Some philosophers of physics and physicists suggest that Einstein’s theory of relativity presents a “block universe” picture of reality, according to which the experience of time as passing duration is illusory. According to such a picture, say some physicists, the concept of causation becomes superfluous. The notion of a kind of Parmenidean block universe was perhaps most famously proposed by Hermann Minkowski. He wrote
“The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.
First of all I should like to show how it might be possible, setting out from the accepted mechanics of the present day, along a purely mathematical line of thought, to arrive at changed ideas of space and time…Three-dimensional geometry becomes a chapter in four-dimensional physics.”
His fundamental, mathematical axiom for this was: c^22dt^2 – dx^2 – dy^2 – dz^2 > 0,
“or what comes to the same thing, that any velocity v always proves less than c.
Accordingly c would stand as the upper limit for all substantial velocities, and that is precisely what would reveal the deeper significance of the magnitude c. In this second form the first impression made by the axiom is not altogether pleasing. But we must bear in mind that a modified form of mechanics, in which the square root of this quadratic differential expression appears, will now make its way, so that cases with a velocity greater than that of light will henceforward play only some such part as that of figures with imaginary co-ordinates in geometry.”
“The basic idea of using the special theory of relativity to prove determinism is that time can be treated mathematically as a fourth dimension. This gives us excellent results for experiments on moving objects and explains the strange Lorentz contraction of objects in space and dilations of clock speeds for observers in fast moving frames of reference (coordinate systems).”
Leibniz used the word “monad” instead of the more traditional term “substance.” The word literally means “that which is one.” It has no parts and is indivisible. They are the most fundamental substances. He believed this could replace the concept of the “atom,” since atomism was becoming popular at this point. While atoms are extended, monads, for Leibniz, are non-extended. For Leibniz, a substance or a monad is the reality which a complete concept represents.
This complete concepts possesses all the predicates of the subject of which it is a concept, and these predicates are related to one another by sufficient reasons, which itself constitutes a vast, monolithic network of mutual explanations. Each monad possesses all the properties it will exhibit in the future, potentially or virtually, as well as possessing traces of everything it has exhibited in the past. These network of explanations are indivisible, since each either partially explains, or is explained by the others. To divide these networks at all, therefore, would mean to disrupt a chain of sufficient reasons for each proposition, and leave the network in a state of absurdity.
“Just as in the analysis of space and time Leibniz argues that all relational predicates are actually interior predicates of some complete concept, so the monad’s properties include all of its relations to every other monad in the universe. A monad, then, is self-sufficient. Having all these properties within itself, it doesn’t need to be actually related to or influenced by another other monad.”
Indeed, keep in mind that for Leibniz, space and time are illusions. They are, however, well-founded illusions. Leibniz says the same thing about causation: it is an illusion, but a well-founded illusions. Monads do not actually interact with one another, but internally contain, as interior predicates, the relation of that monad with every other monad in the universe. One thing “causes” another when the virtual relation between them is expressed “more clearly and simply…in A than B.” Metaphysically, however, it does not matter how this relationship is understood, because the relation, metaphysically, is not even real. Leibniz therefore rejects the existence of causation and replaces it with a theory of pre-established harmony. This is also known as his “hypothesis of concomitance.”
Leibniz’s view of causation can be illustrated by considering the “relation” of two clocks. Suppose that they both tell identical time. One might suppose that one is effecting a causal influence on the other, causing it to behave in an identical manner. However, one who knows how clocks work would know that there is no causal influence at all. They simply both tell them, and work in synchronicity. They are independent yet in sync with one another. Likewise, Leibniz believed that each monad is set in sync with every other monad by God. Monads have no direct contact with each other. In fact, each one expresses the entire universe by containing, as its interior, and in the form of predicates, the entire universe, insofar as it expresses its relation to everything else in the universe. The notion of causation is simply superfluous.
Michael Lockwood, in hs 2005 book, The Labyrinth of Time, argues that the block universe of special relativity eliminates the need for the concepts of both free will and causation. Since the universe is already “there,” causation becomes completely superfluous and unnecessary.
According to C.W. Rietdijk, the problems which Leibniz’s universe seemed to have posed for free will become a reality. He famously denied that there was any room in a Minkowskian universe for free will:
“A proof is given that there does not exist an event, that is not already in the past for some possible distant observer at the (our) moment that the latter is “now” for us. Such event is as “legally” past for that distant observer as is the moment five minutes ago on the sun for us (irrespective of the circumstance that the light of the sun cannot reach us in a period of five minutes). Only an extreme positivism: “that which cannot yet be observed does not yet exist”, can possibly withstand the conclusion concerned. Therefore, there is determinism, also in micro-physics.”
The philosopher Hilary Putnam came to a similar conclusion:
“(1) All (and only) things that exist now are real.
Future things (which do not already exist) are not real (on this view); although, of course they will be real when the appropriate time has come to be the present time. Similarly, past things (which have ceased to exist) are not real, although they were real in the past.
