Process and Reality — the Gifford Lectures, 1929

Certainly, this proposition, construed in the sense ‘one entity and another entity make two entities,’ seems to be properly metaphysical without any shadow of limitation upon its generality, or truth. But we must hesitate even here, when we notice that it is usually asserted, with equal confidence as to the generality of its metaphysical 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 characteristic is inherited by each occasion from its predecessors. A society of this sort is an ‘enduring object.’ Probably, a simple enduring object is simpler than anything 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 ‘corpuscular society.’

Now consider two distinct enduring objects. They will be easier to think about if their defining characteristics are different. We will call these defining characteristics 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.

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entities’ is usually construed in the sense that, given two enduring objects, any act of attention which consciously 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 characteristics, 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 occasion. 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 distinguish the two distinct enduring objects a and b, so as to have knowledge of their distinct defining characteristics 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.

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We hardly ever apply arithmetic in its pure metaphysical 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 ordinary verbal statements make no pretence of discriminating the different senses in which an arithmetical statement can be understood.

There is no difficulty in imagining a world—i.e. a cosmic 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 contemplation 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 conscious mental operations.

SECTION V

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 thep. 304 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.*