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Philosophy of mathematics seems to focus primarily on set theory, which is probably a historical accident (just like it is a historical accident that set theory became the prevalent "foundation" in the 20th century). If you want to see things from other perspectives you could read things like:

• S. Awodey: Structure in mathematics and logic: a categorical perspective. Philosophia Mathematica (3), vol. 4 (1996), pp. 209--237. (See also the subsequent discussion.)

• F. W. Lawvere's "Down with "Foundations"! Up with algebra!" and "Why are we concerned? II" posting on the categories mailing list, which include further references.

Perhaps other, more knowledgable readers, can suggest additional references in this direction.

Philosophy of mathematics seems to focus primarily on set theory, which is probably a historical accident (just like it is a historical accident that set theory became the prevalent "foundation" in the 20th century). If you want to see things from other perspectives you could read things like:

• S. Awodey: Structure in mathematics and logic: a categorical perspective. Philosophia Mathematica (3), vol. 4 (1996), pp. 209--237. (See also the subsequent discussion.)

• F. W. Lawvere's "Down with "Foundations"! Up with algebra!" and "Why are we concerned? II" posting on the categories mailing list, which include further references.

Perhaps other, more knowledgable readers, can suggest additional references in this direction.

Philosophy of mathematics seems to focus primarily on set theory, which is probably a historical accident (just like it is a historical accident that set theory became the prevalent "foundation" in the 20th century). If you want to see things from other perspectives you could read things like:

• S. Awodey: Structure in mathematics and logic: a categorical perspective. Philosophia Mathematica (3), vol. 4 (1996), pp. 209--237. (See also the subsequent discussion.)

• F. W. Lawvere's "Down with "Foundations"! Up with algebra!" and "Why are we concerned? II" posting on the categories mailing list, which include further references.

Perhaps other can suggest additional references in this direction.

Philosophy of mathematics seems to focus primarily on set theory, which is probably a historical accident (just like it is a historical accident that set theory became the prevalent "foundation" in the 20th century). If you want to see things from other perspectives you could read things like:

• S. Awodey: Structure in mathematics and logic: a categorical perspective. Philosophia Mathematica (3), vol. 4 (1996), pp. 209--237. (See also the subsequent discussion.)

• F. W. Lawvere's "Down with "Foundations"! Up with algebra!" and "Why are we concerned? II" posting on the categories mailing list, which include further references.

Perhaps other, more knowledgable readers, can suggest additional references in this direction.

Philosophy of mathematics seems to focus primarily on set theory, which is probably a historical accident (just like it is a historical accident that set theory became the prevalent "foundation" in the 20th century). If you want to see things from other perspectives you could read things like:

• S. Awodey: Structure in mathematics and logic: a categorical perspective. Philosophia Mathematica (3), vol. 4 (1996), pp. 209--237. (See also the subsequent discussion.)

• F. W. Lawvere's "Down with "Foundations"! Up with algebra!" posting on the categories mailing list.

Perhaps other can suggest additional references in this direction.

Philosophy of mathematics seems to focus primarily on set theory, which is probably a historical accident (just like it is a historical accident that set theory became the prevalent "foundation" in the 20th century). If you want to see things from other perspectives you could read things like:

• S. Awodey: Structure in mathematics and logic: a categorical perspective. Philosophia Mathematica (3), vol. 4 (1996), pp. 209--237. (See also the subsequent discussion.)

• F. W. Lawvere's "Down with "Foundations"! Up with algebra!" and "Why are we concerned? II" posting on the categories mailing list, which include further references.

Perhaps other can suggest additional references in this direction.