I think that the vast majority of academic papers are considered to be irrelevant. In that sense, it does not matter if the justification supplied is solid or not. Nobody cares anyway — Tarskian
The mathematics of this is precise. A fractal distribution system has a log/log or powerlaw scale of size. That is how a geography can be efficiently covered so every drop of water or wannabe flyer gets an equal chance of participating in a well-organised network of flow — apokrisis
It is where pure mathematics tries to establish a foundation of knowledge that I am disgruntled. The effort is laudable - but mathematicians have gotten themselves stuck in a dead end and appear unwilling to extricate themselves. — Treatid
That is why I have personally never treated and will never treat philosophy or mathematics as more than just hobbies — Tarskian
Mathematics does not have direct practical applications, mostly by design so. That is often a good thing, but it also means that the academic consensus has much more weight than it would have, if there were practical applications — Tarskian
There's just the mutually back-patting consensus, or else meaningless grades on a collection of otherwise irrelevant tests and exams, or even the eternally back-patting citation carousel. That is why I have personally never treated and will never treat philosophy or mathematics as more than just hobbies — Tarskian
Not sure if mathematical logic is just a curiosity — Tarskian
One could say the crisis is still going on, as we don't know whether ZFC is free of contradictions (and perhaps never will). — Lionino
We could spend decades arguing back and forth over whether mathematicians are applying rules consistently to the staircase paradox — Treatid
(1eg) If a theory explains an observation, then the theory is evidenced. — Hallucinogen
I actually did not invent the term "foundational crisis of mathematics" by myself — Tarskian
Here we go again, assuming a stroll along an uneven path is the same as wandering through a minefield. — jgill
So, the idea is that the use of Godel numbering in a logic expression points to making use of the philosophical capability of the language and therefore turns the expression into a philosophical one. There may be exceptions, though. — Tarskian
The origin for what I write, is of course, the foundational crisis in mathematics — Tarskian
How is all this relevant for defining philosophy? How is this the relevant to philosophy in any way? — Ludwig V
Mathematicians have a long career of coming across inconsistencies and hurriedly changing the rules so that this particular inconsistency no longer counts. — Treatid
Math originally came from accounting, believe it or not — frank
Mathematics and accounting are deeply intertwined, but mathematics did not originally come from accounting. Instead, mathematics has a much broader and older origin that spans various domains.
Here’s a brief overview of how these fields are related:
Early Mathematics: The origins of mathematics date back to ancient civilizations such as the Babylonians, Egyptians, and Greeks. Early mathematics involved basic counting, measurements, and arithmetic. These practices were crucial for various practical activities like agriculture, trade, and construction.
Accounting Origins: The practice of accounting, especially systematic bookkeeping, has roots in ancient civilizations as well. For instance, the Sumerians developed one of the earliest known accounting systems around 3000 BCE, which involved recording transactions on clay tablets. Accounting was essential for managing resources, trade, and taxation.
Development of Mathematics: Mathematics evolved from these practical needs into a more abstract and systematic study. Ancient Greeks, such as Pythagoras, Euclid, and Archimedes, made significant contributions to mathematics that went beyond mere accounting and measurements, exploring geometry, number theory, and more.
Interconnection: As mathematics developed, it increasingly influenced and was influenced by accounting practices. For example, the development of algebra and calculus provided tools for more sophisticated financial analysis and modeling.
In summary, while accounting and mathematics are closely related and have influenced each other, mathematics as a discipline predates accounting and encompasses a much broader range of study than accounting alone.
In mathematics - a paradox (inconsistency) demonstrates a faulty set of axioms — Treatid
Describe why arbitrary transfers are philosophically significant — Mark Nyquist
Abraham Robinson's definition of h revolutionised mathematics in the 1960's. — alan1000
Virtually every professional mathematician lives in the world created by this movement. Nobody notices because it's like fish not noticing water. — fishfry
Even worse than Wikipedia, which much too often is, at best, slop. Quora is close to the absolute lowest grade of discussion. It is a gutter of misinformation, disinformation, confusion and ignorance. Quora is just disgusting — TonesInDeepFreeze
"[...] as an introduction to a topic Wikipedia is very good."
I'll fix that: as an introduction to a topic Wikipedia is very good lousy. — TonesInDeepFreeze
Wikipedia articles about mathematics are too often incorrect, inaccurate, poorly organized or poorly edited — TonesInDeepFreeze
It's call the arithmetization of analysis. It's a thing in late 19th century math. Basically founding math, including calculus and continuous processes, on set theory.
https://en.wikipedia.org/wiki/Arithmetization_of_analysis — fishfry
My favorite game on the internet is guessing the number of page views per day for math and other topics. I guessed 126 here, whereas it is 111. Close, but no cigar. — jgill
That's interesting. Which page views? I think you've mentioned in the past that you look at papers written or something like that. — fishfry
So truth and falsity, semantic concepts, are always relative to a particular model. The integers and the integers mod 5 both satisfy the same ring axioms, but 1 +1 + 1 + 1 + 1 = 0 is false in the integers; and true in the integers mod 5.
That's what we mean by truth. Mathematical truth is always:
Axioms plus an interpretation. — fishfry
Mathematicians are starting to use https://en.wikipedia.org/wiki/Proof_assistant , proof assistants and proof formalizer software. It's a big field, going on ten or twenty years now — fishfry
I don't think Jan 6th happens unless Trump gives the speech he gave right before — RogueAI
A sentence in the language of first-order arithmetic is said to be true in N if it is true in the structure just defined.
A sentence in the language of first-order arithmetic is said to be true in N {\displaystyle {\mathcal {N}}} if it is true in the structure just defined
Goldbach's conjecture is one of the oldest and best-known unsolved problems in number theory and all of mathematics. It states that every even natural number greater than 2 is the sum of two prime numbers.
Interesting to hear you arguing against the concept of truth — fishfry
I have a friend who is a math PhD. I have never really had a chance to discuss this sort of thing in depth, but I have asked him before if he though mathematics was something created or discovered. He said "created" but not with any great deal of confidence and waffled on that a bit — Count Timothy von Icarus
You don't believe in the word truth, or that anything in the world is true, even outside of math? — fishfry
Did you think your work was "about" anything? Or pure symbol-pushing?
I'm pressing you on this point because I don't believe you did not believe in the things you were studying! — fishfry
Gravity is true, wouldn't you say? — fishfry