It is allowable to imagine ourselves placed in circumstances not yet
realised, or in possession of information not yet acquired, and
to anticipate or rehearse the reasoning we should employ under the
supposed conditions. Such arguments take in language a conditional or
hypothetical phraseology.
The case may be entirely fictitious, but I cannot find a valid
instance of a whole precedent being fictitious. Its dubiety turns on
our knowledge or ignorance of the applicate. Has a subject such or
such an attribute? Then it may be applied to illustrate a certain
case. 'If it is true that Damon and Pythias are inseparable, _then
Pythias must be in town_, for I have just seen Damon.'
It is more often the case that is dubious. 'If Caius is a European _he
is white_, for all Europeans are white.' 'If Damon is in town _Pythias
is in town_, for they are inseparable.' 'If I were you _I should
defer the voyage to the summer season_, as I have always found winter
travelling disagreeable.' But the word 'if' does not always mark a
hypothetical thought. In the proposition, 'if children are neglected
they will grow up ignorant,' we have a dogmatic or assertorial
judgment--'neglected children grow up ignorant.' (Bain.)
The precedent may be suppressed in hypothetical as in dogmatic
argument. 'If the crops are good, corn will be cheap' implies the
unspoken precedent, 'good crops have been invariably followed by cheap
corn.' 'If logic is useless it deserves to be neglected,' carries the
mind to the more general thesis, 'all useless studies deserve to be
neglected.' 'If Great Britain should be invaded the volunteers will be
called out,' rests on the precedent judgment, 'it is the duty of the
volunteer army to repel invaders.'
Arguments in which both applicate and case are hypothetical are so
very dubious that they cannot be considered of any practical use.
'_If_ opium is poisonous, and _if_ this substance is opium, you will
be poisoned by taking this substance.'
The Aristotelian hypothetical is almost invariably a fallacy,
sometimes on more than one account. It usually consists of--first, a
conditional or doubtful statement; next, a solution of the doubt by
means of positive information; finally and by way of inference the
first statement is given without the doubt. Here is an example from
Jevons: 'If the barometer is falling, bad weather is coming; but the
barometer is falling; therefore bad weather is coming.'
Where did the information that the barometer is falling come from? If
we knew it before uttering the first proposition, we were affecting
an ignorance that did not exist. The second proposition takes away all
occasion for argument; it is an amendment of the first proposition,
and what we get from the theorem as a whole is a _case_, followed by
a prediction for which there is no precedent justification. We are
arguing in a circle.
'If Aristotle is right, slavery is a proper form of society; but
slavery is not a proper form of society; therefore Aristotle is not
right.' If we knew for certain (as the second proposition indicates)
that slavery is not a proper form of society, what is the use or
meaning of treating the question as hypothetical (as is done in
the first)? If we acquired the information after uttering the first
proposition, there was no occasion to go on with the argument; we
should have said simply, 'Slavery is not a proper form of society,
though Aristotle said it was.' It is needless, except for verbal
completeness, to say 'he was not right'--we have _logically_ said so.
When two or more alternative data are presented, of which only one
is valid or relevant to a proposed argument, but we know not at
first which the valid datum is, we have the _dilemma_ (_trilemma_,
_tetralemma_, &c.) of logicians. In such conditions we have a double
process to go through; we must first settle by observation or by an
auxiliary argument which of the alternative data to select, and then
work out the principal argument in the regular dogmatic form.
Suppose we have to determine dialectically the specific gravity of a
piece of metal, but do not know whether it is gold or gun-metal. It is
evident we must first somehow make up our mind as to its identity, and
then proceed on the usual method of argumentation. The 'making up
our mind' is probably itself an argument, and might be of this
character--'A piece of yellow metal stamped with what appears to be
a hall-mark, is more likely to be gold than gun-metal; this piece of
metal has traces of such a stamp; so I conclude _it is gold_.' Then
we proceed to the principal question--'The specific gravity of gold is
19·26; I have concluded that this object is gold; I conclude further
that _it has a specific gravity of_ 19·26.'
