Parallactic Logic
The word parallax comes from the Greek parallaxis, meaning "alternation," "change," or "looking from a different position." In astronomy, parallax is the apparent shift of an object when viewed from two different vantage points. By analogy, parallactic logic means understanding a question by viewing it from several valid perspectives before reaching a judgment.
This differs from:
Deductive logic, which moves from general principles to a necessary conclusion.
Inductive logic, which moves from observations to a probable conclusion.
Etymology
The word parallax comes from the Greek παράλλαξις (parállaxis), meaning "alteration," "change," or "alternation."
It derives from:
para- (παρά) = beside, alongside, beyond
allassein (ἀλλάσσειν) = to change (from allos, "other")
So the original sense is "a change by being viewed from another position."
In astronomy, parallax came to mean the apparent shift in the position of an object when viewed from two different locations. For example, nearby stars appear to shift slightly against the background of more distant stars as Earth moves from one side of its orbit to the other.
More broadly, the word has come to symbolize how changing one's point of view changes what one perceives—a meaning that has made it popular in philosophy, psychology, and literature as a metaphor for the value of multiple perspectives. It's a fitting word: parallax reminds us that changing our vantage point can reveal aspects of reality that were previously hidden.
Briefly, The Talmud and the I Ching
The Talmud is the central work of Rabbinic Judaism. It grew out of centuries of discussion about the Hebrew Bible (Tanakh), especially the Torah. After the destruction of the Second Temple in 70 CE, Jewish teachers preserved and expanded the oral tradition. Around 200 CE, Judah ha-Nasi compiled the Mishnah, a concise collection of Jewish law. Over the next three centuries, rabbis debated and interpreted the Mishnah, producing the Gemara. Together, the Mishnah and Gemara form the Talmud. Two versions exist: the Jerusalem Talmud (completed around the 4th–5th century CE) and the more influential Babylonian Talmud (completed around the 5th–6th century CE).
The I Ching (or Yijing, "Book of Changes") is one of China's oldest and most influential classics. Its origins lie in ancient divination practices dating back at least to the Western Zhou dynasty (roughly 1046–771 BCE), though some traditions place its roots even earlier. It consists of 64 hexagrams, each representing a fundamental pattern of change in nature and human affairs. Over the centuries, especially through the "Ten Wings" commentaries traditionally associated with Confucius (though likely written by later scholars), the I Ching evolved from a divination manual into a profound philosophical text. It became foundational to both Confucian and Daoist thought, emphasizing that wisdom lies in understanding the rhythms of change and acting in harmony with them.
In this sense, parallactic logic is similar to both rabbinic reasoning, which examines multiple valid interpretations before reaching judgment, and the I Ching, which views reality as a dynamic interplay of complementary forces rather than a collection of fixed opposites. Both traditions suggest that wisdom comes not from eliminating tension, but from inhabiting it long enough to discern the right action.
Talmudic Logic
Parallactic logic—reasoning by looking at an issue from multiple vantage points before reaching a judgment—has a strong resemblance to certain patterns of Talmudic reasoning, even though the Talmud does not use that name. Just as an object appears differently when viewed from different locations, a legal or moral question may look different when viewed through different principles.
Holding multiple valid perspectives in creative tension rather than forcing a simple either/or conclusion—finds many parallels in the Talmud. Two classic examples are:
1. "These and those are the words of the living God." In the Talmud (Babylonian Talmud), the schools of Hillel and Shammai disagree on hundreds of legal questions. A heavenly voice declares, "These and those are the words of the living God," even though the law usually follows Hillel. The point is not that only one perspective has value, but that both reveal genuine aspects of divine truth, even though a practical decision must ultimately be made.
2. The "Oven of Akhnai." In Babylonian Talmud, Rabbi Eliezer invokes miracles and even a heavenly voice to prove his legal position. The other rabbis respond that "the Torah is not in heaven." Once the Torah has been given, its meaning is determined through human interpretation and communal reasoning. Here, truth is viewed from two perspectives: divine authority and human responsibility. The tension between them is not eliminated but becomes the foundation of rabbinic law.
Hillel and Shammai: The Talmud often preserves both schools' arguments side by side. Rather than simply discarding one view, it explores the strengths of each before deciding—or sometimes leaving the matter unresolved.
"These and those are the words of the living God." In the Babylonian Talmud, tractate Eruvin 13b, a heavenly voice declares that both Hillel's and Shammai's opinions express divine truth, even though Jewish law generally follows Hillel. This recognizes that more than one perspective can illuminate the truth.
Makhloket (constructive disagreement): Throughout the Talmud, sages debate not merely to win but to refine understanding. The process itself is considered a path to wisdom.
The "on the one hand... on the other hand...on the other hand…on the other hand" style: A typical sugya (Talmudic discussion) repeatedly raises objections, answers them, considers exceptions, and tests alternative cases. The reasoning circles around a problem from several angles before arriving at a conclusion or suspending judgment.
