Questions tagged [philosophy-of-science]

For questions about the branch of philosophy studying science, scientists, the scientific method and related topics.

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42
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4answers
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Was Occam’s razor ever wrong?

In brief, I am looking for an example where Occam’s razor favoured a theory A over another theory B, but theory B turned out to be a better description of reality later. But let me formulate some ...
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5answers
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When did Mathematics stop being one of “the Sciences”?

If you ask a mathematician today, many will tell you that mathematics is not a science. Many physicists, chemists, and scientists in other disciplines would say something similar. Mathematicians will ...
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In ancient times, how did people conclude that the shape of Earth is a sphere?

This is more of a philosophical question, but I want a mathematical explanation. During ancient times, it was well accepted that the surface of Earth was spherical. People first observed this when ...
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1answer
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Examples of Kuhn loss?

A Kuhn loss is: a success, empirical or theoretical, of a prior theory – or paradigm as Kuhn would have preferred – that does not carry over to the theory or paradigm that replaced it. [Midwinter ...
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Hypothesis testing: Fisher vs. Popper vs. Bayes

I try to make my question short. I am familiar with Popper’s philosophy as well as with statistical hypothesis testing after Fisher and Neyman-Pearson. I am not so familiar with the Bayesian approach ...
18
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4answers
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Is the Scientific Method uniquely Western?

I'm studying High School Science teaching in Australia. In our Science curriculum there are "cross-curriculum" priorities "Aboriginal and Torres Strait Islander histories and cultures" and "Asia and ...
17
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4answers
888 views

Conflict between physics and philosophy

In the old days. stars of physicists like Einstein$^{[1]}$, Poincare, Heisenberg, Pauli, $^{[2]}$ Bohr and so on are quite philosophical mind, and like philosophy. $^{[3]}$ But now, it seems to me a ...
14
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5answers
442 views

Which school of philosophy motivated thinking about spaces of higher dimension?

I'm trying to make a link between important mathematical breakthroughs in history and the important philosophical schools at the time. I realize that this topic is awfully broad and could be the ...
13
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298 views

Why did Newton want lines to be generated by continued motion of points rather than by apposition of parts?

The following passage has been extracted from the Newton's (John Stewart's English translated version) "Sir Issac Newton's two Treatises: Of the Quadrature of Curves, and Analysis by equations of an ...
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7k views

What is the origin of polynomials and notation for them?

This may be quite a broad question, but lately I've been wondering about the history behind polynomials. Nowadays these are pretty much the simplest kind of functions to work with, but I'd like to ...
13
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1answer
467 views

Hidden agenda of the Galileo trial?

Redondi argued that Galileo's trial on heliocentrism was merely a show trial concealing the real objection against Galileo among the catholic establishment, which was his atomism thought to be at ...
12
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3answers
606 views

Why and when did some areas separate themselves from philosophy and some not?

When the Greeks invented science and mathematics in around 600 BC, it was considered as a part of philosophy. Thales of Miletus was a mathematician and philosopher. Aristotle was a philosopher, ...
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Grothendieck's Approach to Solving Problems

Alexander Grothendieck is known to have revolutionized several areas of mathematics. His insights were very deep, original and revolutionary. Time after time he showed that he could see in ways that ...
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Why was modern science and mathematics a European phenomenon?

Of course much of this can be debated on what you mean by the word “modern” But most of us would agree that the Arabic World and places like India were the leading mathematical and ...
9
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1answer
165 views

How was difference in water pressure perceived in ancient cultures or the middle ages?

I recently wondered: Even when diving to just 2-3 meters without any modern equipment one can feel the change in pressure. Do we have any evidence how this was perceived and explained back in ancient ...
9
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2answers
784 views

Why was the Vienna Circle so important?

As far as I know the Vienna Circle was very relevant to science in the twentieth century. Why? What was the importance of the members' philosophy in science? Would science be too different from what ...
8
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166 views

Leibniz's stand on axioms and definitions

Recently while discussing with a friend he claimed that Leibniz was fond of proceeding axiomatically and from definitions. I find this hard to believe. My conception is that Leibniz was more ...
8
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246 views

Are there any canonical books on history of science?

