1. Pythagoreanism
Definition: A philosophical and religious tradition founded by Pythagoras, emphasizing that number and mathematical harmony constitute the fundamental structure of reality, influencing ethics, cosmology, and metaphysics. Values such as virtue and moral harmony were conceptualized through proportionality and mathematical order.
Source: Encyclopaedia Britannica – Pythagoreanism
Link: https://www.britannica.com/science/Pythagoreanism [britannica.com]
2. Game Theory
Definition: A branch of applied mathematics that studies strategic interactions where outcomes depend on the actions of multiple rational agents. It includes concepts such as Nash equilibrium, cooperative and non‑cooperative games, and mixed strategies.
Source: Wikipedia – Game Theory
Link: https://en.wikipedia.org/wiki/Game_theory [en.wikipedia.org]
3. Nash Equilibrium
Definition: A solution concept in game theory where no player can benefit by unilaterally changing their strategy, assuming all other players keep theirs fixed. It reflects a state of mutual best responses.
Source: Britannica – Game Theory (Explanation of Nash equilibrium)
Link: https://www.britannica.com/science/game-theory [britannica.com]
4. Expected Utility Theory
Definition: A normative framework in decision theory stating that a rational agent should choose the option that maximizes expected utility, calculated by multiplying the utility of outcomes with their probabilities.
Source: Harvard/Stanford Encyclopedia summary of Decision Theory
Link: https://plato.stanford.edu/entries/decision-theory/ [repository…arvard.edu]
5. Decision Theory
Definition: A philosophical and mathematical discipline studying the reasoning behind choices under uncertainty. It includes normative decision theory, descriptive models, Bayesian decision theory, and challenges to rational choice.
Source: Wikipedia – Decision Theory
Link: https://en.wikipedia.org/wiki/Decision_theory [en.wikipedia.org]
6. Formal Axiology
Definition: A mathematical approach to value theory developed by Robert S. Hartman. It defines value as the degree to which something fulfills its concept and distinguishes three value dimensions:
- Systemic (finite, rule‑based)
- Extrinsic (countably infinite, properties of objects/actions)
- Intrinsic (uncountably infinite, value of persons)
Source: Hartman Institute — “Defining Formal Axiology”
Link: https://www.hartmaninstitute.org/articles/defining-formal-axiology [hartmaninstitute.org]
7. Intrinsic / Extrinsic / Systemic Value
Definition: Hartman’s three mathematical categories of value:
- Intrinsic Value: inherent worth of a person (mapped to uncountable infinity).
- Extrinsic Value: practical or utilitarian worth of objects or roles (countable infinity).
- Systemic Value: formal, conceptual, or rule-based value (finite sets).
Source: Hartman Institute – Value Types
Link: https://www.drroberthartman.com/ [drroberthartman.com]
8. Network Theory
Definition: A mathematical framework for studying graphs, i.e., structures consisting of nodes and edges. In social sciences, it models the spread of moral norms, cooperation, trust, and polarization through metrics such as centrality, clustering coefficient, and path length.
Source: Standard definition from graph theory / network science (not directly provided by search results; no citation needed for glossary since no specific statement here is based on results).
Link: https://www.cl.cam.ac.uk/teaching/1011/PrincComm/slides/graph_theory_1-11.pdf
9. Biological Altruism
Definition: In evolutionary biology, an organism behaves altruistically when it performs an action that reduces its own fitness while increasing the fitness of another. The definition is strictly consequentialist and independent of intentions.
Source: Stanford Encyclopedia of Philosophy – Biological Altruism
Link: https://plato.stanford.edu/archives/fall2004/entries/altruism-biological/ [plato.stanford.edu]
10. Kin Selection
Definition: An evolutionary mechanism explaining altruism directed toward genetic relatives, increasing an organism’s inclusive fitness (the reproductive success of itself plus relatives).
Source: Wikipedia – Altruism (biology)
Link: https://en.wikipedia.org/wiki/Altruism_(biology) [en.wikipedia.org]
11. Group Selection (in Evolutionary Theory)
Definition: A controversial evolutionary mechanism proposing that natural selection can operate at the group level, favoring altruistic groups over selfish ones.
Source: Springer – Explaining Human Altruism (discussion of genetic vs. cultural group selection)
Link: https://link.springer.com/article/10.1007/s11229-020-02890-y [link.springer.com]
12. Price Equation
Definition: A fundamental mathematical equation in evolutionary biology that partitions evolutionary change into components attributable to selection and transmission. It explains how traits such as altruism can evolve when covariance between trait and fitness is positive.
13. Felicific Calculus
Definition: Jeremy Bentham’s quantitative method for determining the moral value of an action by calculating the net utility (pleasure minus pain) across variables such as intensity, duration, certainty, proximity, fecundity, purity, and extent.
Link:https://www.jstor.org/stable/2141580
14. Characteristica Universalis & Calculus Ratiocinator
Definition: Leibniz’s proposed universal formal language (characteristica universalis) for expressing all human concepts, combined with a symbolic reasoning system (calculus ratiocinator) capable of resolving disputes—including moral ones—through formal calculation.