The essay will discuss the differences between numbers and numerals and the philosophy of mathematics. Mainly, numbers and numerals have a relationship but are also distinct concepts between the two. People mostly write numerals but call them numbers. Primarily, a number represents an abstract concept that gets used to count and measure things. A number can have several numerals; however, a number remains as a single numerical value. Importantly, there are number systems that get used in grouping numbers, and they include unary operations and binary operations. The essay will highlight the differences between numbers and numerals and the philosophy of mathematics.
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OBJECTS OF MATHEMATICS AND PHILOSOPHY OF MATHEMATICS
There are several attitudes that people can assume toward the abstract objects of mathematics. One end includes Platonism that involves total; acceptance of mathematical entities as eternally existing and independent of human thought. Notably, the other opposite end includes nominalism, where there is a total rejection of abstract objects’ existence. It’s difficult to lean on one side and ignore the other, which raises the issue of mathematical realism. Thus, it would call for an acceptance of both notions to cover the understanding of mathematics. The article will help in understanding the differences between numbers and numerals and the philosophy of mathematics.
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https://pdfs.semanticscholar.org/af33/245851baa46d685c18ee24edc614005e8717.pdf
PHILOSOPHY OF MATHEMATICS AND MATHEMATICAL PLATONISM
Mathematical Platonism is the view that there exist abstract objects. Moreover, it is the view that there are correct mathematical sentences that give real descriptions of the mathematical objects. According to Platonists, a geometric purpose is nonspatiotemporal, meaning that it can’t get located anywhere in the physical world. Moreover, they are nonmental, yet they always have and will continue to exist. However, this doesn’t preclude one having mental ideas of abstract objects. Platonists also claim that abstract objects are unchanging and completely noncasual. An analysis of the differences between numbers and numerals is essential in understanding the philosophy of mathematics.
For more information on the philosophy of mathematics and mathematical Platonism, click
https://www.britannica.com/science/philosophy-of-mathematics
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