Part 6: Reasoning
Now, to the crux of critical thinking -- Reason. Simply put, reasoning is the process of inferring conclusions from premises. These premises can be evidence in any of the forms we examined previously, or they can be intermediate conclusions based on this evidence. We say that a conclusion has a degree of cogency based directly on the combination of the premises and the reasoning. This is somewhat different from syllogistic logic, but it is absolutely dependent on it. In critical thinking, we can examine questions which may not have syllogistic certainty, essentially using syllogisms to form strong premises, and then using other statements with a high degree of cogency to link them together in what we can rightly call a proof.
There is a continuum on which we can place certainty, probability, and possibility, and correlate them with truth and falsehood. It can be illustrated like this:
Absolute Truth -----------------------------------------------------------------------------------Scintilla of Truth
As I said, this is a continuum, not a set of boxes. There is only one box in this continuum, and that is the far left end of the spectrum, absolute truth or certainty. An absolute truth is one for which there is incontrovertible evidence, or a statement which has no other alternative and so must be true. If you are familiar with syllogistic logic, you realize that things that are axiomatic are certain. Also, syllogistic logic produces certainty with regard to its own validity, since every proposition within logic is derived directly and with certainty from axioms. In critical thinking, we seldom deal with certainties of this type. If they are certain, there is, after all, no question to be asked!
Beyond certainty, we deal with the nebulous concepts of probability, plausibility, and possibility, and we can say that there are relative degrees of each. Probability requires a high degree of likelihood, or a very high degree of cogency. Just as the word implies, something that is probable is not certain, but it is always at least >50% likely. Plausibility is the next step down, and carries very little weight in debate or in critical thinking. Someone seeking to establish the truth of a statement should be seeking to add more cogency to his argument if it is only plausible.
A brief side note about plausibility: It is possible that a debate could be about the plausibility of a concept. This is perfectly acceptable, but a good critical thinker will realize that in order to win the debate, the positive claimant must provide at least a good probability that a concept is plausible! Plausibility is virtually never good enough to carry an idea in a debate, and the good critical thinker should never base individual decisions simply on the plausibility of an idea.
Possibility is correlated with the lowest degree of cogency, and is, of course, the least reliable. A possibility generally has only weak evidence and limited or flawed proofs. It is important to remember that virtually anything you can conceive of is possible in the broadest sense of the word. If we think about our day to day lives, we realize that possibilities very seldom concern us, nor should they. Every time you get into a car, there is a possibility that you will die. It is highly unlikely, but it is a very real possibility. As the highway usage statistics clearly point out, we are generally not concerned with the possibility that driving in a car will lead to our deaths. Each time we eat sushi, there is a possibility that we will get food poisoning, but we still eat it. Food poisoning can possibly lead to death, but sushi restaurants are open all over the world, despite the possibility that raw or undercooked foods are carrying parasites or bacteria not found in cooked food. When we examine the concept objectively, we realize that in day to day life as well as in critical decision making and formal debate, possibility is not really worth considering in most cases.
Induction and Deduction
Leaving aside the particulars of some rather abstract arguments against both induction and deduction which have been covered in other book pages, we will work with the standard definitions, avoiding the descent into pedantic wordplay that often deflects arguments away from the unavoidable realities of day to day life. Induction, for our purpose, is moving from a proposition to a conclusion where the results are not certain, but are highly cogent. A telltale sign of induction is moving from particulars to generalizations.
Every time I have let go of a ball, it has dropped.
Every time anyone lets go of a ball, it drops.
This is moving from a known particular to an uncertain, but highly likely generalization. Inductive arguments are highly susceptible to errors, and should always be examined closely, since they are not as systematically testable as deductive statements. For instance:
A tuna is a fish.
A tuna has one eye on each side of its head.
A flounder is also a fish
Therefore, a flounder has one eye on each side of its head.
Later, when we examine logical fallacies, we will learn more about the specific errors in the previous example, but for now, it is enough that we can see the potential pitfalls inherent in inductive logic.
Following are a few examples of induction as we might see it in day to day life:
X:Y in a sample.
Therefore, X:Y in the population.
"60% of Americans doubt the veracity of evolution, based on a poll of 2000 random Americans."
X in population Y has probability Z
Therefore, individual A in population Y has Z probability of X.
"80% of Republicans are Christian. Bob, a Republican, is 80% likely to be a Christian."
A is similar to B.
A has attribute X.
Therefore, B has attribute X.
"That antique bottle looks very similar to one I saw in a museum. I'll bet it has a stamp on the bottom just like that one."
A has happened X% of the time in the past.
A will happen X% of the time in the future.
"Bob is almost always an angry drunk. He's drinking now, so he'll probably be angry in a little while."
There are other categories of induction, but this essay is not intended as a complete course in logic. The primary goal is that the critical thinker will be able to recognize the telltale signs of induction, most notably its reliance on a high degree of certainty based on similar or previous observations.
