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Despite the author's argument, for me at least, there are an order of a priori "hints" which argue why Mathematics ought to be seen in the natural sciences. In
by ethn 10y ago
Despite the author's argument, for me at least, there are an order of a priori "hints" which argue why Mathematics ought to be seen in the natural sciences.
In the beginning of mathematics, it was likely, if not definitively created to enumerate similar objects in a particular given set. In order to enumerate an object two things must happen. The object must be turned into an object: this means it must be reduced into some abstract concept which holds certain properties to belong in a set. Second, it must be mapped with a further abstract ID, the number. The most significant consequence of this is that the enumerated ID's and objects now hold the property of logic, because in our world all objects seem to exhibit properties of logic (most of the time). This would have begun as simple arithmetic, an early model of a useful description of our world. From this it becomes evident that you can now map any integer to objects, and perform operations on those integers which map onto the real world as if you were performing the operation on those very real objects.
Later, mathematicians would then become less concerned with the objects mathematics served to represent but more on the relationships in between them. In the logical manipulations of these objects, mathematicians began really exploring the very logical relationships between objects (the creation of variables would coincide here over strict numbers). They once represented an object, yet still can be used again to represent an object. It follows, that these objects should now follow these logical relationships.
From these concerns, I reduce mathematics further as a nice description of logical relationships; a derivative of our own model of the universe.
- kruhft 10y agoThank you for that great explanation. Very enlightening.
- akud 10y ago> because in our world all objects seem to exhibit properties of logic This is the thing that needs to be explained. I get that math is just logic, but why should we expect the natural world to follow logical rules?
- eli_gottlieb 10y agoWhat sort of logical rules would we even consider logical if they didn't manage to explain anything about the natural world?
- tomrod 10y agoCounterexample, for instance, assumes a world that may or may not accord with reality.
- ethn 10y agoExactly. >I reduce mathematics further as a nice description of logical relationships; a derivative of our own model of the universe. The rules of logic are the behaviors of objects that we experience and observe. In a differing reality, objects may have properties which could be illogical to the perspective of someone in our own; yet if we move to that strange reality, our brains would slowly process the information into a new model of reality with the ~new logic~. However that ability is mostly pointless as any group of mostly consistent behaviors will have either more but never differing logical relationships as any other reality with mostly consistent behavior (this is also why we see something called duality in mathematics). The further consequence of this, in our studies of natural sciences, we hold our brain's model of reality as supreme. We don't consider something to be ~true~ until at least its conclusions can be witnessed and perceived. The consequence and perhaps also the cause of this, is all of mathematics and natural sciences are mostly attempts to formalize as well as quantify our own brain's unified model of reality.