We may work out all the alternative conclusions first and fix on a
datum afterwards, as in deciding how we shall invest our money. 'If
I put my money in Consols I shall have a small return with good
security; if I buy Patagonian bonds I may have a large interest for a
time, but the security is bad.' The next thing to settle is whether
in our experience or on accepted principles small profit with good
security is, or is not, to be preferred to large profit and bad
security: having decided in favour of the former alternative, we now
choose our investment dogmatically--'A good security with small
profit is to be preferred; Consols are of this character; _they are a
suitable investment for me_.'
We may be unable to decide for any of the alternative data, but we
work out all the possible arguments as hypotheses, and so are prepared
in a degree for all the possible events. A person is seen approaching
our residence, but we cannot discern whether it is A. B., who is
a bore, or C. D., who is an entertaining companion. We argue
rapidly--'If it is A. B. _I shall have a bad half-hour_, for he always
wearies me; if it is C. D. _I shall have an agreeable distraction_,
for he is very amusing.'
According to the syllogists, the dilemmatic premises are a statement
of alternative data and the choice of one of them, and the inference
is the rejection of the remainder: or the rejection may be given as
matter of fact and the selection as conclusion. In neither case have
we argument.
From the moment we select a datum the remaining data are of no import
to us, and they need not be mentioned. The selection of one datum
is logically identical with the rejection of the rest, and this
is therefore not a conclusion from that.--'Do you take tea or
coffee?'--'Tea, please.'--'Then I conclude you do not take coffee.'--A
person who would 'conclude' in this fashion would be justly deemed
irrational. The choice of the tea is a fact, and the rejection of the
coffee is the same fact otherwise expressed, so that the rejection
cannot be a rational conclusion.--'My doctor sends me off every
winter to Nice, Algiers, or Egypt; but I never go to Algiers or
Egypt.'--There is no occasion to say, 'therefore you go to Nice'; that
has been already announced as a matter of fact and is not susceptible
of inference. For the sake of verbal emphasis we might remark, 'So it
is to Nice you go', but this is not logically requisite.
Whately's examples of this kind of theorem are exactly of the model
just given.--'Either the earth is eternal, or the work of chance, or
the work of an intelligent Being; it is not eternal, nor the work of
chance, _therefore_ it is the work of an intelligent Being.' This is
put forward in all gravity as a specimen of reasoning. It is plain
that if we know the premises as matters of fact, we also know the
proposed conclusion as a matter of fact. There is no occasion to
reason about it.
The Aristotelian hypothetical can be reduced to arithmetical
subtraction. Suppose we put five balls into a bag and afterwards take
out three without seeing the remainder: is the judgment that two balls
remain in the bag a logical inference? No--it is matter of fact. Since
we last perceived the objects they have undergone diminution, but that
does not confer on what is left of them the imaginary character proper
to a rational conclusion. What remains is as much fact--recollected
but not imaginary fact--as before the subtraction.
Whately's next example is--'It is either spring, summer, autumn, or
winter; but it is neither spring nor summer; therefore it is either
autumn or winter.' This is aggravated fallacy. Not only is it mere
subtraction, but the remainder is _perceived_--not recollected, as in
the preceding case. The actual season of the year is a known fact, and
is not rendered more certain by an inference drawn from the absence
of some other season. Arguments have no validity as against matters
of fact, and add nothing to their authority. Fact is above, and
independent of, argument. The example just cited may be paralleled
thus--'The cards in my hand are either spades, hearts, clubs,
or diamonds; but they are neither spades nor hearts; therefore
they are either clubs or diamonds'.--I _see_ that they are
either clubs or diamonds: the perceptual judgment renders the
rational--imaginary--judgment superfluous. Reason is intended to
supplement experience--not to supersede it.