world beyond the subject. The past tense of the word ‘thas’ shows that this point of ambiguity is irrelevant, so that the proposition can be framed so as to ignore it. But it need not be so framed: one of Caesar’s old soldiers may in later years have sat on the bank of the river and meditated on the assassination of Caesar, and on Caesar’s passage over the little river tranquilly flowing before his gaze. This would have been a different proposition from the more direct one which I am now considering. Noth- ing could better illustrate the hopeless ambiguity of lan- guage; since both propositions fit the same verbal phrase- ology. There is yet a third proposition: a modern trav- eller sitting on the bank of the Rubicon, and meditating on his direct perceptions of actual occasions can locate, relatively to himself by spatio-temporal specifications, an event which inferentially and conjecturally he believes to include a portion of the past history of the Rubicon as directly known to him. He also, by an analogous process of inference and conjecture, and of spatio-tem- poral specification, locates relatively to himself another event. which he believes to contain the life of Caesar of whom he has no direct knowledge. The proposition med- itated on by this traveller sitting on the bank of the modern river is evidently a different proposition to that in the mind of Caesar’s old soldier. Then there is the proposition which might have been in the mind of one of the crowd who listened to Antony’s speech, a man who had seen Caesar and not the Rubicon.
It is obvious that in this way an indefinite number of highly special propositions can be produced, differing from each other by fine gradations. Everything depends upon the differences in direct perceptive knowledge which these various propositions presuppose for their subjects. But there are propositions of more general type, for which ‘Caesar’ and ‘Rubicon’ have more generalized, vaguer meanings. In these vaguer meanings, ‘Caesar’ and ‘Rubicon’ indicate the entities, if any, located by any one member of a type of routes, starting from a
Dhe Pr Opos Felons 299
certain type of inference and conjecture. Also there are some such propositions in which the fact of there being such entities, to be thus located, is part of the content whereby the judgment is true or false; and there are other propositions in which even this requisite is evaded, so far as truth or falsehood is concerned. It is by reason of these various types of more abstract propositions that we can conceive the hypothetical existence of the more special propositions which for some of us, as judging sub- jects, would be meaningless.
This discussion should show the futility of taking any
verbal statement, such as ‘Caesar has crossed the Rubi-
con,’ and arguing about the meaning. Also any propo-
sition, which satisfies the verbal form so as to be one
of its possibilities of meaning, defines its own locus of
subjects; and only for such subjects is there the possi-
bility of a judgment whose content is that proposition.
A proposition is the potentiality of the objectification of certain presupposed actual entities via certain qualities and relations, the objectification being for some unspeci- fied subject for which the presupposition has meaning in direct experience. The judgment is the conscious affir- mation by a particular subject—for which the presup- position holds—that this potentiality is, or is not, real- ized for it. It must be noticed that ‘realized’ does not mean ‘realized in direct conscious experience, but does mean ‘realized as being contributory to the datum out of which that judging subject originates.’ Since direct, conscious experience is usually absent, a judgment can be erroneous.
Thus a proposition is an example of what Locke calls
an ‘idea determined to particular existences.’ It is the
potentiality of such an idea; the realized idea, admitted
to decision in a given subject, is the judgment, which
may be a true or false idea about the particular things.
The discussion of this question must be resumed (ef.
Part III) when conceptual activity is examined. But it
is evident that a proposition is a complex entity which
300 Process and Reality
stands between the eternal objects and the actual occa-
sions. Compared to eternal objects a proposition shares
in the concrete particularity of actual occasions; and
compared to actual occasions a proposition shares in the
abstract generality of eternal objects. Finally, it must
be remembered that propositions enter into experience
in other ways than through judgment feelings.
A metaphysical proposition—in the proper, general sense of the terms ‘metaphysical’—signifies a proposition which (i) has meaning for any actual occasion, as a subject entertaining it, and (11) is ‘general,’ in the sense that its predicate potentially relates any and every set of actual occasions, providing the suitable number of logical subjects for the predicative pattern, and (111) has a ‘uniform’ truth-value, in the sense that, by reason of its form and scope, its truth-value is identical with the truth-value of each of the singular propositions to be obtained by restricting the application of the predicate to any one set of logical subjects. It is obvious that, if a metaphysical proposition be true, the third condition is unnecessary. For a general proposition can only be true if this condition be fulfilled. But if the general proposition be false, then it is only metaphysical when in addition each of the derivate singular propositions is false. The general proposition would be false, if any one of the derivate singular propositions were false. But the third condition is expressed in the proposition with- out any dependence upon the determination of the prop- osition’s truth or falsehood.
There can be no cosmic epoch for which the singular
propositions derived from a metaphysical proposition
differ in truth value from those of any other cosmic
epoch.
We certainly think that we entertain metaphysical
propositions: but, having regard to the mistakes of the
past respecting the principles of geometry, it is wise to
Ctheipropostelons 301
reserve some scepticism on this point. The propositions
which seem to be most obviously metaphysical are the
arithmetical theorems. I will therefore illustrate the
justification both for the belief, and for the residual
scepticism, by an examination of one of the simplest
of such theorems: One and one make two.’
