BELIEF: AN OWNER’S MANUAL
ARTICLE 9
A CLOSER LOOK AT AMBIGUITY
PART 2: PRECISE BELIEFS
As noted in Article 5, beliefs can be thought of as falling into four categories: precise beliefs, imprecise beliefs, rules of thumb, and catalytic narratives. Some beliefs fit these categories imperfectly, but I think you’ll find these categories work well enough for our purposes.
In the interest of keeping things simple, let’s restrict ourselves, at first, to exploring the effects of ambiguity on informative beliefs.
CHARACTERISTICS OF PRECISE BELIEFS
Precise beliefs provide believers with explicit guidance about the nature of reality and how to achieve their goals. In some ways, precise beliefs resemble the findings of the physical sciences. Some precise beliefs make explicit claims regarding relationships between phenomena, often written in mathematical form and including an “equals sign” (e.g., F=ma; E=mc²; pV=K). Other precise beliefs predict statistical distributions of outcomes.
Precise beliefs can also take the form of
- predictions that those who make observations under well-defined circumstances will witness well-specified phenomena (from tables of material properties to candy–sugar syrup temperature charts)
- convictions regarding the effectiveness with which well-specified procedures, undertaken under well-specified circumstances, will achieve well-specified outcomes
- facts – claims that, while not always directly observable, provide data that can be used to generate specific, precise predictions
- theories – claims that, while not directly observable, provide conceptual frameworks that enable believers to generate specific, precise predictions
Precise beliefs are consistent with only a narrow range of observations. To illustrate this point, let’s imagine a belief that can be expressed by a linear equation (say, something like F=ma). And let’s imagine that our measuring equipment and procedures are imperfect, so that, in practice, the belief’s predictions incorporate a modest margin of error. Under these conditions, only the small percentage of observations that fall close to the nominal prediction will be consistent with the belief. Observations that fall outside that range will raise doubts about the belief.
In addition to precisely specifying the nature of presumably related phenomena and the conditions under which predicted relationships hold, precise beliefs incorporate second-order precepts that encourage believers to repeat tests with greater precision when more sensitive instruments or exacting procedures become available.
The second-order precepts associated with precise beliefs also encourage believers to communicate belief-relevant data and experiences, even if those data and experiences raise questions about the belief’s validity. Furthermore, such second-order precepts encourage or, in many cases, require believers to acknowledge and grapple with the implications of challenging arguments and data. Finally, those precepts encourage believers to test (rather than uncritically accept) suggested explanations for predictive failures.
As such, if a precise belief is wrong, its second-order precepts inspire believers to discover, acknowledge, and communicate its failings. Yet, despite the discipline imposed by the nature of precise beliefs’ predictions and second-order precepts, advocates of precise beliefs (like scientists) are often less than evenhanded when faced with challenges to beliefs they treasure.
In sum, precise beliefs are highly unambiguous. They’re consistent with narrow ranges of observations. And their second-order precepts encourage believers to acknowledge and discuss challenging results and to view attempts to explain the challenges they raise with a critical eye. This combination of characteristics makes it easy for believers to discover that their erroneous beliefs are erroneous. And it enhances the objective significance of confirmatory data.
Newton’s Universal Law of Gravitation has been both the beneficiary and victim of those characteristics and precepts. The precision with which Newton’s Universal Law of Gravitation predicted planetary motion led to the discovery of Neptune on September 23, 1846. Predictions made using Newton’s law led 19th-century astronomers to view the motion of Uranus as inconsistent with their (7-planet) model of the solar system and inspired Urbain Le Verrier, a French mathematician, to propose that an additional planet could account for the Uranus’ motion. Using Newton’s laws, Le Verrier calculated the mass and position of that hypothesized planet and sent its anticipated coordinates to the German astronomer Johann Gottfried Galle. Galle found Neptune – within one degree of the position Le Verrier predicted – the night he received Le Verrier’s letter. The discovery of Neptune was widely considered a triumph of scientific astronomy and a compelling verification of Newton’s Universal Law of Gravitation.
