Ideas from 'Realism, Mathematics and Modality' by Hartry Field [1989], by Theme Structure

[found in 'Realism, Mathematics and Modality' by Field,Hartry [Blackwell 1989,0-631-16303-4]].

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6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics
Fictionalists say 2+2=4 is true in the way that 'Oliver Twist lived in London' is true
                        Full Idea: The fictionalist can say that the sense in which '2+2=4' is true is pretty much the same as the sense in which 'Oliver Twist lived in London' is true. They are true 'according to a well-known story', or 'according to standard mathematics'.
                        From: Hartry Field (Realism, Mathematics and Modality [1989], 1.1.1), quoted by Michèle Friend - Introducing the Philosophy of Mathematics 6.3
                        A reaction: The roots of this idea are in Carnap. Fictionalism strikes me as brilliant, but poisonous in large doses. Novels can aspire to artistic truth, or to documentary truth. We invent a fiction, and nudge it slowly towards reality.