Download Mathematics and the Natural Sciences: The Physical by Francis Bailly, Giuseppe Longo PDF

By Francis Bailly, Giuseppe Longo

This e-book identifies the organizing strategies of actual and organic phenomena by means of an research of the principles of arithmetic and physics. Our goal is to suggest a conversation among diversified conceptual universes and hence to supply a unification of phenomena. The position of 'order" and symmetries within the foundations of arithmetic is associated with the most invariants and ideas, between them the geodesic precept (a outcome of symmetries), which govern and confer team spirit to varied actual theories. furthermore, an try out is made to appreciate causal constructions, a vital section of actual intelligibility, when it comes to either symmetries and symmetry breakings. A contrast among the foundations of (conceptual) development and of proofs, either in physics and in arithmetic, courses many of the paintings.
the significance of mathematical instruments can also be highlighted to explain adjustments within the types for physics and biology which are proposed through non-stop and discrete arithmetic, corresponding to computational simulations.
when you consider that biology is especially advanced and never in addition understood at a theoretical point, we recommend a "unification by means of concepts" which as a minimum should still precede mathematization. This constitutes an overview for unification additionally according to highlighting conceptual ameliorations, advanced issues of passage and technical irreducibilities of 1 box to a different. certainly, we believe the following a really universal monist perspective, particularly the view that dwelling gadgets are "big baggage of molecules". the most query although is to appreciate which "theory" might help larger comprehend those baggage of molecules. they're, certainly, really "singular", from the actual perspective. Technically, we convey this singularity in the course of the suggestion of "extended criticality", which supplies a logical extension of the serious transitions which are identified in physics. The presentation is generally stored at a casual and conceptual point.

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Additional info for Mathematics and the Natural Sciences: The Physical Singularity of Life (Advances in Computer Science and Engineering: Texts)

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In more constructive and recent terms, the breaking of the symmetry between proof principles and construction principles, of an essentially geometric nature, leads us to understand the insufficiency of a sole logico-formal language as the foundation of mathematics and brings back to the center of our forms of knowledge a constitutive mathematics of time and space, thanks to its construction principles. There is concrete incompleteness, a modern version of Gödelian incompleteness, a discrepancy or breaking in provable symmetry between construction principles and proof principles.

A physics which no longer exists, decades after work and debate in relativity, in the physics of critical systems and in quantum physics. The failure of this “realist” epistemology of mathematics is parallel to the absence of an epistemology of physics. ” Alain Badiou (Badiou, 1990) emphasizes the richness of this Platonism, alone, in mathematics, resembling that of Plato: thought envelops the object, while the idea is “already there,” but as the name of that which is thought and which would remain unthinkable if not activated within thought.

Moreover, for Gödel, as we are reminded, “the objective existence of the objects of mathematical intuition . . is an exact replica of the question of the objective existence of the outside world” (Gödel, 1947). This approach, all the while bringing the question of a mathematical ontology closer to that of an ontology of physics, is far more promising than the realism common in mathematics, a funny mix of vulgar empiricism and of idealism, with the worst shortcomings of each of these two philosophies.

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