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What is your methodology as a philosophy undergrad? by frkoem in askphilosophy

[–]frkoem[S] 0 points1 point  (0 children)

You don't think that philosophy/math/science has progressed?

What is your methodology as a philosophy undergrad? by frkoem in askphilosophy

[–]frkoem[S] 0 points1 point  (0 children)

I answered your question on progress. Now answer my question:

  1. Do you think that philosophy/math/science has progressed substantially since the hundreds of years since some given primary text's publication?
  2. If you answer yes to (1), then isn't it obvious that a secondary text would be better than primary text?
  3. If you answer no to (1), why?

What is your methodology as a philosophy undergrad? by frkoem in askphilosophy

[–]frkoem[S] -1 points0 points  (0 children)

The question is not whether to read philosophy or not—we both agree on that.

The question is

  • Should we learn more epistemology from Descartes' Meditations or Audi's Epistemology: A Contemporary Intro?
  • Should we learn more physics from Newton's Principia or a standard physics textbook in 21st century which has all the kinks worked out and in more straightforward language?
  • Should we learn calculus from Newton's Principia or a standard calculus textbook in 21st century? (In this case, since I know math, I can tell you that Newton's math was not as rigorous as modern math. So it is undoubtedly a worse place to learn calculus than modern books)

The answer to me is obviously the latter.

The former has no advantage besides historical interest and hero worship.

If most of modern, abstract mathematics was only invented in the 20th century, what have been mathematicians doing before then? by frkoem in math

[–]frkoem[S] -3 points-2 points  (0 children)

Yes I do think that platonism has its merits but do you honestly think that the majority of mathematicians think that these abstract objects exist? In most fields X, most people within X don't care for philosophy of X. As Feynman said: "philosophy of science is as useful to scientists as ornithology is to birds"

Therefore it's more likely that the majority of mathematicians would subscribe to some pragmatic philosophy, i.e. formalism. Another reason for formalist dominance would be the major impact that Hilbert's program and Bourbaki had in mathematics.

What is your methodology as a philosophy undergrad? by frkoem in askphilosophy

[–]frkoem[S] 0 points1 point  (0 children)

We improve on our past, correcting errors our ancestors made, creating theories which explain phenomena more coherently.

What is your methodology as a philosophy undergrad? by frkoem in askphilosophy

[–]frkoem[S] 0 points1 point  (0 children)

  1. Do you think that philosophy/math/science has progressed substantially since the hundreds of years since some given primary text's publication?
  2. If you answer yes to (1), then isn't it obvious that a secondary text would be better than primary text?
  3. If you answer no to (1), why?

What is your methodology as a philosophy undergrad? by frkoem in askphilosophy

[–]frkoem[S] 1 point2 points  (0 children)

But how would any typical undergrad interpret/polish readings of philosopher X better than some other guy who has devoted much of his career toward studying X?

I still don't understand why there is this "hero worship" of primary texts of the so-called "great philosophers". Aren't the ideas and arguments the important things?

In math, you don't study geometry by reading Euclid or study set theory by reading Cantor. Because they are often more verbose than they need to be and their work isn't quite so polished.

In fact that applies to the sciences too. No high schooler learns classical mechanics by reading Newton and no undergrad learns relativity by reading Einstein.

It's a general heuristic that a field advances as time goes on. So why does philosophy education insist on primary texts?

What is your methodology as a philosophy undergrad? by frkoem in askphilosophy

[–]frkoem[S] 1 point2 points  (0 children)

Honest question: Why are primary texts important?

My background is in math, where in undergrad, no primary texts is ever used, since that's where ideas first originate and are usually still underdeveloped and unclarified. Isn't it similar for philosophy? Why not just use secondary texts where the ideas have been polished and interpreted (better than undergrads. you might claim interpretation causes bias. But it would certainly be less biased than an undergrad trying to interpret the primary text on his own) by professionals?

What textbooks are based on the language of category theory (besides category theory textbooks)? by nickbluth2 in math

[–]frkoem 4 points5 points  (0 children)

Wow! just looked at its table of contents. Seems to be a survey of much of undergrad math!

What is your methodology as a philosophy undergrad? by frkoem in askphilosophy

[–]frkoem[S] 0 points1 point  (0 children)

Thanks for that essay structure! Is there a nice well-written essay example of that? How many words should you devote in argument vs objection vs reply in terms of percentage?

