Introduction to Options
Critical thinking concerns the processes by which we make decisions, and the most basic decisions are made between two choices. We can better understand the consequences of the choices we make, and learn to make better choices, by employing the concepts of critical thinking.
Making a choice involves the apparently simple operation of either affirming one possibility (saying "yes" to it), or denying another (saying "no" to it). Creating a string of such choices, however, can quickly get complicated, and such a binary string ("yes-yes-no-no-no-yes") is actually the basis for computerized computations, where the options are usually expressed as zeros and ones ("110001"). If we go a little further, and establish relations between the choices using conjunctions and disjunctions, we have created a Boolean string: "a and b or (c and not d)."
Let's say you are visiting Avshi, who offers you the use of a car.
Avshi might ask, "Do you want the red car or not?" In this case,
you have been given two options: red or not red. Driving the blue car is
part of "not red," but so is declining both cars. If you are seen driving
"red" (that is, when "red" is true), the implication is that you have not
chosen "not red," and if you are seen driving anything but "red," the
implication is that you have not chosen "red." When you have only two
options, both of which cannot be true and both of which cannot be false,
you are faced with contradictions, or contradictory choices.Avshi might also ask, "Do you want the red car or the blue car first?"
Since "first" makes it clear that the "or" here is exclusive (for more on
this, see the "And" and "Or"
Introduction), you have been given three options: "red," "blue," and
"neither." In this case, if you are seen driving "red" (that is, if "red"
is true), the implication is that you have not chosen "blue" or "neither."
But the implication of "not red" isn't as clear: we can't conclude that you
have chosen "blue" because "neither" is also an option. When you
have two options ("red" and "blue"), and a third option that neither of the
first two are true ("neither"), you are faced with contraries, or contrary
choices.And someone else might ask, "Which car or cars are you going to drive
while you are here?" Now you have four different options: "red," "blue,"
"both," and "neither." In this case, if you are seen driving "red," we can't
determine whether you might also drive "blue" at another time, because "both"
is an option; and if you aren't driving "red," we can't conclude whether
you have chosen "blue," because "neither" is an option. When you
have two options ("red' and "blue"), and two more options (that "both" of
the first two are true, and that "neither" of the first two is true), then
you are faced with open or unrestricted choices.As you can see, those three questions have very different implications. We can summarize the three different possibilities for an option between two things as follows:
Contradictions: both cannot be
true, and both cannot be false.Contraries: both cannot be true,
but both can be false.Choices: both can be true, and both
can be false.In confronting options, then, your job is first to determine whether you are dealing with a contradiction, a contrary, or an open choice, and then to understand the consequences of that.
Example 1. My options are A or B, and I choose "not B." What can you conclude about "A"?
If A and B are contradictories, you can
conclude that "A" is true.If A and B are contraries or open choices, you cannot conclude anything,
because either "A" is true or "neither A nor B" is true.Example 2. My options are A or B. I have chosen "A." You can only conclude that "not B" is true if you know that A and B are either contradictory or contrary.
Example 3. My options are A or B. I have chosen "not A." You can only conclude that "B" is true if A and B are contradictory. If they are contrary or open choices, "neither" is a possibility.
Note: In common speech, words paired as "opposites" are sometimes contradictories and sometimes contraries. Often, this is determined by the context. "Night" and "day," for example, may be understood as contradictory if "night" is the time between sunset and sunrise, and "day" between sunrise and sunset. On the other hand, if "twilight" is recognized as a time that is neither "night" nor "day," then they are only contrary. We usually accept "male" and "female" as contradictory for humans, but contraries or just choices for other kinds of animals, like snails, some of which are asexual or hermaphroditic. In fact, there is always a range of definitions, depending on the context the terms are used: for gender identities, from physical appearance to genetic composition; for "night" and "day," from the common to the meteorological and astronomical. The only way to be sure that two terms are contradictory, therefore, is to use the "A and not-A" format. Thus, "night" and "not-night" are certainly contradictory, whatever "night" and "day" may be. (And even here, common usage may undermine the meanings. Many people, for example, assume that not everyone falls into the categories of the "haves" and the "have nots.")
