Mathematics
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MATHEMATICS

Philosophy of Mathematics

These preliminary notes date back to 1984–2000. They were intended to become a part of an extended version of the already published draft of the Philosophy of Consciousness (Trafford 2009), as a kind of natural-scientific illustration. Here, a few relatively complete fragments are presented, just to illustrate the general direction of thought and to hint on the scientific background of the other expositions of unism. Each note is self-contained, and there is no particular order that would impart a sense of monograph to the whole.

Flames of Math
Mathematics as a Social Science
Mathematical Relativity
Mathematics and Computers
Mathematical Measurement
The Diagonal Fallacy
The Straights of the Circle
Numeral Systems
Perceptive Forms
Elementary Sets
Rational Dimensions
Dreams and Things
Crazy Kantor
A Broken Parity
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Mathematical Notes

Sets vs. Boolean Algebra
Negative Sets
Fuzzy Sets and Relativistic Velocity Addition
Logical Symmetries and Complex-Valued Logic
Points and Limits
Hierarchical Dimension
Quantum Set Theory
Abstract Pictures
Objective Set Theory
Cardinal Hierarchy
The Quality of Negation
Oriented Curves
Virtual Mathematics
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Notes on the Margins
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Remarks

Comments on "Visualization of the Continuum Problem and Mirror Symmetric Proofs in the Transfinite Numbers Theory" by A.Zenkin
Comments on "Fatal Mistake of Georg Cantor" by A.Zenkin

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Qualitative Complexity
Dynamical Computing, Communication and Hierarchical Inference
A Mathematical Model of Scale Perception
Art as creative communication
Nonlinear art
Philosophy of Consciousness


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