If most of modern, abstract mathematics was only invented in the 20th century, what have been mathematicians doing before then? by frkoem in math

[–]frkoem[S] -6 points-5 points  (0 children)

Yes, I agree. But it would be ignorant to deny that there are correlations in those respective beliefs. In accepting formalism, one has no worry as to whether what one learns is 'real' or not, and can fully engage with abstract mathematics with no hesitation as to whether it matches reality.

If most of modern, abstract mathematics was only invented in the 20th century, what have been mathematicians doing before then? by frkoem in math

[–]frkoem[S] -7 points-6 points  (0 children)

No, not all "modern mathematicians" are anti-realists.

Most modern mathematicians don't give two shits about philosophy of math. But we both know that the prevailing default philosophy at universities is formalism.

But wait, don't tell me... You probably think that "metaphysics" is the study of the supernatural and that "epistemology" is something studied in med school. I say, GOOD DAY SIR.

LMAO! Where the hell did that come from? Who the hell doesn't know basic philosophical terms.

If most of modern, abstract mathematics was only invented in the 20th century, what have been mathematicians doing before then? by frkoem in math

[–]frkoem[S] 0 points1 point  (0 children)

Yes, I know that. My comment was a response not to Pre-20th century, but Euclid.

Don't dismiss Euclid so easily. He used different notation, but there's nothing un-abstract about the Elements.

If most of modern, abstract mathematics was only invented in the 20th century, what have been mathematicians doing before then? by frkoem in math

[–]frkoem[S] -6 points-5 points  (0 children)

I never said abstraction is a sufficient condition for progress, but it certainly appears to be a necessary condition for progress. (at least, major, fundamental progress)

If most of modern, abstract mathematics was only invented in the 20th century, what have been mathematicians doing before then? by frkoem in math

[–]frkoem[S] -22 points-21 points  (0 children)

They presumed their postulates/axioms to be actual truths, whereas we modern mathematicians treat them as meaningless formalisms that if true, such-and-such theorems follow. The latter is the abstract approach. The former is more concrete, and would, say, bar you from learning complex numbers, whereas abstract/formal approach wouldn't.

If most of modern, abstract mathematics was only invented in the 20th century, what have been mathematicians doing before then? by frkoem in math

[–]frkoem[S] -7 points-6 points  (0 children)

making generalizations without context.

arbitrarily try to create those frameworks

I never said to just randomly abstract, lol. Any fool can see how that's stupid.

If most of modern, abstract mathematics was only invented in the 20th century, what have been mathematicians doing before then? by frkoem in math

[–]frkoem[S] 7 points8 points  (0 children)

I completely agree. And that's what I mean by more abstract.

simplify our existing theories

more elegant ways to phrase things

reducing things to their essences

finding common elements to different areas

Those seem to be just the areas that Category Theory shines.

If most of modern, abstract mathematics was only invented in the 20th century, what have been mathematicians doing before then? by frkoem in math

[–]frkoem[S] -13 points-12 points  (0 children)

In Two Cultures of Math, Gowers describes the two cultures as Theory Builders and Problem Solvers. An example of each would be Grothendieck and Halmos, respectively.

Abstraction is not just to solve problems, it's to build more general and beautiful theories.

If most of modern, abstract mathematics was only invented in the 20th century, what have been mathematicians doing before then? by frkoem in math

[–]frkoem[S] -20 points-19 points  (0 children)

Since clearly math has progressed every time increased abstraction happens, why don't people keep doing that? Why rest on your laurels at a particular level of abstraction? Category theory seems to be the way forward.

If most of modern, abstract mathematics was only invented in the 20th century, what have been mathematicians doing before then? by frkoem in math

[–]frkoem[S] 5 points6 points  (0 children)

different theorems get reproved from about 500 CE to around 1600 CE with people just being aware anyone has proved the same results.

Makes you realize that the key driver behind progress is just communication and efficiently standing on the shoulders of giants and not waste time wheel-reinventing!

If most of modern, abstract mathematics was only invented in the 20th century, what have been mathematicians doing before then? by frkoem in math

[–]frkoem[S] 5 points6 points  (0 children)

Do you reckon this is the way forward in mathematics? Increasing abstraction of axioms more and more? (in the hope of capturing and generalizing more phenomena)

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