Podcast Summary: New Books Network Episode: Jeremiah Joven Joaquin and James Franklin eds., The Necessities Underlying Reality: Connecting Philosophy of Mathematics, Ethics and Probability (Bloomsbury, 2025) Host: Gregory McNiff Guest: James Franklin Date: December 24, 2025

Episode Theme / Purpose

This episode features Gregory McNiff interviewing Professor James Franklin about his forthcoming book, The Necessities Underlying Reality: Connecting Philosophy of Mathematics, Ethics and Probability. The conversation explores Franklin’s thesis that there are absolute necessities in reality—connections and truths that are objectively and necessarily true, spanning mathematics, ethics, logic, and probability. Franklin advocates for Aristotelian realism, which locates these necessities in the world itself, as opposed to Platonic or nominalist accounts. The episode scrutinizes the implications of this approach for philosophy, education, ethics, and even theology.

Key Discussion Points and Insights

1. Why This Book? [02:47]

• Franklin’s Objective: To reveal that reality includes, beyond mere facts, absolute necessities—connections about how things must be, not merely descriptions of how things are.
• Examples Provided:
  • Mathematical: Any group of four objects has six unique pairs—true universally [02:58].
  • Logical: If an experiment matches a prediction, it necessarily supports that theory [03:13].
  • Ethical: The value of human beings makes killing wrong, necessarily so [03:19].
• Audience: Intelligent general readers with philosophical interests; no heavy prerequisites, open access [04:03].

2. Absolute Necessities vs. Analytic/Linguistic Truths [04:11]

• Distinction:
  • Analytic truths (e.g., "All bachelors are unmarried") depend on definitions and are trivial (“just the way we use language”).
  • Franklin: “The necessities I’m talking about are nothing to do with linguistics or words… They absolutely must be so and are true in all possible worlds.” [04:36]

3. Objective Reality of Mathematical and Ethical Truths [06:09]

• Universality:
  • Mathematical truths (e.g., primes between 1 and 100; digits of π) are locked in and accessible to all by reason [06:21].
  • Parallel in Ethics: “If you understand the nature of humans... then you’ll see that that kind of person is morally valuable… I’m saying that is absolute and accessible to everyone in exactly the same way as mathematical truths.” [06:51]

4. Aristotelian Realism vs. Platonism and Nominalism [07:14]

• Nominalism: Necessities are only linguistic tautologies—rejected.
• Platonism: Necessities “exist” in some abstract, non-physical realm.
• Aristotelian Realism (Franklin’s view): Mathematical necessities “are implemented in this world,” not in another [08:22].
  • Example: “Any set of four real things… you can find six different pairs… it’s about physical things in this world.” [08:36]

5. Decline of Necessity in Modern Education [08:50]

• Causes:
  • Exam-driven education prioritizes simplistic marking over understanding.
  • Humanities lean towards historicism; math neglects proof-based learning.
• Consequence: Necessity and proof are often “hidden” in current curricula [09:39].

6. Perception and Intuition of Necessities [10:27]

• Franklin downplays intuition: Prefers concrete engagement with proof (e.g., working through Euclid’s Elements, Book I) [10:54].
• Training in Necessity: Mathematics and history when done properly both instill the idea of necessary connections, whether in geometry or in evaluating evidence [11:49].

7. Foundations of Ethics—The Realist Notion [12:20]

• Shift of Focus: Not simply a list of rules (“what to do”), but anchored in “what entities are inherently valuable or of worth” [13:05].
• Encourages: Ethics as grounded in “the inherent worth of persons” rather than in rules or social benefit [13:46].

8. Ethics of Almsgiving and Poverty [14:32]

• Ethical obligation comes from the opportunity to aid in “realizing humanness”—not a rigid rule, but a principle [15:13].
• Details (“how much to give”) are left to individual conscience, after principles are understood [15:58].

