Microworlds

The first will be the ever real disjuncture: “John is the father of Peter or John is not the father of Peter.” Any logician would acknowledge that this disjuncture satisfies at all times the requirement for truth, since tertium non datur, it is impossible to be forty percent father and sixty percent nonfather.

Next, let’s work with a complex sentence: “If Peter has sexual relations with his mother, then Peter commits incest.” The implication is a tautological one, since, according to the semantic rules of language, to have sexual relations with one’s mother is tantamount to committing incest. (Our conjunction is not a complete tautology, since incest constitutes a concept broader than sexual relations with a mother, referring, rather, to relations with any person of such close kinship. We could bring the sentence to a perfect tautology, but this would necessitate complexities that would in no way alter the essence of the matter and merely make the argumentation more difficult.)

To simplify matters we shall investigate first the impact of changes on the veracity or falsity of the statement “John is the father of Peter.” We should point out that what is involved here is a truly causative biological relation to the birth of a child, and not the ambiguous use of the designation “father” (since it is indeed possible to be a biological father and not be a baptismal father, or, conversely, to be a godfather, but not a parent).

Suppose John is a person who died three hundred years ago, but whose reproductive cells were preserved by refrigeration. A woman fertilized by them will become Peter’s mother. Will John then be Peter’s father? Undoubtedly.

But then suppose the following: John died and did not leave reproductive cells, but a woman asked a genetic technician to make up in the laboratory a spermatozoon of John from a single preserved cell of John’s epithelium (all the cells of the body having the same genetic composition). Will John, once fertilization is complete, now also be Peter’s father?

Now suppose the following case: John not only died, but also did not leave a single bodily cell. Instead, John left a will in which he expressed the desire that a genetic technician perform the steps necessary to enable a woman to become the mother of a child of John — i.e., that such a woman give birth to a child and that the child be markedly similar to John. In addition, the genetic technician is not permitted to use any spermatozoa. Rather, he is supposed to cause a parthenogenetic development of the female ovum. Along with this he is supposed to control the genic substance and direct it by embryogenetic transformations in such a way that the Peter born is “the spit and image of John” (there are photographs of John available, a recording of his voice, etc.). The geneticist “sculptures” in the chromosomal substance of the woman all the features John craved for in a child. And thus, to the question “Is John the father or not the father of Peter?” it is now impossible to give an unequivocal answer of “yes” or “no.” In some senses John is indeed the father, but in others he is not. An appeal to empiricism alone will not in itself furnish a clear answer. The definition will be essentially determined by the cultural standards of the society in which John, Peter’s mother, Peter, as well as the genetic technician, all live.

Let’s assume that these standards are fixed, and that the child realized in strict accordance with John’s testamental instructions is generally acknowledged to be his child. If, however, the genetic technician, either on his own or at the instigation of others, made up forty-five percent of the genotypical features of the child not in accordance with the stipulations of the will, but in accordance with an entirely different prescription, it would then be impossible to maintain that John, in agreement with the standards of a given culture, either is or is not the child’s father. The situation is the same as when some experts say about a picture reputed to be a work of Rembrandt: “This is a canvas by Rembrandt,” whereas others say: “This is not a canvas by Rembrandt.” Since it is quite possible that Rembrandt began the picture, but that some anonymous person finished the work, then forty- seven percent of the work could be said to originate from Rembrandt, and fifty-three percent from someone else. In such a situation of “partial authorship,” tertium datur. In other words, there are situations in which it is possible to be a father only in part. (It is also possible to achieve such situations in other ways, e.g., by removing a certain number of genes from a spermatozoon of John and substituting another person’s genes for them.)

