_Of the Divisions of Propositions_.


202. The most obvious and the most important division of
propositions is into true and false, but with this we are not
concerned. Formal logic can recognise no difference between true and
false propositions. The one is represented by the same symbols as the
other.

203. We may notice, however, in passing, that truth and falsehood
are attributes of propositions and of propositions only. For something
must be predicated, i.e. asserted or denied, before we can have
either truth or falsehood. Neither concepts or terms, on the one hand,
nor reasonings, on the other, can properly be said to be true or
false. In the mere notion of a Centaur or of a black swan there is
neither truth nor falsehood; it is not until we make some statement
about these things, such as that 'black swans are found in Australia,'
or 'I met a Centaur in the High Street yesterday,' that the question
of truth or falsehood comes in. In such expressions as a 'true friend'
or 'a false patriot' there is a tacit reference to propositions. We
mean persons of whom the terms 'friend' and 'patriot' are truly or
falsely predicated. Neither can we with any propriety talk of true or
false reasoning. Reasoning is either valid or invalid: it is only the
premisses of our reasonings, which are propositions, that can be true
or false. We may have a perfectly valid process of reasoning which
starts from a false assumption and lands us in a false conclusion.

204. All truth and falsehood then are contained in propositions; and
propositions are divided according to the Quality of the Matter into
true and false. But the consideration of the matter is outside the