FUGITIVE TRUTH
By A. N. PRIOR
HAVE argued elsewhere1 that present-tensed utterances, and tensed
utterances generally, do not normally refer to themselves, and therefore not to the time of their own utterance, or at all events do not refer to
the time of their utterance as the time of their utterance. It is nevertheless necessary to refer to the time of their utterance when we are not
using but mentioning such sentences, and discussing their truth-conditions.
For example, the sentence 'I am about to go home', or 'I am now about
to go home', is true if and only if the person who utters it is about to go
home at the time at which he utters it.
In this connexion, some curious puzzles have been raised by Dr.
A. J. Kenny.2 One is that it would seem to be impossible to utter any
true sentence reporting, in the present tense, an instantaneous event. For
the utterance of a sentence always takes some finite time, and during
part of the time when we say, e.g., 'Eclipse is now just past the winningpost', Eclipse will not be just past the winning-post but an appreciable
distance past it. Moreover, Kenny has pointed out, if 'Eclipse was just
past the winning post' is to be analysed as 'It was the case that Eclipse is
just past the winning post', and 'It was the case that p' in general is
true if and only ifp was true, then even 'Eclipse was just past the winningpost' cannot ever be true either.
There are two points to be made here. In the first place, 'It was the
case that Eclipse is just past, etc.' is not about the sentence 'Eclipse is just
past, etc.' but is, rather, a more complicated sentence about Eclipse. And
the rule for its truth is not the one just given, but rather that 'It was the
case that/>' is true if and only if it was the case that p; and we may be able
to say this truly even if we can never say truly that p (not because it is
never the case that p but because saying that p takes too long). The
relation between the complex and the simple sentence could be like that
between 'For some x, I have never said anything about x\ and some
specific sentence of the form 'I have never said anything about x'—any
such specific sentence is self-refuting, yet its existential generalisation
could be, and in fact is, perfectly true.
However, we need not admit that even the present-tense 'Eclipse is
just past the post' can never be uttered with truth. Kenny's puzzle is a
variant of one which bothered some medieval writers, e.g. Buridan. It
would seem, Buridan pointed out, that a self-contradictory sentence,
I
1
See, e.g., Past, Present and Future, pp. 10-15.
In commenting, at a meeting in 1967, on the paper in 'Tense Logic and the Logic of
Earlier and Later' published in my Papers on Time and Tense (1968).
2
5
0
ANALYSIS
e.g. 'Socrates is sitting down and Socrates is not sitting down', may very
well be true since Socrates may be sitting down while we utter the first
part of it but may stand up while we utter the second part1. It is clear that
we need to make our conventions a little more explicit at this point.
We understand a sentence as being true if and only if what it says is the
case throughout the time when it is being uttered, or if and only if what it
says is the case at some instant within the period of its utterance, or if and
only if what it says is the case at the last moment of its utterance, or if
and only if what it says is the case at the.firstmoment of its utterance—or,
if its utterance has no first moment or no last one, if and only if what it
says is the case at the last moment before it begins, or at the first moment
after it ends. If the sentence contains the word 'now', and is supposed
true if things are as it says they are while 'now' is being said, exactly the
same problems arise, since even 'now' takes some time to say; and there
are the same alternative solutions. It is in general best to avoid the
first suggested conventions, since either of them, when we adopt it for a
given sentence, forces the other on us for its negation. There is in fact no
satisfactory way of referring in the present tense to a temporal boundary
(which is what an instantaneous event always is) except by %. temporal
boundary. And even with this there are ambiguities—must the sentence
cease leaving the man's mouth, or must it begin entering the hearer's ear
(or his consciousness), just as the horse ceases passing the post ? However
we decide this point, it will be by good luck as well as good management
that the speaker gets it exactly right, if he does. But it is not impossible
that he should do so.
These solutions, with all their disadvantages, are not unnatural or
ad hoc, they are the ones we do adopt when we are confronted with
Kenny's problem in practical life, e.g. in giving a running commentary on
a race. And the problem is one that arises in practical life: it is not a
pseudo-problem generated by an eccentric view about the relations
between truth and time.
But there is a similar problem, Kenny has observed, about the
validity of inferences. Suppose we run through the following modus
ponens aloud, with Socrates before us:
If Socrates is sitting, he is not standing
Socrates is sitting
Therefore Socrates is not standing
The first premiss is true at all times, and the second might be true because Socrates is sitting at the last moment of its utterance; yet the conclusion might be false because Socrates is standing at the last moment of
its utterance. This is again a type of puzzle which was not unknown to
1
Buridan, Sophismata, Ch. 7, Soph. 4.
