The Synthetic a Priori
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Empiricism, Platonism, Innate Ideas and the A Priori
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Empiricism is the doctrine that all knowledge is derived from sense-experience. The rationalist counterargument to empiricism is that there exists conceptual knowledge that cannot be derived or abstracted from sense-experience. This argument was first put by Plato, so the doctrine that there are abstract entities existing independently of space and time is known as Platonism. (It is also called realism, which can be confusing, since the term "realism" is used for many different philosophical doctrines, and some of these are arguably inconsistent with each other.) Empiricism: All our knowledge is gained through sense-experience. Platonism: There exist abstract entities not located in space and time, and our experience of them explains how we can have knowledge of the general terms of our language. Rationalists also used the term "innate" to describe abstract entities. They called them "innate" because they believed that God planted them in our minds directly. Plato believed that innate ideas must imply pre-existence. Russell rejects the idea that innate ideas derive from experiences that we had as disembodies souls before our birth, and introduces the term a priori when he writes, "It would certainly be absurd to suppose that there are innate principles in the sense that babies are born with a knowledge of everything which men know and which cannot be deduced from what is experienced. For this reason, the word 'innate' would not now be employed to describe our knowledge of logical principles. The phrase 'a priori' is less objectionable, and is more usual in modern writers. Thus, while admitting that all knowledge is elicited and caused by experience, we shall nevertheless hold that some knowledge is a priori, in the sense that the experience which makes us think of it does not suffice to prove it, but merely so directs our attention that we see its truth without requiring any proof from experience." This use of the term a priori was originally introduced into Western philosophy by Leibniz, and became the cornerstone of the thinking of Immanuel Kant. Thus the rationalists' strongest argument would appear to start with the claim that there exists a priori knowledge. This is knowledge that cannot be logically derived from sense-experience, and hence must have a source independently of experience. Rationalists then seek to explain where this knowledge comes from. Descartes says it is directly implanted into our minds by God; Plato says that it derives from our pre-existence; Russell, who is also a rationalist, says that it comes from a direct acquaintance with universals. The term a priori is contrasted to the term a posteriori. A posteriori knowledge is knowledge that is derived ultimately from particular experience. Obviously, if someone walks into a room and sees their cousin, then the knowledge that their cousin is in the room is derived from this particular observation. Scientific generalisations involve laws that refer to all objects or events of a particular kind; however, these laws are also essentially knowledge a posteriori because they are based ultimately on particular observations.
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Contents of
The Synthetic a Priori
1 Empiricism, Platonism, Innate Ideas and the A Priori
2 Analytic a priori
3 Kant and the synthetic a priori
4 Compound (molecular) and atomic sentences
5 Logically atomic sentences and the philosophy of logical atomism
6 Complex sentences and attitudes
7 Subject and predicate, individual and property
8 Synthetic and analytic, definitions offered by Kant
9 A priori and a posteriori
10 The synthetic a priori in Kant - the Critique of Pure Reason
11 Kant, The Critique of Pure Reason, the self and transcendental apperception
12 Empiricist philosophies of mathematics - conventionalism (formalism)
13 Empiricist philosophies of mathematics - the empiricism of J.S. Mill
14 Hybrid empiricist philosophies of mathematics
15 Empiricist philosophies of mathematics - Wittgenstein and non-cognitivism
16 A.J. Ayer and conventionalism - his reply to Kant
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