康德的先天綜合判斷及一種反駁

06-24

康德的先天綜合判斷及一種反駁

? Why Kant wants to establish the existence of synthetic a priori truths?

Kant』s reasoning of synthetic a priori truths (SAP)

In the Introduction of CPR, Kant objects to the view of the sources of

knowledge by Leibniz and Hume. Both of them regard our knowledge as divided

into 2 fundamental types – necessary and a priori knowledge, and contingent and

a posteriori knowledge. Kant』s new distinction – analytic/synthetic – is

independent from these older distinctions. A judgement is analytic if

the predicate is contained in and thought in the concept of the subject. E.g.

『a triangle has three sides』 is analytic because the concept of three-sidedness

is contained in that of triangularity and its negation is contradictory. A

judgement is synthetic if the predicate that it connects with the

concept of the subject is not contained or thought in it. The judgement must be

true by virtue of something other than the principle of contradiction: it rests

on a 『synthesis』. E.g. 『All bodies are heavy [have weight]』is synthetic because

the concept of weight is not contained in that of body and is added to it

through experience. Hence synthetic judgements extend our knowledge, as analytic

judgements cannot.

For L and H, they would expect all necessary and a priori judgements

to be analytic, and all contingent and empirical judgements to be synthetic. But

Kant argues that not all necessary and a priori judgements are analytic.

Metaphysical judgements are a priori (ap) and synthetic. E.g. 『every event has

a cause』. Because it』s necessary, it must be ap. But it』s not analytic, for the

concept of an event doesn』t contain that of being an effect. This judgement is thus

informative and synthetic, whilst being ap. Metaphysical judgements thus can』t

be derived from either logic or experience. This means that the question 『is

metaphysics possible』 can be answered positively only if the question 『are sap

judgments possible』 can be answered positively.

He goes on to argue that mathematical and geometrical judgements are not

analytic but synthetic instead. Consider the judgement 『7+5=12』. If 「7+5=12」 is

analytic, then 「12」 must be contained in 「7+5」. But the concept of 7+5 doesn』t

contain the concept of 12. Synthesis is required. The truth of 7 + 5 = 12 can

only be established through an intuition, that is, if we want to check the

truth of this claim we need to appeal to an aid, like our fingers. It』s an

appeal to experience, but not an appeal to any particular experience. The same is true for

geometrical judgments. 「A straight line is the shortest distance between two

points」 is synthetic because the concept of straightness doesn』t contain any

information regarding the relative lengths of different lines joining two

points. We cannot extract the quantitative predicate 「shortest」 from the

concept 「straight line」 because 「straight line」 is a purely qualitative concept.

In order to establish the truth of the proposition, we must also appeal to

intuition.

Mathematics and geometry

show that it is possible to have knowledge which is necessary but not logically

necessary, so there』s a reason for thinking that metaphysical knowledge, which

lays claim to the same status, may equally be possible. K thus undermines L』s

claim that knowledge of reality is derivable from logical principles, and opens

the door to demonstrating, against Hume, the possibility of metaphysics.

Analysing Kant』s reasoning

Some people argue that

『mathematics is synthetic』 is defensible, but 『geometry is a priori』 is

dubious: geometry is now divided into pure geometry, which consists of formal

systems based on axioms for which truth is not claimed, and which are

consequently not synthetic, and applied geometry, a branch of physics, the

truth of which is determined empirically, and which is therefore not a priori. The

question is, then, what difference is made to the claims of the Introduction if

Kant』s claims about either mathematics or geometry are rejected. If Kant, in

the Introduction, assumes that mathematics and geometry are not open to repudiation,

this might suggest that their truth is premised in this context and thus in the

Critique as a whole. The whole C might be undermined.

However, Gardner argues

that there』s a clear statement in the Critique of Practical Reason that Kant

does not regard the truths of geometry and mathematics as beyond skeptical

doubt and so cannot be operating this strategy. There he says that Hume only

failed to extend skeptical doubt to mathematical and geometrical truths because

he mistakenly regarded their propositions as analytic, and that once it is realized

that they are synthetic, it becomes possible to doubt their alleged necessity,

and indeed that empiricism demands such skepticism. Furthermore, Kant goes on

to describe himself as having followed in the Critique the strategy of first

disposing of the empiricism witnessed in Hume』s critique of causation, and then

overthrowing its inevitable consequence, skepticism, first, in natural science

and, then, in mathematics.

The Critique is intended,

therefore, to secure rather than assume the truth of geometry and mathematics.

Kant』s justification of the metaphysics of experience belongs to the same

project as that which adds to the defense of

mathematics and geometry, but it does not draw on their epistemological

prestige, and the Critique is not undermined by any defects in Kant』s account

of mathematics or geometry. (This interpretation is substantiated by the

discussion of methodology in the Prolegomena. Kant says that he is

proceeding in this expository work on the basis that mathematics, geometry and

even natural science are objectively valid, because he is following a different

methodology from the Critique, one that is analytical or regressive, rather

than synthetical or progressive. Analytical enquiry rests upon something

already known as trustworthy, from which we can set out with confidence and

ascend to sources as yet unknown, the discovery of which will explain to us

what we already knew. The synthetical method, which he follows in the Critique,

is based on no data except reason itself.)

Thus if the appeal to mathematics and geometry is restricted, Kant may still claim to have clarified the problem set by metaphysics, and the central line of argument in the Critique will remain untouched.