FUGITIVE TRUTH
7
medieval logicians, who were tempted to say that an inference is valid if
and only if its premisses cannot all be true and its conclusion false, but
who resisted this temptation precisely because of exceptions of the sort
mentioned by Kenny. One rather nice example given by Buridan is this:
Om-nis syl-la-ba est plu-res lit-te-rae
(Every syllable consists of several letters)
Ergo, Nul-la syl-la-ba est u-nt-ca lit-te-ra
(Therefore no syllable consists of a single letter).1
Here the premiss, when uttered, is true (if understood as referring to
syllables in the argument), but the conclusion, when uttered, is false,
since it contains the one-lettered syllable u in unica. Again, he supposes
God to make the premiss 'All sentences are affirmative' true by annihilating all negative ones, and then some logician spoils His good work by
drawing, and enunciating, the conclusion 'No sentence is negative'.
Buridan's solution is to add to the definition of validity the proviso
'with the premiss and conclusion simul formatis'. This is a somewhat
unrealistic provision; with spoken arguments in particular, the premiss
and conclusion never are completed simultaneously. But for other
reasons Buridan considers that the definition of validity needs more
radical revision anyway. It must be changed at least to: An inference is
valid if and only if things cannot (at any time) be as its premisses say
they are without at the same time being as its conclusion says they are.
My own answer would be that logic is not really about inference but
about implication, i.e. about the truths that make inferences valid, and
that in leaving pure logic for applied, as we do when we use an implication to guide an inference, it needs to be observed that, if our inference is
not to lead us astray, the state of affairs we are arguing about must not
alter while we are arguing about it. Since most of our arguments, when
they are not about what does not alter anyway, are about what has
happened before the argument started or will happen after it ends, this
proviso seldom bothers us. But a semantics which studies the truthconditions of written or spoken sentence tokens, and the conditions
under which arguments involving these are safe or valid, is bound to
notice these complications; it was one of the merits of medieval semantics that it did not ignore them.
There is, however, a genuine difficulty, which I do not know how
to solve, about the representation of past-tense facts as the former
being-the-case of present-tense ones. Since the present is an instant, the
only past-tense facts which we can represent by 'It was the case that p*
or 'It has been the case that p\ where p is in the present tense, are facts
about what was the case at an instant or at a succession of instants. This
1
Buridan, Sophismata, Ch. 8, Soph. 1.
8
ANALYSIS
covers much more than the strictly instantaneous, i.e. what is the case at
one instant only, or at an instant but not at any neighbouring instant.
Whatever goes on for a period of time can be fitted into this pattern, since
it is going on at each instant in the period. But what takes time eludes this
representation. Consider such simple examples as 'I gave a lecture',
'I ate my breakfast', 'I went to London' or simply 'I moved'. It makes no
sense to speak of these as referring to what was the case at an instant,
and it seems to me unplausible to represent what is here stated as somehow constructed out of what was the case at a succession of instants. I
can indeed be moving (eating, lecturing) at an instant, and I can therefore
say 'It was the case that I am moving (eating, lecturing)', i.e. that I am in
the course of or in a state or condition of moving (eating, lecturing);
but these forms seem to be parasitic on the others. It is, in short, not
what is the case at an instant, but what most signally and irreducibly is
not, that presents the hardest problem for the tense-logician.
Balliol College, Oxford
AN INTRODUCTION TO OMNISCIENCE
By WALLACE I. MATSON
A
N omniscient being (hereafter 'o.b.') knows everything there is to
be known. Can we form a conception of such a being ? It seems
we can. I know some things, I am ignorant of others; I can conceive
what it would be like to have the gaps filled in.
However, what I know I have learnt, and learning is a process in
time. If there is an infinite number of things to be known, an o.b. could
not have learned them one by one, nor even (finite) group by group.
Hence if there is an o.b., either (i) there is not an infinite number of
things to be known, or (ii) knowing does not entail having learnt.
(i) In a sense the number of things to be known is infinite, for instance
answers to questions of the form, 'What is the nth. digit in the decimal
expansion of TT ?'. On the other hand, it would seem unreasonable to
deny that some person had knowledge of the 87th digit if he knew the
algorithm for calculating the expansion and could work it out to the 87th
place in a fairly short period of time, say 3 microseconds.
This example suggests that there are two ways of knowing the values
of digits in the decimal expansion of TT : one requires an infinite storage,
the other does not. Let us then be understood to be discussing hence-