# The Scales Argument ## Intro Justice is drawn as a woman holding scales, and the picture is exact. Justice is about balance: the punishment should fit the crime, the wage should fit the work, the share should fit the claim. Those are mathematical ideas. "Fit" means proportion, and proportion is the stuff of geometry. This is not only a modern metaphor. Aristotle said justice is a kind of proportion. The old law "eye for eye, tooth for tooth" was not a license for revenge; it was a limit, one eye and no more. And research finds that toddlers not yet two years old expect a fair split of treats, and expect someone who did the work to be rewarded for it. So justice is a truth with mathematical content, one that holds necessarily, binds us morally, and is grasped by small children before they can count. The Scales Argument says that is just what you would expect if one Mind, the Word through whom all things were made, is the source of both number and goodness. "A just balance and scales are Jehovah's" ([Proverbs 16:11](/codex/proverbs-16-11/), ASV). ## In full The Scales Argument is a likelihood argument from the mathematical structure of justice. Its explanandum is that a central moral truth, that rewards, penalties and shares ought to be proportioned to their grounds, has necessary mathematical content (Aristotle's arithmetic proportion in corrective justice and geometric proportion in distributive justice), carries objective normative force, and is grasped early in development and across cultures. A deductive spine (P1 to P5) argues that this fusion of necessity, normativity and early knowability is far more expected on theism, where one Logos grounds both mathematical and moral truth and fashions minds to know both, than on naturalism, which treats mathematical truths (if real) as causally inert abstracta, moral truths as either unreal or brute, and the fairness sense as a cooperation heuristic. The strongest rival, Ken Binmore's evolutionary account of fairness norms as equilibrium-selecting conventions, is answered: it explains which conventions societies settle on and why we feel fairness, but not why proportion is correct, and it predicts parochial fairness where the norm itself, and the Hebrew law in particular, is universal in scope. The conclusion is confirmatory, not demonstrative. ## Format note This is a **braided case**, the house format for new [Ris3n Arguments](/codex/ris3n-arguments/): a valid spine, each premise with independent strands of evidence, a knot, a likelihood ledger and a defeater gate. It braids four fields. **Mathematics** contributes the formal structure of proportion that justice uses. **Justice** contributes the legal principle that penalties must fit wrongs and shares must fit claims. **Psychology** contributes the evidence that infants and children expect fair distribution, and the evidence of in-group bias. **History** contributes the long career of proportional law, from Hammurabi and Moses to Aristotle. ## The spine | # | Premise | |---|---| | **P1** | **Mathematical form.** Justice has mathematical structure: corrective justice is an arithmetic equality between loss and remedy, and distributive justice is a geometric proportion between shares and their grounds. | | **P2** | **Necessity and force.** That structure is necessary and normative: it could not be otherwise, and it binds. A penalty a hundred times the wrong is unjust in every possible society. | | **P3** | **Early grasp.** Humans grasp this proportional structure early and across cultures, before formal schooling in either mathematics or ethics. | | **P4** | **The hypotheses.** A truth that is at once mathematical, moral and early-known is far more expected if one rational and good Mind grounds both number and good and makes minds to know both, than if mathematical truth, moral truth and the fairness sense have three unrelated sources. Theism posits the first; naturalism the second. | | **P5** | **The likelihood principle.** Evidence far more expected on one hypothesis than on another confirms the first over the second. | | **C** | **Therefore the mathematical form of justice, necessary, binding and known from infancy, confirms theism over naturalism.** | **Validity.** P1 to P3 establish the datum. P4 says the datum is far more expected on theism than on naturalism. P5 converts that into confirmation. The form is a likelihood comparison closed by modus ponens. **Strength of the conclusion.