12.2 Supporting Evidence
Even when we don’t have direct evidence about a claim, evidence about similar or related cases can support the claim. Arguments by analogy and induction rely on this principle.
Table of Contents
- 12.2 Supporting Evidence
12.2.1 Arguments by Analogy
Two things similar in some ways may be similar in other ways.
Arguments by Analogy
In an argument from analogy, we note that since some thing x shares similar properties to some thing y; we conclude that, since y has characteristic A, x probably has characteristic A as well.
For example, suppose that I have always owned Subaru cars in the past and that they have always been reliable, and I argue that the new car I’ve just purchased will also be reliable because it is a Subaru. The two things in the analogy are:
a) the Subarus I have owned in the past, and
b) the current Subaru I have just purchased.
The similarity between these two things is just that they are both Subarus. Finally, the conclusion of the argument is that this Subaru will share the characteristic of being reliable with the past Subarus I have owned:
1. My old car was a Subaru
2. My new car is a Subaru
3. My new car is like my old car (1, 2)
4. My old car was reliable.
C. My new car is reliable. (3, 4)
This is not a valid deductive argument. There is no rule of inference which allows us to conclude that, simply because two things are similar in some ways, they’ll therefore be similar in some other ways. There are too many obvious counterexamples for this to be a good rule of logic: Eisenhower and Clinton were both U. S. Presidents, but it doesn’t follow that Clinton was bald just because Eisenhower was bald.
In fact, it’s an entirely different kind of argument: an inductive argument. Inductive arguments are invalid: the truth of the premises does not guarantee the truth of the conclusion. Nonetheless, they can provide evidence to support the conclusion. Arguments by analogy are the most basic type of inductive argument. Inductive arguments are evaluated as strong or weak depending upon the relevance of the similarities.
Strong and Weak Analogies
Is the Subaru argument a strong or weak inductive argument? Partly it depends on how many Subarus I’ve owned in the past. If I’ve only owned one, then the inference seems fairly weak (perhaps I was just lucky in that one Subaru I’ve owned). If I’ve owned ten Subarus then the inference seems much stronger. Thus, the reference class that I’m drawing on (in this case, the number of Subarus I’ve previously owned) must be large enough to generalize from (otherwise we would be committing the fallacy of “hasty generalization”).
However, even if our reference class was large enough, what would make the inference even stronger is knowing not simply that the new car is a Subaru, but also specific things about its origin. For example, if I know that this particular model has the same engine and same transmission as the previous model I owned and that nothing significant has changed in how Subarus are made in the intervening time, then my argument is strengthened. In contrast, if this new Subaru was made after Subaru was bought by some other car company, and if the engine and transmission were actually made by this new car company, then my argument is weakened. It should be obvious why: the fact that the car is still called “Subaru” is not relevant establishing that it will have the same characteristics as the other cars that I’ve owned that were called “Subarus.”
Clearly, what the car is called has no inherent relevance to whether the car is reliable. Rather, what is relevant to whether the car is reliable is the quality of the parts and assembly of the car. Since it is possible that car companies can retain their name and yet drastically alter the quality of the parts and assembly of the car, it is clear that the name of the car isn’t itself what establishes the quality of the car. Thus, the original argument, which invoked merely that the new car was a Subaru is not as strong as the argument that the car was constructed with the same quality parts and quality assembly as the other cars I’d owned (and that had been reliable for me).
What this illustrates is that better arguments from analogy will invoke more relevant similarities between the things being compared in the analogy. This is a key condition for any good argument from analogy: the similar characteristics between the two things cited in the premises must be relevant to the characteristic cited in the conclusion.
Relevance and The Fallacy of False Analogy
Of course, the most crucial term here is “relevant”. Two similarities are relevant when they are connected by a common chain of explanation. For instance, in the example earlier, similar brand names would not be relevant to the reliability of a Subaru, because a brand name does not explain why a car is more reliable, whereas similar Engines or similar manufacturing plants may be relevant, if those things explain why a car is more reliable. Likewise, the fact that my old Subaru was blue and the new one is red is not a relevant dissimilarity, since color of a car does not explain its reliability. Relevance matters in two ways:
(1) The characteristics of the two things being compared must be similar in relevant respects to the characteristic cited in the conclusion.
(2) There must not be any relevant disanalogies between the two things being compared.
Because principle (2) above requires that there not be any relevant disanalogies, it is not possible to evaluate an argument by analogy simply from looking at similarities: it is essential to have some information about whether there might be dissimilarities. Similarities can be found between almost any two things, but the analogy is still weak if we’ve neglected to investigate whether there are relevant differences.
The Fallacies of False Analogy and False Disanalogy occur when an argument by analogy relies on a similarity (or dissimilarity) which is not relevant to anything which could explain the conclusion.
