Inductive conclusions go beyond the content of the premise(s)

In my textbook A Concise Introduction to Logic, the author states this:

In general, inductive arguments are such that the content of the conclusion is in some way to "go beyond" the content of the premises. The premises of such an argument typically deal with some subject that is relatively familiar, and the conclusion then moves beyond this to a subject that is less familiar or that is little known about.

What does he mean by "go beyond" the content of the premises?

He goes on to say that such inductive arguments take the form of arguments of authority, arguments from analogy, and predictions about the future.

He is referring to the possible miscomprehension of the conclusion or the improbability of the conclusion in inductive arguments?

4 Answers

A paradigmatic example of induction is :

up to now the sun raised every morning; therefore, the sun raises every morning.

This inference is not justified by deductive logic.

Thus, when the author says that :

In general, inductive arguments are such that the content of the conclusion is in some way intended to “go beyond” the content of the premises

it seems that he is alluding to the fact that the premises alone cannot justify (logically) the conclusion, but we have to "add" to the argument some extra-premise, like an implicit assumption about +natural laws* (i.e. the "uniformity" of natural phenomena).

The word 'induction' is unfortunately used in several different senses and invites confusion. It used to be common to use it refer to a kind of simple extrapolation, such as moving from all the ravens I've ever seen are black therefore all ravens are (probably) black. This might be called enumerative induction.

Sometimes induction is used to describe any argument whose conclusion is uncertain. This is unhelpful because at least sometimes an argument may proceed from uncertain premises to an uncertain conclusion in a way that is deductive. Some theorists call such reasoning probabilistic-deductive rather than inductive.

Sometimes induction is used broadly to mean any non-deductive form of inference, while often it is distinguished from abduction, which is usually understood to mean inference to the best explanation. C S Peirce distinguished between explicative reasoning, which draws out the consequences of what is already known, and ampliative reasoning, which provides cogent reasons for accepting a conclusion that is not entailed by its premises. Inductive and abductive inferences are both ampliative, in that their conclusions are not entailed by their premises and so 'go beyond' them.

Consider an example: suppose we entertain the proposition "the defendant is guilty of the murder of which he is charged". Now suppose we have some evidence for this: "the defendant's fingerprints (and no others) were found on the murder weapon". If we think of the evidence as a premise in an argument and the verdict as the conclusion, the premise does not entail the conclusion, but it does render it more plausible. If we add more evidence, e.g. "the defendant was seen arguing with the victim and was heard threatening to kill him", "the defendant was seen fleeing the scene of the murder covered in blood", "video footage shows the defendant repeatedly stabbing the victim", etc., then we have a highly compelling argument for accepting the conclusion. If we allow ourselves to use the language of probability, we might reasonably say that the premises render the conclusion probable. But no matter how much evidence we pile up, the premises will never entail the conclusion - even video footage can be faked. Nor is it simply a question of eliminating alternatives, despite Sherlock Holmes' famous dictum. The conclusion does not entail the premises either: the defendant could have murdered his victim without leaving his fingerprints behind. Eventually the jury must decide whether they believe the conclusion is true, or at least probable, and bring in a verdict, and whatever decision they make 'goes beyond' the data presented in the evidence.

In general the cogency of ampliative reasoning depends on all kinds of considerations, assumptions and background knowledge, which makes it difficult to give a general account of it. Attempts at finding a purely formal account of induction, e.g. by Rudolf Carnap, are widely considered to have failed. But statistical and algorithmic methods are still highly relevant to the issue of establishing whether some hypothesis is plausible on the strength of observed data.

'What does he mean by "go beyond" the content of the premises?' Probably the author means that induction calls upon the uniformity principle: If a given occurrence has caused a certain result, then future similar occurrences will cause similar results (Hume, An Enquiry Concerning Human Understanding, ¶29).

One observation of a raven shows that it is black. So two ravens, then a thousand. Each observation is a premise. But the process never justifies the overall conclusion all ravens will be black; the observer holds only an unconnected collection of premises.

The uniformity principle says that because one raven was black, observed ravens will be black into the future. With the addition of this principle, which goes beyond the premises, it is possible to say that All ravens are black.