The possibilities of the transformations mentioned above, which entail a change in the logical value of the disjunction — “John is the father of Peter or John is not the father of Peter” — lie, one may judge, in the bosom of a not too distant future. Thus a work describing such a matter would be fantastic today, but thirty or fifty years hence it might indeed be realistic. However, the work by no means needs to relate the story of a definite, concrete John, Peter, and mother of Peter. It could describe fictitious persons in a manner typical of any form of literary composition. The relational invariables between father, mother, and child would not have at that time the fictitious nature they have in the present. The invariables that concern paternity are today different from those of a time when genetic engineering would be realized. In this sense a composition written today and depicting a given situation without a “disconnected middle” in the predication of paternity may be considered a futurological prognosis or a hypothesis that may prove to be true.

For a real tautology to become a falsehood, the device of travel in time is necessary. Suppose Peter, having grown up, learns that his father was a very vile person — that he seduced Peter’s mother and abandoned her only to disappear without a trace. Burning with the desire to bring his father to account for so despicable an act and unable to locate him in the present, Peter boards a time vehicle, sets out for the past and seeks out the father in the vicinity of the place where his mother was supposed to have resided at that time. The search, although very thorough, turns out to be in vain. However, in the course of establishing various contacts related to his expedition, Peter meets a young girl who attracts him. The two fall in love and a baby is conceived. Peter cannot remain permanently in the past, though; he is obliged to return to his old mother, for whom he is the sole support. Having been convinced by the girl that she has not become pregnant, Peter returns to the present. He has not succeeded in finding traces of his father. One. day he finds in one of his mother’s drawers a thirty-year-old photograph and to his horror recognizes in it the girl whom he loved. Not wishing to impede him, she committed a white lie, and hid her pregnancy. Peter thus comes to understand that he did not find his father for the simple reason that he himself is the father. So, Peter journeyed into the past to search for a missing father, assuming the name John to facilitate his search by remaining incognito. The upshot of this journey is his own birth. Thus, we have before us a circular causal structure. Peter is his own father, but, as against a superficial judgment, he did not commit incest at all, since, when he had sexual intercourse with her, his mother was not (and could not be) his mother. (From a purely genetic point of view, if we forget that — as is today believed — the causal circle is impossible, Peter is genotypically identical with his mother. In other words, Peter’s mother for all practical purposes gave birth to him parthenogenetically, since, of course, no man inseminated her who was alien to her.)

This structure constitutes the so-called time loop, a causal structure characteristic of an enormous number of science-fiction compositions. The composition I described is a “minimal” loop, yet there is one still “smaller,” created by Robert Heinlein in the story “All You Zombies” (1959).[9] Its plot is as follows: a certain young girl becomes pregnant by a man who then promptly disappears. She bears a child, or, more correctly, gives birth to it by Caesarean section. During the operation, the doctors ascertain that she is a hermaphrodite and it is essential (for reasons not explained by the author) to change her sex. She leaves the clinic as a young man who, because he was until quite recently a woman, has given birth to a child. She seeks her seducer for a long time, until it comes to light that she herself is he. We have the following circular situation: one and the same individual was in time T1 both a girl and her partner, since the girl, transformed into a man by surgical intervention, was transferred by the narrator to time T1 from a future time, T2. The narrator, a time traveler, “removed” the young man from time T2 and transferred him to time T1 so that the latter seduced “himself.”

Nine months after time T1 the child was born. The narrator stole this child and took it back in time twenty years, to moment T0, so he could leave it under the trees of a foundling home. So the circle is completely closed: the same individual comprises “father,” “mother,” and “child.” In other words, a person impregnated himself and gave birth to himself. The baby born as a result of this is left behind in time, bringing about in twenty years the growth of a girl who has in time T1 sex with a young man from time T2. The young man is she herself, transformed into a man by a surgical operation. The fact that a sexual hermaphrodite should not be able to bear a child is a relatively small hindrance, since the puzzling situation of a person’s giving birth to himself is considerably “more impossible.” What we are dealing with here is an act of creatio ex nihilo. All structures of the time-loop variety are internally contradictory in a causal sense. The contradictoriness is not, however, always as apparent as in Heinlein’s story.

Frederic Brown writes about a man who travels into the past in order to punish his grandfather for tormenting