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experience is the source of physics properly so-called, and Ÿinner experience is the basis
for empirical psychology; and metaphysical knowledge cannot come from either of these.
It is thus knowledge a priori - knowledge out of pure understanding and pure reason.
Mathematics also answers to that description. To demarcate metaphysics from
mathematics as well as from empirical enquiries, we shall have to call it pure philosophical
knowledge. In this phrase, ‘pure’ means ‘not empirical’; and ‘philosophical’ stands in
contrast to ‘mathematical’. The difference between these two ways of using reason - the
mathematical and the philosophical - is something I needn’t go into here; I have
adequately described it in my Critique of Pure Reason. So much for the sources of
Section 2: The only kind of knowledge that can be called metaphysical
(a) The distinction between synthetic and analytic judgments in general.
Because of what is special about the sources of metaphysical knowledge - ·namely, that
they do not include experience· - all such knowledge must consist in judgments that are
made a priori. However, a priori judgments can be divided into two groups, according to
their content: (a) those that merely spell out what is already there, adding nothing to the
content of the knowledge, and (b) those that add something, and enlarge the given
knowledge. We can call (a) analytic judgments, and (b) synthetic.
Analytic judgments say nothing in the predicate that was not already thought - though
less clearly - in the concept of the subject. If I say ‘All bodies are extended’, I haven’t
added anything to my concept of body, but have merely analysed it. Extension was already
implicitly thought of in the concept of body, before I made the judgment. So the judgment
is analytic. On the other hand the proposition ‘Some bodies are heavy’ contains something
in the predicate that is not thought - even unclearly or implicitly - in the concept of body.
It thus enlarges my knowledge in that it adds something to my concept, and hence must be
called a synthetic judgment. 9
(b) The common principle of all analytic judgments is the law of contradiction.
All analytic judgments rest wholly on the law of contradiction. The predicate of an
affirmative analytic judgment has already been thought in the concept of the subject, so it
can’t be denied of the subject without contradiction. This is the case with the proposition
‘Every body is extended’. ·That is equivalent to something of the form ‘Everything that is .
. . and extended is extended’, so that to deny it would be to say that something is . . . and
extended and not extended, which is an outright contradiction. The law of contradiction,
which says that no contradiction is true, thus underlies the truth of the analytic proposition
that all bodies are extended·.
So all analytic propositions are a priori judgments, even those which contain
empirical concepts as does the judgment ‘Gold is a yellow metal’. ·I must have experience
if I am to have the concepts of gold, of yellow, and of metal; but· to know that gold is a
yellow metal I need no further experience; all I need is to analyse my concept of gold,
which contains the concept of being a yellow metal.
(c) Synthetic judgments need a different principle from the law of contradiction.
Some synthetic judgments have an empirical origin, and can be known only a posteriori;
other synthetic judgments have a priori certainty, and originate in pure understanding and
reason. No synthetic judgment can come from the law of contradiction alone. Such
judgments must conform to that principle (which is just to say that they mustn’t be selfcontradictory), but they cannot be deduced from it.
·In the rest of this section four kinds of synthetic judgment will be identified and
discussed. Although they are all synthetic - meaning that none of them can be established
merely by analysing concepts - three of the four kinds can be learned a priori·.
(1) Judgments of experience are always synthetic. It would be absurd to base an
analytic judgment on experience: why go to experience when the judgment can derived
purely from my concept? That every body is extended is a proposition that holds a priori,
and not a judgment of experience. For before I look to experience I already have in the
concept of body all that I need for my judgment: I need only to extract the predicate
(‘extended’) from that concept according to the law of contradiction. In doing that, I also
become conscious of the necessity of the judgment - and ·that is further evidence that this
analytic judgment is not based on experience, because· experience can never teach me that
something is necessary.
(2) Mathematical judgments are all, without exception, synthetic. This is certainly
true and is very important, but it seems to have escaped the notice of all previous analysers
of human reason, and indeed to be directly opposed to all their theories. Thos...
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