Go to page 42 for a discussion of our Faculty of Reason which illustrates how our feelings are regulated by emotions in the right hemisphere (related to language), while math is regulated by logic in left hemisphere. Relatedly, go to the integration wheel (of human cognition) on page 24 to get a picture of why concept-formation is fundamental to everything, i.e., math, language, physics, metaphysics, etc.
FYI, I am new to Substack which apparently hides external links. The website I refer to is www (plus a dot) and "find-your-map" plus dot com. Hope that helps. :)
The distinguishing point here is math is well defined (i.e., unit measurement via a defined standard) and thus contextually complete, while language is incomplete and thus implicit. Both are the product of concept-formation, the process that defines us humans relative to other animals via our ability to differentiate time. By differentiating time, we are abstracting ourselves (i.e., our cognitive process) out of reality. This is why we cannot prove a map without the territory. Math is the map, reality is the territory which we can experience but only to a limited extent. Our senses evolved to primarily experience the universe of space and matter. While we can feel the effects of the quantum aspects of the universe, this is largely implicit, with our emotions being the cognitive regulators. You can get a better view of this in a book I recently published at www (dot) find-your-map.com. Look for the Faculty of Reason sub-section under the temporal hypothesis section (which explains how concept-formation works). Cheers.
How can a true statement be unprovable. It’s already proven by the fact that it is true. It needs no proof. It is a definition. Can you prove that my definition of true is true or wrong? Most statements have anti statements that make them provable one way or the other. However a statement whose contradiction does not exist has no anti partner. Akin to photons being their own antiparticles unprovable statements that are true are like bosons. Statements with possible anti statement outcomes cannot be classed as unprovable. However there are those statements whose truth rely on their singular meaning and thus need no proof.
Curt, feel free to share this with Matt.
Does Krishnamurti's statement 'truth is a pathless land' apply to mathematics?
Here's the direct link that will automatically download this book.
https://www.find-your-map.com/__static/jdj5jdewjgvfy0ximkw5vtvxdxrtwfbw/Find-Your-Map-PDF-Download.pdf
Go to page 42 for a discussion of our Faculty of Reason which illustrates how our feelings are regulated by emotions in the right hemisphere (related to language), while math is regulated by logic in left hemisphere. Relatedly, go to the integration wheel (of human cognition) on page 24 to get a picture of why concept-formation is fundamental to everything, i.e., math, language, physics, metaphysics, etc.
FYI, I am new to Substack which apparently hides external links. The website I refer to is www (plus a dot) and "find-your-map" plus dot com. Hope that helps. :)
The distinguishing point here is math is well defined (i.e., unit measurement via a defined standard) and thus contextually complete, while language is incomplete and thus implicit. Both are the product of concept-formation, the process that defines us humans relative to other animals via our ability to differentiate time. By differentiating time, we are abstracting ourselves (i.e., our cognitive process) out of reality. This is why we cannot prove a map without the territory. Math is the map, reality is the territory which we can experience but only to a limited extent. Our senses evolved to primarily experience the universe of space and matter. While we can feel the effects of the quantum aspects of the universe, this is largely implicit, with our emotions being the cognitive regulators. You can get a better view of this in a book I recently published at www (dot) find-your-map.com. Look for the Faculty of Reason sub-section under the temporal hypothesis section (which explains how concept-formation works). Cheers.
How can a true statement be unprovable. It’s already proven by the fact that it is true. It needs no proof. It is a definition. Can you prove that my definition of true is true or wrong? Most statements have anti statements that make them provable one way or the other. However a statement whose contradiction does not exist has no anti partner. Akin to photons being their own antiparticles unprovable statements that are true are like bosons. Statements with possible anti statement outcomes cannot be classed as unprovable. However there are those statements whose truth rely on their singular meaning and thus need no proof.
The sort of provability referenced in the theorem is a model theoretic one about being derivable from the axioms.