"Therefore … !" Proof or Spoof?

Sir, (a+bⁿ)/n = x, therefore God exists. Please respond! -- Euler to Diderot, 1773.

An Unlikely Story. In 1773 atheist philosopher Denis Diderot visited the Imperial Court at St. Petersburg to personally thank Empress Catherine for the patronage which was to spare him an impoverished old age. So that his often disconcerting though entertaining atheistic polemics not remain unremonished by his Christian hosts, it was arranged that he be present at a "mathematical" demonstration of the existence of God.

The mathematician Leonhard Euler was to make the initial statement in what was hoped would be another entertaining debate. Euler, addressing himself to Diderot, declared with a tone of perfect conviction, “Monsieur, (a+bⁿ)/n = x, donc Dieu existe; respondez!" Diderot, totally ignorant of mathematics (according to Dieudonné Thiébault as related to DeMorgan), was dumbfounded. Diderot was granted permission to return immediately to France.

Although this anecdote has become something of a legend, it ignores the fact that Diderot, himself, was quite a good mathematician. He would have easily recognized Euler’s assertion to be a non sequitur. The point here, of course, is not whether God exists or not. Rather it is whether reciting a mathematical formula proves God’s existence when it is connected with the word “therefore.” Does any statement, call it A, prove another statement, B, when we all we do is connect them with the word, “therefore”? For example, “Dogs are mammals; therefore, the moon is not made of green cheese?”

We would hardly deny that dogs being mammals has no connection to what the moon is made of. The Euler-Diderot story illustrates, however, what is to this day a common use of the word “therefore” -- or any of its many synonyms --: to foist off a nonsequitur on an unattentive or naïve audience.

The Many Synonyms of Therefore. Therefore connects a statement or body of statements (sometimes called “premises”) to a concluding statement, generally known as a “conclusion.” In contexts in which the word, therefore, would sound too high-falutin’, there are many other variations available: for example,

so
hence
in conclusion we must recognize that
consequently
it follows that
proves that
the weight of the evidence indicates that

But the most important thing for us to realize -- that which makes them most dangerous -- is that using any of these words or phrases to support possible conclusions rules out what may be real live options. Therefore and its family members insinuate that other possible considerations are not supported by the option already singled out by the therefores. (See An Introduction to Models of Reasoning)

Obscuring or Discarding Live Options. This is far more than a “mere” theoretical lesson. When, for example, we face a problem for which we are considering alternative solutions for decision, we must be on guard that the therefores of different partisan interests be more than attempts to intimidate or seduce us into acceptance of their special concerns. Intimidation and seduction need seldom be employed if everyone -- or a majority, at least -- can be convinced that the selected decision is adequately and reasonably supported.


To continue this train of thought see Rationales for Intervention: From Test to Treatment to Policy: A forensic theory of warrants & rebuttals


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--- EGR

Common Sense, or Merely Common Hubris?

edited120918

“Nothing is more fairly distributed than common sense: no one thinks he needs more of it than he already has.” ― René Descartes, Discourse on Method

Hume was on to something. John Locke had proposed that our senses responded to our experience by presenting sensations to the mind. The mind in turn worked to store these sensations as memories or to connect and then store these sensations as complex memories.

David Hume saw Locke’s theory as disabling the distinction between what we nowadays call “correlation” and “causation.” Our sensations are of events in our experience. All we can observe through our senses, even our senses amplified by instruments, are events. But we are in the habit of believing in cause and effect if one kind of event is consistently followed by events of another, different kind.

Indeed this tendency to connect one predecessor class of events to another following class gives rise to the fallacy of post hoc, ergo propter hoc, “after that, therefore because of that.” For example, people more often feel queasy after eating raw clams, than after eating zucchini; so, they think, "Raw clams cause queasiness more so than does zucchini.” (But what if people who eat raw clams stuff themselves more frequently than those who eat zucchini?}

Between correlated event-classes we do not observe an intermediate event, a causal nexus, as it is sometimes called, that helps us distinguish between causation and “mere” correlation. True. But there is another way to look at this.