For example, the following is a False Analogy:
1. Skyscraper windows should be clear and transparent.
2. Government finances should be clear and transparent.
3. Government finances are like skyscraper windows.
4. Skyscraper windows kill birds.
C. Government finances kill birds.
Here is a false disanalogy:
1. Fire gives off light.
2. Acid does not give off light.
3. Fire is not like acid.
4. Fire burns.
C. Acid does not burn.
We know that these are false (dis)analogies because the (dis)similarities cited on lines 1 and 2 are not relevant to the conclusion, but we know they aren’t relevant in large part because of background information we have outside of the argument. So, some background information is important whenever we evaluate arguments by analogy.
12.2.2 Arguments by Induction
Inductively, we observe a pattern and expect the pattern to continue.
Inductive Arguments
The basic justification behind inductive arguments is our assumption that, in our world, similar inputs tend to produce similar outputs. Two inputs which are similar in a way which is relevant to the output won’t differ unless there is some relevant dissimilarity between them which explains why they will differ. If the same input has produced the same output hundreds of times before, you should expect the same result to happen again, unless you do something relevantly different this time. A simple inductive argument is the following:
1. 100% of 10,000 people studied who had condition A and took drug B recovered.
2. Jake has condition A
3. Jake took drug B.
4. There are no relevant dissimilarities between Jake and the 10,000 people studied.
C. Jake will probably recover.
Of course, Jake could be the exception. There is no logical guarantee that Jake will recover. We would expect, given the way our world typically works, however, that if Jake was the exception there would be some reason he was the exception: some relevant dissimilarity we had failed to appreciate. So, even if the conclusion is not guaranteed by the premises, it is good enough for our purposes.
Six Criteria for Strong Inductive arguments
We have already mentioned that arguments by analogy are the most basic form of inductive argument. Most arguments by analogy are weak. Most scientific conclusions involves inductive reasoning. Does this mean that most scientific conclusions are weak?
Absolutely not! There are a number of criteria which an inductive argument can meet, which make that argument strong. In the sciences and even in everyday life, these criteria are used to help ensure that the data strongly support their conclusion.
Suppose, for example, that I am thinking about buying a new car, this time a Geo Prizm. I’m very likely to speak with friends who have recently bought new cars, noting their experiences with various makes, models, and dealers. Here are some factors which would make their experience better evidence of how the car will work out for me:
- Many instances. If thirty friends instead of three report their satisfaction with the model I intend to buy, that tends to make it even more likely that I will be satisfied, too. In general, more instances strengthen an analogy; fewer weaken it. Induction from too few instances is the fallacy of hasty generalisation. Similarly, a medical scientist would seek to test a drug on many patients, not just a few, to ensure that it works.
- Instance variety. If my friends bought their Prizms from three different dealers but were all delighted, then my conclusion is somewhat more likely to be true, no matter where I decide to buy mine. In general, the more variety there is among the instances, the stronger the analogical argument becomes, because the common thread between the cases is more likely to be responsible for the conclusion. Similarly, a medical scientist’s results are more conclusive if they can be replicated by other scientists living in other places and working with other patients.
- Many similarities. If my new purchase is not only the same make and model from the same dealer but also has the same engine, then my conclusion is more likely to be true. In general, the more similarities there are between the instances and my conclusion, the better for the analogical argument. Similarly, a doctor is more likely to prescribe a drug when a patient has many similarities to other people from whom the drug worked successfully.
- Relevance. Of course, the criteria we’re considering apply only if the matters with which they are concerned are relevant to the argument. Ordinarily, for example, we would assume that the day of the week on which a car was purchased is irrelevant to a buyer’s satisfaction with it. Relevance, as we mentioned earlier, is determined by whether there is an explanatory connection of some sort between the conclusion of the argument and the similarity between cases. For instance, if a drug is supposed to reduce heart attacks, and a study showed it was effective in a population of French teachers who exercise regularly, a Doctor would be more likely to prescribe it for a German teacher who exercised regularly than for a French teacher who never exercised, because exercise has some causal connection to heart disease, but the language one teaches does not.
- Few dissimilarities. If my friends all bought Geos with automatic transmissions and I plan to buy a Geo with a standard transmission, then the conclusion that I will be delighted with my purchase is a little less likely to be true. In general, the fewer dissimilarities between instances and conclusion, the better an analogical argument is. Similarly, if a study showed a drug was effective in an elderly population, a Doctor might still hesitate to prescribe the drug to someone in their 20s.
- Modesty of conclusion. If all three of my friends were delighted with their auto purchases but I conclude only that I will be satisfied with mine, then this relatively modest conclusion is more likely to be true. In general, arguments by analogy are improved when their conclusions are modest with respect to their premises. Similarly, a legitimate medical scientist can more easily support the conclusion that a drug “lowers the risk of heart attacks in conjunction with diet and exercise”, whereas a con artist would promote a product which “cures heart attacks forever and makes your heart 500% younger.”
