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The philosophy of mathematics is the branch of philosophy that studies the assumptions, foundations, and implications of mathematics. It aims to understand the nature and methods of mathematics, and find out the place of mathematics in people's lives.
Nyāya, literally meaning "justice", "rules", "method" or "judgment", is one of the six orthodox (Āstika) schools of Hindu philosophy that affirm the Vedas. Nyāya's most significant contributions to Indian philosophy were systematic development of the theory of logic, methodology, and its treatises on epistemology.
Hilary Whitehall Putnam was an American philosopher, mathematician, computer scientist, and figure in analytic philosophy in the second half of the 20th century. He contributed to the studies of philosophy of mind, philosophy of language, philosophy of mathematics, and philosophy of science. Outside philosophy, Putnam contributed to mathematics and computer science. Together with Martin Davis he developed the Davis–Putnam algorithm for the Boolean satisfiability problem and he helped demonstrate the unsolvability of Hilbert's tenth problem.
Analytic philosophy is a broad movement or tradition within philosophy focused on analysis, which has been dominant within Western philosophy and especially anglophone philosophy since the latter half of the 20th century. The proliferation of analysis in philosophy began around the turn of the 20th century in the contemporary era in Germany, Austria, the United Kingdom, the United States, Canada, Australia, New Zealand, and Scandinavia.
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The Nyāya Sūtras is an ancient Indian Sanskrit text composed by Akṣapāda Gautama, and the foundational text of the Nyaya school of Hindu philosophy. The date when the text was composed, and the biography of its author is unknown, but variously estimated between 6th-century BCE and 2nd-century CE. The text may have been composed by more than one author, over a period of time. The text consists of five books, with two chapters in each book, with a cumulative total of 528 aphoristic sutras, about rules of reason, logic, epistemology and metaphysics.
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In mereology, an area of philosophical logic, the term gunk applies to any whole whose parts all have further proper parts. That is, a gunky object is not made of indivisible atoms or simples. Because parthood is transitive, any part of gunk is itself gunk.
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or logical truths. It studies how conclusions follow from premises due to the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies, critical thinking, and argumentation theory. It examines arguments expressed in natural language while formal logic uses formal language. When used as a countable noun, the term "a logic" refers to a logical formal system that articulates a proof system. Logic plays a central role in many fields, such as philosophy, mathematics, computer science, and linguistics.
The Quine–Putnam indispensability argument is an argument in the philosophy of mathematics for the existence of abstract mathematical objects such as numbers and sets, a position known as mathematical platonism. It was named after the philosophers Willard Quine and Hilary Putnam, and is one of the most important arguments in the philosophy of mathematics.
Mary Leng is a British philosopher specialising in the philosophy of mathematics and philosophy of science. She is a professor at the University of York.
References
- ↑ "Alexander Paseau". University of Oxford.
- ↑ "A.c. Paseau (Oxford University) - PhilPeople". Philpeople.org.
- ↑ "Research Fellowships 2019". The Leverhulme Trust.
- ↑ "Along With The Eggs, Are There Sets Of Eggs In The Fridge Too? And Other Key Questions..." 3:16. Retrieved 2022-06-25.
- ↑ "The Puzzle of Existence: Why Is There Something Rather Than Nothing?". Routledge & CRC Press. Retrieved 2022-06-25.
- ↑ Chudnoff, E. (1 July 2009). "Mathematical Knowledge, edited by Mary Leng, Alexander Paseau, and Michael Potter". Mind. 118 (471): 846–850. doi:10.1093/mind/fzp079.
- ↑ "Mathematical Knowledge". Mathematical Association of America.
- ↑ Stei, Erik (17 October 2023). "Review of One True Logic: A Monist Manifesto". Notre Dame Philosophical Reviews. ISSN 1538-1617.