Another form which seems to contradict the assertion that negative
propositions are infinite is positive evidence in the shape of negation.
If we give an expert a stain to examine and ask him whether it is a
blood stain, and he tells us: “It is not a blood stain,” then this
single scientifically established assertion proves that we do not have
to deal with blood, and hence “negative” proof seems brought in a single
instance. But as a matter of fact we deal here with an actually positive
proof, for the expert has given us the deduced proposition, not the
essential assertion. He has found the stain to be a rust stain or a
tobacco stain, and hence he may assert and deduce that it is not blood.
Even were he a skeptic, he would say, “We have not yet seen the blood of
a mammal in which the characteristic signs for recognition were not
present, and we have never yet recognized a body without the blood
pertaining to it, and hence we may say, we are not dealing with blood
because all of us found the characteristics of the stain to be what we
have been until now accustomed to call the characteristics of rust
stain.”
We have still to touch upon the difference between logical connection
and experience. If I say, “This mineral tastes salty, therefore it is
soluble in water,” the inference depends upon logical relationships, for
my intent is: “If I perceive a salty taste, it has to be brought to the
nerves of taste, which can be done only by the combination of the
mineral with the saliva, hence by its solution in the saliva. But if it
is soluble in saliva it must also be soluble in water.” If I say on the
other hand, “This mineral tastes salty, has a hardness of 2, a specific
gravity of 2.2, and consequently it crystallizes hexagonally,”--this
statement depends on experience, for what I really say is: “I know first
of all, that a mineral which has the qualities mentioned must be rock
salt; for at the least, we know of no mineral which has these qualities
and is not rock salt, and which in the second place crystallizes
hexagonally as rock salt does,--a way which, at least, we find rock salt
never to have missed.” If we examine the matter still more closely we
become convinced that in the first case only the formal and logical
side, in the second the experiential aspect predominates. The premises
of both cases are purely matters of experience and the formal question
of inference is a matter of logic. Only,--at one time the first
question, at another the second comes more obviously into the
foreground. Although this matter appears self-evident it is not
indifferent. It is well known that whenever we are powerfully influenced
by one thing, things of little intensity are either not experienced at
all or only to a very small degree, and are therefore neglected. This is
a fact which may indeed be shown mathematically, for infinity plus one
equals infinity. When, therefore, we undergo great pain or great joy,
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