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Is this level of density typical for some subset of advanced maths texts? I've never seen anything like it and I'm about to receive an undergrad maths degree.

j2kun 9y ago
This appears to be a philosophy text, to my cursory glance. Definitely not like the advanced math texts I have read.
- aphextron 9y ago
  >This appears to be a philosophy text, to my cursory glance. Definitely not like the advanced math texts I have read. It is absolutely not a philosophy text. It's an attempt at defining a rigorous definition of the basic axioms we take for granted in mathematics in terms of pure logic, and then examining whether those basic rules of logic are themselves irreducible forms of nature or further creations of man. Essentially it seeks to support all higher mathematical thought by not just taking axioms for granted, but formally proving every one.
  - aaachilless 9y ago
    This is not a nitpick, I'm actually curious: When you say "absolutely not a philosophy text" do you mean that it's definitely not 100% philosophy? Or do you mean that it's actually 0% philosophy?
  - j2kun 9y ago
    You say that, and I'm aware of the historical context. But you cannot deny that the majority of the text is devoted to questions like which verbs are appropriate and how words as used in mathematics relate to their notions used in math. In my experience, logic falls into two catgeories: using math to study a formal system of logic; and determining "foundations for all math" and determining what is an "irreducible form of nature" and other such prosaic things (can the phrase "such that" be defined?). In my humble opinion, the former is mathematics and the latter philosophy.
justifier 9y ago
this was written in 1903 by bertrand russell who was both a philosopher and a writer which garnered a nobel prize in literature.. russell loved words i am almost positive all of the views recited in this piece where still considered relevant today have since been made more accessible from textbooks to youtube videos do you need to, or even need to want to, read this piece by russell? hardly, but at the same time it was written by a well respected individual in the field and there could be value in trying to dissect the text regardless of your views on any single piece of writing i would wholeheartedly encourage your interest in mathematics much like how i would encourage someone who dislikes or finds shakespeare too dense to still pursue a career in writing if they so desired but i would still recommend them to take another look
jesuslop 9y ago
By no means, you know normaly maths are written leaving tons of detail to context, folklore, references and well-knowns with human checkable sketchy proofs but in contrast here Russell makes one of the first serious attempts to give a self contained and no assumptions, formal presentation of a part of core maths. Something like now the Mizar library or Coq HOTT. Gödel studied deeply this text and proved the epistemological limitations inherent in this program in his famed theorems, in fact Gödel paper title alluded to Russell's ('on the existence of formally undecidable propositions in Principia Mathematica and related systems').

j2kun 9y ago

This appears to be a philosophy text, to my cursory glance. Definitely not like the advanced math texts I have read.

aphextron 9y ago
>This appears to be a philosophy text, to my cursory glance. Definitely not like the advanced math texts I have read. It is absolutely not a philosophy text. It's an attempt at defining a rigorous definition of the basic axioms we take for granted in mathematics in terms of pure logic, and then examining whether those basic rules of logic are themselves irreducible forms of nature or further creations of man. Essentially it seeks to support all higher mathematical thought by not just taking axioms for granted, but formally proving every one.
- aaachilless 9y ago
  This is not a nitpick, I'm actually curious: When you say "absolutely not a philosophy text" do you mean that it's definitely not 100% philosophy? Or do you mean that it's actually 0% philosophy?
- j2kun 9y ago
  You say that, and I'm aware of the historical context. But you cannot deny that the majority of the text is devoted to questions like which verbs are appropriate and how words as used in mathematics relate to their notions used in math. In my experience, logic falls into two catgeories: using math to study a formal system of logic; and determining "foundations for all math" and determining what is an "irreducible form of nature" and other such prosaic things (can the phrase "such that" be defined?). In my humble opinion, the former is mathematics and the latter philosophy.

justifier 9y ago

this was written in 1903 by bertrand russell who was both a philosopher and a writer which garnered a nobel prize in literature.. russell loved words i am almost positive all of the views recited in this piece where still considered relevant today have since been made more accessible from textbooks to youtube videos do you need to, or even need to want to, read this piece by russell? hardly, but at the same time it was written by a well respected individual in the field and there could be value in trying to dissect the text regardless of your views on any single piece of writing i would wholeheartedly encourage your interest in mathematics much like how i would encourage someone who dislikes or finds shakespeare too dense to still pursue a career in writing if they so desired but i would still recommend them to take another look

jesuslop 9y ago

By no means, you know normaly maths are written leaving tons of detail to context, folklore, references and well-knowns with human checkable sketchy proofs but in contrast here Russell makes one of the first serious attempts to give a self contained and no assumptions, formal presentation of a part of core maths. Something like now the Mizar library or Coq HOTT. Gödel studied deeply this text and proved the epistemological limitations inherent in this program in his famed theorems, in fact Gödel paper title alluded to Russell's ('on the existence of formally undecidable propositions in Principia Mathematica and related systems').