Inductive arguments which meet these criteria are strong, and can be used as evidence for a claim. Again, inductive arguments are not a guarantee of truth. Misleading patterns can arise inevitably in any set of data: global warming has increased in the years since people stopped using swords in combat, but you shouldn’t start fencing in order to save the planet. For every pattern we notice, there may be another pattern we fail to notice which is important and more influential: those who rely solely on economic data to predict the outcomes of elections may be neglecting other important influences, like the candidates’ involvement in scandals. On the whole, though, induction can support a conclusion when it meets these criteria, and so the sciences can produce strong evidence for a claim.
12.2.3 Scientific Laws
Claims about what would or will likely happen are supported by lawful regularities.
Scientific Explanations
Modern science over the last four centuries has contributed significantly to our ability to perceive, understand, and manipulate the natural world. As we discussed earlier, inductive reasoning provides the evidence which supports most scientific claims. Because inductive evidence is not a guarantee of truth, scientific explanations are always tentative proposals, offered in hopes of capturing the best outlook on the matter but subject to evaluation, modification, or even overturning in light of further evidence.
At the same time, repeated testing has shown some inductive generalizations about our world to be consistent and reliable in every case we have encountered. These are often called scientific laws. We rely on these laws to make very precise predictions, such as predicting the trajectory of a rocket to send a satellite into orbit, or designing a laser capable of reshaping the cornea of an eye without damaging it. We also appeal to scientific laws to explain why volcanoes erupt, or why the tides ebb and flow.
There are many ways to model scientific explanation. One way that is easy for logic students to understand involves modeling them as deductive arguments. On this “deductive-nomological model” for scientific explanation, a scientific law is one premise of an argument, an observation about the world is the second premise of an argument, and the conclusion of the argument is the event which is being predicted or explained. For example:
1. All objects, if not acted upon by an external force, will remain at rest or in uniform motion.
2. The asteroid is not acted upon by an external force.
3. The asteroid is not at rest.
4. The asteroid, if not acted upon by an external force, will remain at rest or in uniform motion. (1 UI)
5. The asteroid will remain at rest or in uniform motion (2, 4 MP)
C. The asteroid will remain in uniform motion. (3, 5 DS)
Here, premise 1 is an expression of Newton’s First Law of Motion, premises 2 and 3 are statements about observable facts, and the conclusion is a prediction about the behavior of the asteroid. The conclusion of the argument must be true (that is, the asteroid must remain in uniform motion) if all of the premises are true. If we were looking for an explanation of why the asteroid continues moving at the same rate, rather than slowing down or speeding up, we would present this argument as a kind of explanation: the law of motion in premise 1, and the facts about the asteroid in premise 2 and 3, explain why the conclusion is true. Not every explanation seems to fit this structure, and not every deductive argument is an explanation, but it is a useful model for how predictions and explanations work.
Hypothesis and Theory
Because laws have to apply to all possible cases, with no known exceptions. we have discovered relatively few scientific laws. Our observations of the world are also tentative and incomplete. So, most of the time scientists have to formulate a hypothesis, to help fill in the gaps in order to explain what we do observe. A hypothesis is not a “guess”, but a possible fact which would, in conjunction with laws we already know, predict the phenomena we observe. (Alternatively, a hypothesis can be a possible law which would, in conjunction with facts we observe, predict the phenomenon we want to explain.) To give a simple example, if you observe a skateboard rolling across the sidewalk without anybody on it, you might formulate the hypothesis that somebody was riding the skateboard and then jumped off, which might be a good explanation, given your knowledge of the laws of motion, and of how skateboards most often start moving.
Of course, formulating hypothesis is just the first step: the process of testing and attempting to disconfirm a hypothesis, the scientific method, is something you likely are already familiar with. Scientific theories are broad, general hypotheses which would explain a wide variety of phenomena, and which have survived the ordeal of repeated testing. For instance, if we observed dead fish at the side of the river, we might form the hypothesis that the dead fish are the result of mercury poisoning in the water. We’d then attempt to disconfirm this hypothesis, by testing whether there is in fact mercury in the water, by testing whether fish in fact die in water with mercury in it, and by testing whether there are traces of mercury in the blood of the dead fish. If the hypothesis survived repeated testing over time, we would have a theory for the cause of deaths of fish at the banks of rivers. This theory would still be underdetermined by the evidence: there might be competing theories which are equally compatible with our observations, such as that it is not the mercury but the excessive salt in the water which kills the fish. The two theories would then exist side by side until one theory was eventually rejected. A little bit of seemingly contrary evidence would not be enough to reject the theory, since the theory could instead be modified to fit the evidence, but over time, one theory might win out over the other.
In the next submodule, we’ll discuss the methods for developing and weighing competing hypotheses.
Submodule 12.2 Quiz
Licenses and Attributions
Key Sources:
- Watson, Jeffrey (2019). Introduction to Logic. Licensed under: (CC BY-SA).
- Modified with additions, from two sources: (a) Van Cleave, Matthew. Introduction to Logic and Critical Thinking v. 1.4. pp 154-157, licensed under a Creative Commons Attribution 4.0 International License. (b) The Philosophy Pages by Garth Kemerling, and licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License.
- Modified with additions, from The Philosophy Pages by Garth Kemerling, and licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License.
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