Basic Scientific ReasoningBasic Scientific Reasoning

4/25/2007

What is Science?What is Science?Astrology

Psychoanalysis

Physics

Psychophysics

Mathematics

Phrenology

Biology

Psychology

Scientology

Economics

Cognitive Science

Chemistry

Sociology

History

Cognitive Ethology

Defining ScienceDefining Science

• Is science defined by its method of reasoning?– Its results?– The phenomena it studies?– An attitude towards evidence?– A certain methodology?– Scientists?– The power relationships in which it is embedded?– Its value to the larger culture?– Use of (grounding on) mathematics?

Why should I care?Why should I care?

• ‘Science says that…’ ‘The top scientists think that…’

• States that have (or are) debated teaching creationism in elementary science education (2002-present):– Georgia– Kentucky– Kansas– Dover, Pennsylvania– Maryland– The President

A DemonstrationA Demonstration

• So how does ‘real’ science work?• 2-4-6 problem

Preliminary Lessons from Preliminary Lessons from 2-4-62-4-6

1. Science is an activity of real people who work in a social environment

2. There is nothing ‘special’ about the methods of reasoning used in science

3. When scientists ‘converge’ on the answer is often determined by social factors.

Structures of Reasoning Structures of Reasoning on display in 2-4-6on display in 2-4-6

Verification - Affirming the consequent:IF P THEN QQTHEREFORE, P

Example:IF aliens killed JFK, THEN there would be questions

regarding the ‘single-shooter’ theory.

There are questions regarding the ‘single-shooter’ theory.

THEREFORE, aliens killed JFK.

VerificationVerificationIF the rule is ‘Any three numbers such that x

< y < z’, THEN 2-4-6 will fit.2-4-6 does fitTHEREFORE, the rule is ‘Any three numbers

such that x < y < z’

IF the rule is ‘Any three numbers (x, y, z > 0) such that y = x+2 and z = y+2’, THEN 2-4-6 will fit.

2-4-6 does fit.THEREFORE, the rule is ‘Any three numbers (x, y, z

> 0) such that y = x+2 and z = y+2’

Verification’s ProblemsVerification’s Problems

• Can’t ensure the truth of the theory that entails the verified prediction

• Can’t distinguish between two theories that both entail the verified prediction

Structures of Reasoning Structures of Reasoning on display in 2-4-6on display in 2-4-6

Falsification - Modus Tollens:IF P THEN QNOT-QTHEREFORE, NOT-P

Example:IF aliens killed JFK, THEN Jack Ruby is an alien.

Jack Ruby is NOT an alien.

THEREFORE, aliens did NOT kill JFK.

FalsificationFalsificationApplication to 2-4-6:

IF the rule is ‘any three numbers (x,y,z) such that x > y < z’, THEN the sequence ‘4-2-8’ will fit.

The sequence 4-2-8 does NOT fit.THEREFORE, the rule is NOT ‘any three numbers

(x,y,z) such that x > y < z’

IF the rule is ‘any three symbols (x,y,z) such that x < y < z in their standard order’, THEN the sequence ‘a-b-c’ will fit.

The sequence a-b-c does NOT fit.THEREFORE, the rule is NOT ‘any three symbols

(x,y,z) such that x < y < z in their standard order’

Falsification’s Virtues & Falsification’s Virtues & VicesVices

• Still can’t ensure the truth of the theory that entails the verified prediction

• CAN distinguish between two theories, so long as there is at least one prediction that is entailed by one & NOT by the other.

The DN Model of The DN Model of ExplanationExplanation

• Explanations are sound arguments (valid w/ true premises) that entail the event to be explained.

L1, L2, … Ln

F1, F2, … Fn

E

Explanans

Explanandum

Laws (usually conditionals)Facts

Phenomenon Explained

ExampleExample

• Explanations are sound arguments (valid w/ true premises) that entail the event to be explained.

For all cases, if you stimulate the L cone, the subject experiences a sensation of red.

My L cone is stimulated

Therefore, I have a sensation of red.

