QUANTUM METAPHYSICS - E-thesis

Bohr’s way of thinking, touching both language and mathematics, can be considered a step in the
direction of Empiricism. Ever since the days of Descartes, while mathematics has been generally
understood as the sovereign tool of reason, Bohr puts its possibilities in proportion. Language is
a device within which our experiences of the character of the world are stored, and which
changes when our earlier assumptions about the nature of the world turn out to be inadequate.
Even though we continue to visualize space in three-dimensional terms, relativity theory tells us
that this type of observation does not address the nature of reality correctly, and that even though
we still have to use classical language and logic, we know that these tools are not capable of
describing the world with the depth of quantum mechanics. Bohr emphasised that the use of a
descriptive concept in a specific situation depends on the ruling relevant physical conditions.
Concepts only work in specific contexts, and if we see that the assumed conditions do not
prevail, a change in the concept being employed will result. 748
No-one will certainly wish to dispute that mathematics holds a position of fundamental
significance in modern physics. In spite of the powerful development of mathematical theories,
our conception of the reasons for the usefulness of mathematics has not actually progressed since
ancient times. The ontological and epistemological problems of mathematics are foreground
topics in the philosophy of mathematics. It is by no means clear what mathematics is about.
What is the nature of the objects that it studies? What kind of being or kinds of existence are
shared by mathematical entities? Are the concepts and methods of mathematics discovered or
invented? And what kind of knowledge does mathematics provide? In physics, the nature of
mathematics has not been clearly questioned. Is it, as Bohr maintained, primarily a tool for
humans to use in description, or is it something ontologically more concrete, something with
which the human intellect can directly reveal the structure of reality? 749
New light on the foundations of mathematics has resulted from the theorems of Kurt Gödel and
Alain Turing, probably the two most important achievements in twentieth-century
mathematics. 750 Gödel’s incompleteness theorem and Turing’s theorem proved that there will
always be unsolved problems in mathematics and logic. There are mathematical questions that
admit no mechanical solution. This does not imply that certain problems cannot be solved at all.
748 Hooker 1972, 134, 167 & 192.
749 Reichel 1997, 3.
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