I was looking for some fundamental books on history of science. I picked Thomas Kuhn book "The Structure of Scientific Revolutions" but it's not exactly about history of science - it's more on ...
7
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269 views

Mathematics PhD dissertations that opened a new field of research

I propose this as a companion wiki page to the one about PhD dissertations which contain a solution to an open problem in the style of big-list questions, thinking ...
7
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1answer
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What's the origin of the concept of the five senses?

It is commonly said (to children) that we have five senses: taste, sight, touch, smell, and hearing. The term "sixth sense" refers to something supernatural. But we do have more senses. Balance, for ...
7
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2answers
291 views

Did Gödel consider himself primarily a philosopher who is interested in mathematics (instead of the other way round)?

Kurt Gödel is one of the "best" logicians of the 20th century. Here, the user "Jeffrey Kegler" states that: Kurt Gödel considered himself a philosopher who did mathematics, rather than as a ...
7
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2answers
193 views

Who was the first scientist to suggest that objects can keep moving without applied force?

In the old days Aristotels argued that object needs a force to keep going in 'space'. Some philosophers, Philoponus and Buridanus (?), later argued that there was a need for some kind of 'impetus'. ...
7
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1answer
358 views

How did Wittgenstein fulfill eligibility requirements for a PhD in philosophy without having a Bachelor's degree in philosophy?

The Wikipedia article about Wittgenstein says: In Norway it was clear that Moore was expected to act as Wittgenstein's secretary, taking down his notes, with Wittgenstein falling into a rage when ...
7
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1answer
204 views

Debate between relationship of philosophy of mathematics and physics

Did there exist and does there still exist a debate over which school of mathematical thought (i.e. formalism, logicism, intuitionism, etc.) had the most affinity or application for physics? In ...
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1answer
309 views

Philosophy behind category theory

Category theory represented a huge change in the way the community thought about mathematics, leaving its the set theoretic nature behind and bringing up the importance of arrows between the objects ...
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Who was the first to say “Shut up and calculate!”?

The best thing I could find on the internet was this apparently forgotten aricle from 12 years ago.
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245 views

Why statistical moments are called moments?

According to the Jeff Miller's Earliest Known Uses of the Words of Mathematics "Moment was taken into Statistics from Mechanics by Karl Pearson when he treated the frequency-curve (or observation ...
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3answers
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Nowadays I see a distinct “line” dividing people working in Mathematics and the Physical Sciences. Why?

The direction in which leading research is heading in these subjects (Math, Physics) is very much different and don't seem to be in tandem. Is this something that developed in more recent times? This ...
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Why did Aristotle make mistakes in his laws of motion?

I was studying Aristotle's laws of motion and comparing them to Newton's. He states that heavier bodies fall faster than lighter ones. I really can't understand how he could have committed such a ...
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2answers
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How did people react to the realization that Aristotle's ideas had gone without question for way too long?

Recently read the book "Gravity" by George Gamow, in which he says: For centuries Aristotelian philosophy and scholasticism dominated human thought. Scientific questions were answered by dialectic ...
6
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1answer
201 views

When and how did the notion/idea of physical constant emerge?

Physical constants (e.g. c, h, G, alpha and so on) play a central role in our scientific theories and they have yet drawn much of controversial flavor into questions concerning the foundational status ...
6
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2answers
171 views

What are the early examples of taxonomies in the history of science?

When you think of taxonomies, the first thing that comes to mind is Linneaus. But taxonomies were and continue to be used for all kinds of classification, from biology to astronomy and even ...
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What was the major influence of Francis Bacon on the development of modern science?

I am reading "Advice for young investigators" by Santiago Ramón y Cajal , in which the author suggested Francis Bacon had made no impact on the scientific development*: "It would not be wise in ...
6
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392 views

David Hilbert and the limits of science

David Hilbert wrote a couple of anecdotal paragraphs regarding "the limits of science." He recalled that in the early 19th Century the position of a philosopher - or philosophy in general - was that ...
6
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1answer
226 views

Modern critiques of, alternatives to Kuhn's paradigm shifts?