** Confirmatory. The argument does not claim that only theists can be fair or that fairness proves God. It claims that the specific fusion of mathematical necessity and moral authority in one truth fits theism better. ## P1, Mathematical form ### Inductive strand 1. **Aristotle's two proportions.** [Aristotle](/codex/aristotle/), *Nicomachean Ethics* V.3-4, holds that "the just is a species of the proportionate." In distribution, shares should be in geometric proportion to merit (as A is to B, so the share of A to the share of B). In correction, the judge restores arithmetic equality by taking from the gainer what the loser lost, regardless of who they are. 2. **Plato's geometric equality.** In Plato's *Gorgias* (508a), Socrates tells Callicles that he has neglected geometry, and that geometric equality has great power among gods and men. See [Plato](/codex/plato/). 3. **The Pythagoreans.** Aristotle reports (*Nicomachean Ethics* V.5) that the Pythagoreans defined justice simply as reciprocity, and corrects them with his proportional account. 4. **Proportionality in modern law.** Proportionality is a standing principle in sentencing and in the law of armed conflict, where an attack is unlawful if expected civilian harm is excessive in relation to the military advantage anticipated (Additional Protocol I to the Geneva Conventions, 1977, article 51). ### Abductive strand | Explanation of P1's data | Explanatory power | Scope | Simplicity | Ad hoc? | |---|---|---|---|---| | Justice is a real moral order with real proportional structure | Explains why every serious theory of justice uses ratio and equality | Corrective, distributive, retributive and military law | One posit | No | | Proportion is a convenient metaphor imposed on social bargaining | Explains the vocabulary | Weak on why the metaphor yields correct verdicts in new cases | Simple | Partly | ### Convergence Greek philosophy (Plato, Aristotle, the Pythagoreans), Mesopotamian and Israelite law, and modern international humanitarian law all reach P1, for different purposes and in different millennia. ### Objections and rebuttals 1. *"Justice is about more than numbers: mercy, need, relationship."* **Rebuttal.** Agreed. P1 says justice has mathematical form, not that it is nothing but mathematics. Mercy is the subject of [The Justice and Mercy Argument](/codex/the-justice-and-mercy-argument/). 2. *"Merit cannot be measured."* **Rebuttal.** Not precisely, and Aristotle knew it. But the form of the judgment, that greater desert warrants a greater share and that like cases be treated alike, is proportional even when the inputs are rough. ## P2, Necessity and force ### Inductive strand 1. **The limit of talion.** The Laws of Hammurabi (about 1750 BC) prescribe "an eye for an eye" for injury between men of the same class (laws 196 to 197), and [Exodus 21:23-25](/codex/exodus-21-23-25/) states the principle as life for life, eye for eye, tooth for tooth. Scholars widely read the formula as a limit on retaliation rather than a demand for it: one eye, no more. Rabbinic tradition read it as requiring monetary compensation of equal value (Mishnah, Bava Kamma 8:1). 2. **One standard for all.** Hammurabi's law graded penalties by class: injury to a commoner or a slave was compensated in silver rather than in kind. The Torah requires "one manner of law, as well for the sojourner, as for the home-born" ([Leviticus 24:22](/codex/leviticus-24-22/), ASV), and a master who destroys his slave's eye must set the slave free ([Exodus 21:26-27](/codex/exodus-21-26-27/)). The Hebrew law is more strictly proportional and more universal. See [ANE Legal Codes, Comparative Context](/codex/ane-legal-codes-comparative-context/) and [Mosaic Law](/codex/mosaic-law/). 3. **The judgment is modal.