conception of Radical Evil (Religion within the limits of Reason alone). The proposition which poses a conative directedness, has among its corollaries, the claim that an " original negation of self-determination " constitutively belong to individuality and to the possibility of a plurality of minds in reciprocation (Wechselwirkung). Schelling, though, does not fully develop this implication in the System. Radical Evil (original evil, in the System) marks, thus, a systematic jointure of Practical Philosophy, as well as a unaccomplished task. Later, in his Investigations (1809), Schelling explicates the connection of evil and the will, by restating the fundamental propositions of section iv of the System, in the following terms: " […] the question also falls by the wayside: Why is exactly this individual destined to act in an evil and base manner while, in contrast, another is destined to act piously and justly? For the question presupposes that man is not initially action and act and that he as a spiritual being has a Being which is prior to, and independent of, his will, which […] is impossible ". The Philosophical Investigations into the Essence of Human Freedom and Matters connected herewith are the first post-Kantian full account of Evil within Absolute Idealism. In fact, in the Phenomenology (1807), Hegel's treatment of Kant's Radical Evil quite one-sidedly focuses upon the question of moral worth (to act according to and from a sense of duty): for Hegel, the consciousness of natural individuality is taken to be evil (" Hypocrisy to be unmasked ") by the consciousness which " stands by the fact of duty ". But if evil is but a corollary of moral worth, then Goethe's objection to Kant (alleged reintroduction of the doctrine of the original sin) seems more than justified, Evil being the stain of the irrational in the mantle of critical philosophy. What is more, in Hegelian terms, Evil as original sin is a pictorial representation which falls short of transcending the " bare form " of revealed religion, in order to attain absolute knowledge.
In the Subjective Logic (1816) Hegel claims that cognition is the concept's self-comprehension an... more In the Subjective Logic (1816) Hegel claims that cognition is the concept's self-comprehension and opposes " logical life " to the externality of existence and to spirit. In the latter, life obtains its articulations (determinateness) from its externality (presuppositions and purposes): " the objectivity which stands indifferent against it ". Life as a living individual, on the other hand, can be understood as the stage of intuitionistic mathematics: the constructional mental activity of the living individual; both the living individual and spirit rely on " logical life " for the " transition into cognition ". We ask whether the " Idea of Life by itself " , as emancipated from externalities (institutions and conditionings), is compatible with a representation of human reasoning (default reasoning), or does it entail an ideal rational reasoner (omniscience). I. In Legal Hermeneutics, there is no conflict at all between analogue interpretations (interpretatio extensiva) on the one hand, and the reconstruction of a text by its own standards on the other hand. While the latter (technically called intensio) aims at a deep understanding of the mens legis, the sense of a norm; the former intends to develop the logical consequences of the ratio legis, so as to adapt a supposedly complete system of norms to different contexts of application (convenientia rationi). The present essay offers a tentative analogical reading of Hegel's Logic in the context of Knowledge Representation. The attempts at reconstructing Hegel's Dialectical Methods (or, which amounts to the same kind of delusion) at refuting the accountability of Hegel's cognitive enterprise by the means of today's formal techniques are legions. The reasons for their failure to reconstruct the significance of Hegel's insights are: 1. Hegel's critique of logical form, though programmatic and often formulated with an ideological impetus which dismisses his adversaries without appeal to charity (Leibniz and Wolff), presupposes Kant's formal logic: that is, a radically intensional term logic. 2. The attempt to spell out a basis for a formalization of Kantian Logic is idle: if the goal of formalization ought to be the clarification of (formal) categories, then the Kantian project of developing formal logic from a subjective point of view and starting from the logic of concepts (as cognition) cannot be translated in the formalisms of classical propositional calculus or modal logics. 3. Hegel fosters the Kantian undertaking, though he has to dismiss Kant's construction of transcendental logic (which presupposes the confinement of the absolute to the realm of postulates and regulative ideas); but the reference frame of both Kant and Hegel's (transcendental) logic is the absolute (the unconditioned).
