1. Plato’s Allegory of the Cave.
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2. Plato’s Allegory of the Cave
Plato, Republic, Book VII, 514a-c to 521a-e)
Socrates: And now, I said, let me show in a figure how far our nature is enlightened or unenlightened :
"Behold ! , human beings living in a underground den, which has a mouth open towards the light and reaching all along the den.
Here they have been from their childhood, and have their legs and necks chained so that they cannot move, and can only see before them, being prevented by the chains from turning round their heads.”
Plato's Allegory of the cave, Engraving of Jan Saenredam ( ) after a painting of Cornelis Corneliszoon van Haarlem ( )

3. The allegory of the cave, 2
“Above and behind them a fire is blazing at a distance, and between the fire and the prisoners there is a raised way;
and you will see, if you look, a low wall built along the way, like the screen which marionette players have in front of them, over which they show the puppets.“
Glaucon: "I see".
"And do you see", I said, "men passing along the wall carrying all sorts of vessels, and statues and figures of animals made
of wood and stone and various materials, which appear over the wall ?
Some of them are talking, others silent.“

4. The allegory of the cave, 3
Glaucon: "You have shown me a strange image, and they are strange prisoners".
"Like ourselves", I replied.
"And they see only their own shadows, or the shadows of one another, which the fire throws on the opposite wall of the cave ?"
Glaucon: "True", he said. "How could they see anything but the shadows if they were never allowed to move their heads?"

5. The allegory of the cave, 4
And of the objects which are being carried in like manner they would only see the shadows?"
Glaucon: "Yes", he said.
"And if they were able to converse with one another, would they not suppose that they were naming what was actually before them?"
Glaucon: "Very true.“

6. The allegory of the cave, 5
"And suppose further that the prison had an echo which came from the other side… would they not be sure to fancy then one of the passers-by spoke that the voice which they heard came from the passing shadow ?" Glaucon: "No question", he replied. "To them", I said, "the truth would be literally nothing but the shadows of the images". Glaucon: "That is certain."

7. Plato’s Cave & Science
What does Plato’s Allegory of the Cave tell us about scientific reasoning?
We cannot observe “nature” directly, we only see its manifestations or images:
We are trapped in a world of immediate sensation;
Our senses routinely deceive us (they have error).
We cannot get outside our limited sensations to see the underlying “form” of nature

8. Plato’s Cave: constructs & samples
Plato’s Cave and Scientific Reasoning: Core limitations of our knowledge about the world.
Plato’s Cave: constructs & samples
1. Theories (knowledge structures) address hypothetical constructs…
We infer their forms

9. What is a hypothetical construct?
We cannot actually look in the brain and “see” learning.
What we can see are…
…changes in test scores
…faster / better performance
…changes in neuro-anatomy
…other measurable outcomes.
These are “operational definitions” of learning…

10. What is a hypothetical construct?
We cannot actually look in the brain and “see” learning.
What we can see are…
…changes in test scores
…faster / better performance
…changes in neuro-anatomy
…other measurable outcomes.
We infer that what we observe reflects the hypothetical construct “learning”
We make these observations while testing a hypothesis about what might cause learning.

11. Plato’s Cave: constructs & samples
Plato’s Cave and Scientific Reasoning: Core limitations of our knowledge about the world.
Plato’s Cave: constructs & samples
1. Theories (knowledge structures) address hypothetical constructs…
We infer their forms
2. We study samples of people & places, and try to generalize to the larger population

12. Plato’s Cave: Hypothetical constructs
1. We study hypothetical constructs; basic “operating principles” of nature.
e.g., evolution, gravity, learning, motivation…
Processes that we cannot “see” directly…
…that underlie events that we can observe.
We use rational analysis – theory – to deduce what the “form” of these processes must be, and how they work.

13. Why not observe directly?
Why can’t we just observe “nature” directly?
We can only observe the effects of hypothetical constructs, not the processes themselves.
Our theory helps us develop hypotheses about what we should observe if our theory is “correct”.
What is my hypothesis?