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Exercises for "Options"
1. Which of the following pairs is contradictory?
2. Which of the following pairs is contrary?
3. Which of the following pairs is not contradictory?
4. Which of the following pairs is not contrary?
5. Physicists assume that, in any given system,if there is no light, then it is dark; and it has to be one or the other. In physics, then, what are "light" and "dark"?
1. Which of the following pairs is contradictory?
You answered:
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rich and poor
The rule for contradictory pairs is that both cannot be true, and both cannot be false, at the same time. Though someone cannot be both rich and poor at once, he or she can be neither. So, "rich and poor" are contraries.
1. Which of the following pairs is contradictory?
You answered:
-
left and right
The rule for contradictory pairs is that both cannot be true, and both cannot be false, at the same time. If you had in mind "arms" or "legs" when you answered right and left, you might have a point. For humans, at least, an arm must be either right or left, and cannot be both. But in the more general sense, "right and left" are contraries, because there are other options like "middle."
1. Which of the following pairs is contradictory?
You answered:
-
present and absent
The rule for contradictory pairs is that both cannot be true, and both cannot be false, at the same time. Something cannot be both present and absent at the same time, but it must be one or the other.
You answered:
-
early and late
The rule for contradictory pairs is that both cannot be true, and both cannot be false, at the same time. Early and late are contraries. A bus cannot be simultaneously "early and late," but it can be neither of these, by being "on time."
2. Which of the following pairs is contrary?
You answered:
-
good and bad
Good and bad are contraries, because both cannot be true, but both can be false. The last movie you saw cannot have been both good and bad at the same time, but it might have been neither by being "average"--as in "one thumb up," or "two stars."
2. Which of the following pairs is contrary?
You answered:
-
good and not good
Good and not good are contradictory: everything must be one or the other, because "not good" includes everything that is not "good."
2. Which of the following pairs is contrary?
You answered:
-
good and not bad
Good and not bad are open choices. Since "not bad" includes "good," something (for example, a movie) can be both.
2. Which of the following pairs is contrary?
You answered:
-
good and ready
Good and ready are choices: you can be one, or the other, or both, or neither. In contraries and contradictories, "both" is impossible.
3. Which of the following pairs is not contradictory?
You answered:
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literate and illiterate
Literate and illiterate are contradictories. The suffix here, "il-," means "not," and so this is equivalent to "A and not-A," the paradigm of a contradiction.
3. Which of the following pairs is not contradictory?
You answered:
-
perfect and imperfect
Perfect and imperfect are contradictories. The suffix here, "im-," means "not," and so this is equivalent to "A and not-A," the paradigm of a contradiction.
3. Which of the following pairs is not contradictory?
You answered:
-
explored and unexplored
explored and unexplored are contradictories. The suffix here, "un-," means "not," and so this is equivalent to "A and not-A," the paradigm of a contradiction.
3. Which of the following pairs is not contradictory?
You answered:
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well-known and unknown
Well-known and unknown are not contradictory, because someone or something can be neither. I've driven to Santa Barbara before, so the way is not unknown to me, but it was years ago, so I can't say the way is well-known, either. These are contraries, since both cannot be true.
4. Which of the following pairs is not contrary?
You answered:
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tall and short
Tall and short are contraries. Both cannot be true at the same time, but they both might be false. Sujata, for example, may be of average height.
4. Which of the following pairs is not contrary?
You answered:
-
young and restless
Young and restless are not contraries, because a person could be both and, in contraries, both cannot be true.
4. Which of the following pairs is not contrary?
You answered:
-
happy and sad
Happy and sad are contraries. Both cannot be true at the same time, but they both might be false. Sujata, for example, may have an even disposition, neither happy nor sad.