If we assume classical physics and take the relation R to be the relation of simultaneity, then, on the view (1), it is true that all and only the things that stand in the relation R to me-now are real.
We now discover something really remarkable. Namely, on every natural choice of the relation R, it turns out that future things (or events) are already real!”
Roger Penrose, in his 1989 book The Emperor’s New Mind, comes to a similar conclusion:
“Two people pass each other on the street; and according to one of the two people, an Andromedean space fleet has already set off on its journey, while to the other, the decision as to whether or not the journey will actually take place has not yet been made. How can there still be some uncertainty as to the outcome of that decision? If to either person the decision has already been made, then surely there cannot be any uncertainty. The launching of the space fleet is an inevitability.”
The observers cannot see what is happening in Andromeda. It is light-years away. The paradox is that they have different ideas of what is happening “now” in Andromeda.”
Leibniz’s notion of a world utterly devoid of causation and duration may seem quite strange to us. Indeed, Leibniz postulated different “spheres” of reality. The most fundamental level of reality is the metaphysical reality, which consists of monads, their perceptions and their desires. The monads “unfold” spontaneously according to the kind of substance it is. On the descriptive or phenomenal level, the finite human mind describes its empirical, illusory reality. The object of science is totally illusory, and nothing happens in it that is not based upon what is really happening from the metaphysical level. This is what Leibniz means when he describes the illusions of science as “well-founded.” The mechanistic laws of physics are correct as a description but at the metaphysical level, there is no mechanistic causation, or any sort of causation, for that matter.
“A serious error would arise only if one took the “objects” of science (matter, motion, space, time, etc.) as if they were real in themselves. Consider the following analogy: in monitoring a nation’s economy, it is sometimes convenient to speak of a retail price index, which is a way of keeping track of the average change in the prices of millions of items. But there is nothing for sale anywhere which costs just that amount. As a measure it works well, provided one does not take it literally. Science, in order to be possible for finite minds, involves that kind of simplification or “abbreviation””
In addition, to this, Leibniz contributed to the psychological concept of the “unconscious.” This is because the monad, keep in mind, mirrors the entire universe. This means that the individual soul has an infinite number of highly complex perceptions. One does not “apperceive” these things, however. One merely perceives them; but one is unconscious of perceiving these things because one does not have a complete concept of oneself and is not cognizant of the relation one bears to all other things, even though one bears a distinct relation to every other thing in the entire universe. Indeed, a complete concept of oneself gives an account of the entire universe, insofar as it gives an account of one’s relation to everything in the entire universe.
“Further, where one is conscious of some perception, it will be of a blurred composite perception. Leibniz’s analogy is of the roar of the waves of the beach: the seemingly singular sound of which one is conscious is in fact made up of a vast number of individual sounds of which one is not conscious–droplets of water smacking into one another.”
These little perceptions contribute to our understanding of the infinite minor habits and customs which each individual possesses as a component of their personality.
“Such habits accumulate continuously and gradually, rather than all at once like decisions, and thus completely bypass the conscious will. Further, these little perceptions account for one’s pre-conscious connection with the world. For Leibniz, one’s relation with the world is not one just of knowledge, or of apperceived sensation. An individual’s relation with the world is richer than either of these, a kind of background feeling of being-a-part-of. (Thus, a thorough-going skepticism, however plausible at a logical level, is ultimately absurd.)”
Leibniz’s concept of the little perception is more than a psychological insight, however. It plays a key role in his physics and his metaphysics. It is an important element of his principle of continuity, according to which nature “never makes leaps.” This follows from the principle of sufficient reason and the notion of the perfection of the universe. Little perceptions, Leibniz believed, allowed him to account for how continuity happens in everyday circumstances.
“Finally, Leibniz’s idea of little perceptions gives a phenomenal (rather than metaphysical) account for the impossibility of real indiscernibles: there will always be differences in the petite perceptions of otherwise very similar monads. The differences may not be observable at the moment, but will “unfold in the fullness of time” into a discernible difference”
For Leibniz, everything perceived as a unified being is a single monad. Other things are composed of an infinite number of monads, and each thing only looks like a single monads because all of the monads are acting simultaneously. The soul, however, is a single monad that controls a composite body. Individual organisms, therefore, are substantial forms. The substantial form (a term and concept borrowed from Aristotle) constitutes the principle of unity of living composites (as opposed to inanimate ones, which are constituted by an infinite number of monads acting together). The monad is the substantial form of the individual’s aggregate body.
Leibniz believed that the composite body is constituted by an infinite number of monads, just as inanimate monads. The universe is “the richest in controlled complexity,” for Leibniz. Leibniz believed that it would be a “waste” of possible perfection to only allow living beings to have bodies at particular, phenomenally familiar levels. This is reminiscent of the notion, mentioned in the last article, of how the human person extends throughout the temporal length of eternity as a four-dimensional “worm.” In Leibniz’s own words, “Every portion of matter can be thought of as a garden full of plants, or as a pond full of fish. But every branch of the plant, every part of the animal, and every drop of its vital fluids, is another such garden, or another such pool. […] Thus there is no uncultivated ground in the universe; nothing barren, nothing dead.”
