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Medieval realism is the Platonic doctrine that universals and other abstract entities (like humanity and whiteness) exist independently of the mind; the mind may discover them, but it can't create them.
The corresponding view in contemporary philosophy of mathematics is
{ 1 } - formalism -- which denies that abstract entities exist but keeps mathematics as a useful system of symbols that's literally meaningless (and makes no truth claims).
{ 2 } - logicism -- which uses bound variables (like "some") to refer to abstract entities (like numbers and sets) known and unknown, indiscriminately.
{ 3 } - intuitionism -- which uses bound variables (like "some") to refer only to abstract entities (like numbers and sets) that we have constructed in advance.
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1 is wrong. Please try again.
Medieval realism is the Platonic doctrine that universals and other abstract entities (like humanity and whiteness) exist independently of the mind; the mind may discover them, but it can't create them.
The corresponding view in contemporary philosophy of mathematics is
{ 1 } - formalism -- which denies that abstract entities exist but keeps mathematics as a useful system of symbols that's literally meaningless (and makes no truth claims).
{ 2 } - logicism -- which uses bound variables (like "some") to refer to abstract entities (like numbers and sets) known and unknown, indiscriminately.
{ 3 } - intuitionism -- which uses bound variables (like "some") to refer only to abstract entities (like numbers and sets) that we have constructed in advance.
This is closer to medieval nominalism.
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2 is correct!
Medieval realism is the Platonic doctrine that universals and other abstract entities (like humanity and whiteness) exist independently of the mind; the mind may discover them, but it can't create them.
The corresponding view in contemporary philosophy of mathematics is
{ 1 } - formalism -- which denies that abstract entities exist but keeps mathematics as a useful system of symbols that's literally meaningless (and makes no truth claims).
{ 2 } - logicism -- which uses bound variables (like "some") to refer to abstract entities (like numbers and sets) known and unknown, indiscriminately.
{ 3 } - intuitionism -- which uses bound variables (like "some") to refer only to abstract entities (like numbers and sets) that we have constructed in advance.
On this view, numbers and sets are real entities that are discovered, not created.
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3 is wrong. Please try again.
Medieval realism is the Platonic doctrine that universals and other abstract entities (like humanity and whiteness) exist independently of the mind; the mind may discover them, but it can't create them.
The corresponding view in contemporary philosophy of mathematics is
{ 1 } - formalism -- which denies that abstract entities exist but keeps mathematics as a useful system of symbols that's literally meaningless (and makes no truth claims).
{ 2 } - logicism -- which uses bound variables (like "some") to refer to abstract entities (like numbers and sets) known and unknown, indiscriminately.
{ 3 } - intuitionism -- which uses bound variables (like "some") to refer only to abstract entities (like numbers and sets) that we have constructed in advance.
This is closer to medieval conceptualism.
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the end