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Response to yeoman6987 (Reply #11)

Tue Oct 14, 2014, 03:32 PM

12. You may be right in a narrow pragmatic way, but wrong if the larger scope of things is considered...

Philosophy is about developing questions and attempting to show others the possibilities inherent in questioning. The history of what questions led to what results is important if one wants to pass knowledge on with any meaning attached to it. Presenting answers without questions and context is not useful. It robs the student.

Engineering when badly taught is pragmatic to a fault. Even physics and mathematics can be taught badly when they are taught with the instructor's mindset firmly fixed on "Get 'er done.", "Just do it." or "Shut up and calculate."

To leave philosophy out denies the fact that one needs to appreciate the questions and their boundaries as much as one needs to know the answers and their boundaries.

Here is a semi-technical piece by V.I. Arnold that you might find interesting:

On teaching mathematics
by V.I. Arnold


The scheme of construction of a mathematical theory is exactly the same as that in any other natural science. First we consider some objects and make some observations in special cases. Then we try and find the limits of application of our observations, look for counter-examples which would prevent unjustified extension of our observations onto a too wide range of events (example: the number of partitions of consecutive odd numbers 1, 3, 5, 7, 9 into an odd number of natural summands gives the sequence 1, 2, 4, 8, 16, but then comes 29).

As a result we formulate the empirical discovery that we made (for example, the Fermat conjecture or Poincaré conjecture) as clearly as possible. After this there comes the difficult period of checking as to how reliable are the conclusions .

At this point a special technique has been developed in mathematics. This technique, when applied to the real world, is sometimes useful, but can sometimes also lead to self-deception. This technique is called modelling. When constructing a model, the following idealisation is made: certain facts which are only known with a certain degree of probability or with a certain degree of accuracy, are considered to be "absolutely" correct and are accepted as "axioms". The sense of this "absoluteness" lies precisely in the fact that we allow ourselves to use these "facts" according to the rules of formal logic, in the process declaring as "theorems" all that we can derive from them.

It is obvious that in any real-life activity it is impossible to wholly rely on such deductions. The reason is at least that the parameters of the studied phenomena are never known absolutely exactly and a small change in parameters (for example, the initial conditions of a process) can totally change the result. Say, for this reason a reliable long-term weather forecast is impossible and will remain impossible, no matter how much we develop computers and devices which record initial conditions.



The above is an inherently philosophical discussion.

Robbing mathematics of geometry is very similar to robbing science (and one's knowledge) of any philosophy.

So, yes, one may need to adopt the pragmatic view that you espouse, but at the same time one should realize that exactly this need is the result of a system that limits and devalues education.

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