¹ In physics there are essentially three types of metaphysical concepts. 1. Geometric and kinematic concepts, such as “point,” “line,” “motion,” etc. 2. Physical methodological concepts, such as “frictionless surface,” “a body left to itself,” “100% efficient engine,” etc. These concepts are arrived at by allowing certain factors in a complex symbol to become zero in extent, and by this method we get a new concept, useful methodologically but having no referent in the factual world. E.g. if the height of a pyramid becomes zero in extent, we have a triangle. This method, I should say, was impossible before the introduction of zero as a number. It is the basis, I presume, of the null class. 3. Physical concepts which transcend experience, or concepts referring to interphenomena. (see below)

² Nicod writes: “If one wishes to obtain the last word about the exact sensory meaning of any physical proposition whatsoever, he must seek it right in the realm of experience which is subject to the laws of physics. Energy, matter, object, space and time—all these physical terms and, generally, every word that physics employs outside of terms having simple designations, derive their meaning and utility from the tyrannical desire for simple and forceful embodiments of the laws of the sensible world …. One might say that the mind remains attached to these new terms because of their aesthetic appeal. Thus the objective world becomes eclipsed by its representation; and in physics where we paint this picture, we must learn once more how to see the natural world.” Foundations of Geometry and Induction., Harcourt, Brace & Company, pp. 12–13. 1930.

³ Rudolf Carnap writes: “If we believe that propositions, such as, say, ‘in twelve years the polar star will have changed its position relative to the axis of the earth by four minutes,’ have any other signification than a reassertion of my momentary impressions, we are entirely mistaken. ‘I see a sparkling spot on a black line and some numbers on a brass instrument’ is all that astronomy aims to say; and it cannot wish to say more because that would be impossible.” Journal of Philosophy, Vol. 33, p. 157. It is safe to conclude from this statement that, according to Carnap, all statements must refer to experienced objects in order to be significant. Clearly “electron,” according to him can refer only to sensed objects; i.e., to phenomena, and not to interphenomena. Carnap writes further: “… only the propositions of mathematics and empirical science have sense, … all other propositions are without sense.” Philosophy and Logical Syntax, London, 1935, p. 36. Feigle and Blumberg write: “The meanings of propositions is identical with the conditions of their verifications.” Journal of Philosophy, Vol. 28, p. 293.

⁴ B. Russell, Our Knowledge of the External World, W. W. Norton and Company, 1929. p. 121.

⁵ The logical positivists (or logical empiricists) have persistently ignored at least one phase of physics absolutely essential in making physics an intelligible and practical science; namely, they do not fill the gap between phenomena. Let us consider the consequences of not positing interphenomena as physical entities. In prediction we do not restate past or present experiences. Furthermore, prediction is impossible without a calendar in which every possible interval and instant of time is included. The same must be said of space, distances, and points. This is the case inasmuch as prediction concerns events which will transpire in a future. Similarly a complete system one can predict for any future instant and at any place beginning with any previous event. This requires the positing of interphenomena. A law, which is a means of prediction, enables us to predict a great and indefinite number of instances quite unlike the instances used in formulating the law. Consider the law of falling bodies: s = gt²/2. It is very ambiguous in that potentially it has an infinite number of possible referents inasmuch as s, g, and t have an infinite number of possible values. Is this law a restatement of present or past experiences as Carnap would contend? Or why would one want to be so foolish as to restate his present experiences? Isn't having those experiences enough, since restatement leaves room for error? Obviously the law is other than a restatement or a summation of experience. And inasmuch as it is other than experiences we have had, it posits, in metaphysical fashion, that which includes more than the experiences upon which it is based. The completion of a system, through metaphysical speculation, makes experience intelligible and the world knowable. Logical positivism, if carried to its proper conclusion, will put human beings to shame for not having such keen sensitivities as do “lower” animals. But according to the positivists’ doctrine we still have something to do; now we can continually restate our experiences, and, in tautological fashion, restate what we have restated, through the use of formal logic.

One can never account for, predict, or control events by restating experiences. In the world of applied science we cannot simply’ repeat the present or the past. The construction and reconstruction of the industrial world, say, requires speculation and the transcedence of our present.