14. Constructs and hypotheses
Theory
(Hypothetical constructs)
Hypothesis: If
eye tracking & task time are higher
Then
scores & paper quality will be greater.
Attention
Learning
Operational Definitions
Eye tracking
Time on task
Quiz scores
Paper quality

15. Constructs and hypotheses
Theory
(Hypothetical constructs)
Hypothesis
Attention
Learning
Inference
Inference
Results
Eye tracking
Time on task
Quiz scores
Paper quality

16. Why not observe directly?
Why can’t we just observe “nature” directly?
We can only observe the effects of hypothetical constructs, not the processes themselves.
Our theory helps us develop hypotheses about what we should observe if our theory is “correct”.
We test our hypotheses to infer how nature works.
Our inferences contain error: we must estimate the probability that our results are due to “real” effects versus chance.
The link from hypothetical constructs to empirical evidence can be deductive (“top-down”) or inductive (“bottoms-up”).

17. The link between theory & data
Deductive:
We begin with a well articulated theory
…then to data collection:
Theory
Hypothetical Constructs
Not directly observed
Specific hypotheses
Research methods
(operational definitions)
Empirical observations
Deductive
Inductive
Inductive: we begin with empirical observations,
then:
formulate a theory that may account for them
develop further testable hypotheses
gather more data in a specific hypothesis-testing process .

18. 2. Theories are tested with samples, not the entire population.
Generalizability
2. Theories are tested with samples, not the entire population.
Just as we infer the hypothetical constructs underlying our observations, we infer how well those results generalize to:
The larger population our sample is drawn from
Other physical or social settings
Other conditions or forms of the Independent Variable
Other outcomes or forms of the Dependent Variable.
As with all inferences, our generalizing beyond the experiment is probabilistic and is subject to error.

19. Flash question: operational definition
What is an operational definition?
A general statement about how a variable works.
The specific procedures we use to manipulate or measure a variable.
A dictionary-like definition of a hypothetical construct.
Another expression for a hypothesis.

20. Flash question: operational definition
What is an operational definition?
A general statement about how a variable works.
The specific procedures we use to manipulate or measure a variable.
A dictionary-like definition of a hypothetical construct.
Another expression for a hypothesis.
No.
A theory is a general statement of how two or more variables “work” or are related to each other.

21. Flash question: operational definition
What is an operational definition?
A general statement about how a variable works.
The specific procedures we use to manipulate or measure a variable.
A dictionary-like definition of a hypothetical construct.
Another expression for a hypothesis.
Yes!
An operational definition takes our general construct and turns it into a specific variable that we can directly observe or assign numbers to.

22. Flash question: operational definition
There is one particular operational definition for any hypothetical construct.
True
False

23. Flash question: operational definition
There is one particular operational definition for any hypothetical construct.
True
False
No.
General constructs from behavioral or medical science, economics, even physical sciences – much less History or Literary Criticism - may be operationally defined in a variety of ways.
A Public Health researcher may operationally define “health disparity” in purely economic terms, as distance to health facilities, as care qualified by morbidity, and so one.
Social – behavioral constructs can often be operationalized either as experimental or measurement variables, a major distinction.

24. Flash question: operational definition
There is one particular operational definition for any hypothetical construct.
True
False
Yes.
The creativity of science lies in developing ways of manipulating or measuring abstract constructs such as learning, stress, or arousal.

25. Flash question: operational definition
A good operational definition corresponds exactly to the hypothetical construct we are studying.
True
False

26. Flash question: operational definition
A good operational definition corresponds exactly to the hypothetical construct we are studying.
True
False
No.
A hypothetical construct is a general principle or process – think about “economic contraction” – that we manipulate or measure in a particular way for any specific study.
Any particular way we assess “economic contraction” will not capture the concept perfectly.
This is the core point of the Plato’s Allegory of the Cave: we do not see the complete “form” of a process, we can see (manipulate, measure…) only the particular way it appears in our study…

27. Flash question: operational definition, 3
There is one particular operational definition for any hypothetical construct.
True
False
Yes!
Many hypothetical constructs are complex or have many aspects to them. No one study will capture all aspects of a complex construct, such as depression:
Verbal behavior
“vegetative”: sleep, eating
Depression
Appearance
Suicide, drug use, work…
Survey / questionnaire answers…

28. Plato’s Cave and scientific logic
Summary
Plato’s allegory of the cave can be taken as a metaphor for the “problem” of knowledge;
Processes that govern the natural world are not easy for us to see directly, and..
Almost invariably we are studying only a sample of the population we are interested in.
As a result, we must infer how nature works by:
Positing hypothetical constructs (the building blocks of a theory) that may explain natural processes
Gathering data and testing hypotheses to infer whether our theory is correct.
Gathering data requires that we operationally define our variables, by specifying measures or manipulations that express them.
All our observations and inferences are made with error: we never see the world perfectly clearly.