4. Which of the following pairs is not contrary?
You answered:
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here and there
Here and there are contraries. Both cannot be true at the same time, but they both might be false. Sujata, for example, may be at home, which is neither "here" nor "there" but somewhere else.
5. Physicists assume that, in any given system,if there is no light, then it is dark; and it has to be one or the other. In physics, then, what are "light" and "dark"?
You answered:
-
Contradictions
In this case, light and dark are contradictory, because "it has to be one or the other," meaning that both cannot be simultaneously true, and both cannot be simultaneously false.
5. Physicists assume that, in any given system,if there is no light, then it is dark; and it has to be one or the other. In physics, then, what are "light" and "dark"?
You answered:
-
Contraries
If light and dark were contraries, both could be false. But you were told, "it has to be one or the other," meaning that both cannot be simultaneously false.
5. Physicists assume that, in any given system,if there is no light, then it is dark; and it has to be one or the other. In physics, then, what are "light" and "dark"?
You answered:
-
Choices
If light and dark were simply choices, both could be false and both could be true. But you were told, "it has to be one or the other," meaning that both cannot be simultaneously true, and both cannot be simultaneously false.
6. Physicists assume that, in any given system, if there is no light, then it is dark; and it has to be one or the other. In physics, then, if a system is "not dark," what must it be?
7. Nguyen is choosing whether to listen to jazz or rock music. Assuming "jazz" and "rock" are contraries here, what are his options?
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He can listen to jazz only, or to rock only.
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He can listen to jazz only, to rock only, to both, or to neither.
8. Trying to remember the colors of a dress, Cathy has narrowed it down to two options: blue and green. She knows that if blue is correct, then green cannot be, and if green is correct, then blue cannot be. In this case, therefore, blue and green are:
9. According to a news report, the senator contradicted her former position when she said that a flat tax would benefit the middle class. What must her former position have been, to create a contradiction?
10. Contrary to Kim's expectations, the critical thinking class was completely full. Assuming this case is indeed one of "contraries," what might Kim's expectations have been?
6. Physicists assume that, in any given system, if there is no light, then it is dark; and it has to be one or the other. In physics, then, if a system is "not dark," what must it be?
You answered:
-
Light
It must be light. As we saw in Question 5, light and dark here are contradictory, meaning that "light" is "not dark," and "dark" is "not light."
6. Physicists assume that, in any given system, if there is no light, then it is dark; and it has to be one or the other. In physics, then, if a system is "not dark," what must it be?
You answered:
-
Light and Dark
As we saw in Question 5, light and dark here are contradictory, meaning that "light" is "not dark," and "dark" is "not light."
6. Physicists assume that, in any given system, if there is no light, then it is dark; and it has to be one or the other. In physics, then, if a system is "not dark," what must it be?
You answered:
-
Neither
As we saw in Question 5, light and dark here are contradictory, meaning that "light" is "not dark," and "dark" is "not light."
7. Nguyen is choosing whether to listen to jazz or rock music. Assuming "jazz" and "rock" are contraries here, what are his options?
You answered:
-
He can listen to jazz only, or to rock only.
Jazz or rock only (but not "both" or "neither") would be contradictory
7. Nguyen is choosing whether to listen to jazz or rock music. Assuming "jazz" and "rock" are contraries here, what are his options?
You answered:
-
He can listen to jazz only, to rock only, or to neither.
In contraries, either or neither can be true, but not both. So either jazz, or rock, or neither would be contrary.
v
7. Nguyen is choosing whether to listen
to jazz or rock music. Assuming "jazz" and "rock" are contraries here,
what are his options?
You answered:
-
He can listen to jazz only, to rock only, to both, or to neither.
Jazz or rock or both or neither would be an unrestricted choice.