Maintaining Cause and Effect. Immanuel Kant attempted a rescue by proposing that Locke had gotten it wrong. The Mind (in German, Verstand, translated both as “mind” and as “understanding,” -- not Seele, Gemüt, or Sinn also translatable as “mind”) does not merely make connections of sensation brought in through the senses. The Mind’s very structure tends to process correlative event classes as cause and effect. We can hardly help but understand -- at least initially -- repeated correlation as indicating cause. This theory has been found to be much more attractive in the US since the withering of radical Behaviorism in the later 20th Century. (See A Critical Review of B.F. Skinner's Philosophy )

However, invoking some logic, there is a more direct way of thinking about it. We can accept Hume, yet maintain the distinction between correlation and causation. Consider universal negatives, which are statements that propose that, at any place or at any time, something is not; or, that nothing is, a certain way or thing.

For example, “There are no such thing as dragons,” or, what is logically equivalent, “There are no dragons, anywhere, ever.” The issue here is not whether the claim of the non-existence of dragons is true or false; but, whether there is an observation we -- or beings like us, of limited breadth of experience in space and time -- can perform to establish it.

Note that it is easier to disprove a negative universal than to establish it. The find of one dragon disproves it. But despite a very, very large number of failures to find a dragon, any claim that they don’t exist is not proven by that failure. It was, in fact, widely believed in the 19th Century and earlier that there was no such thing as a black swan. There are, in Australia. Also, tomatoes were considered to be poisonous, e.g. there was no such thing as a tomato that could safely eaten by humans. We know differently.

Disproving "No Swans are Not White."

Reconsider the example given above about the relation of eating raw claims and queasiness. The very argument against its being causation demonstrates that we bring much more to such a causal claim than a narrow consideration of correlation: we consider possible alternatives, or intermediaries, standardly characterized as confounding or mediating variables. A host of assumptions and presuppositions supports our observational reports.(See Identifying Trans-ideological Epistemological Presuppositions)

The “Common Sense” of American (School) Reform. There is always the possibility of hidden, overlooked or disregarded causes or effects that undermine an assertion that one situation causes another. As many have discovered, an apparent “common-sense” causal relation can disappear under closer scrutiny due to confounding or mediating variables.

There are a host of causal myths involved with all sorts of reform efforts, in particular, American education, primary, secondary, and higher, be it public, private or parochial. For example:

Bad or insensitive teachers are the primary cause of failing students.

Students have learning styles. Teachers can teach to them, i.e. no child is unteachable.

College is a pure waste of time, i.e. nothing worth the cost is learned.

Today’s schools are in a position to forestall 21st Century employment problems.

(See References to Schooling Myths.)

Such “common sense” beliefs underlie the hubris that drives a great many of today’s school reform undertakings. Their prospect is to continue on in a century-long American tradition: the cavalier waste of mis-aimed scarce resources leading to reform failure.

To examine these and related issues at greater length, see Moral Responsibility in the Education Industry: 
how much can school reform enhance a student's occupational fitness?)


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--- EGR

Critical Thinking About “Critical Thinking”?

There are more than 16,000 school districts in the United States and nearly all of them say they teach critical thinking. Google “critical thinking” and “mission statement” and you will find page after page of heart-warming affirmations like this one from the Lordstown, Ohio School District: “We believe in the development of critical thinking skills.”

Commendable; but what would happen if critical thinking actually were effectively taught? Suppose the youngsters in Lordstown learned to truly, seriously and boldly scrutinize the nation’s customs, principles, and beliefs. Suppose they even learned to critically examine the authorities that most of us defer to in directing our lives and defining the good, the true, the beautiful? No doubt that they would be thinking critically. But would educators who facilitate this sort of inquiry receive hearty congratulations or have to flee a mob of angry, torch-wielding villagers?

Let’s be clear, by “critical thinking” we do not mean mere logic chopping. You know, the “these are the premises” and “this is a conclusion,” sort of thing that sometimes passes for critical thinking. That sort of thing is harmless because it rarely results in serious challenges to anything deeply believed.

No, by critical thinking we mean systematically reconsidering the deep assumptions that most of us take for granted. And we also include questioning authority — including sacred and semi-sacred source documents as well as those who interpret them. Thinking critically has to include this sort of thing or it is hardly critical.

To get kids thinking, for instance, educators could familiarize them with the well-known argument from evil. It maintains that a loving God would permit only as much physical suffering as is absolutely necessary to achieve the greater good. Yet the world is stuffed full of seemingly unnecessary misery. What, we could ask students, is one to make of this?

