Think: A Compelling Introduction to Philosophy (29 page)

LANGUAGE AND LOGIC

The logician studies the forms of information that we have just described, and of course such other complex forms as come to light.
But there is another side to the work of the philosopher, which is to
decide when information couched in the idioms of ordinary
speech indeed displays one or another of these forms. This proves
a surprisingly fraught business.

Consider, for instance, the difference between `She was poor and
she was honest, and `She was poor but she was honest'. The first
clearly illustrates the form `p & q'. But what about the second? It
certainly suggests something else, along the lines that it is surprising or noteworthy that someone poor should be honest. But does
it actually say that? A simpler suggestion might be that it strictly
says only what the first says, but says it in a way to insinuate or suggest that the combination is surprising or noteworthy. Perhaps
only the simpler information is strictly given, but it is given in a
way that carries its own suggestions (which may, as in this example,
be seriously unpleasant). So philosophers of language are led to
distinguish what is strictly said or asserted-the information carried by the utterance, called its truth-condition-from what is suggested or implied, not as a strict logical consequence, but by the
way things are put, called the implicature.

Language is such a flexible and subtle instrument, that there is
almost no limit to the way nuances in the presentation of information affect the implicatures. A famous example is the way in which
simply not saying something can have weighty overtones:

`What do you think of the new professor of logic?'

`They tell me he is famous for his tomatoes.'

Here what is strictly said has little or no bearing on whether the
new professor is competent. But the fact that this response is all
that is given shows unmistakably that the respondent thinks the
professor is no good. Choice of terminology can have its own implicatures: consider the difference between

John is Fred's brother.

Fred has a male sibling, John.

Here, the second way of putting what is in fact the same information suggests some kind of significance-sinister psychoanalytic
overtones, perhaps. Order of telling also carries implicatures about
the order of events. It would be misleading, although what is said is
strictly true, to report the life of a child who learned to read and
then wrote poetry, by saying that she wrote poetry and learned to
read.

The way in which implicatures are generated is part of the study
of language called pragmatics, whereas the structure of information is the business of semantics.

Consider the dreaded lawyer's question, used to discompose
married male witnesses: `Have you stopped beating your wife-yes
or no?' The witness cannot answer `Yes', without admitting that he
once did; he cannot answer `No', without giving the strongest impression that he still does. So he is embarrassed, and the trick
works. How can we do better? Well, suppose we analyse `X stopped
doing Y' as a conjunction: `X once did Y & X does not now do Y.'
This explains why saying `Yes' to the lawyer is had: it follows that you once did beat your wife. Saying 'No', on the other hand, is interesting. If we look at the truth-table for conjunction we see that a
conjunction can be false in three different ways: p true, q false; p
false, q true; and both false. And each of these three ways are ways
in which the negation of a conjunction can be true (negation reverses truth-value). Now in the lawyer case it is vital to the innocent
husband to establish that his is the middle case: false that he once
did it, and true that he does not now do it. The trouble is that the
one word `no' is insufficient to establish which way it is, and the risk
is that the jury thinks he hasn't stopped because he continues (true
that he once did, true that he does it now, so false that he stopped).

The innocent witness needs enough words to specify which
combination describes him. So he cannot stick with the one-word
answer `No' (true thought it is). The right thing for the witness to
say is (in one breath) `No I haven't stopped because I never started,
or words to that effect. If we handle the lawyer's question this way,
we can say that it `presupposes' that the witness once beat his wife,
but only in the pragmatic sense, that anyone asking that question
would normally be taking this for granted. Uncovering the hidden
presuppositions behind questions and opinions is an important
part of thinking.

Some presuppositions even raise questions about the assumption we made when interpreting`and,'not',`or', and especially'If...
then' as truth-functions, adequately described by the tables. They
sometimes seen, to do more complex things. For instance, consider
a party to which Fred is invited, but to which he in fact does not go.
Suppose two assassins are trying to establish Fred's whereabouts.
One says, `If Fred goes to the party, he will go by taxi.' The other says, `If Fred goes to the party, he will go by elephant.' Intuitively, at
most one of these is true-in the West, probably the first. But if we
look at `Fred goes to the party - ..: we will see that both of them
are true. Because it is false that Fred goes to the party, and the table
for - gives the outcome true, whatever the truth-value of the
other proposition. Philosophers used to argue a great deal about
whether this shows that the English conditional `If ... then' means
the same as the truth-function -b. Nowadays there is often a
slightly more relaxed attitude, it being conceded that at any rate
gives the core of the notion, and the rest can be handled either semantically or pragmatically.

Before we leave this brief sketch of formal logic, we might pause
to consider one kind of reaction it sometimes provokes. People
sometimes think that logic is coercive (`masculine') or that it implies favouring some kind of'linear thinking' as opposed to `lateral
thinking'. Both these charges are totally mistaken. Formal logic is
too modest to deserve them.