Deduction is the kind of reasoning associated with syllogistic logic. Deduction is the process of deriving necessary conclusions from premises. When no other conclusion is possible, you are using deduction. It's important to note that deduction involves two very different concepts -- validity and truth. In a proper deductive argument, 100% of the conclusions will be valid. That is to say, a deductive argument is valid if it cannot possibly have all true premises and a false conclusion. Truth is a trickier concept, and this is where induction and deduction often meet. In the real world of critical thinking, almost all decisions are based on a combination of deduction and induction. To the logician, this might cause justified consternation, but the reality for virtually everybody else is that we rely on induction as if many things were absolutely certain because they are so probable as to discount the remote possibility that they are not true.
A very important concept in the understanding of deduction is that of an axiom. An axiom is a statement that is self-evidently true, and exists without the need for a proof. The reason that this is possible is that axioms are proven true through something called retortion. The simplest way to explain it is to say that a question which must rely on that which it is questioning is true through retortion. The most famous example, of course, is the question of whether or not I exist. To ask the question of existence is to rely on the fact of my own existence. So, in a sense, the retortion is the proof, even though it is not considered a proof in the logical sense. It simply is, because there is no other alternative. To make a very long and complicated story short, deductive logic (syllogism) is derived from axioms, and so their conclusions must be valid. Each step of the way, the premises are necessitated by the previous premises, all the way back to an axiom.
The following is an example of a simple deductive argument:
All bachelors are unmarried.
Tom is a bachelor.
Therefore, Tom is unmarried.
As you can see, there is no possibility of anything except Tom being unmarried. By definition, a bachelor is unmarried, so the first statement is guaranteed to be true. Once we know for certain that Tom is a bachelor, there is no way that he can be anything except unmarried, since he is a member of the group "bachelors."
This is one of the hallmarks of deductive logic, and is essentially the mirror image of induction. When we take a known quantity of a group and then isolate a member, we are using deduction. Moving from generalizations to specifics is typical of deduction.
This presentation is woefully lacking in depth, but again, the purpose is to recognize the differences in types of reasoning, not to give the reader a thorough understanding of the intricacies of formal logic. At this point, we will move beyond the two types of reasoning and examine more real world tests of reasoning.
REASONING BY EXAMPLE
This is a very common, and largely inductive style of reasoning that everyone uses on a regular basis. Essentially, this is where we examine a number of individual cases and arrive at a conclusion based on the consistency of evidence between cases. "Each time I have purchased avocados, the squeeze test has proven effective for determining the quality of the avocados. Therefore, I feel certain that today when I go to the store, I can employ the squeeze test, and will purchase high quality avocados as a result." While the language is a bit forced, the logic is properly stated. In fact, in the same moment that we make the decision of which test to use, we might also reach the following conclusion: "In the past, if I have squeezed three or four of the avocados in a bin, and they have all been good quality. It stands to reason that today, I only need to squeeze three or four before determining the quality of most or all of the avocados in the bin."
This silly little example shows how we use different types of reasoning intuitively, and almost without any thought. In deciding to squeeze a couple of avocados before buying several, we have induced that a number of cases (our past experience) is sufficient evidence to believe that today's shopping trip will be comparable. We have also induced that testing a sample will give us accurate knowledge of the group. So, we have actually made two important decisions by inductive reasoning. If we were to get really nit-picky about it, we could list hundreds, perhaps even thousands, of induced truths, down to the most mundane conclusions, such as whether or not the grocery store will even be in the same place it was last time we went shopping!
Now, how did we subconsciously test our hypothesis that we can squeeze a few avocados to test the group?
1. Relevance: Any set of cases from which we are going to reach a conclusion must be relevant to the conclusion we are seeking.
2. Pool Size: How many cases do we have from which to judge? Are there enough examples to allow for the reasonable expectation of consistency?
3. Time Period: Are the examples from a time period which is relevant and up to date?
4. Are the examples typical and sufficiently random? Have we eliminated the possibility of artificially tainting the pool by our selection methods?
5. Are negative examples non-critical? In other words, if there have been times when the test did not work, are there sufficient reasons why we can say there is minimal possibility that the test will not work this time?
With a little imagination, you can ask each of those questions of the avocado testing, and see again that these questions are not necessarily consciously asked, but the conditions have indeed been satisfied. Even though it is unconscious most of the time, it's important for us to realize that when we are consciously trying to arrive at a decision about something, we need to be aware of these tests of validity.
REASONING BY ANALOGY
As the name implies, this is the process by which we examine two things which are similar and reach conclusions about unknown parts of one or both of the analogous things. Essentially, reasoning by analogy follows this form:
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In the diagram above, A and C are our analogous items. "Bb" a known item about A, and "Bx" represents an unknown item about C that shares qualities with Bb. If A is a type of fish with certain external qualities and flaky white meat (Bb) then we might reach the conclusion that C, a very similar fish from the same family with very similar external qualities might also have flaky white meat (Bx). The degree of cogency in this kind of reasoning is determined by the answers to several important questions:
1) Are there a large enough number of similarities?
2) Are the points of similarity relevant to the comparison?
3) Are the points of difference non-critical to the analogy?
4) Is the analogical reasoning cumulative? Remember cumulative evidence, where each case adds to the credibility of the proposition? This is essentially the same thing. If we can show 5 similar fish that are all analogous and all have flaky white meat, our reasoning is much more sound than if we only have one.
