Wednesday, May 6, 2015

Is the Mathematics Imagined or Discovered?

For a very, very long time I have been meaning to read up on contemporary views of the philosophy of mathematics and the relevance of phenomenology.  I have not had the time.  Yet the topic haunts me.  I think about it a lot.  I would nonetheless like to share my current thoughts on the subject, despite the present ignorance and incompleteness.  So below are my thoughts.....


On the question as to whether mathematics is a part of reality or a mere mental construct, I offer the following account. I hold to a mathematical realism. That is, mathematical reality - the truth value of mathematical statements, for instance – are discovered, not constructed. That said, I will add that the reality(and properties) of mathematics are dependent on the mind. It is important to note that just because something's existence depends on the mind does not mean that it is “created” by the mind. There being an “out” depends on there being an “in.” The point is that mathematics is real because the mind is real. Mathematics is areal aspect of the real finitude of the mind.

The truth of mathematics depends on the reality of the mind being conditioned from without. That is, it derives from the fact that the mind is necessarily conditioned by that which is beyond it. The fact that the human mind is impinged upon by what's beyond it is an aspect of the mind and this aspect is key in understanding the reality of mathematics.

All philosophy from mathematics should start here. Beyond that I adhere to some extent to a form of mathematical structuralism which suggests that mathematical objects are constituted by their relation in a system. In this sense mathematical objects are also meanings. The details of the phenomenology of mathematics beyond this are yet to be spelled out tome.

This is the starting point of the discussion of the relationship between mathematics and hermeneutics. They both rest on the finitude of human perspective.  

I should end by saying a philosophical theologian with whom I'm connected on Facebook, said to me that this view is, which I consider a kind of "realism" is closer to a "Kantian Idealism." That may be. However, I'm actually not fully convinced. At this time I suspect that if I can flesh out my ideas, then they would provide an interesting argument for realism.

Then, again, as I said, I have not given this subject the time and thought it diserves for a long, long time. At the moment, I think Euler's identity e^(iπ) = -1 will make more intuitive sense to the mathematical community in the future, because their are aspects of it that is yet to be discovered.

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