Stony Brook University

in mathematics, the measures of right and wrong might be made out, to
anyone that will apply himself with the same indifferency and attention to
the one as he does to the other of these sciences. (E 4.3.18)
Locke thinks that moral truths may be demonstrated in only two ways: either by
beginning with self-evident propositions (propositions consisting of self-evident ideas),
or by reducing propositions to self-evident ideas. 16 Locke goes on to say that, “we have
an intuitive knowledge of our existence, and a demonstrative knowledge of God” and
only a sensitive knowledge of everything else (E.4.3.21). He does not go on to provide a
demonstration of God’s existence, nor to show how knowledge of God or of oneself
makes morality demonstrable. He does however provide two morally related propositions
that he says are as demonstrably certain as any in mathematics.
Where there is no property there is no justice,’ is a proposition as certain
as any demonstration in Euclid. For the idea of property being a right to
anything, and the idea to which the name ‘injustice’ is given being the
invasion or violation of that right, it is evident that these ideas, being thus
established, and the names annexed to them, I can as certainly know this
proposition to be true, as that a triangle has three angles equal to two right
ones. Again: ‘No government allows absolute liberty.’ The idea of
government being the establishment of society upon certain rules or laws
which require conformity to them; and the idea of absolute liberty being
for any one to do whatever he pleases; I am as capable of being certain of
the truth of this proposition as of any in the mathematics. (E.4.3.18)
Both propositions fulfill the “analytic” criterion he laid out earlier: a self-evident
proposition is one that “carries its own light and evidence” so that “he that understands
the terms assents to [the principle] for its own sake . . .” (E 1.2.4). Applied to the first
proposition, this means that the idea of property analytically, necessarily, contains the
ideas of right and justice; thus, without property there is no justice. Applied to the second
proposition, the idea of ‘government,’ necessarily contains ‘restriction of freedom,’ an
idea which logically excludes absolute freedom. Thus, deduced from self-evident ideas,
each proposition is demonstrably certain. They are as certain as the properties of a
triangle deduced from the self-evident idea of a triangle. It should be noted however that
Locke takes these ideas to be self-evident; once they are taken to be self-evident, the
deduction is certain. However, as we will see Leibniz argues that Locke’s idea of
property is mistaken and his idea of government is derivative. For Leibniz both ideas
depend on the meaning of right.
At the same time, Locke then claims that such propositions and moral ideas
similar to them are not really demonstrably certain, mainly for two reasons: (1) we have
no “sensible marks” for them and thus cannot be sure the ideas remain the same from
person to person; (2) “moral ideas are commonly more complex” than mathematical and
geometrical ideas, so again their signification is uncertain, making it difficult to maintain
consistency through a chain of reasoning, and difficult to maintain consistency with other
16 It is interesting to note in comparison with Leibniz that for Locke “the science of morality” begins with
self-evident propositions; whereas for Leibniz “the science of right” begins with real definitions.
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