5) Are only literal analogies used as logical proof? Also a very important concept! Only literal analogies have any validity in critical thinking. Figurative analogies are good in literature and sales meetings, but they have no place in critical thinking. Let me say that again. Only literal analogies may be used in critical thinking.
What is the difference, you ask? A literal analogy involves items in the same classification. For instance, we may compare U.S. states because they are all under the same federal law. We might also compare types of wood, or models of Dell Laptops. The famous cliche, "You're comparing apples to oranges" is a way of saying, "You're making a figurative analogy." Any analogy in which the two things being compared are not within the same category is a figurative analogy. Clearly there can be debate over whether an analogy is valid, since humans have an almost limitless desire to classify every conceivable aspect of everything we can describe. The ultimate question always comes down to the relevance of the classifications. (See question 2 above.)
When we infer that a certain thing resulted from another thing, or that a certain thing caused another thing, we are using causal reasoning. This can be an extremely difficult form of reasoning to use correctly because there are many confounding variables in most events, and many events cannot be said to have a single cause. Nevertheless, there are several questions that we must ask ourself if we are to attribute a cause to an effect or vice versa.
1) Is the alleged cause relevant to the effect? In other words, is there a relevant potential cause/effect relationship between the two? While it is true that moments after I walked into my home this afternoon, rain started to fall, it is clearly not the case that my movements had any effect whatsoever on the time that the rain fell, or for that matter, the fact that the rain fell or did not fall.
2) Is this the sole or distinguished causal factor? In some cases, we can say that a certain thing is the sole cause of another thing. For instance, I can say that my flipping of the switch on the wall caused the light to come on. In practical terms, nothing else directly caused the light to come on. Here, the careful reader will object, of course. Electrons and wires and filaments are all involved in the light coming on, and without any one of those things involved, the light would not have come on. Here is where we get to distinguishing causal factors. The question being asked is not concerned with how light bulbs work or how electricity is produced or how neurons in the brain cause muscles in my fingers to contract. The question is, "Who turned on the light bulb?" So, in terms of the question, there is only one cause -- me.
3) Can we say with high probability that we have eliminated other possible causes? Even when it seems obvious that a certain thing is causing something else, we must be careful to ask ourselves if we have truly examined enough possibilities to say that it is so. Magic tricks are an easy example. We all know that misdirection and sleight of hand are involved in magic, so when we see a magic wand being waved over a hat, we can easily reach the conclusion that the magic wand was not responsible for the rabbit appearing in the hat. Other examples, however, are not so obvious, and we must be diligent in exploring all available possibilities before settling on one.
When we infer a relationship between two variables, we often decide that the presence or absence of one variable is sufficient evidence for the presence or absence of another. This is called Sign Reasoning. If one variable can be said to be a sign of another variable, and vice versa, we say that they have a reciprocal relationship. A non-reciprocal relationship is one in which one variable is a sign of the other, but the reverse is not necessarily true.
Perhaps an example or two will make this kind of reasoning clearer. If a man is at least 35 years of age, he is eligible to be the President of the U.S. So, if I show you a man and tell you that he is the President, you can reasonably conclude that he is at least 35 years of age. However, if I show you a man and tell you that he is forty four years old, you cannot reasonably conclude that he is the President of the United States. This is a non-reciprocal relationship.
If I note that the leaves are turning brown, I can conclude that they will fall from the tree soon. Conversely, if I tell you that the leaves will fall soon, you can conclude that they are turning brown. This is a reciprocal relationship.
Sign reasoning is essentially relating an attribute of a larger whole to either the whole itself, or to another attribute within the whole. Sign reasoning is actually a catch-all, and can include reason by analogy, example, and causal reasoning. When you recognize sign reasoning, you should ask the following questions:
1) Are the two attributes relevant to each other? Remember me entering my home and the rain falling? Same test.
2) Is the relationship between the two inherent? In other words, for sign reasoning to work, the two things being cited must be intrinsically linked, not just superficially related. If leaves often turn brown and fall from trees at all seasons, we cannot say that they are inherently linked to Fall, and the observation that Fall is coming because the leaves are turning brown would not be valid, in and of itself.
3) Are there any other factors that could be disrupting the relationship?
4) Is there cumulative reasoning?
GENERAL TESTS OF REASONING
Finally, regardless of which kind of reasoning we are using, we must ask two final questions before we can safely declare our conclusion valid.
1) Are all the propositions true and is all the evidence real? This seems obvious, but it is surprising how many people reach conclusions without doing basic fact checking. This relates back to a previous essay, in which I discussed evaluating evidence, but it's so important that I've mentioned it again. Proper critical thinking involves meticulous and complete fact checking, along with cross checks and tests of internal coherence.
2) Is the conclusion relevant? It is possible to build a case and make a conclusion that is perfectly cogent and which contains nothing but true statements and real evidence, and then find that your conclusion doesn't have anything to do with what you are trying to determine. This is actually a convoluted way of saying something that we all heard beginning in grade school: "Make sure you answer the question that has been asked!"