Yes, you did see it right. Apparently, numbers do not exist. My mind is still trying to process how such a concept could even be possible after believing all my life that numbers are the fundamental basis of mathematics. After much time pondering and challenging this, it appears to be true…
We use numbers everyday, from the numerals on our watches, the numbers on our calendars to the sizing on our clothing. Each of these numbers we use represent something, but what if we substituted our common base-ten numbers for something different? Would we still be able to count, tell the time, use money etc?
Collins (1998) suggests that by taking a nominal view of numbers, we can. He suggests that we can use any number system in the world (or a completely new one if we wished) to represent a size and it would still make sense, as long as we knew what each symbol represented. Society has constructed these notions that 1 is less than 4, and 4 is 3 more than 1 etc. However, Collins (1998) argues that we could equally use the symbol ‘4’ to represent one item and the symbol ‘1’ to represent four items, thus showing the flexibility of numbers as we know it. This is something I would never have considered as I thought the number system was a rigid structure, something which could never be changed. Nominalists see numbers as ‘fictions’ – symbols which aid and support our understanding of mathematics and everyday life, meaning we could use other symbols or entities to do the exact same job. The fact that we use different number systems around the world, such as octal, mayan and Arabic, supports this theory, and suggests that numbers are something which we have been predisposed to use through the work of many mathematicians which have came before us.
On the other hand, Collins (1998) explores the view that many realists take. We use numbers everyday in order to make sense of, and complete a wide variety of tasks everyday and thus, numbers must be real if we use them. Fine (2009) suggests the links that we have formed between numbers and the properties we have given them suggests that their existence must be true. For example, we have developed the concept of ‘prime’ numbers within our number system. Although, is this not another made up concept used to help us understand and make links within our made up number system? Confusing, isn’t it!
We could have used the word prime to represent another property of numbers, such as those divisible by 2, or every number ending in 1. Thus, this could be applied to other items we represent using language in our everyday lives. We could use the word ‘table’ to represent a ‘chair’ or vice versa, as long as we had an agreed understanding as a society that a ‘table’ actually represented what we know today to be chair.
Randy Palisoc develops this idea is his ted talk (see video below) by suggesting that numbers are a language we use to make sense of the world around us (TEDx Talks, 2014), just like we have constructed the letter system (the alphabet) and thus words to be able to communicate with one another.
Overall, I believe that the debate on the existence of numbers is an incredibly interesting one. I acknowledge that we use numbers everyday to perform basic functions, and thus they must be real as such. I also share Collin’s (1998) nominalist view that we could substitute other symbols for our base-ten number system and would still be able to perform basic arithmetic and daily tasks involving what our numbers represent, whether that be time, quantity of money or clothes sizes – the list goes on. The language we use for numbers, whatever this may be, is one which we will most likely always require to be a fully functioning member of society. Through this, is it clear to see that is imperative that we have a number system in place which allows us to represent different quantities and sizes etc, even if it is made up!
Collins, A.W. (1998) On the Question ‘Do Numbers Exist?’, The Philosophical Quarterly, 48 (190), pp. 23-36. Available at: https://www.jstor.org/stable/2660370?seq=1#page_scan_tab_contents [Accessed 8 October 2018].
Fine, K (2009) The question of ontology, Metametaphysics: New Essays on the Foundations of Ontology, pp. 157-177. Available at: https://philpapers.org/rec/FINTQO-2 [Accessed 8 October 2018].
Image – Wikipedia (2018) Numeral Systems of the World. Available at: https://commons.wikimedia.org/wiki/File:Numeral_Systems_of_the_World.svg [Accessed 8 October 2018].
Video – TEDx Talks (2014) Math isn’t hard, it’s a language | Randy Palisoc | TEDxManhattanBeach. Available at: https://www.youtube.com/watch?v=V6yixyiJcos [Accessed 8 October 2018].