Nach Herrmann Broch ist jeder säkulare Intellektuelle ein Häretiker, wie auch jeder Held ein Rebe... more Nach Herrmann Broch ist jeder säkulare Intellektuelle ein Häretiker, wie auch jeder Held ein Rebell gegen die Platonische Ordnung ist. Es ist demnach ironisch genug, dass Kurt Gödel auf dem Gebiet der mathematischen Logik Entdeckungen machte, deren Tragweite voll zu durchmessen (philosophisch wie fachspezifisch) der Arbeit von kommenden Jahrzehnten vorbehalten bleibt 1 , während er zeitlebens an einem (zugegeben sehr differenzierten) Platonismus 2 festhielt. In den Jahren 1928-1939 legte Gödel einige der wichtigsten Ergebnisse für die Formale Logik seit Aristoteles vor: Die Vollständigkeit der Logik erster Stufe; die Unvollständigkeit axiomatischer Systeme, welche die elementare Zahlentheorie enthalten; die Konsistenz des Auswahlaxioms und der Kontinuum-Hypothese mit den übrigen Axiomen der Zermelo-Fränkel'schen Mengenlehre. In den selben Jahren, in denen er sich mit dem Entscheidungsproblem und dem Begriff der Berechenbarkeit befasste (beide stellen Grundlagen der Künstlichen Intelligenz dar), oder eine zukunftsweisende Interpretation der intuitionistischen Logik erarbeitete, reifte in dem evangelisch getauften (tatsächlich aber nie einer Kirche angehörenden) Mathematiker ein rationalistischer Theismus heran, der sich gut in die Tradition des Böhmischen Reform-Katholizismus einfügt (wie dieser z.B. von Bernard Bolzano verkörpert wird). Gödels wohl bekannteste Ergebnisse, die Unvollständigkeitssätze, grenzen die Leistung der Axiomatischen Kalkülisierung (David Hilberts formalistischer Ansatz) auf die Ermöglichung eines unscharfen kartographischen Blicks ein, während eine durch die Axiomatisierung vorgeblich zu leistende apodiktische Evidenz für das Ganze der Mathematik prinzipiell in Zweifel gezogen wird. Ein ausreichend starkes formales System enthält nach dem ersten Gödel'schen Unvollständigkeitssatz wahre, im selben System jedoch formal unbeweisbare Sätze 3 , wobei dieses Ergebnis auch für die Eigenschaft der Widerspruchsfreiheit des fraglichen Systems selbst gilt (so dass ein ausreichend starkes formales System nicht vollständig und widerspruchsfrei sein
Structuralism as Transcendental Aesthetic In his early work on the theory of case (La Catégorie d... more Structuralism as Transcendental Aesthetic In his early work on the theory of case (La Catégorie des Cas, Kopenhagen 1935-1937), Hjelmslev's focuses on the general problem of the delimitation of categories; this issue, obviously, has a direct import on the question how categorial form is given and which distinctions in a given substance contribute to schematize the categorial form (constitution of a symbolic domain). With the question of the delimitation of a category, thus, the inquiry manifests a transcendental turn, which is all the more remarkable in view of the predominance of ontology in contemporary European culture. When the author says that the three categories of case, number and genus pose an entanglement (enchevêtrement), he takes issue with two different questions latent in traditional grammar: the relation between formal and material categories (the interpretation of numerus as quantity, of genus as gender); and the problem of the differential definition of a symbolic structure (delimiting the categories one against the other). While these themes prefigure the famous differentiation (form of content/form of expression, substance of content/substance of expression) of the deSassurean scheme in the Prolegomena (1943); the necessity of a mediation (in traditional philosophical terminology: schematism) of categorial form in an expressive medium is stressed throughout Hjelmslev's early work. Also the diacronic considerations point in the same direction, for example when, following the path opened by another great danish linguist, Otto Jespersen, H. says that the shift from a synthetic language (latin), which expresses grammatical roles through desinences, to an analytic language like french with prepositional forms, enacts a relocation (remplacement) of the categorial matter. By 1951, when Merleau-Ponty wrote Sur la Phénoménologie du Langage (published also in Signes, 1960, the author's last published book before his death 1961), this morphological distinction between synthetic and analytic languages must have been a common place; even if we are not in the position to reconstruct Merleau-Ponty's direct source, much in the contest of that essay speaks for Hjelmslev.) Sub-Structure The central idea of Hjelsmlev's reflection on the theory of case, however, is that the articulation of linguistic categories and mathematical (logical) categories are indifferent to one another. The discovery of the symbolic realm is, at the same time, the discovery that what Husserl calls categorial intuition, presupposes a radical disconnectedness between symbolic order and logical form: " the linguistic system is free in relation to the logical realm to which it corresponds " (La Catégorie, op.cit., p. 102). In the early Hjelmslev, the problem of a transcendental schematisme, that is the problem of constructing the relation of possible objects in relation to given rules and a given categorial matter (language), is taken issue with by positing a sublogical system (the claim is that the clarity with which the author develops the problem of a sublogic, remains unattained in his later work, with one exception). Both the associative oppositions (partecipative) of the symbolic system (grammatical forms) and the mathematical oppositions of the logical system, are founded in a sublogical tripartite systems of distinctions (positive, negative and neuter). This dimensionality is foundational in a double sense: it is through operational derivations of a given symbolic order from the sublogical categories, that the formal categories operational in a symbolic and logical domain are apprehended. Secondly, the sublogical operations constitute the relation object-subject, that is reflections concerning the historicity and relativity of a system of categories are motivated by reflections on the contingency of the symbolic order. Structures as semantic-pragmatic interface