** It is not merely that our society forbids hanging pickpockets. A society that did so would be doing wrong. The verdict holds in every possible society, as mathematical truths hold in every possible world. ### Abductive strand | Explanation of P2's data | Explanatory power | Scope | Simplicity | Ad hoc? | |---|---|---|---|---| | Moral truths of proportion grounded in a necessary, good God | Explains both the necessity and the binding force | All proportional norms | One posit | No | | Godless moral realism: necessary brute moral facts (Erik Wielenberg) | Explains necessity | Leaves the link to mathematics unexplained | Brute | No, but brute | | Convention: fairness is whatever a society settles on | Explains variation | Cannot say a society with grossly disproportionate penalties is wrong | Simple | Gives up the datum | ### Convergence The comparative history of law (Hammurabi to Moses), rabbinic interpretation, and moral philosophy from Aristotle to the present agree that disproportion is a defect of justice itself, not only of a local code. ### Objections and rebuttals 1. *"Eye for an eye is barbaric."* **Rebuttal.** As a cap on vengeance in societies without police, it was a moral advance, and Jesus's teaching against personal retaliation ([Matthew 5:38-39](/codex/matthew-5-38-39/)) presupposes it as the law of courts, not the rule of private life. 2. *"Necessity belongs to logic, not morals."* **Rebuttal.** Most moral philosophers, realist and anti-realist alike, accept that if there are moral truths about kinds of acts, the basic ones are necessary. The Scales Argument needs only that. ## P3, Early grasp ### Inductive strand 1. **Toddlers expect fair splits and fair pay.** Stephanie Sloane, Renée Baillargeon and David Premack, "Do Infants Have a Sense of Fairness?" (*Psychological Science* 23, 2012), found that 19-month-olds looked longer when an experimenter divided items unequally between two puppets, and that 21-month-olds expected an experimenter to reward two workers equally when both had worked, but not when only one had. 2. **Fifteen-month-olds.** Marco Schmidt and Jessica Sommerville, "Fairness Expectations and Altruistic Sharing in 15-Month-Old Human Infants" (*PLoS ONE* 6, 2011), found infants attended longer to unequal distributions, and that this sensitivity was related to their own sharing. 3. **Every society departs from pure self-interest.** Joseph Henrich and colleagues, "'Economic Man' in Cross-Cultural Perspective: Behavioral Experiments in 15 Small-Scale Societies" (*Behavioral and Brain Sciences* 28, 2005), found that no society behaved as the selfish model predicts in bargaining games, though what counted as a fair offer varied widely with local economic life. 4. **A contested primate parallel.** Sarah Brosnan and Frans de Waal, "Monkeys Reject Unequal Pay" (*Nature* 425, 2003), reported capuchins refusing a lesser reward after seeing a partner receive a better one. Later work disputed it: Alan Silberberg and colleagues (*Animal Cognition*, 2009) found no inequity effect in a design without role switching and argued the earlier effect depended on frustration-inducing procedures. It carries little weight here. ### Abductive strand | Explanation of P3's data | Explanatory power | Scope | Simplicity | Ad hoc? | |---|---|---|---|---| | Minds made to know the moral and mathematical order, so the form is recognized early | Explains early onset, cross-cultural presence and the link to number | Wide | One posit | No | | Evolved cooperation heuristic (Robert Axelrod; Ken Binmore) | Explains early onset and variation well | Predicts parochial scope | Moderate | No | | Cultural learning alone | Explains variation | Weak on preverbal infants | Simple | Struggles with the infant data | ### Convergence Infant cognition labs (Baillargeon, Sommerville), experimental economics in fifteen societies (Henrich and colleagues), and comparative primatology (Brosnan and de Waal, with its critics) reach P3 by different methods. They agree that a sense of proportion is early and widespread; they disagree on its origin. ### Objections and rebuttals 1. *"Henrich shows fairness is cultural."* **Rebuttal.** Henrich shows the calibration is cultural: what share counts as fair. The structure, that some departure from pure self-interest is required and that offers can be too low, appeared in every society tested. 2. *"Looking time is not moral judgment."* **Rebuttal.** Agreed; the infant data show an expectation of proportion, not a theory of justice. That is all P3 needs: the form is known before it is taught. ## P4, The hypotheses ### Inductive strand 1. **Theism.** On Christian theism the same Word through whom all things were made ([John 1:1-3](/codex/john-1-1-3/)) is the ground of their order and measure ([Isaiah 40:12](/codex/isaiah-40-12/)), and the same God loves justice and requires just weights ([Proverbs 11:1](/codex/proverbs-11-1/)). Mathematical and moral order share one source, and human beings, made in his image ([Imago Dei](/codex/imago-dei/)), are fitted to know both. The fusion in P1 to P3 is predicted. 