9. The Central Question of Philosophy: Knowledge and Reality

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Lecture Notes

Main Topics #

Aristotle’s Solution: Reason and Sign #

Aristotle grounds his solution in two sources:

• The Reason: Drawn from the definitions that underlie geometry and natural philosophy

  • Geometric definitions (sphere, cube) contain no reference to matter or motion
  • Natural philosophy definitions necessarily involve matter and motion
  • Since definitions are foundational to reasoned-out knowledge, the way a science defines its objects determines its scope

• The Sign: Taken from mathematical sciences of nature

  • When mathematics is applied to nature, the need for application proves separation
  • Example: Before application, mathematics exists independently
  • Historical cases: Kepler applied conic sections to planetary orbits; Einstein applied Riemann’s mathematics to relativity
  • Often the mathematician has no knowledge of future applications

The Central Question of Philosophy #

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

Two Possible Answers:

• Yes (Plato): If we truly know something, it must exist in the way we know it
• No (Aristotle): We can know things truly in a different way than they are

Plato’s Position and Its Consequences #

Plato answers “yes” to the central question and combines this with:

1. The premise that we have genuine truth in geometry
2. The observation that geometry knows objects in separation from sensible matter
3. The premise that definitions give us truth
4. The observation that definitions know universals in separation from singulars

Consequence: Since we truly know cubes and spheres in separation from matter, they must exist in separation from matter. Since we truly know universals in separation from singulars, universals must exist in separation. Therefore, there must be a mathematical world and a world of forms.

Plato’s method of knowing involves turning the soul away from the material world through mathematical study toward immaterial realities.

Aristotle’s Counter-Position #

Aristotle denies that answering “yes” to the central question is necessary. His key insight:

• We can know things in separation without falsity if they are knowable in separation
• The falsity comes only if we claim they exist in separation
• Separation in thought (abstraction) is not the same as separation in reality

The Critical Principle: “There’s no falsity in understanding in separation things that don’t exist in separation if they are knowable one independently of the other.”

Historical Divergences Following the Central Question #

William Ockham (14th century):

• Answers “yes” to the central question
• Agrees with Aristotle that universals don’t exist in separation from singulars
• Conclusion: We cannot know universals because they don’t exist in separation, yet all our sciences know universals in separation
• Result: Universal skepticism spreads through universities—students learn nothing

Spinoza:

• Answers “yes” to the central question
• Claim: “The order in ideas and the order in things is the same”
• Consequence: The order of thought must be the order of reality

Hegel:

• Most full-blown rationalist position
• Answers “yes” to the central question
• Takes the most general and most confused idea of the human mind (being itself)
• Makes this correspond to the beginning of reality

Kant:

• Answers “yes” to the central question but sees the way we know is not the way things are
• Conclusion: We don’t know things in themselves (noumena remain unknown)

Key Arguments #

Knowing in Separation Without Falsity #

Aristotle establishes that separation in thought does not entail separation in reality:

1. The Philosopher and Grandfather Example (from Thomas Aquinas’s explanation):

   • A student knows the teacher as a philosopher without knowing he is a grandfather
   • A nurse knows the teacher as a grandfather without knowing he is a philosopher
   • Both know truly; neither is mistaken
   • The knowledge is incomplete but not false
   • Falsity would come only if one claimed “this philosopher is not a grandfather”

2. Properties of Sugar:

   • Taste knows sweetness without whiteness
   • Eyes know whiteness without sweetness
   • Both are true; knowledge is incomplete but not false
   • Falsity would come only if we claimed sweetness exists without color

3. The Cube Example:

   • Geometry knows the shape (cube) without wood, plastic, ice, etc.
   • No falsity in understanding cube-ness without any particular matter
   • Falsity would come only if we claimed the cube exists outside all matter
   • The shape is knowable without matter even though all actual cubes have matter

4. Universals and Singulars:

   • We can know what humans have in common (universal “man”) without knowing individual differences
   • The universal is knowable in separation from the singulars
   • But this doesn’t mean the universal exists in separation from all singulars
   • Falsity would come only if we claimed “man exists without any individual humans”

