MonoRealism Philosophy Site

Induction Rules

Part C: Principles & Fallacies

If a thing exists, its existence is felt: anything that exists affects other things that exist, directly or indirectly. To postulate an entity which exists but cannot ever affect the rest of existence is the essence of an arbitrary claim: by definition, no evidence for such an entity can ever be obtained.

This basic principle has a number of specific consequences for inductive reasoning.

Onus of Proof

Asserting the positive is asserting that something exists. Therefore it is asserting that there will be an effect on other existents. Therefore it is asserting that there will be evidence for it. This is why the onus of proof lies on those asserting the positive: such an assertion requires predicting an effect. Denying a claim is merely saying there will be no effect because there's nothing to cause one: that is, we won't see anything we can't explain by what we already know. And that's already consistent with the evidence!

Asserting the positive while refusing to offer predictions or evidence is an admission that the claim is arbitrary – which is worse than being disproved (see Philosophical Reflections 26). It is like pleading guilty to murder to escape a manslaughter charge.

Evidence of Absence

It is often stated that "absence of evidence is not evidence for absence." This is true, but not in a way that lends credence to the arbitrary – which is, unfortunately, often the motive for quoting this truism.

If a belief lacks evidence because it is an arbitrary claim, then the absence of evidence is a consequence and proof of its being arbitrary and hence meaningless. One does not need evidence of absence in such cases. "Evidence" – for or against – is the one thing that has nothing to do with arbitrary claims. Proof that a claim is arbitrary is sufficient reason to dismiss it.

However, absence of evidence is not necessarily evidence of being arbitrary. For example, a physicist might posit the existence of a particle whose existence is felt only at energies higher than currently reachable, or a palaeontologist might predict the existence of certain fossil forms not yet found. While these propositions might have no proof at present, they are not arbitrary if they are consequences of theories developed to explain other facts, and if there are specific reasons why direct confirmation hasn't yet been found. Indeed, all scientific theories are tested by their ability to make predictions about the not-yet-observed. In that context, the lack of evidence for those specific claims is a strength, not a weakness.

As always, the basic principle is testing against reality. Any claim which avoids such a test is dishonest, arbitrary and without merit. Any claim designed to be put to such a test is honest and worthwhile.

Occam's razor

Occam's Razor is a well known principle of reasoning which states that in explaining something, no more assumptions should be made than are necessary. Or, the simplest explanation is the best.

Occam's Razor is just another consequence of the principle that anything which exists affects other things. Tacking on unnecessary extras to an explanation is effectively postulating existents which have no effect, making them arbitrary and without explanatory value.

Of course, a theory that assumes more existents than another might not have merely tacked them on for no reason: it might just be a more complex theory. But all else being equal, the simpler theory is still to be preferred: but not regarded as true. It is to be preferred, because each previously unheard-of existent requires some explanation as to why, if it exists, it is unheard of. So prima facie, the simpler theory has less problems. But of course reality can be complex, and the only way to really tell is by the appropriate observational tests. Occam's Razor is a general guide, not a law.

The overriding principle here is propose no more and no fewer existents than needed to explain the facts.

Hempel's Paradox

Hempel's Paradox notes that since each observation of a black crow is evidence that all crows are black, so is each observation of an orange cat! This is because "all crows are black" is logically equivalent to "all non-black things are not crows." Thus, as each non-black thing that isn't a crow is evidence of that, an orange cat is evidence that all crows are black! (Hempel's Paradox was described in more detail in TableAus a few years ago by Peter Bloxsom.)

The fundamental issue here is that any thing that exists is a positive existent. It exists and is what it is: that which is cannot properly be defined as "the absence of that which it is not." Light is not "the absence of darkness,"and matter is not "the absence of nothing." This is our principle that knowledge is positive, which has two implications for Hempel's Paradox.

A purely logistical problem is that there are far more non-black things and things which aren't crows, than there are either black things or crows respectively. This principle is true of all things in reality. To attempt to gain knowledge of a thing by specifically looking at everything that is not that thing is a fool's errand, for there is so much variety in the universe that looking for a needle in a haystack is trivial by comparison.