Certainly, this proposition, construed in the sense ‘one entity and another entity make two entities,’ seems to be properly metaphysical without any shadow of limi- tation upon its generality, or truth. But we must hesi- tate even here, when we notice that it is usually asserted, with equal confidence as to the generality of its meta- physical truth, in a sense which is certainly limited, and sometimes untrue. In our reference to the actual world, we rarely consider an individual actual entity. The objects of our thoughts are almost always societies, or looser groups of actual entities. Now, for the sake of simplicity, consider a society of the ‘personal’ type. Such a society will be a linear succession of actual occasions forming a historical route in which some defining char- acteristic is inherited by each occasion from its prede- cessors. A society of this sort is an ‘enduring object.’ Probably, a simple enduring object is simpler than any- thing which we ordinarily perceive or think about. It is the simplest type of society; and for any duration of its existence it requires that its environment be largely composed of analogous, simple, enduring objects. What we normally consider is the wider society in which many strands of enduring objects are to be found, a ‘corpuscu- lar society.’
Now consider two distinct enduring objects. They will be easier to think about if their defining character- istics are different. We will call these defining character- istics a and b, and also will use these letters, a and 6, as the names of the two enduring objects. Now the proposition ‘one entity and another entity make two
? For the proof of this proposition, cf. Principia Mathematica, Vol. II, *110.643.
302 Process and Reality
entities’ is usually construed in the sense that, given two enduring objects, any act of attention which con- sciously comprehends an actual occasion from each of the two historic routes will necessarily discover two actual occasions, one from each of the two distinct routes. For example, suppose that a cup and a saucer are two such enduring objects, which of course they are not; we always assume that, so long as they are both in existence and are sufficiently close to be seen in one glance, any act of attention, whereby we perceive the cup and perceive the saucer, will thereby involve the perception of two actual entities, one the cup in one occasion of its existence and the other the saucer in one occasion of its existence. There can be no reasonable doubt as to the truth of this assumption in this particular example. But in making it, we are very far from the metaphysical proposition from which we started. We are in fact stating a truth concerning the wide societies of entities amid which our lives are placed. It is a truth concerning this cosmos, but not a metaphysical truth.
Let us return to the two truly simple enduring objects, a and b. Also let us assume that their defining charac- teristics, a and b, are not contraries, so that both of them can qualify the same actual occasion. Then there is no general metaphysical reason why the distinct routes of a and b should not intersect in at least one actual occa- sion. Indeed, having regard to the extreme generality of the notion of a simple enduring object, it is practically certain that—with the proper choice for the defining characteristics, a and b—intersecting historic routes for a and b must have frequently come into existence. In such a contingency a being who could consciously dis- tinguish the two distinct enduring objects a and b, so as to have knowledge of their distinct defining character- istics and their distinct historic routes, might find a and b exemplified in one actual entity. It is as though the cup and the saucer were at one instant identical; and then, later on, resumed their distinct existence.
The Propositions 303
We hardly ever apply arithmetic in its pure metaphys-
ical sense, without the addition of presumptions which
depend for their truth on the character of the societies
dominating the cosmic epoch in which we live. It is
hardly necessary to draw attention to the fact, that ordi-
nary verbal statements make no pretence of discrimi-
nating the different senses in which an arithmetical
statement can be understood.
There is no difficulty in imagining a world—i.e. a cos- mic epoch—in which arithmetic would be an interesting fanciful topic for dreamers, but useless for practical people engrossed in the business of life. In fact, we seem to have been only barely rescued from such a state of things. For amid the actual occasions located in the wilds of so-called ‘empty space,’ and well removed from the enduring objects which go to form the enduring material bodies, it is quite probable that the contempla- tion of arithmetic would not direct attention to any very important relations of things. It is, of course, a mere speculation that any actual entity, occurring in such an environment of faintly co-ordinated achievement, achieves the intricacy of constitution required for con- scious mental operations.
We ask the metaphysical question, What is there in the nature of things, whereby an inductive inference, or a judgment of general truth, can be significantly termed ‘correct’ or ‘incorrect’? For example, we believe now— July 1, 1927—that the railway time-tables for the United States, valid for the previous months of May and June, represent the facts as to the past running of the trains, within certain marginal limits of unpunctuality, and allowing for a few individual breakdowns. Also we believe that the current time-tables for July will be exemplified, subject to the same qualifications. On the evidence before us our beliefs are justified, provided that we introduce into our judgments some estimate of the
304 Process and Reality
high probability which is all that we mean to affirm. If
we are considering astronomical events, our affirmations
will include an estimate of a higher probability. Though
even here some margin of uncertainty may exist. The
computers of some famous observatory may have made
an unprecedented error; or some unknown physical
law may have important relevance to the condition of
the star mainly concerned, leading to its unexpected
explosion.*