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Single Idea 5526

[filed under theme 12. Knowledge Sources / A. A Priori Knowledge / 9. A Priori from Concepts ]

Full Idea

It is clearer that all arithmetical propositions are synthetic if we take larger numbers, for it is then clear that, twist and turn our concepts as we will, without help from intuition we could never find the sum by means of the mere analysis of concepts.

Gist of Idea

With large numbers it is obvious that we could never find the sum by analysing the concepts

Source

Immanuel Kant (Critique of Pure Reason [1781], B016)

Book Ref

Kant,Immanuel: 'Critique of Pure Reason', ed/tr. Guyer,P /Wood,A W [CUO 1998], p.144

A Reaction

I don't see this. Obviously we may not know the name of the number which is the answer. We must analyse 'plus' as well as the component numbers. How can it be synthetic if no experience is involved?

The 15 ideas with the same theme [a priori knowledge only arises from our concepts]:

1824 To name something, you must already have an idea of what it is [Epicurus, by Diog. Laertius]
2191 Relations of ideas are known by thought, independently from the world [Hume]
18262 For Kant analytic knowledge needs complex concepts, but the a priori can rest on the simple [Coffa on Kant]
5526 With large numbers it is obvious that we could never find the sum by analysing the concepts [Kant]
16915 A priori intuitions can only concern the objects of our senses [Kant]
4430 All a priori knowledge deals with the relations of universals [Russell]
5411 We can know some general propositions by universals, when no instance can be given [Russell]
9353 We explain away a priori knowledge, not as directly empirical, but as indirectly holistically empirical [Devitt]
13406 A priori knowledge is analytic - the structure of our concepts - and hence unimportant [Papineau]
12389 Knowledge is a priori if the experience giving you the concepts thus gives you the knowledge [Kitcher]
9341 Meanings and concepts cannot give a priori knowledge, because they may be unacceptable [Horwich]
9334 If we stipulate the meaning of 'number' to make Hume's Principle true, we first need Hume's Principle [Horwich]
2727 Red and green being exclusive colours seems to be rationally graspable but not analytic [Audi,R]
2728 The concepts needed for a priori thought may come from experience [Audi,R]
17726 Examining accurate, justified or grounded concepts brings understanding of the world [Jenkins]