It's not often that I blog about philosophy itself, although it is central to much of what I do. This one is about mathematics -- and my own thinking on the subject. Is mathematics a separate language? Is it an objective language? I say no to both questions. For three reasons mainly:
• Mathematics is a degree of abstraction in the midst of our everyday experience and language. Whether I say to the greengrocer: "Give me an apple," or :"Give me one," the difference is the degree of abstraction. Therefore, also, we can freely mix mathematics with our daily conversation.
• Secondly, mathematical units are not cast in stone. They are always the product of human judgement. Einstein wrote that a mathematical unit "singles out a complex from nature", while Peirce wrote before him: "Every new concept first comes to the mind in a judgment." Whether one speaks of an apple or an orchard, therefore, one has created the unit.
• Thirdly, mathematical language is merely a distillation of the real world. When we individuate things, we strip away their sensible qualities. What we end up with, then, is something not really representative of the real world. Thomas Mautner writes: "All abstraction involves some falsification." I used the example recently of a soccer match which South Africa lost (I think) 2:0. But when one heard an interview with the Minister of Sport, that score hid massive subterfuge.
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