27. Axioms, First Principles, and the Central Question of Philosophy

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Lecture Notes

Main Topics #

The Problem of Investigating Axioms #

• Initial Objection: Axioms are obvious to everyone; why investigate what all people already know?
• Berquist’s Resolution: While axioms are universally known, people often hold confused rather than distinct knowledge of them
• Evidence: Some people deny axioms in words and give reasons most people cannot answer
• Conclusion: Investigation moves people from confused to distinct knowledge of axioms

The Equivocation on “Whole” and “Part” #

• Example: “The whole is greater than a part”
• Two Senses:
  • Composed whole: A whole put together from parts (man = animal + reason)
  • Universal whole: A universal predicated of particulars (animal includes dog, cat, horse)
• The Equivocation: Saying “animal is part of man” (in sense 1) but “animal is a whole of dog” (in sense 2) leads to the false conclusion that a part is greater than a whole
• Lesson: The word “more” has different meanings in each context; people don’t have completely distinct knowledge of the axiom until they see these distinctions

The Central Question of Philosophy #

The Question: Does truth require that the way we know be the way things are?

Plato’s Answer: Yes #

• We know mathematical things (like cube) in separation from sensible matter
• We know universals (like man) in separation from individual men
• If truth requires correspondence between knowing and being, then:
  • Mathematical objects must exist separately (mathematical world)
  • Universals must exist separately (world of forms)
• Result: Plato’s threefold ontology (sensible world, mathematical substances, forms)

Aristotle’s Answer: No #

• We can truly know things in separation from how they exist in reality
• Falsity comes only from attributing the order of our knowing to the order of things
• Examples of true knowledge in separation:
  • Eye knows whiteness of sugar without sweetness; tongue knows sweetness without whiteness—neither is false
  • We know cube in separation from wood, ice, or sugar—not false
  • We know a person as a philosopher without knowing he is a grandfather—not false
  • We know water before hydrogen (hydrogen named from water), though hydrogen is prior in nature—not false
• The key principle: “What you say about the thing has got to be with it” (falsity requires claiming separation where none exists)

Historical Trajectory of the Question #

• Most philosophers since Plato implicitly answer “yes,” though they reach different conclusions
• William of Ockham: No universals exist → universal knowledge impossible → skepticism
• Kant/Experimental Science: We know only by making → we know only what we make
• Hegel: Identifies most confused thought (being itself) with the divine principle → pantheism
• Spinoza: Order of thoughts = order of things
• Medieval Agreement: Boethius, Albert the Great, Thomas Aquinas, Arab philosophers all follow Aristotle on this question

The Question’s Centrality #

• The question unites truth (the end of philosophy) with the two subjects of philosophy:
  • The way things are (natural philosophy, political philosophy, wisdom)
  • The way we know (logic, epistemology)
• All philosophical investigation involves either knowing or being; this question connects them

Questions About Immaterial Substances (Third and Fourth Questions) #

• Are there immaterial substances besides sensible/material substances?
• If so, are there one kind or many?
• These questions are technically about things themselves, not about what wisdom is about, but they are “intertwined” because they affect what wisdom investigates
• Common opinion: “Whatever is must be somewhere” → only bodies exist (because we always imagine bodies)
• Evidence for immaterial substances in natural philosophy:
  1. Order in nature: The order in plants and animals (like order in houses) requires a cause; we know minds cause such order; therefore, a greater mind exists
  2. The human soul: Reason understands universals; understanding is an operation not dependent on matter; therefore the soul has an immaterial operation
  3. The definition example: Definition of square is discontinuous (genus and differences don’t share a boundary), yet square is continuous; reason knowing continuous thing discontinuously cannot itself be continuous; therefore reason is immaterial

Key Arguments #

The Argument for Investigating Axioms #

1. Axioms are known by all and obvious
2. Yet people sometimes deny axioms in words with reasons most cannot answer
3. When they deny them, they equivocate on the meanings of terms
4. Therefore, people have confused rather than distinct knowledge of axioms
5. Conclusion: Investigation of axioms is necessary for moving to distinct knowledge and refuting objections