2. **Naturalism.** On naturalism, mathematical truths, if they exist, are abstract and causally inert; objective moral truths are either denied or posited as brute; and the fairness sense is an evolved heuristic. These have three unrelated sources, and their meeting in one early-known moral-mathematical truth is a coincidence. ### Abductive strand Naturalism's best move is to collapse the three into one: fairness is just an evolved equilibrium norm, and its "mathematical" look comes from the game theory that describes it. That is the defeater gate. ### Convergence The convergence on P4 is theological and philosophical: Augustine's identification of number and wisdom (*On Free Choice of the Will*, book II), the medieval transcendentals, and the contemporary arguments that mathematics needs a Mind ([Argument from Mathematical Truth](/codex/argument-from-mathematical-truth/); [Mathematics Requires Christian Theism](/codex/mathematics-requires-christian-theism/)) and that morality does ([Moral Argument](/codex/moral-argument/)). ### Objections and rebuttals 1. *"This is two arguments glued together, one from math and one from morals."* **Rebuttal.** It is one argument from one truth that has both features. The datum is not "there is math" plus "there is morality" but "a single moral truth has necessary mathematical content." 2. *"Why the Christian God?"* **Rebuttal.** The argument confirms one rational, good Mind. Scripture's specific claim, that the Logos is creator and judge, and that the Judge weighs ([Daniel 5:27](/codex/daniel-5-27/)), fits it closely. ## P5, The likelihood principle ### Inductive strand The principle is standard in probability theory and scientific confirmation. ### Abductive strand Rejecting it would undercut the comparative reasoning of the very experiments cited in P3. ### Convergence Bayesian and likelihoodist schools agree on this comparative use. ### Objections and rebuttals 1. *"Priors decide."* **Rebuttal.** The ledger is prior-agnostic; see [Cumulative Case for Christian Theism](/codex/cumulative-case-for-christian-theism/). ## The knot The strands are independent: ancient philosophy (Plato, Aristotle), ancient Near Eastern and Israelite law, infant cognition (Sloane and colleagues; Schmidt and Sommerville), cross-cultural experimental economics (Henrich and colleagues), and developmental economics (Fehr and colleagues). Two overlaps are counted once: the two infant studies form one family, and the primate row is weak and contested, so it is not counted. The decisive datum is the conjunction of necessity (P2) with early grasp (P3) in a truth whose content is mathematical (P1). ## The ledger Prior-agnostic: the ledger asks only how expected each datum is under each hypothesis. The ratings are reasoned judgments from the sections above, not measurements. | Datum | How expected on theism | How expected on naturalism | Favours | Why | Independent? | |---|---|---|---|---|---| | Justice has proportional mathematical form (Aristotle) | High | Moderate | Theism, slightly | Game theory also yields proportional norms | Yes | | Disproportion is wrong necessarily, in every society | High | Low (convention) to moderate (brute realism) | Theism, modestly to clearly | Naturalism must deny or leave it brute | Yes | | Infants expect fair splits and fair pay (Sloane et al.; Schmidt and Sommerville) | High | High | Even | An evolved heuristic predicts it | Yes (one family) | | Every society departs from self-interest (Henrich et al.) | High | High | Even | Cooperation theory predicts it | Yes | | Capuchin inequity aversion | Moderate | Moderate | Not counted | Contested data | Not counted | | Children's fairness is parochial (Fehr et al.), yet the reflective norm and the Torah are universal | High | Moderate | Theism, modestly | Heuristics predict in-group scope; the norm outruns it | Partly overlaps the necessity row | | One truth that is mathematical, moral and early-known | High | Low | Theism, clearly | Three unrelated sources must coincide | The conjunction | **Net.** The developmental rows do not favour theism by themselves; an evolved sense of fairness is expected on both views. The weight sits on necessity and on the conjunction: a moral truth whose content is mathematics, binding in every possible society, is what a world grounded in one Logos would contain. ## The defeater gate **Binmore's natural justice.