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R. Barrett and P. P. Delsanto
(2) Does logic, which is a product of our brains, have any existence outside
of us?
(3) Assuming that other rational beings exist in the universe, would they
necessarily develop the same system of logic that we have, or could they
possibly find some other system equally capable of explaining their world?
Mathematics is often described as a priori, meaning that it exists independently of the outside world, in contradistinction to an a posteriori knowledge,
which is obtained by empirical observation. This implies that mathematics
would exist even if the world around us vanished. The brains of humans,
and presumably other intelligent beings, harness this universal resource in the
development of science. The term Platonism is used to describe this philosophical tenet. Eccentric 20th Century mathematician, Paul Erdös, often
referred to “The Book”, in which God keeps the most elegant proof of each
mathematical theorem. He once said in a lecture: you don’t have to believe in
God, but you should believe in The Book [8].
Other philosophers deny that mathematics is a priori at all, claiming that
it arose in the search for the best description of experience, and in that sense
is no different from the other sciences. This viewpoint is known as Empiricism, and has been propounded by 20th Century philosophers, Willard Van
Orman Quine and Hilary Putnam. A criticism of an empirical view of mathematics is that if mathematics is just as empirical as the other sciences, then
its results are just as fallible as theirs.
The empiricist explanation opens the way for the evolution of logic and
mathematics in the brains of early humans as a survival aid in the process of
Darwinian natural selection, and gives insight into why mathematical logic
works so well at describing the physical world. Of course, once developed,
logic can be applied to any other abstract field not connected with survival.
This is nothing new: our eyes did not evolve to read computer screens, but
serve that purpose just as well.
We will re-examine these two alternative views of the nature of logic (and
mathematics) in Part 3, after a review in Part 2 of what we have learned from
the last century of progress in physics.
2.3 Pattern Recognition
Leaving aside these questions, which will no doubt occupy philosophers for
another few centuries, it is worth considering whether mathematics and logic
are the only approaches to a rational understanding of the universe. Formal
R. Barrett and P. P. Delsanto
(2) Does logic, which is a product of our brains, have any existence outside
of us?
(3) Assuming that other rational beings exist in the universe, would they
necessarily develop the same system of logic that we have, or could they
possibly find some other system equally capable of explaining their world?
Mathematics is often described as a priori, meaning that it exists independently of the outside world, in contradistinction to an a posteriori knowledge,
which is obtained by empirical observation. This implies that mathematics
would exist even if the world around us vanished. The brains of humans,
and presumably other intelligent beings, harness this universal resource in the
development of science. The term Platonism is used to describe this philosophical tenet. Eccentric 20th Century mathematician, Paul Erdös, often
referred to “The Book”, in which God keeps the most elegant proof of each
mathematical theorem. He once said in a lecture: you don’t have to believe in
God, but you should believe in The Book [8].
Other philosophers deny that mathematics is a priori at all, claiming that
it arose in the search for the best description of experience, and in that sense
is no different from the other sciences. This viewpoint is known as Empiricism, and has been propounded by 20th Century philosophers, Willard Van
Orman Quine and Hilary Putnam. A criticism of an empirical view of mathematics is that if mathematics is just as empirical as the other sciences, then
its results are just as fallible as theirs.
The empiricist explanation opens the way for the evolution of logic and
mathematics in the brains of early humans as a survival aid in the process of
Darwinian natural selection, and gives insight into why mathematical logic
works so well at describing the physical world. Of course, once developed,
logic can be applied to any other abstract field not connected with survival.
This is nothing new: our eyes did not evolve to read computer screens, but
serve that purpose just as well.
We will re-examine these two alternative views of the nature of logic (and
mathematics) in Part 3, after a review in Part 2 of what we have learned from
the last century of progress in physics.
2.3 Pattern Recognition
Leaving aside these questions, which will no doubt occupy philosophers for
another few centuries, it is worth considering whether mathematics and logic
are the only approaches to a rational understanding of the universe. Formal