Ironically, that same precision later led to the refutation of Newton’s view of gravitation in favor of Einstein’s. For Newton, space was an absolute, unmoving reference in which events occurred, neither affecting nor affected by whatever might happen within it. Similarly, time, for Newton, was absolute and immutable. By contrast, General Relativity described space and time as inextricably interwoven and subject to warping by mass and energy. What Newton attributed to gravitational attraction, Einstein attributed to the effects of mass and energy on spacetime.
While most of the predictions generated by Newton’s and Einstein’s equations were indistinguishable to the measurement tools of the early 20th century, their predictions about gravitational lensing differed significantly. Gravitational lensing occurs when a large amount of matter lies between a distant light source and an observer, altering the path of the light roughly as a lens would. While both classical (Newtonian) mechanics and Einstein’s General Theory of Relativity predicted gravitational lensing, classical mechanics predicted half the effect that relativity did. On May 29, 1919, a solar eclipse off the east coast of Africa made it possible to measure shifts in the apparent positions of stars whose light passed close to the sun. Those measurements, made by Sir Arthur Eddington on the island of Principe, clearly supported Einstein’s model rather than Newton’s, making Einstein an instant celebrity and contributing to the acceptance of General Relativity – rather than Newton’s conception – as the best explanation for such phenomena as motion and force.
HOW TO DETERMINE WHETHER YOU VIEW A BELIEF AS PRECISE
If you rely on a belief to tell you what’s going to happen, how to achieve your goals, or to provide an easily falsified framework that helps you explain events, you’re treating that belief as if it were precise.
EXERCISE 9
DETERMINING WHETHER BELIEFS
ARE APPROPRIATELY CLASSIFIED AS “PRECISE”
1. Refer to the list of beliefs you generated during Exercise 7A. If that list isn’t readily available, identify one or two beliefs that guide you in each of the areas below, for a total of about ten. Keep a record of those beliefs, many of which you’ll be examining in exercises to follow. Suggested areas from which to draw beliefs are:
• where you find joy
• where you find meaning and purpose
• your view of others – especially those whose views differ from your own
• your personal life
• your vocational/professional life
• advice/guidance you offer others
• political positions you advocate
2. Choose three or more beliefs you rely on for guidance and are interested in examining. Using the questionnaire found in Exercise 7A, determine whether those beliefs are informative or reassuring.
3. Print the appropriate number of copies of the tool below.
4. Write each belief in the space containing the sentence stem, “I believe that . . .”.
5. Keeping the pertinent belief in mind, answer each of the questions in “A Tool to Help You Determine Whether a Belief is Properly Classified as ‘Precise’”
6. Note that beliefs are properly classified as precise only if they satisfy all of the major criteria specified by the tool.
7. Record any thoughts, feelings, or questions that arise during this exercise in the space provided.
A TOOL TO HELP YOU DETERMINE WHETHER A BELIEF IS PROPERLY CLASSIFIED AS “PRECISE”
Belief to be examined: I BELIEVE THAT . . .
To determine whether the belief in question is “precise,” determine whether that belief satisfies criteria 1), 2) and 3), i.e., whether the belief
1) satisfies criterion a), b), c), or d), i.e., whether it
a) makes a clear and precise claim (whether definite or statistical) about relationships between phenomena and specifies the circumstances under which the alleged relations occur
b) predicts that well-specified procedures, undertaken under well-specified circumstances, will achieve well-specified (definite or statistical) outcomes
c) predicts that those who make observations under well-defined circumstances will witness precisely (definitely- or statistically-) specified phenomena
d) provides data and/or concepts that enable believers to generate specific, precise predictions
2) satisfies criteria e) and f), i.e., whether it incorporates second-order precepts that encourage believers to
e) seek, generate, acknowledge, and honestly grapple with challenging arguments and data
f) thoroughly assess suggested explanations for predictive failures
3) satisfies criterion g) and/or criterion h), i.e., whether it incorporates second-order precepts that encourage believers to
g) subject the belief to increasingly challenging tests as more sensitive instruments or exacting procedures become available
h) communicate belief-relevant data and experiences, even if they raise questions about the validity of the belief
What thoughts, feelings, or questions arose during this exercise?