** The strongest objection is Ken Binmore's *Natural Justice* (Oxford, 2005), building on Robert Axelrod, *The Evolution of Cooperation* (1984). Binmore argues that fairness norms are evolved conventions for selecting among the many equilibria of the repeated "game of life." Their mathematical look comes from the game theory that models them; their felt authority from the emotions that stabilize them; their early onset from biological and cultural evolution. No moral truth is needed, and none is being tracked. The reply has three steps. 1. **The account explains the norm, not its correctness.** Binmore explains why societies settle on proportional norms and why we feel them. It does not explain why a society that hanged pickpockets would be wrong rather than merely different. On Binmore's naturalism, fairness norms are relative to the conventions a society has evolved, and that is the cost. 2. **It predicts parochial fairness.** Ernst Fehr, Helen Bernhard and Bettina Rockenbach, "Egalitarianism in Young Children" (*Nature* 454, 2008), found that inequality aversion grows strongly between ages 3 and 8, and that it is shaped by parochialism: children favour equality with their own group. That is what an evolved cooperation heuristic predicts. But the reflective norm, and the Torah's "one manner of law, as well for the sojourner, as for the home-born," extend proportion to strangers and slaves. The norm outruns the heuristic in exactly the direction a moral truth would. 3. **Mathematics is not the model's projection.** The proportional verdicts are not artifacts of modelling; Aristotle and the lawgivers of Babylon and Israel reached them two thousand years before game theory existed. What the gate concedes: evolution and culture shape our fairness sense, and the infant data are expected on both views. The argument rests on the necessity and universality of the norm, not on its early onset alone. ## Concessions - *Grant:* fairness has an evolutionary history. *Now collect:* so does arithmetic sense; neither history makes the truths it tracks conventional. - *Grant:* cultures disagree about what is fair. *Now collect:* they disagree about inputs (who deserves what), not about the form (that the share must fit the claim). - *Grant:* "eye for eye" sounds harsh. *Now collect:* it was a limit, and the Torah applied it across class lines where Hammurabi did not. ## Cheatsheet **The 30-second version (read aloud).** Justice is mathematics with a conscience. The punishment must fit the crime, the pay must fit the work. Aristotle called it proportion. The old law of "eye for eye" was a limit: one eye, no more. And toddlers under two expect a fair split and expect the worker to be paid. So a truth that is mathematical, moral and known from infancy runs through the world. If one Mind made both number and goodness and made us to know both, that is what you'd expect. If math, morality and our sense of fairness came from three blind sources, their meeting is a coincidence. **Fast facts:** 1. Aristotle (*Nicomachean Ethics* V): "the just is a species of the proportionate." 2. Sloane, Baillargeon and Premack (*Psychological Science*, 2012): 21-month-olds expect equal pay for equal work. 3. Henrich et al. (*BBS*, 2005): no society of fifteen tested behaved as pure self-interest predicts. 4. Fehr, Bernhard and Rockenbach (*Nature*, 2008): children's fairness is strongly shaped by in-group favouritism. 5. [Leviticus 24:22](/codex/leviticus-24-22/): one law for the sojourner and the home-born. **The closing line.** The scales of justice are calibrated, and calibration needs a standard. ## Cross-examination ### Round 1, The form - **Q:** Is it unjust to hang a man for stealing a loaf of bread? - **If they say yes:** then you hold that punishment must be proportioned to the wrong. Proportion is mathematics. - **If they say only by our standards:** then a society that did it would not be wrong. Do you accept that? ### Round 2, The necessity - **Q:** Could there be a society where punishing a pickpocket a hundred times more severely than a murderer was just? - **If they say no:** then proportion binds in every possible society, like a theorem. - **If they say yes:** then