80. Scientific Hypothesis, Contradiction, and the Road to Knowledge

Subscribe in Podcast App | Download Transcript

Lecture Notes

Main Topics #

The Nature of Scientific Hypothesis #

• A hypothesis is freely imagined with no justification from what is already known
• Its only justification comes from the predictions it makes
• When predictions match observation—especially precise, unexpected observations—confidence increases, but the hypothesis remains a “tested guess,” not certain knowledge
• Einstein emphasizes that confirmation is not a syllogism: from “If A then B” and “B is so,” one cannot conclude “A is so”
• Historical example: Newton’s physics was so successful that when planetary orbits deviated, scientists predicted unknown planets rather than abandoning the theory. Later, Einstein’s theory predicted the same phenomena plus others Newton could not explain, showing Newton’s theory was ultimately provisional

The Problem of Apparent Contradiction #

• Following the senses often leads to apparent contradictions (e.g., “the healthy becomes sick,” “day becomes night”)
• Parmenides rejects the road from the senses, claiming it leads to the impossible contradiction of something being and not-being simultaneously
• Parmenides proposes instead the road from reason: the impossibility of contradiction in reality
• He calls those who accept apparent contradictions “two-headed mortals”—creatures that would require two heads to think contradictory thoughts
• Yet we commonly speak this way: “the good became bad,” implying genuine change

Aristotle’s Resolution: The Role of Accident #

• Aristotle accepts both the principle of non-contradiction AND the reality of change
• The key is distinguishing between what something is essentially (per se) and what happens accidentally (per accidens)
• Example: A cook who is also a pianist. The cook as such cooks; the pianist as such plays piano. But the cook happens to be a pianist, so we can say “a pianist cooks” without contradiction
• Similarly, the healthy as such does not become sick, but the body (to which health happens) becomes sick
• The subject of change is always the underlying thing (the body), not the quality itself
• This resolves Heraclitus’s apparent contradictions: there is no real contradiction because change occurs in the subject, not in the quality as such

Zeno’s Paradoxes and Infinite Divisibility #

• Zeno argues that traversing any finite distance requires passing through infinite points
• If each point requires some time, infinite points require infinite time
• Therefore, motion should be impossible
• Aristotle’s response (ad hominem): Even accepting Zeno’s assumption that a line consists of infinite points, time is divisible in exactly the same way as magnitude
• For every point on a finite line, there is a corresponding instant (now) in finite time
• Therefore, one can traverse infinite points in finite time
• The resolution depends on recognizing that time and magnitude are equally divisible or undivisible

The Hidden Harmony: How Contradictions Point to Truth #

• Apparent contradictions are not real contradictions in things but signs of something hidden in our understanding
• Heraclitus: “The hidden harmony is better than the apparent harmony”
• When reason encounters an apparent contradiction (e.g., light behaving as both particle and wave in modern physics), it signals that something remains to be discovered
• The untying of the apparent contradiction constitutes genuine discovery
• Modern examples: Quantum mechanics arose to resolve the contradiction between light’s wave and particle nature; string theory attempts to reconcile general relativity and quantum theory

The Limits of Scientific Method #

• Claude Bernard (biologist) naively assumes the scientific method is the only valid method of inquiry
• He distinguishes: scientists test ideas; philosophers deduce but never test; theologians merely posit ideas
• This misses that philosophy and theology operate by different principles than experimental science
• Modern scientists often make claims about ancient thinkers (Plato, Aristotle, Thomas Aquinas) without reading them, thus failing to apply their own experimental method consistently
• Warren Murray jokes about this: e.g., claiming the ancients thought there was a maximum speed in the universe, when Einstein first proposed this idea

Habit and Custom in Thinking #

• Those accustomed to the experimental method may assume all ideas are hypotheses requiring testing
• Custom can blind us to the existence of other kinds of knowledge (philosophical, theological, mathematical)
• This illustrates how habit shapes our view of what is knowable and how

Key Arguments #

The Ad Hominem Response to Zeno #

1. Zeno assumes: a finite line is composed of infinite points
2. Zeno concludes: traversing these points requires infinite time (absurd)
3. Aristotle grants the assumption but points out: time is divisible in the same way as magnitude
4. Therefore: for every point in a finite line, there is an instant in finite time
5. Conclusion: infinite points can be traversed in finite time without absurdity

The Accident Argument Resolving Contradiction #

1. Apparent contradiction: “X becomes not-X” (e.g., healthy becomes sick)
2. Analysis: This is not saying X as such becomes not-X, but that the subject of X becomes not-X
3. Resolution: When the cook plays piano, the cook is not as cook becoming pianist; rather, one who happens to be a cook is as a pianist playing
4. Similarly: The healthy (quality) does not become sick, but the body (subject to which health happens) becomes sick
5. No contradiction: The subject can bear opposite qualities in succession because the qualities are accidentally related to the subject

Important Definitions #

Hypothesis (ὑπόθεσις) #

• Freely imagined without justification from prior knowledge
• Justified only by the predictions it generates
• Remains a “tested guess” even after confirmation

