The objective view of mathematical truth holds that mathematical truths are true independently of human beliefs or opinions. This view is often associated with the idea that mathematics is a discovery rather than an invention.

Platonism is a philosophical position that holds that mathematical objects exist independently of the human mind. Platonists believe that mathematical truths are objective and eternal, and that they can be discovered by reason.

There are a number of objections to Platonism, including the following: (1) Mathematical objects are abstract and cannot exist independently of the human mind. (2) Mathematical truths are not always certain. (3) Mathematical objects are not physical objects.

Formalism is a philosophical position that holds that mathematical objects are mental constructions. Formalists believe that mathematics is a game or a calculus, and that mathematical truths are simply rules of the game.

There are a number of objections to formalism, including the following: (1) Formalism cannot explain the applicability of mathematics to the real world. (2) Formalism cannot explain the creativity of mathematics. (3) Formalism cannot explain the objectivity of mathematics.

Intuitionism is a philosophical position that holds that mathematical objects are created by the human mind. Intuitionists believe that mathematics is a creative activity, and that mathematical truths are justified by their self-evidence.

There are a number of objections to intuitionism, including the following: (1) Intuitionism cannot explain the objectivity of mathematics. (2) Intuitionism cannot explain the applicability of mathematics to the real world. (3) Intuitionism cannot explain the creativity of mathematics.

Conventionalism is a philosophical position that holds that mathematical truths are simply conventions. Conventionalists believe that mathematics is a human invention, and that mathematical truths are true only because we have agreed to accept them as true.

There are a number of objections to conventionalism, including the following: (1) Conventionalism cannot explain the objectivity of mathematics. (2) Conventionalism cannot explain the applicability of mathematics to the real world. (3) Conventionalism cannot explain the creativity of mathematics.

Relativism is a philosophical position that holds that mathematical truths are relative to the individual or culture. Relativists believe that there is no one true mathematics, and that what is true in one culture may not be true in another culture.

There are a number of objections to relativism, including the following: (1) Relativism cannot explain the objectivity of mathematics. (2) Relativism cannot explain the applicability of mathematics to the real world. (3) Relativism cannot explain the creativity of mathematics.

Fictionalism is a philosophical position that holds that mathematical truths are simply fictions. Fictionalists believe that mathematics is a game or a story, and that mathematical truths are true only within the context of the game or story.

There are a number of objections to fictionalism, including the following: (1) Fictionalism cannot explain the objectivity of mathematics. (2) Fictionalism cannot explain the applicability of mathematics to the real world. (3) Fictionalism cannot explain the creativity of mathematics.

Constructivism is a philosophical position that holds that mathematical objects are constructed by the human mind. Constructivists believe that mathematics is a creative activity, and that mathematical truths are justified by their constructibility.

There are a number of objections to constructivism, including the following: (1) Constructivism cannot explain the objectivity of mathematics. (2) Constructivism cannot explain the applicability of mathematics to the real world. (3) Constructivism cannot explain the creativity of mathematics.