8. Trying to remember the colors of a dress, Cathy has narrowed it down to two options: blue and green. She knows that if blue is correct, then green cannot be, and if green is correct, then blue cannot be. In this case, therefore, blue and green are:
You answered:
-
contradictory only
All we know is that blue and green both cannot be true. Whether they both can be false is not clear. To put it another way, if blue is not correct, can we conclude that green is? If so, blue and green are contradictory. If not, they are contrary. But we are not given that information.
8. Trying to remember the colors of a dress, Cathy has narrowed it down to two options: blue and green. She knows that if blue is correct, then green cannot be, and if green is correct, then blue cannot be. In this case, therefore, blue and green are:
You answered:
-
contrary only
All we know is that blue and green both cannot be true. Whether they both can be false is not clear. To put it another way, if blue is not correct, can we conclude that green is? If so, blue and green are contradictory. If not, they are contrary. But we are not given that information.
8. Trying to remember the colors of a dress, Cathy has narrowed it down to two options: blue and green. She knows that if blue is correct, then green cannot be, and if green is correct, then blue cannot be. In this case, therefore, blue and green are:
You answered:
-
either contradictory or contrary
Either contradictory or contrary, because all we know is that blue and green both cannot be true. Whether they both can be false is not clear. To put it another way, if blue is not correct, can we conclude that green is? If so, blue and green are contradictory. If not, they are contrary. But we are not given that information.
9. According to a news report, the senator contradicted her former position when she said that a flat tax would benefit the middle class. What must her former position have been, to create a contradiction?
You answered:
-
That a flat tax would benefit the wealthy.
Saying that it would benefit the rich and benefit the middle class is neither contradictory nor contrary because they both can be true. So these are just unrestricted choices.
9. According to a news report, the senator contradicted her former position when she said that a flat tax would benefit the middle class. What must her former position have been, to create a contradiction?
You answered:
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That a flat tax would not benefit anyone.
It would be only contrary if her position had been that it did not benefit anyone. Though these cannot both be true--that it benefits no one and that it benefits the middle class--they both can be false: it could benefit only the rich, for example.
9. According to a news report, the senator contradicted her former position when she said that a flat tax would benefit the middle class. What must her former position have been, to create a contradiction?
You answered:
-
That a flat tax would benefit everyone.
Saying that it would benefit everyone and benefit the middle class is neither contradictory nor contrary. For example, since the middle class is part of "everyone," these both can be true. And if "everyone" does not benefit, they are both false. So these are just unrestricted choices.
9. According to a news report, the senator contradicted her former position when she said that a flat tax would benefit the middle class. What must her former position have been, to create a contradiction?
You answered:
-
That a flat tax would not benefit the middle class.
Since contradictions follow the form, "A and not-A," this contradiction is "benefit the middle class" and "not benefit the middle class."
10. Contrary to Kim's expectations, the critical thinking class was completely full. Assuming this case is indeed one of "contraries," what might Kim's expectations have been?
You answered:
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The critical thinking class was not completely full.
"Completely full" and "not completely full" are contradictory, fitting the form of "A and not-A."
10. Contrary to Kim's expectations, the critical thinking class was completely full. Assuming this case is indeed one of "contraries," what might Kim's expectations have been?
You answered:
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The critical thinking class was popular.
And if a class is popular, it might also be "completely full" (both), so this is simply a choice.
10. Contrary to Kim's expectations, the critical thinking class was completely full. Assuming this case is indeed one of "contraries," what might Kim's expectations have been?
You answered:
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The critical thinking class was completely empty.
"Not completely full" would mean that there was at least one seat open. And there would be "at least one seat open" in a class that was completely empty, so that would be the contrary. Notice, therefore, that when we say things like "contrary to her expectations," we may not be using the word "contrary" accurately.
10. Contrary to Kim's expectations, the critical thinking class was completely full. Assuming this case is indeed one of "contraries," what might Kim's expectations have been?
You answered:
-
The critical thinking class was not completely empty.
If something is not completely empty, it might be "completely full," which would make these both true; and "empty" would then be neither, so they are unrestricted choices.
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