Parallactic logic captures a style of reasoning that values changing perspective rather than merely moving from premises to conclusions. It also resembles Tevye's habit in Fiddler on the Roof of saying, "On the one hand... on the other hand...on the other hand…on the other hand…"—and, in a deeper sense, reflects the dialectical spirit that has characterized rabbinic study for centuries.
Tevye’s Logic in Fiddler on the Roof
Tevye's "On the one hand... on the other hand...on the other hand…on the other hand" reasoning is parallactic logic. He does not try to prove a theorem; he weighs competing truths—tradition, compassion, family, and faith—to arrive at the wisest practical decision.
This style of reasoning is deeply rooted in rabbinic Judaism. In the Talmud, rabbis frequently present opposing interpretations, explore the strengths of each, and only then reach—or sometimes deliberately leave open—a conclusion. The goal is often not simply to "win" an argument but to illuminate the truth by seeing it from multiple angles. In that sense, parallactic logic captures very well the spirit of Tevye's reasoning and a long tradition of rabbinic deliberation.
Deductive logic begins with general principles and arrives at a conclusion that necessarily follows.
Inductive logic begins with observations and arrives at a probable general conclusion.
Parallactic logic, as in Tevye's "On the one hand... on the other hand...on the other hand…on the other hand" reasoning, examines an issue from multiple valid perspectives. Instead of trying to prove a conclusion, it weighs competing truths, values, and circumstances to reach a balanced practical judgment.
So, Tevye's reasoning is best described as parallactic logic: looking at the same situation from different angles before deciding what is wisest.
I Ching and Parallactic Logic
Reality is understood by viewing it from complementary standpoints and by recognizing that different perspectives become appropriate as circumstances change, rather than by insisting on a single, fixed viewpoint.
The truth emerges not by erasing one viewpoint, but by seeing how different standpoints illuminate the same reality.
Rather than asking, "Which side is right?", the I Ching asks, "What phase of change am I in?" A hexagram often contains tensions—strength and yielding, advance and retreat, danger and opportunity—that are all true from different perspectives. The wisdom lies in holding these perspectives together until the proper course becomes clear.
Hexagrams 63 (Already Across / After Completion) and 64 (Not Yet Across / Before Completion) are perhaps the clearest expression of parallactic logic.
Hexagram 63 – After Completion appears to describe a perfect ending: everything is in its proper place. Yet the I Ching immediately warns that this is precisely when one must be most vigilant. Completion already contains the seeds of decline. From one perspective, the work is finished; from another, it has just entered its most precarious stage.
Hexagram 64 – Before Completion appears unfinished and uncertain. Yet it is full of possibility. What looks like disorder from one viewpoint is the very condition from which new order can emerge. Failure is not the opposite of success; it is often its necessary precursor.
Read together, these hexagrams reject a simple either/or logic. Completion and incompletion are not opposites but phases of the same process. Parallactic logic would say that genuine wisdom comes from holding both perspectives at once: every ending is also a beginning, and every beginning already contains the outline of its eventual completion. That is one of the deepest themes of the I Ching.
Two additional examples from the I Ching that illustrate parallactic logic are:
Hexagram 11 – Peace (Tai) and Hexagram 12 – Standstill (Pi). These are almost mirror images of one another. The same forces—Heaven and Earth—are present, but their relationship has changed. From one perspective, the situation is flourishing; from another, communication has broken down. The lesson is that the meaning of events depends on the configuration of relationships, not on isolated facts.
Hexagram 1 – The Creative (Qian) and Hexagram 2 – The Receptive (Kun). Neither is presented as superior to the other. The Creative represents initiative, strength, and leadership; the Receptive represents responsiveness, nurture, and support. Wisdom comes from discerning which mode fits the moment. The I Ching does not ask, "Which is right?" but rather, "Which perspective is appropriate now?"
In Conclusion:
Parallactic logic begins from the recognition that truth may appear differently from different positions without thereby becoming arbitrary. Like Tevye’s “on the one hand—and on the other hand,” it resists the demand that every tension be prematurely resolved. The perspectives do not cancel one another; each discloses something the others cannot see, while the truth emerges through their continuing relationship.
The Talmud embodies this logic through argument. It preserves majority and minority opinions, questions and counterquestions, sometimes even the reasoning of a defeated position. Its pages suggest that disagreement need not be a failure to reach truth: it may be the very discipline by which truth is approached. The unresolved argument remains fruitful because no single human standpoint can exhaust the meaning of Torah.
The I Ching embodies a related logic through transformation. Its yin and yang are not fixed opposites but interdependent tendencies continually becoming one another. A hexagram describes a situation from one angle; its changing lines reveal another situation already forming within it. Thus wisdom lies less in declaring which side is absolutely correct than in perceiving the movement, timing, and hidden reversal within the present moment.
The Talmud and the I Ching therefore arrive by different roads at a common insight: contradiction may be something to inhabit intelligently rather than eliminate. The Talmud places truth in the sacred conversation among contending voices; the I Ching places it in the ceaseless transformation of circumstances. Parallactic logic draws these insights together—not by merging the traditions, but by showing how both teach intellectual humility: truth is approached through multiple perspectives, and wisdom begins when we can hold them together long enough to see more than any one of them reveals alone.