Order of Knowledge vs. Order of Being #

We can know things in a different order than they come to be without being mistaken:

• We know children before we know their parents, yet parents came before children
• We typically know effects before causes, yet causes come before effects
• The reversal of order in knowledge does not involve falsity
• Falsity would come only if we claimed the order of knowledge is the order of being
• Example: Sherlock Holmes must “reason back” from effect to cause; this is valid reasoning, not false knowledge

Important Definitions #

Nature (φύσις): A beginning and cause of motion or change and rest in that which it is, first as such, not by happening

Mathematical Object: Something considered in separation from sensible matter and motion

Natural Object: Something considered insofar as it exists in matter and motion

Abstraction (ἀφαίρεσις): The mental separation of things that don’t exist in separation

Truth: The agreement (ἀδύναμις) of the mind with things; conformity of mind to reality

Central Question: The question that brings together how we know and how things are, converging upon the end of philosophy, which is truth

Examples & Illustrations #

The Envelope and Stamp #

• An envelope with a built-in stamp requires no application
• An envelope with a separate stamp requires application to attach it
• The Point: The need to apply the stamp shows it was separate before application
• Applied to Mathematics: The need to apply mathematics to nature shows that in mathematics, these things are separated from nature
• If mathematics were already part of nature, application would be unnecessary

Physical vs. Geometric Properties #

• Lead Balloon: Would fall when released (has weight)

• Helium Balloon: Would rise when released (lighter than air)

• Geometric Sphere: Neither rises nor falls; it is neither heavy nor light

  • Falsity would occur only if we claimed the geometric sphere exists this way
  • But knowing it in separation from weight involves no falsity

• Ice Cube: Has a melting point (around 0°C)

• Wooden Cube: Burns at a certain temperature

• Geometric Cube: Has no melting point or burning point

  • Again, knowing the cube in separation involves no falsity

• Rubber Ball: Bounces when thrown against a wall

• Glass Ball: Shatters when thrown against a wall

• Steel Ball: Penetrates or dents the wall

• Geometric Sphere: None of these apply; it’s knowable without these properties

The Snubbed Nose #

Aristotle’s classical example:

• Geometry: Knows “curve” abstracted from flesh and cartilage
• Natural Philosophy: Knows “snubbed nose” as a curve in matter
• Both are true; they consider the same thing differently
• The difference is the mode of considering, not falsity in either

Questions Addressed #

Can we know mathematical objects truly if they don’t exist in separation from matter? #

Resolution: Yes. We can know things in separation without falsity if they are knowable in separation. The falsity comes only if we claim they exist in separation. Knowing incompletely (leaving aside some aspects) is not the same as knowing falsely.

Does the order in which we know things have to match the order in which things come to be? #

Resolution: No. We can know effects before causes, universals before singulars, and still know truly. The order of knowledge can be the reverse of the order of being without falsity. Falsity comes only if we claim the order of knowledge is the order of being.

Why did Plato posit a world of forms separate from the sensible world? #

Resolution: Because he answered “yes” to the central question and observed that we know mathematical objects and universals in separation from matter and singulars. To preserve truth, he concluded these must exist in separation. His premises are sound, but his answer to the central question is what leads to the forms.

Why does William Ockham conclude we know nothing? #

Resolution: Because he answers “yes” to the central question but agrees with Aristotle that universals don’t exist in separation from singulars. This creates a logical bind: we know universals in separation, but universals don’t exist in separation, so we don’t know the way things are, so we don’t have truth. The result is universal skepticism.

Why is application of mathematics to nature a sign that mathematics is separated? #

Resolution: Because application requires taking something external (mathematics) and fitting it to something else (nature). If mathematics were already internal to nature, no application would be needed. The very fact that we must go and get mathematics and then apply it proves it was separate from nature to begin with.

Notable Quotes #

“For they are separated in thought from motion. And it makes no difference, nor does a falsehood come to be in those separating.” — Aristotle

“There’s no falsity in understanding in separation things that don’t exist in separation if they are knowable one independently of the other.” — Aristotle (as explained by Berquist)

“You wouldn’t have to apply it if it was in the thing to begin with.” — Berquist, on why application of mathematics is a sign of separation