Action failure is tied to different types of incompleteness. The conjecture is advanced that a pr... more Action failure is tied to different types of incompleteness. The conjecture is advanced that a proposition defining the type sensitiveness of action tokens should be taken as a starting point for structuring the syntax of a modal logic of action, if the multifaceted phenomenon of action incompleteness is to be accounted for. In the following, the focus on actions which " consume " their type features is functional to the interest in acting on / within institutions: the design of minimal institutions must take a completeness criterion into account, unless unplayable games are to be cast upon agents. Since an agent's performance involves reference to a composite frame (resource spaces, e.g. varying availabilities; epistemic spaces, i.e. changing preferences; time points, paths, histories), it seems to make sense to assume that the notion of action incompleteness allows for different general interpretations. As a matter of fact, action incompleteness is part of the very fabric of agency in at least three respects: 1. Learning (reiteration as a device for designing and planning): given a training routine, for learners it is crucial to distinguish between weak and strong default (to use the jargon of programmers), with the former involving reference to an object which is not being retained for retrieval in subsequent implementations of the program, whereas the latter typically defines conditions for an object to be retrieved if a policy requests such revision or update. Learning by doing is systematically linked to a specific iteration pattern performed, while this same feature ties learning (belief update) to a radical contingency: if the choice to deliberate and change the agent's intentions is designed as functional to running routines, then reconsidering and updating are modeled as mechanisms triggered by some intervening collapse or breakdown or unavailability (an agent might go on indefinitely on the basis of unrealistic assumptions); whereas an agent constantly reconsidering and updating its delete list would run out of time for the realization of any proposed task. 2. Linguistic representation: since the seminal distinction by Vendler (Vendler, 1957) between achievements and accomplishments has been under some criticism of late1, a finer grained modeling and formalization of agency default is likely to help in discriminating between purely lexical meaning and grammatical structure of natural language expressions relating to 1 See the summary of the discussion in Hagit Borer, The Normal Course of Events. OUP 2005 (vol. II of Structuring Sense); p. 326. States and Activities are the other two categories of events which Vendler distinguishes. In the context of this paper, I decide to focus on achievements and accomplishments, for the sake of the peculiar relation they entertain to planning. Furthermore, by studying the design (Pollock) of accomplishments and achievements one may better understand the role of operations in the performance of specific action chains. See on this aspect Pollock (1995), ch. 6, The Logical Structures of Plans.
After Kant's dictum in the Preface of Metaphysical Foundations of Natural Science"in any special ... more After Kant's dictum in the Preface of Metaphysical Foundations of Natural Science"in any special doctrine of nature there can be only as much proper science as there is mathematics therein."* (A IX) After introducing the distinction between a philosophy of nature and a pure doctrine of nature (a determination of causality as connectedness of matter), K. states in the same context: "And, since in any doctrine of nature there is only as much proper science as there is a priori knowledge therein, a doctrine of nature will contain only as much proper science as there is mathematics capable of application there."* In trying to spell out the notion "capable of application", recent commentators have failed to exploit the difference between intuition and sensation. Consequently, a focus on but extensive quantity has conditioned the discussion. What is said in Phoronomy about the composition of motions (systems of bodies) as well as in Proposition 8. of the Dynamics, is textual evidence for a conception of mathematical applicability from the point of view of intensive quantity and the second mathematical Grundsatz (KrV B 208).
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Kantian Equilibrium, Natural History of Fairness and the fictitious play of the Critiq... more Abstract
Kantian Equilibrium, Natural History of Fairness and the fictitious play of the Critique. A Critique of Dekanting, Detranscedentalizing, Putting into Operation of the Categorical Imperative. This inquiry deals with the import of moral arguments for a political theory of income distribution. The restriction to a ‘political theory’ is essential, since occasional considerations about the economic and/or ethical theory of resource allocation in the following are to be taken as functional to a theory of politics. In particular, as of late it has been claimed that a version of the Categorical Imperative can be used to function as a constraint in modelling transitional processes of resources distribution. Such claims have to be carefully considered in the light of Kant’s own Political Theory, which he began to articulate systematically as a system of norms in the last stage of his work in esoteric and exoteric work. The claim that a Theory of Politics and Justice can be constructed based on the textual basis of the Kantian Corpus, although not at all consensual, will not be further justified. At some points, a construction has to be submitted following hints in the Kantian texts. The reason is that certain relevant aspects are not systematically developed by Kant, especially in Metaphysics of Morals (MS) and in the popular treatises Perpetual Peace and On the Old Saw and Religion within the Boundaries of mere Reason.
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Kantian Equilibrium, Natural History of Fairness and the fictitious play of the Critique. A Critique of Dekanting, Detranscedentalizing, Putting into Operation of the Categorical Imperative.
This inquiry deals with the import of moral arguments for a political theory of income distribution. The restriction to a ‘political theory’ is essential, since occasional considerations about the economic and/or ethical theory of resource allocation in the following are to be taken as functional to a theory of politics. In particular, as of late it has been claimed that a version of the Categorical Imperative can be used to function as a constraint in modelling transitional processes of resources distribution. Such claims have to be carefully considered in the light of Kant’s own Political Theory, which he began to articulate systematically as a system of norms in the last stage of his work in esoteric and exoteric work. The claim that a Theory of Politics and Justice can be constructed based on the textual basis of the Kantian Corpus, although not at all consensual, will not be further justified. At some points, a construction has to be submitted following hints in the Kantian texts. The reason is that certain relevant aspects are not systematically developed by Kant, especially in Metaphysics of Morals (MS) and in the popular treatises Perpetual Peace and On the Old Saw and Religion within the Boundaries of mere Reason.