Mathematics was Discovered, not invented
Debate Rounds (4)
Mathematics was discovered, the evidence can be set firmly in place. When we look at the world around us, we see mathematics everywhere, mathematics did not need to be invented to exist. An example is, when we see four apples on a tree, there are four apples on the tree, we didn't invent that value, but we did invent the name/character for that value, which, in this case is the number four. Numeric value existed before any human did, before the big bang when the universe was singularity, it was one.
Mathematics: the abstract science of number, quantity, and space.
Pro must support the metaphysical view that mathematics exists independent of us and our language. However, it’s hard to tell if he’s arguing for mathematical Platonism, since he seems to be implying that mathematics has a physical, rather than abstract, existence. That’s extremely problematic, however, since math is quite evidently non-physical. It has empirical applications but its entities are abstract.
Pro says we can see math everywhere. He says the 4 apples on a tree is a value independent of us. This is erroneous. Mathematical values only make sense as idealized entities that are inexact in their representation of reality. Math is a language that we tailor to articulate reality. The symbols of math are conceived of as absolute (1 is exactly the same as 1), but empirically, math is only approximate. For an elementary example, when you add physical objects, such as coins, you are only adding objects approximately similar to each other. It does not follow an exact 1+1=2 model. The entities being added are not equal to each other, even though they’re represented as identical in math. We can conceive of adding one electron to another, thus creating two electrons, but the electrons have different properties and by the uncertainty principle, their positions and momentum are inexact. There are no pure triangles, circles, or numbers in reality, only approximations of those entities. This makes sense under the view that math is a creation used to describe a fluid and blurry reality through the means of abstract absolute symbols. Though math is extraordinarily useful, there’s a disconnect between it and reality.
Math is also only successful on certain scales. For example, in the 1970s, when transistor behavior was on the level of micrometers, they could be elegantly described with equations. With the submicrometer transistors of today, compact equations fail and computer software is required.
The numeric characters; 1, 2, 3, 4 etc were created by us to represent values so we could understand the mathematics and science of the universe more fully. Back to my example of four apples on a tree, that value exists, the fact and meaning that their are four apples on a tree has not been created by us, we simply create the name of the value (in this case is four) to help us interpret those values.
Part of my argument from the last round was actually taken from another article inspired by the one Pro mentions called The Reasonable Ineffectiveness of Mathematics. While math is vastly effective on one level, as shown, it breaks down at certain scales and is only an approximation of reality. Pro's argument is especially erroneous since he's assuming a non-Platonist position that math is not abstract but physical. The fact that math invented centuries ago has functions even now only testifies to the widespread usefulness of math and that math can be built upon, which no one denies. However, the effectiveness of math is overstated by Pro. For example, Maxwell's equations were standard for modelling integrated electromagnetic devices and structures. Modern devices abandoned analytical calculations, instead reverted to simulation programs. "When we carry out engineering in different circumstances, the way we perform mathematics changes. Often the reality is that when analytical methods become too complex, we simply resort to empirical models and simulations". http://ieeexplore.ieee.org...
Pro agrees that numbers are invented. I ask how anything else in math is different. The concept of multiplicity and singularity are concepts invented by humans. Reality is not inherently categorized into distinct entities. Humans make it so. We categorize it and give it labels. Moreover, mathematical equations assumes the terms in the equation stand for absolutes all equal to each other. Entities in nature, on the other hand, are unique.
An example of my point from my argument before, Pi. Pi as you would know was discovered hundreds of years ago yet we have not discovered all the digits of Pi. It is a mathematical concept is it not? An invention is a device or concept that we create, when we create something, we are able to understand every aspect and function of the invention. Mathematics cannot be defined as an invention because we still have mathematical concepts that are unknown to us and need to be discovered.
Addressing your question in the third paragraph, I only said that the character that represents numeric value was created by us, and so numeric value is the thing that all math is comprised of. The characters we create called numbers are again, as I have stated before in my arguments before, a representation of numeric value.
Pro’s first paragraph is perplexing since the very notion of debate entails a continued dialogue. By leaving my arguments unopposed Pro is neglecting his burden.
You can’t discover all the digits of pi because they’re endless and non-repetitive. Pi is an irrational number, which does not really help Pro’s case because it can only be approximated. It’s hard to conceive of a number with non-terminating decimals (and no repeating pattern) existing in nature. We can represent 5 and 2.5 with objects, but that’s impossible to do with irrational numbers. For all practical purposes, it is not a problem, but it does threaten the view that math is discovered.
Pro's entirely wrong that we know everything about that which we create. When chess was invented, the countless strategies for winning the game were all unknown. We’ve built on math from the past and used technology to help us arrive at further knowledge. Invoking new concepts (such as imaginary numbers) makes math more functional. We continually develop new ideas and analyze our current mathematical knowledge to build on what we know. Derivations can be made from previous mathematical notions, which itself explains how new mathematical knowledge grows. Math is not a complete system. We’ll very likely have more mathematical knowledge in the future, not because we discover it, but because we do not fully understand math and all its derivations, and because reshaping may be necessary as well as new concepts.
Pro’s last paragraph is difficult to understand. I realize at least that he’s claiming our names for numbers are created, and I assume he’s not saying numeric value is created by us since that would contradict his case. Obviously, something exists behind the symbols we give objects: matter. But the notion that this can be categorized into individual entities is a human conception. Overall, Pro only elucidates his meaning and does not really give a response to the argument.
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