smcder
Paranormal Adept
Isn't that 'expectation' a reaction to Godel's Incompleteness Theorums and others named in the wikipedia article that have recognized the limitations of our tendency toward formalist thinking based in reified concepts of that which is experienced? Kafatos attempts to move us beyond that tendency.
["Gödel's incompleteness theorems are two theorems of mathematical logic that demonstrate the inherent limitations of every formal axiomatic system containing basic arithmetic.[1] These results, published by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The theorems are widely, but not universally, interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all mathematics is impossible.
The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an effective procedure (i.e., an algorithm) is capable of proving all truths about the arithmetic of the natural numbers. For any such formal system, there will always be statements about the natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem, an extension of the first, shows that the system cannot demonstrate its own consistency.
Employing a diagonal argument, Gödel's incompleteness theorems were the first of several closely related theorems on the limitations of formal systems. They were followed by Tarski's undefinability theorem on the formal undefinability of truth, Church's proof that Hilbert's Entscheidungsproblem is unsolvable, and Turing's theorem that there is no algorithm to solve the halting problem."
Gödel's incompleteness theorems - Wikipedia]
Steve's post continues:
I'm impressed to learn that Feynman broached the qualitativeness behind/beneath mathematical expression [where most mathematicians and physicists evidently have not]. From the paper Steve linked we can follow the notes to read more of what Feynman said on that occasion.
Thought experiments are apparently all we have to work with at this point, having come up against the incompleteness of our understanding in both physics and mathematics and also regarding the nature of consciousness. But the prospects for more comprehensive thought experiments undertaken by Kafatos and the author of the paper linked by @Soupie are most promising. As often, Wallace Stevens provides a phrase that bubbles up for me from thirty years ago providing a sense of the scope of our inquiry at this point, in which we are sensing our approach to "the outlines of Being and its expressings."
@Soupie wrote in his first post today:
"If consciousness is fundamental and continuous (as we've been discussing), then we still need to understand how the structure of the organism/brain shapes consciousness into specific contents of consciousness. And if all processes are fundamentally conscious, why does it seem that some processes are conscious and some are not?"
What we need to explore is the spectrum of evolution/increasing complexity of living organisms developed from original 'awareness' to prereflective consciousness and the nature of subconscious mind that arises within it, as the phenomenologists have been arguing.
I'll be reading with interest both the paper @Soupie linked today and this additional Kafatos paper linked by Steve as soon as I finish reading the rest of the new posts in the thread today. It feels, to me, like we are now coming to the edge of a desert in our attempts to understand consciousness/mind and confronting an ontological mountain we will need to scale in order to understand more about the nature of 'reality'/what-is. It looks like there will five of us making the climb now that @william has joined us and @Pharoah has told me that he is rejoining the thread. Happy days.
the Kafatos paper takes a Platonist approach to mathematics (the paper about the qualitative interpretation of mathematical formulas) - the other paper I posted on the "reasonable" effectiveness of mathematics would not agree ... but it's an open question, what makes me uneasy is the move in the Kafatos paper from formula to reality. As I said, we haven't discussed the philosophy of mathematics much and it's not on the main subject line - so maybe we can come back to this later.