First, what could be meant by the charge of coercion? Formal
logic enables you to determine whether a set of propositions implies a contradiction. It also interprets contradictions as false. Most
of us will want to avoid holding sets of propositions that imply
things that are false, because we care that our beliefs are true. If
someone is not like that, then we may indeed be minded to moralize against them. But we are not wearing the hats of formal logicians as we do so. The work of the formal logician was finished with
the result.

Perhaps someone might feel coerced by the assumption mentioned right at the outset-that every proposition is true or false, and no proposition is both. Perhaps we ought to try more complex
assumptions: for instance, we might welcome vague propositions
that are true to a degree, or propositions that are neither true nor
false but have some third status. That is fine too: these are respectable ideas, and there are alternative logics that develop them.
But it is fair to warn that, for various reasons, they become awkward and uncomfortable. It is usually wise to be grateful for the
simple `two-valued' assumption.

A third source of the feeling of coercion introduces wider issues.
If someone voices a number of views, or comes up with a piece of
reasoning, it can be crass and coercive to insist on seeing them as of
such-and-such a form and therefore contradictory, or therefore
invalid. This may well be insensitive to the other factors we have
mentioned already: presuppositions, suppressed premises, and so
on. But this was not the fault of the logic, but of the uncharitable
way of taking what was said. By itself logic is indifferent, even to
sayings that look as if they embody direct contradictions. In the
short story `The Lady with the Pet L)og' by Chekhov, Anna
Sergeyevna tells her husband that she is going to Moscow every so
often to visit a doctor, `and her husband believed her and did not
believe her: Formal logic does not tell us to jump up and down on
Chekhov for this blatant contradiction. We know that Chekhov is
suggesting something else, which is that her husband half-believes
her, or alternates between confidence and mistrust. It is the flat
contradiction that prompts us to look for other interpretations.

What of the charge that formal logic privileges `linear' th inking?
This too is nonsense. Formal logic does not direct the course of
anyone's thoughts, any more than mathematics tells you what to count or measure. It is gloriously indifferent between propositions
that arrive through speculation, imagination, sheer fancy, sober
science, or anything else. All it tells you is whether there is a way in
which all the propositions in a set, however arrived at, can be true
together. But that can he a pearl beyond price.

PLAUSIBLE REASONINGS

Formal logic is great at enabling us to avoid contradiction. Similarly, it is great for telling us what we can derive from sets of
premises. But you have to have the premises. Yet we reason not only
to deduce things from given information, but to expand our beliefs, or what we take to be information. So many of our most interesting reasonings, in everyday life, are not supposed to be valid
by the standards we have been describing. They are supposed to be
plausible or reasonable, rather than watertight. There are ways in
which such an argument could have true premises but a false conclusion, but they are not likely to occur.

Nevertheless, we can go a little further in applying some of the
ideas we have met, even to plausible reasonings. Why is it silly, for
instance, to be confident that my bet at roulette will be a winner?
Because my only information is that I have placed my bet on x, and
most ways that the wheel might end up do not present xas the winner. What we are dealing with is a space of possibilities, and if we
could show that most possibilities left open by our evidence are
ones in which the conclusion is also true, then we have something
corresponding to plausible reasoning. In the roulette case, most possibilities left open by our evidence are ones in which the conclusion that x is the winner is false.

Roulette and other games of chance are precisely little fields designed so that we know the possibilities and can measure probabilities. There are fifty-two outcomes possible when we turn up a
card, and if we do it from a freshly and fairly shuffled pack, each
possibility has an equal chance. Probabilistic reasoning can then go
forward: we can solve, for instance, for whether most draws of
seven cards involve two court cards, or whatever. Such probabilistic reasoning is precisely a matter of measuring the range of
possibilities left open by the specification, and seeing in what proportion of them some outcome is found.

What underlies our assignments of probabilities in the real
world? Suppose we think of our position like this. As we go
through life, we experience the way things tall out. Within our experience, various generalizations seem to hold: grass is green, the
sky blue. Water refreshes; chocolate nourishes. So we take this experience as a guide to how things are across wider expanses of
space and time. I have no direct experience of chocolate nourishing in the eighteenth century, but I suppose it did so; I have no direct experience of it nourishing people tomorrow, but I suppose it
will continue to do so. Our beliefs and our confidence extend beyond the limited circle of events that fall within our immediate
field of view.

Hume puts the problem this way:

As to past Experience, it can be allowed to rive d irect and certain information o~ those prec iseobjects only, and that precise
period of time, which 11,11 under its cognizance: but why this experience should be extended to future times, and to other
objects, which for aught we know, may be only in appearance
similar; this is the main question on which I would insist ...
At least, it must be acknowledged, that there is here it consequence drawn by the mind; that there is a certain step taken;
a process of thought, and an inference, which wants to be explained. These two propositions are being the same, I
have found that such an object has always been attended
with such an effect, and I foresee, that other objects, which
are, in appearance, similar, will be attended with similar effects. I shall allow, if you please, that the one proposition may
justly be inferred from the other: I know in fact, that it always
is inferred. But if you insist, that the inference is made by a
chain of reasoning, I desire you to produce that reasoning.