Combining Texts

Ideas for 'Mahaprajnaparamitashastra', 'unfinished dialogue' and 'Philosophy of Mathematics'

unexpand these ideas     |    start again     |     choose another area for these texts

display all the ideas for this combination of texts

4 ideas

6. Mathematics / A. Nature of Mathematics / 1. Mathematics
9604 Mathematics is the only place where we are sure we are right [Brown,JR]
     Full Idea: Mathematics seems to be the one and only place where we humans can be absolutely sure that we got it right.
     From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 1)
     A reaction: Apart from death and taxes, that is. Personally I am more certain of the keyboard I am typing on than I am of Pythagoras's Theorem, but the experts seem pretty confident about the number stuff.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
9622 'There are two apples' can be expressed logically, with no mention of numbers [Brown,JR]
     Full Idea: 'There are two apples' can be recast as 'x is an apple and y is an apple, and x isn't y, and if z is an apple it is the same as x or y', which makes no appeal at all to mathematics.
     From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 4)
     A reaction: He cites this as the basis of Hartry Field's claim that science can be done without numbers. The logic is ∃x∃y∀z(Ax&Ay&(x¬=y)&(Az→z=x∨z=y)).
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / n. Pi
9648 π is a 'transcendental' number, because it is not the solution of an equation [Brown,JR]
     Full Idea: The number π is not only irrational, but it is also (unlike √2) a 'transcendental' number, because it is not the solution of an algebraic equation.
     From: James Robert Brown (Philosophy of Mathematics [1999], Ch.10)
     A reaction: So is that a superficial property, or a profound one? Answers on a post card.
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
9621 Mathematics represents the world through structurally similar models. [Brown,JR]
     Full Idea: Mathematics hooks onto the world by providing representations in the form of structurally similar models.
     From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 4)
     A reaction: This is Brown's conclusion. It needs notions of mapping, one-to-one correspondence, and similarity. I like the idea of a 'model', as used in both logic and mathematics, and children's hobbies. The mind is a model-making machine.