Part 10 (1/2)

FOOTNOTES:

[29] _Proc. Arist. Soc._, 1909-1910, pp. 191-218.

[30] On this subject, compare _A Theory of Time and s.p.a.ce_, by Mr.

A.A. Robb (Camb. Univ. Press), which first suggested to me the views advocated here, though I have, for present purposes, omitted what is most interesting and novel in his theory. Mr. Robb has given a sketch of his theory in a pamphlet with the same t.i.tle (Heffer and Sons, Cambridge, 1913).

[31] ”Natural Realism and Present Tendencies in Philosophy,” _Proc.

Arist. Soc._, 1908-1909, p. 165.

[32] _Die Erfahrungsgrundlagen unseres Wissens_, p. 28.

[33] Cf. _Principia Mathematica_, Vol. I, * 14, and Introduction, Chap. III. For the definition of _existence_, cf. * 14. 02.

[34] Cf. Edwin B. Holt, _The Place of Illusory Experience in a Realistic World._ ”The New Realism,” p. 303, both on this point and as regards _seeing double_.

IX

ON THE NOTION OF CAUSE

In the following paper I wish, first, to maintain that the word ”cause” is so inextricably bound up with misleading a.s.sociations as to make its complete extrusion from the philosophical vocabulary desirable; secondly, to inquire what principle, if any, is employed in science in place of the supposed ”law of causality” which philosophers imagine to be employed; thirdly, to exhibit certain confusions, especially in regard to teleology and determinism, which appear to me to be connected with erroneous notions as to causality.

All philosophers, of every school, imagine that causation is one of the fundamental axioms or postulates of science, yet, oddly enough, in advanced sciences such as gravitational astronomy, the word ”cause”

never occurs. Dr. James Ward, in his _Naturalism and Agnosticism_, makes this a ground of complaint against physics: the business of those who wish to ascertain the ultimate truth about the world, he apparently thinks, should be the discovery of causes, yet physics never even seeks them. To me it seems that philosophy ought not to a.s.sume such legislative functions, and that the reason why physics has ceased to look for causes is that, in fact, there are no such things.

The law of causality, I believe, like much that pa.s.ses muster among philosophers, is a relic of a bygone age, surviving, like the monarchy, only because it is erroneously supposed to do no harm. In order to find out what philosophers commonly understand by ”cause,” I consulted Baldwin's _Dictionary_, and was rewarded beyond my expectations, for I found the following three mutually incompatible definitions:--

”CAUSALITY. (1) The necessary connection of events in the time-series....

”CAUSE (notion of). Whatever may be included in the thought or perception of a process as taking place in consequence of another process....

”CAUSE AND EFFECT. (1) Cause and effect ... are correlative terms denoting any two distinguishable things, phases, or aspects of reality, which are so related to each other that whenever the first ceases to exist the second comes into existence immediately after, and whenever the second comes into existence the first has ceased to exist immediately before.”

Let us consider these three definitions in turn. The first, obviously, is unintelligible without a definition of ”necessary.” Under this head, Baldwin's _Dictionary_ gives the following:--

”NECESSARY. That is necessary which not only is true, but would be true under all circ.u.mstances. Something more than brute compulsion is, therefore, involved in the conception; there is a general law under which the thing takes place.”

The notion of cause is so intimately connected with that of necessity that it will be no digression to linger over the above definition, with a view to discovering, if possible, _some_ meaning of which it is capable; for, as it stands, it is very far from having any definite signification.

The first point to notice is that, if any meaning is to be given to the phrase ”would be true under all circ.u.mstances,” the subject of it must be a propositional function, not a proposition.[35] A proposition is simply true or false, and that ends the matter: there can be no question of ”circ.u.mstances.” ”Charles I's head was cut off”

is just as true in summer as in winter, on Sundays as on Mondays. Thus when it is worth saying that something ”would be true under all circ.u.mstances,” the something in question must be a propositional function, i.e. an expression containing a variable, and becoming a proposition when a value is a.s.signed to the variable; the varying ”circ.u.mstances” alluded to are then the different values of which the variable is capable. Thus if ”necessary” means ”what is true under all circ.u.mstances,” then ”if _x_ is a man, _x_ is mortal” is necessary, because it is true for any possible value of _x_. Thus we should be led to the following definition:--

”NECESSARY is a predicate of a propositional function, meaning that it is true for all possible values of its argument or arguments.”

Unfortunately, however, the definition in Baldwin's _Dictionary_ says that what is necessary is not only ”true under all circ.u.mstances” but is also ”true.” Now these two are incompatible. Only propositions can be ”true,” and only propositional functions can be ”true under all circ.u.mstances.” Hence the definition as it stands is nonsense. What is meant seems to be this: ”A proposition is necessary when it is a value of a propositional function which is true under all circ.u.mstances, i.e. for all values of its argument or arguments.” But if we adopt this definition, the same proposition will be necessary or contingent according as we choose one or other of its terms as the argument to our propositional function. For example, ”if Socrates is a man, Socrates is mortal,” is necessary if Socrates is chosen as argument, but not if _man_ or _mortal_ is chosen. Again, ”if Socrates is a man, Plato is mortal,” will be necessary if either Socrates or _man_ is chosen as argument, but not if Plato or _mortal_ is chosen. However, this difficulty can be overcome by specifying the const.i.tuent which is to be regarded as argument, and we thus arrive at the following definition:

”A proposition is _necessary_ with respect to a given const.i.tuent if it remains true when that const.i.tuent is altered in any way compatible with the proposition remaining significant.”

We may now apply this definition to the definition of causality quoted above. It is obvious that the argument must be the time at which the earlier event occurs. Thus an instance of causality will be such as: ”If the event [Math: e_{1}] occurs at the time [Math: t_{1}], it will be followed by the event [Math: e_{2}].” This proposition is intended to be necessary with respect to [Math: t_{1}], i.e. to remain true however [Math: t_{1}] may be varied. Causality, as a universal law, will then be the following: ”Given any event [Math: t_{1}], there is an event [Math: e_{2}] such that, whenever [Math: t_{1}] occurs, [Math: e_{2}] occurs later.” But before this can be considered precise, we must specify how much later [Math: e_{2}] is to occur.

Thus the principle becomes:--