Explanans

Explanandum

H-DH-D

• Notice the relation to falsification’s H-D method:

For all cases, if you stimulate the L cone, the subject will experience a sensation of red. I am not experience red

Therefore, my cone is not stimulated

Explanans

Explanandum

Notice also that all explanandi are potential predictions!

Real scientists don’t work that way.

Quine-Duhem ThesisQuine-Duhem Thesis

Any hypothesis can be defended in light of any evidence. (if you’re willing to make “drastic enough adjustments elsewhere” in your system of beliefs.)

IF Hypothesis is true, THEN Prediction.

Prediction is NOT true

THEREFORE, the hypothesis is NOT true

VALID

DogmatismDogmatism

Any proposition can be made consistent with any scientific theory, if one tries hard enough– Gender, Intelligence, Variability and

Pre- and Post-Darwin Biology– Myths of Gender by Anne Fausto-

Sterling

Here, the Devil lurksHere, the Devil lurks

IF my Hypothesis is true,

Prediction is NOT true

THEREFORE, at least one of (1) – (N) is NOT true

(1) AND My apparatus works,

(2) AND My experiment is correctly designed,

(3) AND My subject is of interest to others, …

THEN, prediction.

(N) AND ….

Summary: Biases creep:Summary: Biases creep:

1. Shifting categories2. Ambiguous measurements will

reveal prejudices (artifacts of instruments)

3. Failure to consider alternative hypotheses (I.e. body size / gender)

4. Miscalculations (confirmation bais)

(Brief) History of Color (Brief) History of Color ScienceScience

Basic Schema:

Hermann von HelmholtzHermann von Helmholtz(1821-1894)(1821-1894)

Short = Purple Middle = Green Long = Red

Historical Note:Historical Note:• In 1877, Ladd-Franklin became the first woman

to attend (albeit unofficially) Johns Hopkins where she studied mathematics.

• She wrote a dissertation under the supervision of C.S. Pierce. It was published in 1883, but her Ph.D. was not awarded until 1926!

• Even though she had studied under Helmholtz and had published a great deal in psychological journals, she was never admitted to the American Psychological Association meetings to present her papers.

• While she lectured at John Hopkins, Columbia, Clark, Harvard and Chicago, she never held an official academic post, and she was rarely paid.

• Her book Color and Color Theories was finally published in 1929, one year before her death.

Ladd-Franklin (1847-1930)Ladd-Franklin (1847-1930)IF stimulating the long-wavelength cone yields a red experience, and stimulating the middle-wavelength cone yields a green experience, THEN stimulating both the long and middle-wavelength cone would….

yield an experience of reddish-green

L-F’s argument (L-F’s argument (≈≈1892)1892)

IF stimulating the long-wavelength cone yields a red experience, and stimulating the middle-wavelength cone yields a green experience, THEN stimulating both the long and middle-wavelength cone would yield an experience of reddish-green

Stimulating L and M yields an experience of yellow.

THEREFORE, Helmholtz’s theory is NOT true

Yellow does NOT look like reddish-green.

THEREFORE, yellow is NOT reddish-green.

Good Argument Right?

Why not?Why not?“Helmholtz deemed it illegitimate or at least

untrustworthy to draw conclusions as to physiological processes from the direct psychological character of the sensations”-Von Kries

Q-D for HelmholtzQ-D for Helmholtz

IF stimulating the Long-wavelength cone yeilds a red experience, and stimulating the middle-wavelength cone yields a green experience, THEN stimulating both the Long and Middle-wavelength cone would yield an experience of reddish-green

Stimulating L and M yields an experience of yellow.

THEREFORE, Helmholtz’s theory is NOT true

THEREFORE, Yellow is NOT reddish-green.

Yellow does NOT look like reddish-green.

BUT: One cannot draw conclusions about the physiology of color from this fact, so it does not follow that:

yellow is not reddish-green or greenish-red.

Note:Note:

The Gestalt Psychologist David Katz made the phenomenology of color appearance the starting point for a theory of color (1908).

