PHIL 2100: Introduction to Philosophy
Dr. Robert Lane
Lecture Notes: Thursday June 10, 2010



[2.5.2.] Induction.[1]


induction (df.): an inductive argument is one that takes a description of some sample and extends that description to items outside the sample (for example, the pro-choice and crow arguments stated above.)

·         Inductive arguments that are good from a logical point of view are said to be inductively strong. Inductive arguments can be extremely strong, very strong, moderately strong… all the way down to being not strong at all (weak).

·         There are two factors that influence inductive strength:

·         size of the sample: have you examined 1000 crows or only 10? Were there 100 people in the class you surveyed, or only 5?

·         representativeness (or unbiasedness) of the sample: how representative of the entire population is the sample? The more the sample has in common with the entire population, the stronger the argument.




biased sample

reason for bias

all crows

what % are black?

crows living around the paper mill

pollution could have caused them to be darker

residents of Atlanta

what % are Republicans?

people who listen to Rush Limbaugh’s radio program

Limbaugh’s audience tends to be conservative and is more likely to be Republican



[2.5.3.] Abduction.


The second sort of non-deductive reasoning that is sometimes logically strong is abduction:


abduction, a.k.a.. inference to the best explanation (df.): an abductive argument is one that begins with surprising facts and concludes with a proposed explanation of those facts. 


A famous example of an important abductive inference was made by the Czech biologist Gregor Mendel (1822-1884), the discoverer of genes, “the particles in living things that allow parents to transmit characteristics to offspring in reproduction.” (Sober 24)[2]


Mendel’s reasoning involved inferring the existence of something that he could not observe (he never observed a single gene—the microscopes available to him were not nearly powerful enough to make such observations possible).


He inferred the existence of genes in order to explain facts that he did observe. “Mendel reasoned that the observations he made could be explained if genes existed and had the characteristics he specified.” (Sober 24)


His observations were of a species of pea plant (pisum sativum). This plant has several characteristics (“traits”) that come in pairs—each plant has one or the other of each pair of traits; these traits include

·         having smooth peas / wrinkled peas

·         having yellow peas / green peas

·         being tall / short.


His first breeding experiment:


Mendel called them:




“true breeding”



all short



all tall




some tall, some short


His second breeding experiment:





true breeding tall

true breeding short

all tall


His third breeding experiment:





tall hybrid (offspring from ex #2)

tall hybrid (offspring from ex #2)

some tall, some short (proportion of 3:1)



Mendel’s surprising observation: (O) Whatever is responsible for determining whether a plant is tall or short is transmitted across a generation of all tall plants. (This is surprising, since it is not apparent how a trait can be “carried” by a plant that doesn’t itself exhibit that trait.)


Mendel’s hypothesis: (H) There are particles transmitted from parent to offspring that determine the traits of those offspring, and these particles operate according to definite rules.



If H is true, then O is explained.


Mendel’s abductive reasoning—his inference to the best explanation—took this form:


Surprising observation O has been made.

If it were the case that H, then O would not be surprising

It is the case that H.



[] General Facts About Abduction.


·         Abduction is similar to induction in that the conclusion goes beyond what is contained in the premises (i.e., there is some degree of informativeness) and is therefore less than maximally secure.


·         Abduction is dissimilar to induction in that abduction concludes with an explanation of surprising observations described in the premises.  Had Mendel made an inductive inference, it might have looked something like this:


The tall hybrids that I bred yielded offspring that were tall/short in a proportion of 3:1.

Therefore, breeding tall hybrids always yields offspring that are tall/short in a proportion of 3:1.


·         Abduction is very much unlike deduction. To see this, let us recast Mendel’s reasoning in the form of a prediction:


If H is true, then O is true (I will make surprising observation O).

O is true (I make surprising observation O).

Therefore, H is true.


Understood as an attempt to give a deductive argument, Mendel’s reasoning takes the form of affirming the consequent, which is always invalid:


If p, then q.


Therefore, p.


So Mendel’s abductive argument has an invalid argument form.


This indicates something very important about scientific reasoning in general


·         The truth of a theory’s predictions does not guarantee that the theory is true. This is because affirming the consequent is an invalid argument form. But the truth of a theory’s predictions can serve as supporting evidence for the theory. In general, the more predictions made by a theory that come true, the better supported the theory is.


