31 votes
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Was Occam’s razor ever wrong?

By way of throat-clearing, what is Occam's razor? John Baez has a useful essay giving the history and some examples. William of Ockham's original formulation was Entities should not be multiplied ...
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25 votes
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Did ancient Greek mathematicians consider numbers independently of geometry?

The answer is yes. There was a split. First of all, for the Greek mathematics (and very long after them) "numbers" were integers. "Rational numbers" were called fractions, and no ...
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23 votes
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Hypothesis testing: Fisher vs. Popper vs. Bayes

According to Mayo, Popper did not designate statistical tests implementing his logic of falsification, or as Hilborn and Mangel put it "Popper supplied the philosophy, and Fisher, Neyman and ...
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23 votes

How were irrational numbers accepted by mathematicians?

Let me clarify a couple of things. No student of Pythagoras discovered irrational numbers, although this is a common misconception, Pythagoreans and even Euclid did not associate numbers with ...
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18 votes

When did Mathematics stop being one of "the Sciences"?

Let's start with everyone's first go-to source: Wikipedia. Right in the long introduction at the top lies the passage Carl Friedrich Gauss (1777–1855) referred to mathematics as "the Queen of the ...
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18 votes
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Is the Scientific Method uniquely Western?

In a word, yes, but only interpreting "western" broadly. The tradition of precise and systematic astronomical observations comes from ancient Babylonians, i.e. from Mesopotamia, and even Alexandria, ...
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15 votes
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What is the origin of polynomials and notation for them?

Although many problems that we now reduce to polynomial equations were solved since time immemorial early occurences are coached in verbal and/or geometric terms, and polynomials are not treated as ...
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15 votes
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What was Kolmogorov’s point of view in the philosophy of mathematics?

Kolmogorov was not exactly free to express his views considering the situation in the Soviet Union. Philosophical issues, even concerning mathematics, were ideologically sensitive, and everyone had to ...
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12 votes

In ancient times, how did people conclude that the shape of Earth is a sphere?

Eratosthenes of Cyrene did an experiment that confirmed that the Earth was roughly spherical, and estimated its circumference around 200 BC. Note that the lunar eclipse observation mentioned by ...
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12 votes
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The Greeks did not discover "a single scientific law"

It is a strange idea that scientific laws can be only expressed with algebraic means. The Greek did discover several scientific laws. The oldest one is attributed to Pythagoras himself: it relates the ...
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12 votes
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Who said that math or statistics is not free from class interest?

The quote is from Lenin, in his instructions to Popov when discussing the project of organizing Soviet statistics in summer of 1918:"Statistics, as any other scientific discipline, poses problems ...
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11 votes

Was Occam’s razor ever wrong?

In the 1960s the mathematical structure of Turing degrees was conjectured to be rather simple and homogeneous. This was consistent with what was known at the time. It later turned out that the ...
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11 votes

Why did Aristotle make mistakes in his laws of motion?

Air or more generally medium resistance was not yet treated as a separate effect in Aristotle's time. Nor was there a clear idea of motion in a vacuum, in fact most ancient Greek philosophers, ...
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11 votes
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Why and when did some areas separate themselves from philosophy and some not?

The area of knowledge separates itself from philosophy as soon as a reliable method of obtaining exact knowledge in this area is invented. Thus mathematics separated from philosophy at its very ...
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11 votes

What's the origin of the concept of the five senses?

It goes back at least to Aristotle's De Anima, Book II, ch. 7-11 (these five chapters being respectively devoted to sight, hearing, smell, taste, and touch). This is perhaps where it started, since ...
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11 votes
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Does Lakatos' argument in favour of 'informal mathematics' hold up in most cases?

I do not agree with the assumptions made in the title and in main text of this question, namely that Lakatos rejects the Euclidean methodology and exposition of mathematics. In the way I read it, ...
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10 votes

Conflict between physics and philosophy

The modern conflict is not so much between physics and philosophy, as between physics and "half" of philosophy, the continental philosophy. Scientists, and physicists in particular, see culturally ...
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10 votes

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

Problem: classical geometry is not happy with infinitesimals Newton is systematically trying to avoid basing calculus on infinitesimal geometric quantities. We can see this from how he emphasizes ...
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10 votes
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How was difference in water pressure perceived in ancient cultures or the middle ages?

One has to distinguish static pressure from the dynamic pressure in a flow. Static pressure was understood to some extent by Archimedes and later Hellenistic writers like Hero and Ctesibius. At least ...
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10 votes

Hidden agenda of the Galileo trial?

The Assayer & Redondi's "G3" Michele Camerota's 2008 Complete Dictionary of Scientific Biography entry on Galileo describes this theory in a section entitled "Atomism and the ...
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10 votes

Did the Idea of Universal Gravitation predate Newton?

The idea, yes, Aryabhata speculated about something like that as early as c. 500 AD, Brahmagupta called it gurutvākarṣaṇ. So did Kepler, at about the same time as Ahmad Baba al Massufi (late 1500-s), ...
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10 votes

Gauss on philosophers

The quote is not accurate but Gauss actually wrote something similar to Schumacher in the letter of 1 November 1844 cited here, where he complains about concepts and definitions given in math books by ...
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9 votes

When did Mathematics stop being one of "the Sciences"?

Some people would still call mathematics a science. (V. I. Arnold is a notable example). The distinction became commonly accepted in the first half of the 20-s century, but the process was slow and it ...
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9 votes

Nowadays I see a distinct "line" dividing people working in Mathematics and the Physical Sciences. Why?

You do not say what field of mathematics you are working in, and perhaps there are signs of separation there. Overall however, lively interaction between mathematics and physics is alive and well. ...
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9 votes

Mathematics PhD dissertations that opened a new field of research

John Forbes Nash Jr. got a Nobel Prize for his. Nash earned a Ph.D. degree in 1950 with a 28-page dissertation on non-cooperative games. The thesis, written under the supervision of doctoral advisor ...
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9 votes

What was Kolmogorov’s point of view in the philosophy of mathematics?

Kolmogovov expressed his views in this paper: MR2278817 Kolmogorov, A. N. Modern debates on the nature of mathematics. (Russian). With a commentary by V. A. Uspenskiĭ. Reprinted from Nauchnoe Slovo ...
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8 votes
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Which school of philosophy motivated thinking about spaces of higher dimension?

Leibniz and Newton never thought of manifolds outside of ambient space as far as I know, Newton is credited with forging the concept of absolute space, and Leibniz with reducing it to a relational ...
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8 votes
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Why was the Vienna Circle so important?

The Vienna circle, and more broadly logical positivism that it promoted, was the key link connecting philosophy of classical physics in 19-th century, positivism and neo-Kantianism of the Marburg ...
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8 votes
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History of the study of indeterminism in classical mechanics

Perhaps, the most insightful analysis (possibly to this day) of indeterminism in classical mechanics and its implications was given by Joseph Boussinesq, best known for his work on solitons, in a book ...
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