Induction and Analogy

The traditional definition of induction as any argument proceeding from the particular to the general is mistaken.
 

Examples

All the people surveyed thusfar said they preferred brand X.
So, it is likely that the next person surveyed will also claim to prefer brand Z.
 

Most actors are extroverts.
Jerry is an actor.
So, it is likely that Jerry is an extrovert.
 

All cows are mammals and have lungs.
All whales are mammals and have lungs.
All humans are mammals and have lungs.
So, it is probable that all mammals have lungs.
 
 

Inductive generalization.

Case a was observed to be an F and a G
Case b was observed to be an F and a G
Case c was observed to be an F and a G
So, probably the next F observed will be a G
 

Case a was observed to be an F and a G
Case b was observed to be an F and a G
Case c was observed to be an F and a G
Nothing was was observed to be an F and not a G
So, probably all Fs are Gs
 

Size and representativeness of the sample are important factors.

Inductive arguments are not valid or invalid.

Inductives arguments are strong or weak depending on the degree to which the premises support the conlusion.

A strong argument with true premises is said to be cogent.
 

AnalogiesÖ

B is like A in many ways.
A has property G.
So, B has property G.
 

On her first paper Joan spent time in the library doing research, wrote several drafts and cosulted with a writing tutor early in the semester. She received an A for the paper. For her second paper Joan also spent time in the library doing research, wrote several drafts and cosulted with a writing tutor early. Probably Joan will get an A on this paper, too.

Principles for evaluating arguments from analogy

1. Relevance of the similarities: The greater the relevance the stronger the argument

2. Number of similarities: The more relevant similarities to better the argument.

3. Nature and degree of disanalogy: The more relevant disanalogies, the weaker the argument

4. Number of primary analogates: the more primary analogates the better the argument

5. Diversity of the primary analogates: The greater the diversity of the primary analogates, the better the argument

6. Specificity of the conclusion: the more specific the conclusion the weaker the argument

Rats are like people in many ways: They have very similar systems of enzymes and hormones, they adapt well to a wide variety of environments, they are omnivores, etc.
People carry umbrellas.
So, rats carry umbrellas, too.

The ways in which A and B are similar should be relevant to having G.
 

You can get a large audience together for a striptease act-that is, to watch a girl undress on the stage. Now suppose that you came to a country where you could fill a theatre simply by bringing a covered plate onto the stage and then slowly lifting the cover so as to let everyone else see, just before the lights went out, that it contained a mutton shop or a bit of bacon, would you not think that in that country something had gone wrong with the appetite for food? (C. S. Lewis)

What is the conclusion?

What general principle is illustrated here?

How reasonable is the general principle?
 

If people will pay to have an appetite teased by a theatrically unveiled peek at an example of the object of that appetite, then the appetite itself in not operating in a healthy way.

All things that are F are also G
B has F
So B is G

Could also support a weaker principle: Most/many Fs are (likely to be) Gs, or Something that is F is likely to be a G.
 

As for one who is choosy about what he learnsÖ we shall not call his a lover of learning or a philosopher, just as we shall not say that a man who is difficult about his food is hungry or has an appetite for food. We shall not call him a lover of food but a poor eater. Ö But we shall call a philosopher the man who is easily willing to learn every kind of knowledge, gladly turns to learning things, and is insatiable in this respect. (Plato)
 

The Argument from Analogy

In crossing a heath, suppose I pitched my foot against a stone and were asked how the stone came to be there, I might possibly answer that for anything I knew to the contrary it had lain there forever; nor would it, perhaps, be very easy to show that absurdity of this answer. But suppose I found a watch upon the ground, and it should be inquired how the watch happened to be in that place, I should hardly think of the answer which I had given, that for anything I knew the watch might have always been there. Yet why should not this answer serve for the watch as well as for the stone; why is it not admissible in that second case as in the first? For this reason, and for no other, namely, that when we come to inspect the watch, we perceive-what we could not discover in the stone-that its several parts are framed and put together for a purpose, e.g., that they are so formed and adjusted as to produce motion, and that motion so regulated as to point out the hour of the day; that if the different parts had been differently shaped from what they are, or placed in any other manner or in any other order than that in which they are placed, either no motion at all would have carried on in the machine, or none which would have answered the use that is now served by it.

ÖThis mechanism being observedÖthe inference we think is inevitable, that the watch must have had a makerÖ.

[E]very indication of contrivance, every manifestation of design, which existed in the watch, exists in the works of nature, with the difference on the side of nature of being greater and more, and that in a degree which exceeds all computation. I mean that the contrivances of nature surpass the contrivances of art, in the complexity, subtlety, and curiosity of the mechanism; and still more, if possible, do they go beyond them in number and variety; yet in a multitude of cases, are not less evidently mechanical, not less evidently contrivances, not less evidently accommodated to their end, or suited to their office than are the most perfect production of human ingenuity. (Paley)

We may observe a great similitude between this earth which we inhabit, and the other planets, Saturn, Jupiter, Mars, Venus, and Mercury. They all revolve around the sun, as the earth does, although at different distances and in different periods. They borrow all their light from the sun, as the earth does. Several of them are known to revolve around their axis like the earth, and by that means, must they have a succession of day and night. Some of them have moons, that serve to give them light in the absence of the sun, as our moon does to us. They are all, in their motions, subject to the same law of gravitation, as the earth is. From all this similitude, it is not unreasonable to think that those patterns may, like the earth, be the habitation of various orders of living creatures. There is some probability in this conclusion from analogy. (Thomas Reid)

Some look on preemployment testing of teachers as unfair-a kind of double jeopardy. "Teachers are already college graduates," they say. "Why should they be tested?" That's easy. Lawyers are college graduates and graduates of professional school, too, but they have to take a bar exam. And a number of other professions ask prospective members to prove that they know their stuff by taking and passing examinations: accountants, actuaries, doctors, architects. There is no reason why teachers shouldn't be required to do this too. (Albert Shanker)

If you cut up a diamond into little bits, it will entirely lose the value it had as a whole; and an army divided up into small bodies of soldiers, loses all its strength. so a great intellect sinks tot he level of an ordinary one, as soon as it is interrupted and disturbed, its attention distracted and drawn off from the matter in hand: for its superiority depends upon its power of concentration-of bringing all its strength to bear on one theme, in the same way as a concave mirror collects into one point all the rays of light that strike upon it. (Schopenhauer)