Is that one too religious for public school? Then how about a high school assignment such as this? “We are often told that the United States is the greatest nation on earth. Working together, decide what standards you think should be used to measure a nation’s greatness; then use those standards to compare the United States with other nations.

Some might argue that it isn't necessary to tackle such issues head on; that by teaching generic critical thinking methods learners will eventually bring these tools to bear on those deep assumptions and basic authorities that are central to their lives. But such transfer of learning cannot be relied upon. If we want young people to really think critically, we must provide them with direct and well-focused opportunities to do so. Just be prepared to find another job shortly thereafter.

T0 examine these issues further, see Additional Reflections on Critical Thinking)


Sincerely,

Gary K. Clabaugh, Ed. D.

Blocking Inquiry

Upon this first, and in one sense this sole, rule of reason, that in order to learn you must desire to learn, and in so desiring not be satisfied with what you already incline to think, there follows one corollary which itself deserves to be inscribed upon every wall of the city of philosophy: Do not block the way of inquiry.
-- C. S. Pierce (1889) The First Rule of Logic

But even in this, our Land of the Free, Of, For and By the People, blocking inquiry is seen as an indispensible technique to proper socialization, called “good citizenship.” And the basic rule of “good citizenship” is “Don’t question either this directive, or those who have (claim?) the authority to tell you what to do.” Little wonder that “critical thinking” is little more than an empty buzzword in the mouths of those who govern American educational institutions.

Of course, much lip service is given to the idea that education should nourish and encourage a child’s curiosity. But unspoken is the reality that such curiosity must be constrained within bounds whose existence is seldom acknowledged, much less subject to inquiry. For the sake of a “peaceful, orderly society.”

In fact, it is not only teachers, but parents, too, who breathe sighs of relief once they perceive that their children have given up on asking “Why?” and, instead, just pay if only very perfunctory obedience when told to do things.

Much money is wasted when people are given a costly education in which they don’t learn to tell when they are being given a runaround. Much of our formal education is flawed in this way. Even most higher education fails to give people a practical introduction to the many words, phrases and modes of speech used to dissuade us from asking potentially embarrassing questions.

So instead of explanations that might give insight and control to those who ask for them, they are offered terms, inquiry blockers, like “human nature,” “mystery,” “intuition,” “faith,” “feelings” and similar obscurities as “explanations” for many of the important problems they encounter. Such education aims not at empowerment and mastery, but obedience and resignation.

Students in higher education are subjected to myriad "introductory" courses that serve up buzzwords, seldom critically examined, like "market," "ecology," "transcendence," "power," "society" that they may sport as knowledge, even though very little if any practical application is acquired with them. (See Masks: words that hide agendas)

Even worse, the semi-literate condition a great number of people end up in after years of formal education cements their belief that any skills requiring careful attention to the fine points of writing or discourse are dispensible for everyday, practical activities, except for, perhaps, those of lawyers or college professors.

The sad irony is that there appears to be no small number of lawyers, college professors and other “professionals” for whom careful, critical use of language is as much a confused exercise as it is for the average guy-on-the-street. Politicians, advertisers and hucksters of salvation know this and rely on it to make their living.

To examine these issues further, see Inquiry Blockers


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--- EGR

Inverting Risk: misdescription for the sake of punditry.

The children involved with the Atlanta schools cheating scandal are “the victims of … massive fraud, the helpless pawns of adults who callously overlooked the needs of their charges and focused on preserving their careers.” -- C. Tucker, 4/10/13 Phila Inquirer, A18

Punditry tempts one to great (see) moral hazard. Once you have a newspaper column that guarantees an audience, you can, if you wish, sacrifice fact and logic for the sake of seducing sympathy for your latest enthusiasm. (Besides, getting to ride the high horse of moral superiority is so delightful!)

First, let’s give but short shrift to the likely false assumptions in Tucker’s diatribe:

a. Did any students or their parents, relatives etc. protest against the high scores announced before the “scandal” broke? (Not likely.)

b. Did the adults involved, i.e. school staff, “callously overlook the needs of their charges? (More likely they did so with trepidation and feelings of guilt. Educators are, to my taste, entirely too sensitive to what kids and their parents claim to want or need.)

c. Which “needs” is Tucker talking about? Is there much agreement as to what they are and which among them takes priority? (Disregarding slogans for the consumption of the ill-informed, the answer is NO. See The Need for and Possibilities of Educational Reform)

d. And, horrors! What kind of adults might overlook the “needs” of others (children included) and focus on preserving their careers? Not just teachers and principals and school superintendents; but, also, presidents, popes, preachers, corporate CEO’s, as well as you, me, members of Congress, definitely, and even pundits! (But see The Mea Culpa Culture in Public Education.)