·         On the other hand, the falsehood of a theory’s predictions does guarantee that the theory is false. Imagine that Mendel had made completely different observations than those predicted by this theory, e.g., every time he crossed two tall plants, all the offspring were tall.  In that imaginary case, he would reason as follows:



If H is true, then O is true.

It is not the case that O is true.

Therefore, it is not the case that H is true.


This argument is valid, since it has the form modus tollens, which is always valid:


If p, then q.


Therefore, not-p



This illustrates that:

·         If a theory’s predictions are false, then you can be sure that the theory itself is false.

·         You cannot be sure that a theory is true just because its predictions are true. But you can take a theory to be (more or less) plausible based on the truth of its predictions, and the more true predictions it yields, the more plausible it is.


There are two rules of thumb that, when followed, can increase the strength of abductive arguments:

1.      Remember the Surprise Principle

2.      Avoid the Only Game in Town Fallacy



[] The Surprise Principle. 


Not every true prediction that a theory implies is evidence for that theory. E.g., the theory that all Alabamians are cannibals implies that all Alabamians eat. It’s true that all Alabamians eat, but this in no way increases the strength of the relevant abductive argument:


If all Alabamians are cannibals, then they eat.

All Alabamians do eat.

Therefore, all Alabamians are cannibals.


So we need a way of distinguishing supportive predictions from non-supportive predictions. The Surprise Principle will help us to do that.


Suppose your car won’t start, and you think the problem is that the battery is dead.



observation A

observation B

H1: My car doesn’t start because the battery is dead.


H2: The battery is fine; the car doesn’t start for some other reason.


My car has a battery.


My car starts when my battery is connected to someone else’s.

does the observation help discriminate between H1 and H2?

NO – This would be expected, whether or not the battery was dead.

YES – This would be expected were H1 true, but it would be surprising were H2 true.


Sober states the principle that explains why observation B but not observation A favors H1 over H2 (quoting from p.30):

The Surprise Principle: “[a]n observation O strongly favors one hypothesis (H1) over another (H2)” if both of the following conditions are satisfied, but not otherwise:

1.      If H1 were true, you would expect O to be true.

2.      If H2 were true, you would expect O to be false.[3]


Let’s apply the Surprise Principle to the car example:

·         Consider observation B (my car starts when my battery is connected to someone else’s). If H1 (the battery is dead) were true, then we would expect B, i.e., we would expect the car to start when the battery is jumper-cabled; but if H2 (the battery is OK; the problem is something else) were true, we wouldn’t expect B at all.

·         This is very different than with observation A, which we would expect no matter which of the two hypotheses is true.

So observation B favors H1 over H2, since both of the two conditions are satisfied:

·         If H1 were true, we would expect B to be true.

·         If H2 were true, you would expect B to be false.


But observation A does not favor H1 over H2, since the one of the conditions is not satisfied:

·         If H1 were true, we would expect A to be true.

·         If H2 were true, you would expect A to be false. (We would expect observation A—that the car has a battery—to be true even if the problem was something else.)




·         To use the Surprise Principle, you must have more than one hypothesis to choose from. The principle only tells you whether a given observation supports a given H more than it supports another H.


·         Whether or not an O supports one H over another depends on what the competing Hs are. A given observation may not help at all to discriminate between two Hs, but can be decisive relative to a different pair of Hs. In the first example, A was not supportive of either H1 or H2. But that same observation would have helped discriminate between a different pair of hypotheses:



observation A

H1: My car doesn’t start because the battery is dead.

H3: My car doesn’t start because my battery has been stolen.

My car has a battery.

helps discriminate between H1 and H3?

YES – This would be expected were H1 true, but it would be surprising were H2 true.


·         The Surprise Principle has nothing to say about whether the hypotheses are surprising, or whether one hypothesis is more surprising than the other. The issue this Principle addresses is whether a given observation is surprising or to be expected given a pair of competing hypotheses. 





Another example: suppose you come home and find your house in complete disarray. Two ideas that might explain this cross your mind…



observation A

observation B

H1: My house has been burglarized.

H2: My roommate had a party.

The phone line was cut, deactivating the alarm system.

There are a few pieces of dog food lying around my dog’s food bowl.

Does the observation help discriminate between H1 and H2?

YES – This would be expected were H1 true, but it would be surprising were H2 true.

NO – This would be expected whether H1 is true or whether H2 is true.


So in this example, observation A favors H1 over H2, while observation B does not.



[] The “Only Game in Town” Fallacy.


A fallacy is a mistake in reasoning.