Per Se vs. Per Accidens #

• Per se (in itself): what something is essentially
• Per accidens (accidentally): what happens to happen to something
• The cook as cook cooks; the pianist as pianist plays; but the cook happens to be a pianist

The Road from the Senses vs. The Road from Reason #

• Road from senses: Proceeds from observation but leads to apparent contradictions
• Road from reason: Proceeds from the impossibility of contradiction but seems to deny change
• Aristotle’s solution: These are not two roads but stages along one road; apparent contradictions in sense-data point to deeper truths discoverable by reason

Examples & Illustrations #

Dirac’s Prediction of the Positron #

• Dirac worked out Heisenberg’s theories mathematically
• From the mathematics emerged a prediction: a particle with the same mass as an electron but positive charge
• No one had observed such a particle
• Months or years later, the positron was discovered experimentally
• Illustrates how hypothesis leads to precise predictions of previously unknown facts

Newton’s Planets #

• Newtonian physics predicted planetary orbits with high precision
• Observations revealed small deviations from predictions
• Rather than abandon Newton, scientists hypothesized unknown planets
• Using Newton’s mathematics, they predicted where these planets would be
• Telescopes found the predicted planets, validating Newton’s theory
• Yet Einstein later showed Newton’s theory was incomplete

The Cook and Pianist #

• A cook is also a pianist
• The cook cooks dinner (per se as cook)
• The pianist plays piano (per se as pianist)
• We can say “a pianist cooked dinner” because the pianist happens to be a cook
• But the pianist as such (through the art of playing) does not cook, and the cook as such (through the art of cooking) does not play
• This illustrates how something can bear contrary properties without real contradiction

Light as Wave and Particle #

• 19th century: experiments showed light behaves as waves
• 1905: Einstein explained the photoelectric effect only by treating light as particles
• Modern physics: light exhibits both wave and particle properties (apparent contradiction)
• Quantum mechanics arose to reconcile this apparent contradiction
• Shows that hidden beneath apparent contradictions is deeper truth

Zeno’s Paradox: Leaving the Room #

• To leave the room, I must traverse a finite distance
• A finite distance contains infinite points (on Zeno’s assumption)
• To reach each point takes some time
• Infinite points would require infinite time
• Therefore, I can never leave the room
• Aristotle’s response: Time is divisible as magnitude is; infinite instants fit in finite time

Parmenides’ Two-Headed Mortals #

• Those who claim “day is night” seem to think opposite things simultaneously
• Would need one head to think day is day, another to think day is night
• But one head cannot hold contradictory thoughts
• Thus they speak like monsters (what is contra naturam)
• Yet we naturally speak of change, suggesting a resolution beyond mere denial

Notable Quotes #

“Being freely imagined, [the hypothesis’s] whole justification is what you might predict on the basis of it.” — Einstein, on the nature of scientific hypothesis

“After you confirm the scientific hypothesis, it remains a guess. It’s a tested guess, but you still don’t know it’s so.” — Einstein, on the limits of experimental confirmation

“The confirmation is not a syllogism. You’re saying, if A is so, B is so. B is so. It doesn’t fall into saying that A is so.” — Berquist, on the logical invalidity of confirming hypotheses by observing consequences

“The hidden harmony is better than the apparent harmony.” — Heraclitus, on how apparent contradictions point to deeper truth

“Men admire Hesiod…and he didn’t even know day and night. For there one [Heraclitus], because day becomes night and night becomes day.” — Heraclitus fragment, on the apparent contradiction of change

“We should not act and speak like those asleep.” — Heraclitus fragment, suggesting he distinguishes clearly between waking and sleeping despite speaking of their unity

“You need one head to think it is so, and another head to think it is not so. But one in the same head couldn’t think that both is and is not.” — Berquist, paraphrasing Parmenides on the impossibility of contradiction

Questions Addressed #

Can We Ever Know What Scientists Hypothesize? #

• Answer: Not with certainty. Even extensively confirmed hypotheses remain tested guesses. Confirmation does not logically entail truth because from “If A then B” and “B is true,” one cannot validly infer “A is true.”

How Can Apparent Contradictions in Experience Be Reconciled with the Principle of Non-Contradiction? #

• Answer: Apparent contradictions are not real contradictions in things but signs of something hidden. By distinguishing per se from per accidens, we see that the subject of change bears opposite qualities successively, not simultaneously. The quality as such does not become its opposite; the subject acquires a different quality.

How Can One Traverse Infinite Points in Finite Time (Zeno’s Paradox)? #

• Answer: Time is divisible in exactly the same way as magnitude. For every point on a finite line, there is a corresponding instant in finite time. One can traverse infinite divisible points in infinite divisible instants, both within finite bounds.

Why Do Modern Thinkers Deny the Principle of Non-Contradiction? #

• Answer: Because something seems to contradict it. But they unknowingly assume the principle in their very objection—they must assume it to even pose the contradiction. This shows they implicitly know it, though they deny it in words.

Is the Scientific Method the Only Valid Form of Inquiry? #

• Answer: No. Philosophy and theology operate by different principles. The error is to assume that custom in one domain exhausts all valid knowledge. Scientists often fail to apply their own experimental method when making claims about history (e.g., about ancient thinkers).