The Aristotelian Refutation of Plato #

1. We can know things truly in separation from how they exist
2. Example: Sugar is white and sweet; eye knows whiteness without sweetness and is not false
3. Falsity occurs only when we claim things are separated that are not actually separable
4. Plato mistakenly identified the order of our knowing (universal before singular, mathematical before sensible) with the order of things
5. Conclusion: The way we know need not be the way things are; Plato’s multiplication of worlds (sensible, mathematical, forms) is unnecessary

The Argument for Immaterial Substances #

• The order in natural things (plants, animals) requires a cause of that order
• Such causes must themselves be immaterial minds (as we observe that material minds cause order in material things like houses)
• Therefore, immaterial substances exist

Important Definitions #

Axiom (ἀξίωμα) #

• A statement known by itself, obvious to all
• A beginning of all reasoned-out knowledge
• Example: “The whole is greater than a part”; “Nothing is before itself”; “The same cannot be affirmed and denied simultaneously”

Composed Whole (ὅλον κατὰ σύνθεσιν) #

• A whole put together from distinct parts
• Example: Man = animal (the body and soul as principles) + reason
• In this sense, “more” means put together for more than just one of its parts

Universal Whole (ὅλον κατὰ πρέδικατον) #

• A universal that is said of multiple particulars
• Example: Animal is a universal whole; it is said of dog, cat, horse
• In this sense, “more” means a universal is a set of more than any one of its subordinates

Separated/Immaterial Substance (οὐσία χωριστή) #

• Substance that exists independently of matter
• Examples: Anaxagoras’s greater mind, Plato’s forms and mathematical substances
• The question of whether such substances exist divides Plato (yes, many) from Aristotle (no, except possibly God)

Examples & Illustrations #

The Equivocation on Whole and Part #

• “Animal is part of man” (in definition: man = animal + reason)
• “Animal is a whole” (universally: animal is said of dog, cat, horse)
• Conclusion: “Part is greater than whole” (fallacy)
• Shows: The same words (whole, part, more) have different meanings in different contexts

Knowledge in Separation #

• Sugar example: White and sweet; eye knows whiteness without sweetness, tongue knows sweetness without whiteness; neither is false
• Cube example: We truly know cube in separation from wood, ice, sugar, plastic; not false
• Person example: Knowing Berquist as philosopher without knowing he is grandfather—not false, merely incomplete
• Water example: We know water before hydrogen (hydrogen is named from water), yet hydrogen is prior in nature; not false

The Immateriality of Reason #

• Definition of square: “equilateral and right-angled quadrilateral”
• Definition itself: discontinuous (genus and differences do not share a boundary)
• Square itself: continuous thing
• Conclusion: Reason knowing a continuous thing in a discontinuous way must itself be non-continuous and therefore immaterial

Questions Addressed #

Why investigate axioms if everyone knows them? #

Resolution: People have confused knowledge. Objectors equivocate on terms. Investigation moves toward distinct knowledge and enables refutation of objections.

What is the relationship between truth and the correspondence of knowing and being? #

Plato’s answer: Truth requires the way we know to be the way things are → multiple worlds (sensible, mathematical, forms) Aristotle’s answer: We can truly know things in separation from their mode of existence; falsity arises only from claiming separation where none exists → one world suffices

Are there immaterial substances besides material bodies? #

Evidence: (1) Order in nature requires a greater mind as cause; (2) Our reason understands universals without matter; (3) Reason’s discontinuous knowing of continuous things shows it is immaterial

Notable Quotes #

“You can’t equivocate on [axioms], and you can’t confuse people obviously. But then, you know, there are people who do object to them…” — Berquist, on why axioms must be investigated

“[People] think they don’t know what they do know.” — Berquist, explaining why investigation of axioms is necessary

“What you say about the thing has got to be with it.” — Aristotle (cited by Berquist), on the principle of falsity

“We can know in separation things that don’t exist in separation.” — Aristotle, on the non-correspondence of knowing and being

“More doesn’t have exactly the same meaning, does it?” — Berquist, showing equivocation on “more” in different senses of whole and part