Now that we are fatigued from wagging our fingers, let’s consider a deeper issue: the degradation of our natural sense of logic and experience by the persistent hammering in of emotional confusions.

By the time a normal child is ten years old, he or she has learned through experience the following three rules for survival:

Rule 1: A sure bet is definitely not the same as a distant possibility;

Rule 2: Sure bets are lower, much lower, risks than distant possibilities; from which follows

Rule 3: Avoid betting things you value on distant possibilities, unless the payoffs are proportionately (inversely) unequal, i.e. massive payoffs may be worth an increased risk, even though small or equal ones are not.

As the headmaster of a private, academic school, grades seven through twelve, I attempted to solicit financial support for our programs from corporations around the Philadelphia area. I was never successful in the face of the reasons given by almost every one of those who refused: “High school kids are too distant a prospect for us to bet on. Too much can happen before they get to us. We only contribute to programs for upper-class students in college, because we’ll see them presently.”

No dummies, they! They have retained their childhood knowledge of Rules 1-3 given above. They put their money on the surer bet.

But, in this cruel world we live in, who in their right mind -- unless well-endowed (or a hopelessly optimistic educator) -- makes a bet on the future prospects of a school kid at the much surer risk of destroying their career? That is, discarding a career they have poured much time, sweat and money into, along with the pension they cannot recover through new employment? Tucker seems to think this would have been the reasonable option for the educators involved.

“Reasonable” for educators, but not a newspaper columnist, I am sure.

For references and to examine these issues further, see Illogic and Dissimulation in School Reform


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--- EGR

Critical Thinking: weapon, or tool for self-development?

updated 8/5/20

"He who asks a question is a fool for five minutes; he who does not ask a question remains a fool forever." - Chinese Proverb

One of the most persistent suggestions for curing what ails American education at all levels is to help students develop "critical thinking." Everywhere, you find people complaining that college graduates don't know how to think critically. Neither do younger students.

But why is critical thinking often praised but seldom implemented in the schools? There are four important reasons. This first is that, in casual conversation, “critical” implies nasty, often disrespectful, mocking evaluation and complaint. Parents don't want to have their kids coming home even better equipped to do what many are already too inclined to. And they certainly don’t want it applied to what they, as adults, esteem.

Secondly, critical thinking is conceived of, by many people, as little more than a weapon. Parents only want weapons pointed at the things and people they disapprove of. Many would sooner trust their kids with firearms. You can’t destroy Faith with a bullet; but you can sure weaken it with critical reflection. So it is that critical thinking is shunned if it focusses back on one’s families’ own beliefs and values.

The third reason why it is not taught is that it is not sufficiently emphasized that, in order to avoid indoctrination, all reasoning in critical thinking classes, is hypothetical. It examines what connections among thoughts might exist. It need not take the additional step of advocating action. People outside of schools tend to be, or pretend to be, action oriented. To think something is to act on it. Teachers -- indeed instructors at all levels of education -- often overstep the boundary here and try to surreptitiously press students to act, rather than let those students reflect on whether they have good, personal grounds for action.

But messages here are mixed. Parents, and social leaders, want teachers to get their students to act in ways those higher-ups approve of. The incessant worry about values education reflects this. But teachers who get kids to act, no matter how morally and rationally, in ways their superiors find discomforting, are liable to criticism, even dismissal.

The forth and final reason is that critical thinking instruction is seldom thought of by non-educators as teaching how to "get down to facts" or "uncover basic values.” (See Authority, Fact & Value). Assuring that indoctrination will be avoided, critical thinking skills could be seen as even more important when applied to things we value. For example, most people when they want to sell their house, overprice it and try to show it to prospective buyers full of the memorabilia that makes it a home for them, the present owners. They don’t see the faults and don’t consider that piles of books, souvenirs and pillows they personally find comforting and homey, are likely to be just junk in the eyes of a prospective buyer.

