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

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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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29 views

What are some good metrics for intellectual progress (of all sorts)?

My thinking about this topic is vague, and I'm looking to clarify it. I'm not sure what "intellectual progress" is or if that's even a useful abstraction, but it seems like it should include things ...
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3answers
135 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 ...
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1answer
154 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 ...
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2answers
116 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 ...
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4answers
219 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 ...
6
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1answer
280 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 ...
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1answer
41 views

Suggestions for hosting a Scientific Salon of Paris in Émilie du Châtelet's time

My students just learned about Émilie du Châtelet's Salon with Voltaire in her husband's residence in Paris and in their country estates. I want to give them a homework assignment for extra credit of ...
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1answer
79 views

Who invented the term “Kuhn loss”?

This term has been discussed on this forum, e.g. under Examples of Kuhn loss?, and has been attributed to Kuhn himself. The term refers to the loss of explanations and predictions of the prior ...
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1answer
144 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 ...
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1answer
119 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 ...
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56 views

Gentzen and computer science

This is a cross-post from mathstack: https://math.stackexchange.com/questions/2584003/gentzen-and-computer-science?noredirect=1#comment5333947_2584003 I would like to learn a bit about the ...
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32 views

Are there any undergraduate research/internship opportunities in math/science education/history?

(Apologies if this isn't the right place for such a post. I see lots of information out there for math/science students wanting to do research, but haven't seen anything about doing things on the "...
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2answers
65 views

Canonical examples of successful scientists giving detailed advice about doing science/mathematics?

I've read this long transcript of a speech given by Richard Hamming: http://www.cs.virginia.edu/~robins/YouAndYourResearch.html It was an amazingly good speech in my view, and extremely interesting. ...
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6answers
397 views

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 ...
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2answers
138 views

Books on scientific method for laymen

Could anyone recommend books that introduce to a layman science and its method/spirit? In particular, it should talk about what is science, what is the scientific method and why it works. After ...
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2answers
117 views

Does the word 'science' mean what's been found so far, or the way that human discovers unknown?

I'm writing a piece of paper and trying to understand, the meaning of word 'science' in the context of history. I'm not a native English speaker and I know I could look up in the dictionary, but my ...
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0answers
40 views

Did Turing ever mention Protagoras regarding the Imitation Game?

Based on the period when Turing went to school, it is fairly inconceivable he was not well familiar with Protagoras, and the statement that: "Man is the measure of all things" *I asked a question ...
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1answer
95 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 ...
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2answers
370 views

Did Karl Popper argue against Bayesian inference?

I am somewhat familiar with the works of Karl Popper and his opposition to using past data to induce prospects of future events, however disclaimed as uncertain, AKA historicism. He contributed to ...
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3answers
224 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 ...
5
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1answer
513 views

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 ...
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1answer
183 views

Has mathematicians read/reacted to speculative realism, specifically to philosophy of Quentin Meillassoux? [closed]

There has been a recent uprise in philosophy (and it seems to me to be a very popular topic there), which is called Speculative Realism or Object-Oriented Ontology. One of the founding texts there is ...
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2answers
488 views

Who is the philosopher Feynman cites as saying that existence of science requires the same conditions to produce the same results?

In part 6 of his lecture series "Character of Physical Law", Richard Feynman remarks: A philosopher once said, "It is necessary for the very existence of science that the same conditions always ...
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52 views

Carnap's last theory Of probability

According to Bar-Hillel, Carnap's coauthor in a 1952 report on probability, Carnap had, as of 1956 an unpublished but circulated theory distinguishing "random" refers to methods of production of ...
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0answers
57 views

How important were serendipitous scientific discoveries (objectively)?

I'm interested in examining the efficiency of the scientific process. Part of this involves examining what actually goes into making a discovery. One common objection is: Half of all important ...
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2answers
132 views

Were there any famous Asian philosophers who were also mathematicians?

New here, had a question: Were there any famous Asian philosophers who were also mathematicians? Happy Xmas!
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2answers
279 views

Why is pure mathematics important? More generally, why do some scientists deal with inaplicable notions?

I am a freshman, mathematics. I have a presentation assignment for a class. I am expected to talk about the necessity of abstract sciences. The thesis I need to argue is the following: ''Some people ...
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3answers
1k views

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 ...
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2answers
247 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? ...
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67 views

Was Joseph Priestley describing fundamental interactions in the 18th century?

In 1777, Joseph Priestley wrote a book called Disquisitions relating to Matter and Spirit, in which he says: It is maintained in this treatise, that neither matter nor spirit (meaning by the latter ...
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2answers
228 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 ...
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2answers
166 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'. ...
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1answer
333 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 ...
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1answer
61 views

Are there fields of science that became more successful after becoming less clearly understood?

In machine learning, people have been more and more letting go of the idea that they should understand how a particular algorithm works, and accepting it on the basis that it "just works". Are there ...
6
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1answer
180 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
60 views

Was interpretivism always considered scientific by part of the people?

I always was amazed by how disciplines which can give very different grades of accuracy (exact sciences in contrast to others which fails in its predictions more times than they are successful) can ...
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1answer
98 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 ...
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63 views

Galileo's pendulum and any references

In some texts about the simple pendulum we use to see references about some "experiments" Galileo Galilei did realize and whereby he found some important results, including that the period of the ...
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61 views

Cauchy's real line and math philosophy till XIX

I have to write an essay concerning philosophy of mathematics until the end of XIX century. I've heard that the reason why the Cauchy's theorem (if continuous functions $fn→f$ then $f$ is continuous ...
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26 views

Where did the idea of modularization come from?

I have a wild guess that science flew when we started to take the concepts, fragment it and examine it piece by piece, fragmenting it again when needed for a better understanding. It seems that this ...
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1answer
60 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 ...
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4answers
446 views

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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68 views

Have humans gotten better at the methods of science over time? [closed]

Im currently reading the book A Short History of Nearly Everything by Bill Bryson, and as I'm reading about the history of many fields of science (e.g. paleontology, geology, astronomy, etc.) it seems ...
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1answer
121 views

If the lens wasn't discovered/invented what current technologies wouldn't be possible [closed]

When I'm thinking of the most crucial discoverys of science than I think of the lens invented in the 16e century. By using a lens man could make microscopes and telescopes. When I think about that ...
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1answer
451 views

When and who was the first mathematicians to prove rigorously that $\sqrt[3]{2}$ was impossible number? [closed]

The purpose of the question is to understand why the number $\sqrt[3]{2}$, that was proven rigorously by ancient Greek is an impossible number (even at infinity), by their three famous impossibility ...
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1answer
126 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 ...
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329 views

When or why & who originated this puzzle, $0.999… = 1$ [duplicate]

The problem is the infinite or endless repeated digits of $9's$ after zero digit and the decimal notation, Despite its apparent simplicity & the huge talk about it every where in mathematics or ...
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1answer
145 views

Did a divide/gap develop in recent times between people working in Mathematics and in Physics, Astronomy and Cosmology?

The direction in which leading research is heading in these subjects is very much different and doesn't seem to be in alignment, there is no sense of parallelism. Is this something that developed in ...
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4answers
665 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) ...