Most importantly, the argument only works if the non-black thing might be a crow. If on a diagram of all things you draw a circle labelled "black" and a circle labelled "crow", the question is whether the latter is entirely contained within the former. Whether yes or no, there are vast tracts of reality which cannot be crows. A crow is a bird of a specific nature. Whatever their colour, you cannot find crows by sending a probe to Venus or looking into a microscope. You cannot use your orange cat as proof that crows are black because a cat cannot be a crow: if you already know it is a cat, it is excluded from the evidence. Thus, the only way one could use Hempel's inverted reasoning to test the blackness of crows is to send a robot probe searching in places where crows might be found, detecting non-black things, and then identifying those things.

Thus while Hempel's Paradox is a curious logical puzzle, it has no epistemological value. The purpose of epistemology is to aid in discovering knowledge, not to work out the most impractical ways to do it.


Some fallacies of inductive reasoning have been touched on earlier, but it is useful to give a brief summary of common "standard" inductive fallacies (the following are based on the very useful site Stephen's Guide to the Logical Fallacies:

  • Hasty Generalisation: the sample is too small to support an inductive generalisation about a population, as in judging all men by the actions of one.
  • Unrepresentative Sample: the sample used to generalise about a group is known to belong to a subgroup with different properties, as in "all the swans in Perth are black, therefore all swans are black."
  • False Analogy: two things are similar in some ways and it is argued that therefore they share another common quality: but they differ in a way which affects whether they can both have that property. For example, "men and women are all human beings, so they should wear the same clothes."
  • Slothful Induction: the conclusion of a strong inductive argument is denied despite the evidence, as in "I've had 15 accidents in the last 6 months, but I'm a good driver who's just unlucky."
  • Fallacy of Exclusion: evidence which would change the outcome of an inductive argument is ignored. For example, "my team has won the last 8 games so will probably win this time", when the last 8 games were against poor teams and this one is against the best.

The following "statistical fallacies" are related to inductive reasoning because they concern misuse of generalisations:

  • Accident: a generalisation is applied when circumstances suggest that there should be an exception, as in "it is good to be honest, so you should tell the Nazis about the Jews you're hiding."
  • Converse Accident: an exception is applied in circumstances where a generalisation should apply: that is, the generalisation is discounted because of one exception. For example, "If lying to protect a Jew from the Nazis is moral, all lying is moral."

The following "causal fallacies" are also related to induction because they are often part of explanations based on generalisations (especially, with statistics):

  • Post hoc (fully: post hoc ergo propter hoc): because one thing follows another, it is held to cause the other, as in "he died at sunrise, therefore the sun killed him."
  • Joint effect: one thing is held to cause another when in fact they are both effects of an underlying cause, as in "your fever is giving you a rash" when both are symptoms of an underlying disease.
  • Insignificant: one thing is held to cause another, and it does, but it is insignificant compared to other causes, as in "exercise causes heart attacks".
  • Wrong Direction: the direction between cause and effect is reversed, as in "cancer causes smoking".
  • Complex Cause: the cause singled out is only a part of the entire cause of the effect, as in "the accident was caused by the rain" (when you were driving at 150 kph).

Inducing Principles

If you consider the derivation of why inductive reasoning is valid, and the various rules discussed above, you can see that the rules of induction can mostly be summarised under two main principles, one positive and one negative.

On the positive side, induction is induction from reality. Sir Francis Bacon wrote that "nature to be commanded must be obeyed." To this we can add: nature to be understood must be listened to. All knowledge of the world comes from studying the world: from seeing, hearing, touching, smelling and tasting, and using reason to integrate the resulting evidence into a consistent whole. Induction consists of observation: what is? Reason: what does it mean? And experiment: if it really means what I think it does, what will happen if I do this? These must be the tools you use in your own life: and the tools used by others, if you are to have any trust in their claims.

On the negative side, the main thing to beware of when evaluating evidence is accidental coincidence. Most of the errors discussed previously, associated with anecdotal evidence, statistics and logical fallacies, can be grouped under this umbrella. It is not enough to see that B follows A. You must then show that B follows A more frequently than it would by chance alone. And then you must find out why. Only when you have reached the second stage can you say that there is any connection. Only when you have reached the third stage can you say you understand it.

© 2003 Robin Craig: first published in TableAus.