9. Mathematics as Antidote to Relativism [16:31]

• Mathematics offers “the easiest way into understanding certainty” [17:01].
• Training in mathematics (historically, Greek mathematics) was intended to instill principles and necessary thinking, resisting relativism [17:24].

10. Relationship Between Humanities and Mathematics [18:42]

• There’s a divide; Franklin notes that both sides often accuse the other of lacking depth or breadth [18:49].
• “We do need both sides… to be properly human and properly educated.” [19:09]

11. Literature and the Concrete Value of Persons [19:26]

• Literature “rounds out” our understanding of what it is to be human—novelists, Shakespeare, etc., illuminate the concrete aspects of human worth [19:38].

12. Koenigsberg Bridges Problem—Necessity in the Real World [20:12]

• Euler’s solution showed mathematical necessity realized among “actual bridges in an actual city”—a vivid example of necessity in reality [21:26].
  • “Absolute. It’s not as if any change in the laws of nature… could make it possible… it’s a necessity much stronger than any scientific or linguistic… necessity.” [21:39]

13. The Mystery of Human Understanding and AI [22:05]

• Key Quote: “We don’t see how any physical object could truly understand… it must have some mysterious properties that are beyond the physical.” [22:46]
• AI: Even as AI achieves “human-like” outputs, it lacks real understanding or consciousness—no computer, as of yet, truly gets at necessity or modality [24:08].
• Human vs. animal minds: “Animals are very poor at even the simplest things about necessity.” [24:33]

14. Teaching Proofs in Mathematics [25:26]

• Proofs are not being taught with sufficient rigor (“too much computation, too much rules, too much content without concentrating on proof techniques”) [26:47].
• Franklin authored “Proof: An Introduction” to fill this gap; explicit teaching of proof technique is essential [26:21].

15. Ratio, Symmetry, and Philosophy’s Failings [27:54]

• Western philosophy has neglected “relations” like ratio and symmetry, which are essential to mathematical thought [28:22].
• Quote: “Somehow people are not focusing on [ratios] as a topic… and the same with symmetry.” [29:13]

16. Who's to Blame? [30:09]

• “I blame everyone… different things have gone wrong, so I’m trying to bring it all together…” [30:34]

17. Personal Background and Catholic Influence [31:01]

• Catholic education, via natural law and scriptural tradition, provides some grounding in objective ethics (“training in the idea that ethics is objectively true and not because of divine commands, but because of how humans are”) [31:42].
• Examples from Psalms and the Declaration of Independence highlight the universality of these concepts [32:33].

18. Worth of Persons and Everyday Ethics [33:13]

• Even small acts (e.g., “being polite to the receptionist at the doctor”) are ethically significant, based on the inherent dignity of persons [33:32].

19. Logical Probability vs. Bayesian Probability [34:03]

• Logical Probability: Concerns the necessary logical relation between evidence and conclusion (“an absolutely certain fact” that evidence points to a conclusion “on the balance of probabilities”).
• Different from subjective or Bayesian approaches—more about necessity than about changable credences [34:31]–[36:59].

20. Mathematical Necessities and Divine Omnipotence [39:04]

• Even God cannot change mathematical necessities. “God can’t make any of the digits of PI other than what they are. It’s just an absolute necessity.” [39:13]
• These necessities “should not be subject to divine omnipotence,” but must be allowed for in creation [39:40].

21. Leibniz, God, and the Best Possible World [40:43]

• Franklin aligns with Leibniz: The world is the best possible, given all necessary constraints—including the mathematical “engineering” of reality [40:53].
• “Any small change… can’t just be swapped out; everything affects everything.” [41:27]

22. Ethics Closer to Mathematics than to Empirical Science [42:47]

• Both are “abstract sciences of absolute necessities, subject matter which you can understand by pure thought,” whereas empirical science demands observation [42:52].

23. Is There a Universal, Objective Ethics? [43:41]

• “Yes… it’s for cultures to get a better understanding of the worth of persons.” [43:46]

24. How Cultures Discover Ethical Truths [44:21]

• Not all cultures discovered mathematics or ethics independently; it took Greek and Hebrew cultures, respectively, to formalize them.
• Universal Declaration of Human Rights cited as a modern expression of discovered ethical necessities [45:20].