The “Only Game in Town” fallacy happens when you assume that you have to accept a given explanation of surprising events simply because it is the only explanation available.


Sober explains the fallacy by telling a story of hearing strange rumblings from the attic of a cabin in the woods. I will use a different example:


During the 1980s and 1990s, hundreds of Americans, most of whom didn’t know each other,  claimed to have been abducted by odd-looking humanoids traveling in what appear to be spaceships. Suppose that the only available explanation for this is that there really are such creatures and they are abducting humans (this isn’t the only available explanation, of course; just suppose for the sake of argument that it is). You might be tempted to reason as follows:


Hundreds of Americans have reported abducted by space aliens.

The only currently available explanation of this fact is that they really have been abducted by space aliens.

Therefore, hundreds of Americans really have been abducted by space aliens.


However, this is not a strong abductive argument. Even if it is the only available explanation, that fact does not obligate us to believe it. Instead we can say: “That explanation is too outlandish. There is an explanation, but we just don’t have it yet.”



[] Preliminaries to the Philosophy of Religion.


Sober’s approach to philosophy, including to the philosophy of religion, is known as naturalism:

naturalism (df.): “A view that locates human beings wholly within nature and takes the results of the natural and human sciences to be our best idea of what there is.”[4]

·         In philosophy, naturalism maintains that we should “do what good scientific practice itself does in deferring to our present background state of general scientific understanding as the best story we now have about the universe and its furnishings. It is no doubt a flawed, imperfect story still very much in progress, but far more to be trusted than the rival guidance we might seek from theology...”[5]


A contemporary philosopher named Susan Haack has articulated the difference between genuine and pseudo-inquiry, based on some observations first made by the classical American philosopher Charles Peirce (1839-1914):


genuine inquiry vs. pseudo-inquiry: distinguished by motive.


genuine inquiry (df.): inquiry that is motivated by the desire to find the truth, no matter what that truth happens to be. This desire is what Peirce called “the scientific attitude.”


pseudo-inquiry (“pseudo” = false) is motivated by the desire to make a case for a claim that you have already settled on in advance; there are two kinds:


sham reasoning (df.): making a case for a claim your commitment to which is sincere (you care that the claim is true), but also immune to evidence or argument—no matter what the evidence shows, you will not change your mind about it.


fake reasoning (df.): making a case for a claim, not because you have a sincere commitment to it (you don’t really care whether the claim is true or false), but because you think doing so will be to your advantage.


Deciding in advance that God exists, emphasizing evidence for that claim, and ignoring or discounting any evidence against it, is sham reasoning, not genuine inquiry.


As we begin examining arguments for and against the existence of God, try your best to be a genuine inquirer rather than a sham reasoner.



Stopping point for Thursday June 10.  Reading for next time:

·         Chapter 5 (pp.53-60). The very beginning of this chapter refers to some things in chapter 4, which we haven’t read. Don’t worry about that; just dive into the reading. By p.54, you should be able follow what’s going on without having read chapter 4.

·         Chapter 6 (pp.61-75).

·         At the beginning of tomorrow’s class we will have a pop quiz on today’s lecture notes and/or this reading.


Optional readings (these will not be covered on tomorrow’s pop quiz—read them only if you have time to do so):

·         Scientific American’s “15 Answers to Creationist Nonsense”:

·         William Paley, “The Design Argument” (pp.120-22)

·         David Hume, “Critique of the Design Argument” (pp.123-28)

The last two writings are some of the original philosophical writings that Sober discusses in chapter 5. They will be more difficult to read than Sober’s explanations, but if you have time, it would be great for you to work through them.



[1] For more on the general topic of induction, see James Hawthorne, “Inductive Logic,” The Stanford Encyclopedia of Philosophy (Fall 2009 Edition), Edward N. Zalta (ed.), URL = <>.


[2] For more information on Mendel’s experiments see Michael R. Cummings, “Mendelism,” in AccessScience@McGraw-Hill,, DOI 10.1036/1097-8542.414500 .

[3] Sober gets this from A. Edwards (Likelihood, Cambridge UP, 1972), who calls it the Likelihood Principle; see Sober, Philosophy of Biology, pp.31ff.

[4] Norman Melchert, The Great Conversation, glossary, G-4.


[5] James Lenman, "Moral Naturalism", The Stanford Encyclopedia of Philosophy (Fall 2006 Edition), Edward N. Zalta (ed.), URL = < >.


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