I blame YouTube.
Unfolding confusions is conceptual clarification. We might ask if we want a coherent, incomplete story, or a complete, incoherent story. The latter is easy. The former, philosophy.
Not as I intended it in that sentence. I meant relishing confusions and celebrating obscurantism.
well, this solves everything. I donāt think anyone would disagree with the idea that mathematicians have an independent body of knowledge or that mathematicians do converge on truth pretty often. And if mathematicians are philosophers then philosophers too.
The paper is a find. I read only an AI summary of the article. Matches Sunyās output, point to point, almost.
I drew up this analogy to assist me in understanding the paper. 2 astronomers must know what āstarā refers to, what object it points to, much, much before they can argue about supernovae. Thatās to say the 2 star-studiers have to know what a star is in order to have a convo on supernovae. This is the typical face of what a fact is to the author.
My only issue is with 200, too low. Shouldnāt it be in the 1000s?
Glad you found it interesting.
Iād adjust your analogy a bit. Your two star gazers should agree as to what they are discussing, if the discussion is to progress. Thatās a bit different to knowing what āstarā refers to. So one might think it a ball of mostly hydrogen, the other the glowing eye of a dragon; in which case they do not agree on what āstarā refers to, but do agree as to what they are discussing.
They agree on the extension but not the description. But the general point is sound: disagreement presumes agreement.
If I recall correctly, Frances deliberately cut down the number of items, and restricted himself to one areaāepistemologyāfor the sake of avoiding tedium. So he probably agrees with you that it should be thousands.
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Mr. BF is onto something and a very general statement that seems to vindicate his stance is, exposure to even just the basics of philosophy can make a person a better thinker. Consider the fact that science/math biggies (Nobel Laureates) of the scientific golden age of the 1900s, like Einstein, Bohr, Heisenberg, Pauli, Russell, Whitehead, etc. were also philosophers/deeply interested in philosophy. Is scientific and mathematical progress indebted to philosophy?
Certainly, at least in so far as there is a common ground in reasoning. Were science presumes reason, I suppose philosophy at least in part studies reason. The folk you name were very keen on conceptual clarity.
Less so these days, maybe; or maybe itās the less clear scientistic thinkers who are popular.
Can we zero in on the X factor(s)? What about philosophy improves scientific/mathematical thinking, in a way that produces real results, theories/theorems?
Perhaps Iām seeing things. Gƶdel pops up (re his refinement of Anselmās ontological argument and his eponymous incompleteness theorems). Then thereās the alleged mysterious connexion between quantum physics and eastern religions/philosophies, which some have dismissed as woo-woo (re Heisenberg, Bohr) though.