Vindication:Vindication:In 1957, Dorothea Jameson & Dale

Hurvich proposed what is now called the ‘opponent-processing’ model of color perception. According to it, colors are given by mixing 4 primary colors which are arranged in opponent pairs:Red GreenBlue Yellow

This is now the dominant theory in color science

VindicationVindicationPerformed by Jameson and Hurvich in 1957. A test light is shown to a subject. If the light appears greenish, a red-appearing light is added until the test light no longer appears at all greenish.

Jameson and Hurvich Jameson and Hurvich ResultsResults

Cone Sensitivity CurvesCone Sensitivity Curves

Mathematical Transformation Mathematical Transformation of Cone Sensitivity Functionsof Cone Sensitivity Functions

• We decorrelate the responses of the L, M and S cones by weighting each signal with a constant, and combining those results:

C1() = 1.0L() + 0.0M() + 0.0S()

C2() = -0.59L() + 0.80M() + -0.12S()

C3() = -0.34L() + -0.11M() + 0.93S()

Opponent Processing Opponent Processing ModelModel

Falsification (finally)Falsification (finally)• In 1977, Edwin Land produced a

falsification:The particular relationship between the stimulus of the L, M and S cones is both NECESSARY and SUFFICIENT for determining a particular color sensation. (Given trichromatic perceivers and normal conditions)

Helmholtz

(sufficiency) Produce a case where two objects stimulate the L, M and S cones in exactly the same way, but produce two different color sensations(necessity) Produce a case where two objects stimulate the L, M and S cones in different ways, yet produce the same color sensation.

Two falsifications required:

MondriansMondrians

5.8 (L)3.2 (M)1.6 (S)

These values held for red, green and blue patches, yet the patches still appeared red, green and blue!

5.8 (L)3.2 (M)1.6 (S)

Tristimulus values Tristimulus values sufficient for color sufficient for color

appearanceappearanceAccording to the Helmholtz theory, IF objects reflect the same tristimulus values, THEN they will appear to be the same color.

A patch in the first Mondrian reflects the tristimulus values of 5.8(L), 3.2 (M) and 1.6 (S), yet looks red.A patch in the second Mondrian reflects the tristimulus values of 5.8(L), 3.2 (M) and 1.6 (S), yet looks blue.

(from 1) IF the Helmholtz theory is correct, THEN the patch in the first Mondrian will appear to be the same color as the patch in the second Mondrian.They do NOT appear to be the same color.

THEREFORE, the Helmholtz theory is NOT correct.

Tristimulus values Tristimulus values necessary for color necessary for color

appearanceappearanceAccording to the Helmholtz theory, IF two objects appear to be the same color, THEN they will reflect the same tristimulus values.

Before Land turned the projectors on, the red patch looks red.

After Land turned the projectors on, the red patch looks red.

(from 1) IF the Helmholtz theory is correct, THEN the patch that continues to look red must reflect the same tristimulus values when the projectors are on & off.

The patch that continues to look red does NOT reflect the same tristimulus values when the projectors are on as it does when they are off.

THEREFORE, the Helmholtz theory is NOT correct.

Helmholtz’ responseHelmholtz’ response(from 1) IF the Helmholtz theory is correct, THEN the patch that continues to look red must reflect the same tristimulus values when the projectors are on & off.

The patch looks red w/ the projector OFF and it reflects tristimulus values x, y, z

THEREFORE, the Helmholtz theory is NOT correct.

The patch looks red w/ the projector ON and it reflects tristimulus values a, b, c

BUT: One cannot draw conclusions about the physiology of color from this fact, so…

The patch looks red w/ the projectors OFF, but it is really isn’t. (or vice versa)

TimelineTimeline

1856: Helmholtz proposes his theory

1892: Christine Ladd-Franklin formulates her argument.

1957: Theory change following Jameson & Hurvich

1977: Land’s Falsification

64 years! 20 years

1908: Gestalts.

Why Theory Change?Why Theory Change?

• New Technology (Galileo's Telescope)

• Socio-cultural factors (Ladd-Franklin)

• Mathematics (Jameson & Hurvich)

Alternatives for Alternatives for DemarcationDemarcation

1. Verification2. Falsification3. Lakatos’ ‘Progressive v.

Degenerative’4. Sociological factors5. Explanation in terms of

mechanism.