The English works of Thomas Hobbes of Malmesbury, Volume 01 (of 11) — Thomas Hobbes — John Shaqi
The English works of Thomas Hobbes of Malmesbury, Volume 01 (of 11)
Thomas Hobbes · en
_Subcontrary_, are particular propositions of different quality; as,
_some man is learned_, _some man is not learned_; which cannot be both
false, but they may be both true.
_Contradictory_ are those that differ both in quantity and quality; as,
_every man is a living creature_, _some man is not a living-creature_;
which can neither be both true, nor both false.
[Sidenote: Consequence, what it is.]
18. A proposition is said to _follow_ from two other propositions, when
these being granted to be true, it cannot be denied but the other is
true also. For example, let these two propositions, _every man is a
living creature_, and, _every living creature is a body_, be supposed
true, that is, that _body_ is the name of _every living creature_, and
_living creature_ the name of _every man_. Seeing therefore, if these be
understood to be true, it cannot be understood that _body_ is not the
name of _every man_, that is, that _every man is a body_ is false, this
proposition will be said to _follow_ from those two, or to be
necessarily _inferred_ from them.
[Sidenote: Falsity cannot follow from truth.]
19. That a true proposition may follow from false propositions, may
happen sometimes; but false from true, never. For if these, _every man
is a stone_, and _every stone is a living creature_, (which are both
false) be granted to be true, it is granted also that _living creature_
is the name of _every stone_, and _stone_ of _every man_, that is, that
_living creature_ is the name of _every man_; that is to say, this
proposition _every man is a living creature_, is true, as it is indeed
true. Wherefore a true proposition may sometimes follow from false. But
if any two propositions be true, a false one can never follow from them.
For if true follow from false, for this reason only, that the false are
granted to be true, then truth from two truths granted will follow in
the same manner.
[Sidenote: How one proposition is the cause of another.]