Suppose you, the seller, were buying a house. What would you be concerned about? The age of the roof? A wet basement? Termite or mold damage? Make a list of questions. Now ask yourself what the answers might be for this beloved domicile, this home you are putting up for … sacrifice, er… sale? Don’t make excuses or cover-ups. An astute buyer wouldn’t. Use critical thinking methods to guide your actions. If you won’t, a good real estate agent will.

The practice of systemizing and standardizing questioning has long been followed in many occupations, especially, the law. Sets of broad, standardized questions are called “Interrogatories.” Many kinds of legal activity, for example, require that interrogatories be completed, before time is spent by specialists in judicial proceedings.

Here is a hypothetical example for educators: suppose we were considering whether to incorporate computer literacy into a class on printmaking. Important questions in developing an interrogatory might be:

1. Is there a consensus among specialists in both printmaking (and computer literacy) as to what pertinent knowledge computer literacy offers?
2. Do the students already have that knowledge?
3. If they already "know" computer literacy, in some sense, is it in a form they can use?
4. Will computer literacy enhance their skills as practitioners in printmaking ?
5. Will computer literacy enhance their performance in those many activities that support printmaking as an enterprise, e.g. academically or vocationally?

Notice that merely to answer these questions does not automatically commit you to the change, or even, to resisting the change.
(For more on this see Evaluating Proposed Program Expansion)


A useful, non-formal approach to critical thinking is to get familiar with formulating and using interrogatories. For example of interrogatories and their applications, see Developing Interrogatories to Aid Analysis, 
Problem-Solving and Conflict Resolution


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--- EGR

Avoiding Controversy: a survival necessity?

What’s the connection?

1. Students, particularly (shockingly,) college students, do not learn, or learn well, critical thinking skills; (NYT)
2. High school teachers do not teach, or teach well, Evolution; (NYT)
3. College students are seldom invited to examine the assumptions on which their professor’s course material is based; particularly, not graduate students.

Exceptions are more likely found in religious colleges than in public ones. Why is this?

Here are some possible answers:

a. the teachers or professors don’t know their subject matter.
b. Students, who don’t know how to handle controversy, evaluate their professors for promotion and tenure.
c. Professors have not studied formal logic.
d. Neither students nor professors know how to reason well on their feet.

Let’s dismiss a and c as unlikely. This is not a matter of knowing something, but of being able to teach it, especially, if it provokes debate. Merely studying formal logic does not help here.

Option b is close to the matter. Evolution and other controversial items are perceived by students to threaten their “sacred values.” They strongly dislike the apparent threat. They get their revenge by giving their instructors low ratings. (I have noticed during my 17+ years as a college professor that the same person, teaching a basically “technical” course would get higher ratings from his or her students than in a course where controversial material was dealt with.)

Option d is crucial. Teaching, if it is a face-to-face encounter requires either suppressing questioning, or having argumentative (or debate) skills to use. Except in religious environments where boundaries are clear – you still risk skating on thin ice --, secular, pluralistic schools and universities have disregarded argumentative and debate skills so long that few now command them to the degree they can be used for teaching purposes.

More than once have I heard professors at professional conferences declare that “There are, without exception, no absolute truths.” When asked about the truth of that very statement, which if true, is false, they shrugged it off with the retort, “You’re just playing word games.”

To examine these issues further, and avoid intellectual lobotomy, see An Introduction to Models of Reasoning


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--- EGR

Mental Meringue: conjecture as educational theory

edited 5/21/20

Two groups (among others) abet the destruction of our public schools as educational systems: boards of education and professional educators .

Board members -- pursuing megalomaniac visions and frequently not understanding what it takes to run a real school with real warm bodies in it -- are too often ready to sell out to any political interest that assures them continuity of office.

Professional educators -- through their formal and in-service education -- have been so stuffed with flatulent conjecture, minimally substantiated, often contradictory, sketches of theory, mental fluff that passes for science, that they cannot deal effectively with simple organizational and classroom problems.

Undisciplined conjecture, expanded through leaps of logic and magnified by fear or fervent hope generates the bulk of topics of discussion not only in Education, but also in the world at large.

Public schools, especially, are vulnerable to political meddling, to intrusions by ideologues of all kinds, for whom conjecture is a way of life, so long as others bear its consequences.

To examine these issues further, see Conjecture Pollution: Poisoning Educational Practice


-- EGR