Scientism

[Tinker Grey]

Not really. No one ever puts 3 apples on a table, takes 7 away, and photographs the -4 apples on the table to determine the outcome of the experiment. Euclid didn't use a protractor to determine that the sum of the angles in a triangle is 180 degrees.

Euclidean geometry is a game based on assuming a set of axioms, and seeing what logically follows. No empirical evidence is necessary. All mathematics is the same. It may have utility in empirical science; certain branches may have been motivated by empirical questions, but it is not really empirical itself.

I would say the foundations are both empirical and inductive in nature. We observe that 1 + 1 = 2. I would, however, agree that things like negative number are conceptual extensions in cases like negative apples. However a vector with a negative magnitude can be real. For example, if I am heading -5 miles/hr north, I am heading +5 mph south. It's real.

 

[essentialsaltes]

I would say the foundations are both empirical and inductive in nature. We observe that 1 + 1 = 2.

No one has ever observed a 1. It is an idea.

 

[Tinker Grey]

In a sense, I suppose. But I have observed a single object. Having observed that single object and then placing another object with the previous object, I arrive at an idea of distinguishing the quality of the first situation from the quality of the second. We give names to those ideas and observe that it is never the case that 1 + 1 doesn't equal two. We have arrived at a generalized mathematical principle through induction by observing reality.

The foundation of the concept of 1 is empirical. The quibble here, I'm guessing, is that I would agree that the concept of 1 is abstract, but I'm saying we arrived at the concept and the need for the concept by processing reality.

 

[essentialsaltes]

We give names to those ideas

Yes, these are our mental descriptions of the world.

 

[.Mikha'el.]

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