The individual monads of which one is constituted are constantly changing, although not simultaneously. The substantial form consists, on the one hand, of a “unified explanation of bodily form and function” in addition to continual flux, diversity and connection with other entities. Leibniz distinguished four kinds of monads: animals, plants, matter and humans, and argued that all of these have “percpetions” in the sense that they possess internal properties and exhibit external relations. Only humans, animals and palnts, however, have appetition, since they possess substantial forms. Animals and humans both have memory, however, and humans alone are seen as having reason.
Leibniz occupied a unique presence among the early modern philosophers, as one of the historically important “rationalists.” On the one hand, the empiricists, such as Locke, believed that the human mind was a “tabula rasa,” or blank slate, upon which impressions were pressed. Rationalists, such as Descartes and Leibniz, emphasized the importance of pre-empirical innate ideas possessed by the mind. Leibniz believed in innate ideas on the metaphysical level. Indeed, since the monad lacks a “window” through which something can pass, it is therefore the case that absolutely all ideas are innate. For the monad to possess an idea is just one of many properties of that monad. The property of the innate idea, like any other property of the monad, can be entirly accounted for on a purely interior level, since monads never interact with other monads. It is in terms of the complete concept of the monad that innate ideas, as well as other properties of the monad, can be understood. On the phenomenal level, however, many ideas are “represented” as “arriving” by means of the senses. Keep in mind, however, that the phenomenal world is illusory, as the spatio-temporal world in which it has its being is itself illusory; space and time, for Leibniz, are not real.
This is quite interesting and it makes Leibniz difficult to pigeonhole. On the purely phenomenal level, Leibniz seems to have been okay with a thoroughgoing empiricism. This is true, at least, on a descriptive level. Indeed, it is useless, so far as the scientist is concerned, to know that, on a metaphysical level, all ideas are innate. Indeed, the scientist who is unconcerned with the metaphysical level does not really need to be concerned with “truth” at all, provided he is concerned only with methodological and pragmatic considerations. The metaphysical level, however, for Leibniz, represents the basis of all reality.
Leibniz distinguished between different kinds of innate ideas. Some exhibit universal necessity, such as ideas in logic, metaphysics, morality, geometry and theology. Such universal necessity, however, cannot be derived from experience, and must be known through reason. Next, the innate idea is not necessarily possessed consciously. Keep in mind that little perceptions operate on the unconscious of the individual, yet they are not conscious; they are perceived without being “apperceived.” Finally, Leibniz believed that innate ideas exhibiting universal necessity, such as in physics, were useful:
“Consider the possibility of foreseeing an event that is not similar to (and thus merely an associated repetition of) a past event. By using rational principles of physics, for example, one can analyze a situation and predict the outcome of all the masses and forces, even without ever having experienced a similar situation or outcome. This, Leibniz says, is the privilege of humans over animals (“brutes”), who only have the “shadow” of reason, because they can only move from one idea to another by association of similars.”
“…at the phenomenal level, Leibniz can distinguish between innate and empirical ideas. An empirical idea is a property of a monad which itself expresses a relation to some other substance or which arises from another internal property that is the expression of an external substance. Although the difference between empirical and innate is in fact an illusion, it does make a difference, for example, to the methodology of the sciences. This is similar to the distinction made above between the idea of truth (as the containedness of the predicate in the subject), and the pragmatic/methodological issue of how one comes to know that truth. The latter is not irrelevant, except to the foundation and definition of truth. (Leibniz’s most extensive discussion of innate ideas, not surprisingly, is in the New Essays on Human Understanding.)”
Finally, the monad possesses an active power. He sees predicates as “folded up” within the monad. In his Monadology, Leibniz uses the Aristotelian and medieval notion of “entelechy.” This involves the becoming-actual or achievement of a monad’s potential. It is derived from the idea of a “perfection.” This involves an actual striving to finish or perfect its potential. In order for a monad to actualize its complete concept, it must unfold itself perfectly. Keep in mind that its entirety is contained implicitly or virtually in its beginning. He refers to this property o the monad as “active power,” “entelechy,” “conatus,” “nisus” (effort, striving, urge, or desire), “primary force,” “internal principle of change” and “light.”
This externalization of its internal properties is found, not just in the human soul, but in all forms of monads. It is an inner activity, meaning that it is both the source of action and that it is also capable of being affected or resisted. The unfolding of its complete concept is exhibited empirically in the illusion of cause and effect. Keep in mind that this power to act is not merely a monad’s capacity to do stuff. It is the determination of specific kinds of actions at specific times and in specific ways, and it is merely its expression of its virtuality or potentiality.