justice is local fashion. ### Round 3, The origin - **Q:** If fairness is an evolved heuristic, why does it tell us to treat strangers fairly, when the heuristic was tuned for our own group? - **If they say culture extended it:** then culture discovered something the heuristic did not contain. What was it? ### Dodge table | Dodge | What it concedes | Reply | |---|---|---| | "Fairness is just evolved." | Fairness is real as a sense | "So is the number sense. Evolution explaining a sense does not make what it senses fiction." | | "Cultures disagree about fairness." | Fairness norms exist everywhere | "They disagree about inputs. None think the share should have nothing to do with the claim." | | "Math is a human invention." | We use math to state justice | "Then the injustice of a hundredfold penalty is an invention too. Is it?" | | "Babies just like symmetry." | Infants detect equality | "And they expect the worker to be paid but not the idler. That is proportion to merit, not symmetry." | ## Live-cite kit **Scripture (ASV):** - [Leviticus 19:35-36](/codex/leviticus-19-36/): Ye shall do no unrighteousness in judgment, in measures of length, of weight, or of quantity. Just balances, just weights, a just ephah, and a just hin, shall ye have: I am Jehovah your God ([Leviticus 19:35-36](/codex/leviticus-19-35-36/), ASV) - [Job 31:6](/codex/job-31-6/): Let me be weighed in an even balance, That God may know mine integrity ([Job 31:6](/codex/job-31-6/), ASV) - [Proverbs 11:1](/codex/proverbs-11-1/): A false balance is an abomination to Jehovah; But a just weight is his delight ([Proverbs 11:1](/codex/proverbs-11-1/), ASV) - [Proverbs 16:11](/codex/proverbs-16-11/): A just balance and scales are Jehovah's; All the weights of the bag are his work ([Proverbs 16:11](/codex/proverbs-16-11/), ASV) - [Daniel 5:27](/codex/daniel-5-27/): TEKEL; thou art weighed in the balances, and art found wanting ([Daniel 5:27](/codex/daniel-5-27/), ASV) - [Exodus 21:23-25](/codex/exodus-21-22-25/): thou shalt give life for life, eye for eye, tooth for tooth, hand for hand, foot for foot, burning for burning, wound for wound, stripe for stripe ([Exodus 21:23-25](/codex/exodus-21-22-25/), ASV) - [Leviticus 24:22](/codex/leviticus-24-22/): Ye shall have one manner of law, as well for the sojourner, as for the home-born: for I am Jehovah your God ([Leviticus 24:22](/codex/leviticus-24-22/), ASV) **Scholarly:** - Aristotle, *Nicomachean Ethics* V.3: "the just is a species of the proportionate." - Plato, *Gorgias* 508a: geometric equality has great power among gods and men. - Sloane, Baillargeon and Premack, *Psychological Science* 23 (2012). - Fehr, Bernhard and Rockenbach, *Nature* 454 (2008). **Aphorism:** "Fairness is a ratio, and ratios are not made by votes." ## Connection to Scripture - [Leviticus 19:35-36](/codex/leviticus-19-36/), just weights and measures are tied directly to the character of the God who redeemed Israel. - [Proverbs 11:1](/codex/proverbs-11-1/) and [Proverbs 16:11](/codex/proverbs-16-11/), the scales belong to God: measure is his before it is ours. - [Isaiah 40:12](/codex/isaiah-40-12/), the Creator who weighed the mountains in scales: the same God measures the world and the deed. - [Isaiah 28:17](/codex/isaiah-28-17/), justice the line and righteousness the plummet: the builder's tools of measure used for morals. - [Exodus 21:23-25](/codex/exodus-21-22-25/) and [Leviticus 24:22](/codex/leviticus-24-22/), proportion as a limit, applied equally. - [Daniel 5:27](/codex/daniel-5-27/) and [Matthew 7:2](/codex/matthew-7-2/), the measure we use is the measure used on us. ## Scholarship Published academic works this page draws on, each matched to a publisher, index or library catalog record. - Robert M. Axelrod, *The evolution of cooperation* (Basic Books, 1984). [Open Library](https://openlibrary.org/works/OL2620286W) - Ken Binmore, *Natural Justice* (Oxford University Press, 2005). [doi:10.1093/acprof:oso/9780195178111.001.0001](https://doi.org/10.1093/acprof:oso/9780195178111.001.0001) - Sarah F. Brosnan and Frans B. M. de Waal, "Monkeys reject unequal pay," *Nature* 425 (2003). [doi:10.1038/nature01963](https://doi.org/10.1038/nature01963) [PubMed 13679918](https://pubmed.ncbi.nlm.nih.gov/13679918/) - Ernst Fehr, Helen Bernhard and Bettina Rockenbach, "Egalitarianism in young children," *Nature* 454 (2008). [doi:10.1038/nature07155](https://doi.org/10.1038/nature07155) [PubMed 18756249](https://pubmed.ncbi.nlm.nih.gov/18756249/) [open access](https://www.zora.uzh.ch/id/eprint/3833/11/2008_Fehr_NatureV.pdf) - Martha T. Roth, *Law Collections from Mesopotamia and Asia Minor* (SBL Press, 1997). [doi:10.2307/jj.25577265](https://doi.org/10.2307/jj.25577265) - Marco F. H. Schmidt and Jessica A. Sommerville, "Fairness Expectations and Altruistic Sharing in 15-Month-Old Human Infants," *PLoS ONE* 6 (2011). [doi:10.1371/journal.pone.0023223](https://doi.org/10.1371/journal.pone.0023223) [PubMed 22003380](https://pubmed.ncbi.nlm.nih.gov/22003380/) [open access](https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0023223&type=printable) - Stephanie Sloane, Renée Baillargeon and David Premack, "Do Infants Have a Sense of Fairness?" *Psychological Science* 23 (2012). [doi:10.1177/0956797611422072](https://doi.org/10.1177/0956797611422072) [PubMed 22258431](https://pubmed.ncbi.nlm.nih.gov/22258431/) [open access](https://www.ncbi.nlm.nih.gov/pmc/articles/3357325) ## See also - [Ris3n Arguments](/codex/ris3n-arguments/), the hub of ris3n's original arguments - [Arguments](/codex/arguments/), the master index - [Mathematics Requires Christian Theism](/codex/mathematics-requires-christian-theism/), which Mind mathematics needs; this page is about one moral truth with mathematical content - [Argument from the Beauty-Mathematics Convergence](/codex/argument-from-the-beauty-mathematics-convergence/), beauty as a guide to truth in physics, a different fit between value and mathematics - [Argument from Mathematical Truth](/codex/argument-from-mathematical-truth/), the general case that mathematical truth needs a Mind - [The Ought-Owe Argument](/codex/the-ought-owe-argument/), the grammar of moral debt; this page concerns the measure of the debt - [Argument from Justice](/codex/argument-from-justice/), the standard of justice and the final Judge - [ANE Legal Codes, Comparative Context](/codex/ane-legal-codes-comparative-context/) and [Mosaic Law](/codex/mosaic-law/), Hammurabi and the Torah compared - [Aristotle](/codex/aristotle/) and [Plato](/codex/plato/), the classical sources - [Moral Argument](/codex/moral-argument/), the family this argument belongs to - [Cumulative Case for Christian Theism](/codex/cumulative-case-for-christian-theism/), where this argument contributes ## Common questions this page answers **Q: Do babies have a sense of fairness?** Studies suggest they do, in a basic form. Sloane, Baillargeon and Premack (2012) found that toddlers around 19 to 21 months expect items to be split equally and expect a worker, but not an idler, to be rewarded. Schmidt and Sommerville (2011) found related expectations at 15 months. **Q: Why is justice described in terms of balance and proportion?** Because justice has mathematical structure. Aristotle said "the just is a species of the proportionate": shares should be proportioned to merit, and a court restores equality between what was lost and what is repaid. Scripture uses the image of just scales for the same reason. **Q: Did "an eye for an eye" mean revenge?** Most scholars read it as a limit: one eye and no more, in place of escalating feuds. Later Jewish tradition applied it as monetary compensation of equal value. The Torah also applied one law to native and stranger alike, where the Code of Hammurabi graded penalties by social class. **Q: Isn't fairness just an evolved instinct for cooperation?** Evolution and culture shape our sense of fairness, and researchers like Ken Binmore argue that is the whole story. But an evolved instinct explains why we feel fairness, not why disproportion is actually wrong, and children's fairness starts out favouring their own group, while the moral norm, and the biblical law, extend it to strangers. **Q: How can mathematics and morality be connected?** In justice they meet in a single truth: that rewards and penalties must fit their grounds. The Scales Argument says a truth that is both mathematical and moral, and known from infancy, is best explained if one Mind is the source of both number and goodness. **Q: Is this the same as the argument from mathematics for God?** No. The argument from mathematics asks what grounds mathematical truth in general. The Scales Argument starts from one specific moral truth whose content is mathematical, and argues from that fusion.