25. The Return of Aristotelian Science [46:08]

• The scientific revolution combined a “Baconian,” fact-collection method with a mathematical focus on necessary connections (Galileo, Newton).
• Now, mathematical necessity is more fully appreciated in the sciences as underlying contingent truths [46:23].

26. Loss and Recovery of Contact with Necessity [48:17]

• Despite technological and mathematical progress, human understanding has regressed in recognizing ethical necessity—blaming in part the “humanities crowd” and historicist philosophy (notably Hume) for neglecting necessity [49:24].
• Franklin’s advice: Go back to Aristotle’s Posterior Analytics (“programmatic”) and Euclid’s Elements (“how to do it”); modern philosophers and scholars have lost sight, so start again [51:18].

Notable Quotes and Memorable Moments

• “The necessities I’m talking about are nothing to do with linguistics or words… They absolutely must be so and are true in all possible worlds.” (James Franklin, [04:36])
• “If you understand the nature of humans… you’ll see that that kind of person is morally valuable in a way that just atoms or something are not.” (James Franklin, [06:43])
• “[Mathematical] truths are accessible to everyone… accessible to everyone by pure thought.” (James Franklin, [06:26])
• “Intuition is important, but it’s a rather vague term… It’s better to just sit down with Euclid’s Elements…” (James Franklin, [10:35])
• “Mathematics itself stands as an unanswerable challenge to any relativist undermining of truth.” (James Franklin, paraphrased and discussed at [16:31])
• “We don’t see how any physical object could truly understand… it must have some mysterious properties that are beyond the physical.” (James Franklin, [22:46])
• “I blame everyone… but a different thing.” (James Franklin, [30:34])
• “I think Catholics have a little bit of a head start… because of the background in natural law philosophy.” (James Franklin, [31:42])
• “God can’t make any of the digits of PI other than what they are. It’s just an absolute necessity.” (James Franklin, [39:13])
• “We have to go and read Aristotle…” (James Franklin, [51:11])

Timestamps for Major Segments

• [01:28] Introduction of guest
• [02:47] Why write the book? What are absolute necessities?
• [04:27] Distinction from analytic/language-based truths
• [06:09] Connection of mathematics and ethical necessities
• [07:14] Aristotelian realism explained; contrast with Platonism/Nominalism
• [08:50] Problems in modern education regarding necessity
• [10:27] How to perceive and “train in” necessity
• [13:18] Foundations of ethics in the worth of persons
• [14:46] Almsgiving, ethics, and duties to the poor
• [16:31] Mathematics versus relativism
• [20:12] Koenigsberg bridges and necessity in the real world
• [22:05] The brain, human understanding, and artificial intelligence
• [25:26] The proper teaching of mathematical proof
• [27:54] Neglect of relations (ratio, symmetry) in philosophy
• [31:01] Personal background and Catholic perspective
• [34:03] Logical probability versus Bayesian approaches in evidence
• [39:04] Mathematical necessities and the limits of divine power
• [40:53] Leibniz, God, and the possible worlds
• [42:47] Ethics as an abstract, universal science
• [46:08] Aristotelian science and the scientific revolution
• [48:17] Why knowledge of necessity has been lost; blame historicism, especially Hume
• [51:11] Final recommendation: return to Aristotle and Euclid

In Summary

Franklin’s work and this podcast episode synthesize the philosophy of mathematics, ethics, and probability into a framework asserting the existence and significance of absolute necessities in reality. Mathematics is not just about symbols or calculation but reveals universal, necessary truths about the world—truths that should serve as a model for thinking about ethics, logic, and scientific evidence. The episode calls for a renewed appreciation of necessity in human thought, education, and culture, and recommends a return to foundational sources like Aristotle and Euclid to rediscover lost intellectual virtues.