Whether the uniformity principle itself stands on firm ground is a different question. But that is what I think the author means.

I don't know what the author of the book you cite means. However, induction is impossible and unnecessary as pointed out be Karl Popper, see "Realism and the Aim of Science" especially chapter I, "Objective Knowledge" by Popper chapter 1 and Chapters 3 and 7 of "The Fabric of Reality" by David Deutsch and Chapter 1 of "The Beginning of Infinity" by Deutsch. It is impossible because an explanation, an account of how the world works, does not follow from any finite set of observations. Such an explanation has an infinite set of consequences, some of which may be unobservable. For example, our current physical theories have implications for the temperature at the core of the sun, but it may be impossible to measure that temperature.

Knowledge is created by noticing a problem, proposing solutions to the problem and criticising the solutions until only one is left and it has no known criticisms. No induction is necessary to guess and criticise guesses, so no induction is necessary for progress.

Alleged examples of induction are all examples of guessing and no amount of fancy terminology can change that. For example, "up to now the sun raised every morning; therefore, the sun raises every morning". Taken literally this is false. The sun often doesn't rise at the north pole. And if the Earth's orbit decays so that it falls into the sun or is ejected from the solar system it will fail. The sun rising every morning so far has nothing to do with it rising tomorrow except in the light of an explanation of why it rises: celestial mechanics or whatever. And then the explanation is doing the heavy lifting, not induction. Admitting that you've guessed an explanation and some consequences for the sun rising is the honest way to go. Saying anything else involves stupidity and/or self deception.

The idea that induction can be rescued by assuming the uniformity of natural law is no good.If such a uniformity principle does nothing to explain in what respects natural laws are uniform, then it selects no specific explanation. If the principle does try to explain in what respects the laws of nature are uniform, then it is a law of nature and so can't be used as a foundation for some attempt to justify some set of laws of nature.

• Induction is guessing, a particular type of it, but it is still a form of inference. Both induction and abduction are particular cases of (non-deductive) ampliative inference, and as such do not have to be deductively valid, only explanatory, see SEP plato.stanford.edu/entries/abduction/#DedIndAbd Popper's notion of induction was too narrow, and is rarely used today. – Conifold Oct 13 '16 at 0:13
• The example of abduction given in the article takes for granted an explanation and then works out consequences of that explanation. "96 per cent of the Flemish college students speak both Dutch and French" is a statement about reality that takes for granted a load of explanations. The rest of the argument takes for granted explanations about the connection between frequency statements and what you can conclude about individual guesses. Since epistemology is about how to create new knowledge, this has very little to do with the subject. – alanf Oct 13 '16 at 7:33
• If epistemology was only about how to create new knowledge Popper was not doing epistemology, "the act of conceiving or inventing a theory, seems to me neither to call for logical analysis nor to be susceptible of it... there is no such thing as a logical method of having new ideas, or a logical reconstruction of this process". To create a new idea the explanation is guessed, but it can be reconstructed as guessed according to forms of ampliative inference. Popper missed the logical aspects of creative process exactly because his notion of logic was reduced to deductive one. – Conifold Oct 13 '16 at 22:06
• Knowledge creation requires guessing and criticising the guesses. First, note that nothing in the article you cited explains anything about the creation of guesses. It takes for granted that the guess has been made. Second, Popper was right that there is no possibility of a logical reconstruction. Knowledge arises by evolutionary processes of variation and selection. The variation step involves some mechanism that makes produces variations in an unbiased way, e.g. - random mutation in biological knowledge creation. – alanf Oct 14 '16 at 7:35
• Anything a person sez has gone through multiple rounds of variation and selection in his brain before he sez it. Note that whatever is going on you can't give a purely logical account of it since the details of the mechanism matter for how it works, its degree of universality and possibly other stuff. Ampliative inference is a vague name for something philosophers don't understand. For more explanation, see "Evolutionary epistemology,rationality and the sociology of knowledge" ed by Radnitzky and Bartley and "the beginning of infinity" chs 4, 15,16 by David Deutsch. – alanf Oct 14 '16 at 7:45