Kuhn's theory of paradigm shifts dates back over 50 years. Are there modern critiques of or alternatives to his theory? It seems to have been controversial from the start, with some people apparently ...
6
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1answer
134 views

Different models for the development of mathematics: Latin versus butterfly

Ian Hacking's new book *Why is there philosophy of mathematics at all?", see here, contains many interesting ideas. One of the ideas is the dichotomy of two distinct models for the development of a ...
6
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1answer
102 views

What are the earliest known accounts of the demarcation problem (science versus pseudo science)?

The demarcation problem, i.e. the problem of differentiating science from pseudo science has been on my mind recently. This might be considered a philosophy topic for philoSE but since my question has ...
5
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3answers
204 views

The Greeks did not discover “a single scientific law”

The title is drawn from a sentence in a Jim Holt article, "The Dangerous Idea of the Infinitesimal," now a chapter in his book collection.1 I found this a striking claim, and perhaps true, as the ...
5
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2answers
258 views

What did it historically mean in physics for something to “exist”?

What is the history of influential definitions of objective existence --- This Is Real, It Exists --- in physics? Where did they appear in the literature and in what context were they put forward? ...
5
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1answer
461 views

History of the study of indeterminism in classical mechanics

The classic Norton's dome problem, space invaders and other examples, show that Classical Mechanics, held as the paragon of determinism for ages having inspired Laplace's statements on determinism, is ...
5
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2answers
218 views

What is the origin of “normal” in normal coordinates and normal modes?

I am trying to understand why vibrational modes of polyatomic molecules are called "normal" mode of vibrations and with corresponding normal coordinates. What is the origin of the term normal here? I ...
5
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1answer
64 views

Is there an explicit description of Landis-Petrovskiĭ's mistake in their “solution” to Hilbert's 16th problem?

The second part of the Hilbert's 16th problem (determination of the upper bound on the number of limit cycles for two-dimensional polynomial vector fields of given degree), proposed in 1900, is still ...
5
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1answer
101 views

To constructivists, is “mind” more than a convenient synonym for “algorithm”?

I could give (but, not being a professional historian, nor a native Dutch speaker, only few) references and background-remarks, but I will keep this short, to make more use of what a Q&A-sites ...
4
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4answers
867 views

How were irrational numbers that are not constructible accepted by mathematicians?

What was behind accepting the existence of irrational numbers historically? Especially numbers that are not constructible on the real number line, say for example $\sqrt[3]{2}$. Was it a (somewhat) ...
4
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1answer
149 views

Does Lakatos' argument in favour of 'informal mathematics' hold up in most cases?

Lakatos, in his Proofs and Refutations, rejects the Euclidean methodology and exposition of mathematics: where axioms and definitions precede the proofs. In other words, a Euclidean mathematician ...
4
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2answers
129 views

Reference Request: Books on the work of Imre Lakatos

What are the best works summarizing, discussing or criticizing the work of Imre Lakatos? What are the pros and cons of said works? Which would you recommend picking up first if one has read some but ...
4
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1answer
179 views

Who influenced Gauss in his abstract approach to mathematics?

I have studied that Gauss was one of the firsts mathematicians to defend this idea, about the Abstract Math and the conception of number, claiming that "What is calculated (in the sense of things ...
4
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1answer
207 views

Can we identify Paul Benacerraf in these photos

This question is about Paul Benacerraf, who worked on the philosophy of mathematics, and wrote the 1965 essay What numbers could not be (see: Benacerraf's identification problem). He was at Princeton ...
4
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263 views

How did the early chemists make a connection between gram formula weight with 1 mole and Avogadro's number?

According to one historian Mustafa Sarikaya's article in Foundations of Chemistry DOI 10.1007/s10698-011-9128-7, the mole concept was introduced to chemistry earlier than Avogadro’s number. The mole ...
4
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3answers
359 views

“Tension” between Electromagnetism and Newton's laws

When talking about the inconsistencies in physics that led up to Einstein's discovery of relativity today's professors always say that Maxwell's discovery of the constant speed of light $c$ created a ...