[continued from previous message]   
      
   >>>      Axiomless Natural Deduction and the "Constructed" Nature of Truth:   
   >>>          Axiomless natural deduction, with its focus on inference rules,   
   >>> aligns with this constructivist view. The "truths" it derives are not   
   >>> necessarily reflections of pre-existing realities but rather the logical   
   >>> consequences of the rules and assumptions we employ.   
   >>>          Therefore, the results are "true" within the system that   
   >>> created them.   
   >>>      Metaphysical Implications:   
   >>>          This distinction has profound metaphysical implications. It   
   >>> challenges the traditional view of mathematics as a realm of objective,   
   >>> eternal truths and opens up the possibility of multiple, equally valid   
   >>> mathematical systems, each with its own set of "truths."   
   >>>   
   >>> In essence, the quotation marks were a way of acknowledging the   
   >>> philosophical debate surrounding the nature of truth, particularly in   
   >>> the context of idealism and its challenge to Platonistic ideals.   
   >>>   
   >>>   
   >>>   
   >>>   
   >>> Thanks GG. Actually one might usually identify the idealistic and   
   >>> platonistic together, and separate instead the analytical tradition as   
   >>> nominalism. Comment for example as about these, then for example with   
   >>> regards to Derrida's reading of Husserl's geometry and the   
   >>> pre-geometric, pre-geometric world as a merest silver thread connecting   
   >>> an idealistic tradition and metaphysics, and truth, providing a   
   >>> justification of the analytical tradition.   
   >>>   
   >>>   
   >>>   
   >>> You've raised a very important and subtle point about the complex   
   >>> relationship between idealism, Platonism, and the analytical tradition.   
   >>> It's true that in many contexts, idealism and Platonism share a common   
   >>> ground, particularly in their opposition to nominalism, which is more   
   >>> aligned with the analytical tradition. Here's a breakdown:   
   >>>   
   >>> Idealism, Platonism, and Nominalism:   
   >>>   
   >>>      Idealism and Platonism (Shared Ground):   
   >>>          Both emphasize the existence of abstract entities or ideals   
   >>> that transcend the physical world.   
   >>>          They often prioritize reason and intellectual intuition over   
   >>> empirical observation.   
   >>>          In mathematics, they tend to believe in the objective existence   
   >>> of mathematical truths, even if those truths are not directly   
   >>> observable.   
   >>>          They both find a place for the mind, or consciousness, as an   
   >>> important part of the structure of reality.   
   >>>      Nominalism (Analytical Tradition):   
   >>>          Nominalism, associated with the analytical tradition, rejects   
   >>> the existence of abstract entities.   
   >>>   
   >>> It argues that universals (like "redness" or "triangularity") are merely   
   >>> names or concepts, not real entities.   
   >>>   
   >>>          It emphasizes the importance of language, logic, and empirical   
   >>> observation.   
   >>>          It is more concerned with the way that language, and logic, are   
   >>> used to describe the world, instead of the world itself.   
   >>>          The analytical tradition often favours formal systems, and the   
   >>> symbolic manipulation of those systems, over the intuitive appreciation   
   >>> of idealistic systems.   
   >>>      Derrida, Husserl, and the Pre-Geometric:   
   >>>          Derrida's reading of Husserl's "Origin of Geometry" is crucial   
   >>> here. Husserl, though often considered an idealist, sought to ground   
   >>> geometry in a primordial, pre-geometric experience.   
   >>>          Derrida, however, deconstructs this attempt, highlighting the   
   >>> inherent instability of any attempt to ground knowledge in a pure,   
   >>> unmediated experience.   
   >>>          The "pre-geometric" becomes a site of tension, a "silver   
   >>> thread" connecting idealism's quest for foundational certainty with the   
   >>> inevitable slippage and ambiguity that Derrida exposes.   
   >>>          This pre-geometric world, is the world of experience, before it   
   >>> has been formally defined. This world is the world of the senses, and of   
   >>> subjective experience.   
   >>>      The Analytical Tradition's Justification:   
   >>>          Derrida's critique, and the focus on the instability of   
   >>> foundations, provides a kind of justification for the analytical   
   >>> tradition's emphasis on language and formal systems.   
   >>>          If there is no stable, pre-geometric ground, then the focus   
   >>> shifts to the rules and conventions that govern our language and   
   >>> reasoning.   
   >>>          The analytical tradition, with it's focus on formal logic, and   
   >>> symbolic manipulation, is well suited to deal with systems that do not   
   >>> have a firm foundation.   
   >>>          The analytical tradition, then, is justified by the failure of   
   >>> the idealistic tradition to establish a firm foundation. The analytical   
   >>> tradition provides a way to deal with the instability that is left   
   >>> behind.   
   >>>   
   >>> In essence, the tension between idealism/Platonism and   
   >>> nominalism/analytical tradition is revealed in the struggle to ground   
   >>> knowledge. Derrida's reading of Husserl exposes the limitations of   
   >>> idealistic attempts to find a pure foundation, thereby indirectly   
   >>> validating the analytical tradition's focus on language and formal   
   >>> systems.   
   >>>   
   >>>   
   >>>   
   >>>   
   >>> Thanks GG. One may actually read Derrida reading Husserl and find that   
   >>> instead both are sure of the truths of geometry that arrive via the   
   >>> pre-geometric as geometry, and that both are quite platonistic while yet   
   >>> so compliant to logicist positivism, then that their reviews mostly   
   >>> reflect the lens of logical positivism as its own justification, which   
   >>> may be no more than a science. Comment on this as from various   
   >>> perspectives.   
   >>>   
   >>>   
   >>>   
   >>>   
   >>> You've presented a fascinating and provocative reading of Derrida and   
   >>> Husserl, challenging the conventional interpretation. You're suggesting   
   >>> that, despite their apparent differences, they share a deep-seated   
   >>> Platonism and a compliance with logicist positivism, and that their   
   >>> critiques primarily serve to reinforce the latter. Let's explore this   
   >>> from various perspectives:   
   >>>   
   >>> The Shared Platonism and Logicist Compliance:   
   >>>   
   >>>      Geometry's Inherent Truth:   
   >>>          You're right to point out that both Husserl and, arguably, even   
   >>> Derrida, don't fundamentally question the validity of geometric truths.   
   >>> Husserl seeks to ground them in a pre-geometric intuition, while   
   >>> Derrida, even in his deconstruction, acknowledges the persistence of   
   >>> geometric ideals.   
   >>>          This could be interpreted as a form of Platonism, where   
   >>> geometric truths possess a certain independence and necessity.   
   >>>      Logicist Positivism's Influence:   
   >>>          The emphasis on logical rigor and formal systems, even in   
   >>> Husserl's phenomenological project, reflects the pervasive influence of   
   >>> logicist positivism in the early 20th century.   
   >>>          Derrida, despite his critique of Husserl, operates within a   
   >>> philosophical landscape shaped by this logicist emphasis. His   
   >>> deconstruction often relies on precise linguistic analysis and logical   
   >>> argumentation.   
   >>>          This is shown in the precise way that Derrida analyzes the   
   >>> texts of Husserl.   
   >>>      The Self-Justifying Lens:   
   >>>          Your point about their reviews primarily reflecting the lens of   
   >>> logical positivism is crucial. You're suggesting that their critiques,   
   >>> rather than dismantling the logicist framework, actually reinforce it by   
      
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