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1. link.springer.com › referenceworkentry › 10Thought Experiments in Mathematics: From Fiction to Facts

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   Apr 27, 2024 · As in science and philosophy, thought experiments in mathematics link a problem to new epistemic resources that are unavailable in a given practice, e.g., Euclidean geometry. Thought experiments invite us to perform an imaginary scenario involving counterfactual, deductive and sensory elements.

   • Author: Irina Starikova

2. sites.ualberta.ca › ~francisp › Phil488THOUGHT EXPERIMENTS IN MATHEMATICS - University of Alberta

   sites.ualberta.ca › ~francisp › Phil488

   prototypical cases. Occasionally, authors talk about mathematical thought experiments (MTEs). There the situation becomes even more complex: first, few authors actually believe that there are such things as MTEs and those that do believe so, put forward nearly contradictory definitions.

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4. link.springer.com › referenceworkentry › 10Experimental Mathematics in Mathematical Practice

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   Nov 4, 2023 · Others have claimed that thought experiments are just a variation of mathematical reasoning that obviously depend on thought. In contrast, Starikova maintains that thought experiments do exist in mathematics and argues that they should be considered as an independent form of mathematical reasoning.

   • Author: Jessica Carter

   • Email: jessica@css.au.dk

5. philsci-archive.pitt.edu › 12823 › 1THOUGHT EXPERIMENTS IN MATHEMATICS - University of Pittsburgh

   philsci-archive.pitt.edu › 12823 › 1

   THOUGHT EXPERIMENTS IN MATHEMATICS. Irina Starikova1 and Marcus Giaquinto. It is not news that we often make discoveries or find reasons for a mathematical proposition by thinking alone. But does any of this thinking count as conducting a thought experiment? The answer to that question is “yes”, but without refinement the question is uninteresting.

6. www.semanticscholar.org › paper › Thought[PDF] Thought Experiments in Mathematics - Semantic Scholar

   www.semanticscholar.org › paper › Thought

   Jun 8, 2016 · Thought Experiments. Edmond Goblot Eugenio Rignano. Philosophy, Mathematics. 2022. : Since the beginning of the twentieth century, prominent authors including Jean Piaget drew attention to Edmond Goblot’s account of mathematical thought experiments. But his contribution to today’s…

7. philpapers.org › rec › STATEI-8Thought Experiments in Mathematics: From Fiction to Facts

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   Thought experiments invite us to perform an imaginary scenario involving counterfactual, deductive and sensory elements. This chapter aims to pinpoint the beneficial peculiarities of thought experiments in mathematics in comparison with inferences, diagrams and calculative procedures.

8. People also ask

   Do thought experiments exist in mathematics?

   • Irina Starikova’s “Thought experiments in mathematics: from fiction to facts” consider the particular case of thought-experiments in mathematics. Starikova notes that philosophers have argued that thought experiments cannot exist in mathematics since experiments are a form of a posteriori reasoning whereas mathematics is a priori.

   Experimental Mathematics in Mathematical Practice

   link.springer.com/referenceworkentry/10.1007/978-3-030-19071-2_121-1

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   Why are thought experiments important?

   • Looking at the development of the discussion about thought experiments over the past thirty years, it is fair to say that thought experiments were primarily an important topic in the philosophy of science and the philosophy of philosophy (“metaphilosophy”), before the scope widened up at a later point. There is a simple reason for that path.

   Thought Experiments (Stanford Encyclopedia of Philosophy)

   plato.stanford.edu/entries/thought-experiment/

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   What is a mathematical experiment?

   • Mathematicians have since long performed “experiments,” for example, in the form of computations, trying out and rejecting ideas. Tradition, however, prescribes that mathematics is presented in the form of definitions, propositions, and proofs that hides the work that came before.

   Experimental Mathematics in Mathematical Practice

   link.springer.com/referenceworkentry/10.1007/978-3-030-19071-2_121-1

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   Can thought experiments be tested by physical experiment?

   • At least thought experiments in science, the skeptic claims, can be tested by physical experiment. However, this is clearly false, since frictionless planes and universes empty of all material bodies cannot be produced in any laboratory. True, the results of philosophical thought experiments cannot be even approximately tested.

   Thought Experiments (Stanford Encyclopedia of Philosophy)

   plato.stanford.edu/entries/thought-experiment/

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   Is thought experiment still useful in science in present time?

   • Do you think thought experiment is still useful in science in present time? Yes. It is useful until now. Some people might think that thought experiment is no longer useful in these present times for the reason that there’s a growing presence of evolving technology.

   Do you think thought experiment is still useful in science in present time?

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   Are mathematical experiments based on a computer?

   • This is also noted in the aims of the journal Experimental Mathematics: “Many mathematical experiments these days are carried out on computers, but others are still the result of pencil-and-paper work, and there are other experimental techniques, like building physical models.” 1

   Experimental Mathematics in Mathematical Practice

   link.springer.com/referenceworkentry/10.1007/978-3-030-19071-2_121-1

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9. www.researchgate.net › publication › 370210916Thought experiments in mathematics: from fiction to facts

   www.researchgate.net › publication › 370210916

   Apr 23, 2023 · Like science and philosophy, thought experiments in mathematics link a problem to new epistemic resources that were unavailable earlier. Performing an imaginary scenario can involve...