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Single Idea 12933

[filed under theme 12. Knowledge Sources / A. A Priori Knowledge / 3. Innate Knowledge / a. Innate knowledge ]

Full Idea

I would name the propositions of arithmetic and geometry as innate. ...The actual knowledge of them is not innate. What is innate is what might be called the implicit knowledge of them, as the veins of marble outline a shape for the sculptor.

Gist of Idea

Arithmetic and geometry are implicitly innate, awaiting revelation

Source

Gottfried Leibniz (New Essays on Human Understanding [1704], 1.01)

Book Ref

Leibniz,Gottfried: 'New Essays on Human Understanding', ed/tr. Remnant/Bennett [CUP 1996], p.86

A Reaction

This seems to walk straight into the empiricist guns. The marble example shows the problem, because the 'veins' will hardly outline David in the block. Locke's challenge is to show that merely 'implicit' ideas have demonstrable reality.

The 16 ideas with the same theme [knowledge that arise from within the mind]:

5052 When Gentiles follow the law, they must have the law written in their hearts [Paul]
22169 Initial universal truths are present within us as potential, to be drawn out by reason [Aquinas]
3630 Our thinking about external things doesn't disprove the existence of innate ideas [Descartes]
24022 Our souls possess divine seeds of knowledge, which can bear spontaneous fruit [Descartes]
7570 Innate ideas are trivial (if they are just potentials) or absurd (if they claim infants know a lot) [Locke, by Jolley]
12472 If the only test of innateness is knowing, then all of our knowledge is innate [Locke]
7709 A proposition can't be in the mind if we aren't conscious of it [Locke]
4018 Innate ideas were followed up with innate doctrines, which stopped reasoning and made social control possible [Locke]
12929 All of our thoughts come from within the soul, and not from the senses [Leibniz]
12933 Arithmetic and geometry are implicitly innate, awaiting revelation [Leibniz]
12991 Children learn language fast, with little instruction and few definitions [Leibniz]
21081 We are equipped with the a priori intuitions needed for the concept of right [Kant]
14774 Innate truths are very uncertain and full of error, so they certainly have exceptions [Peirce]
2990 Contrary to commonsense, most of what is in the mind seems to be unlearned [Fodor]
3008 Evolution suggests that innate knowledge of human psychology would be beneficial [Fodor]
3009 Sticklebacks have an innate idea that red things are rivals [Fodor]