Definition of
   a priori






Induction within epistemology implies that when a certain phenomenon always has been observed in connection with certain conditions, these conditions at a later occasion create an expectation that the phenomenon will occur.

The result of an induction hence implies a synthesis of related phenomena. Induction is a basal reasoning that is responsible for a large amount of our experience.

Due to this importance, clearly expressed within scientific methodology, it is often erroneously criticized by anti-scientific flavoured writers. This motivates a more detailed discussion here.


David Hume called such a process "Custom" or "Habit" [Hume] and claimed that the predictions of the future were not logically inferred but implied probability arguments. This gave impact within epistemology, in spite of that it actually is sufficient to note two factors that are discussed at this website:

- every perception or observation results in probability arguments.

- a probability argument can, through reasoning, never be transformed into "absolutely certain", even though many trustworthy observations together may result in such a high certainty that it is easily confused with such a certainty.


Vitally important

Everybody agree that experience based on induction exists and that is necessary for our survival.

We use inductive based experience during every moment awake:

- When we take a breath we expect to get air.

- At each step we expect the support will receive the foot as it always used to do.

- We do not believe that we the next moment will be transformed into a flying parrot.


What we believe about the world and about the future is, at best, very often based on induction.



The credibility of an inductive inference is formed by the credibility of every separate premise, together with the number of similar premises.

An example of this is given in the section "Very credible induction", below.


Induction with uncertain premises

In case I walk in the wood at a dark and windy night (with the monotonous hooting of owls), and in the moonshine glimpses a moving shadow, the phantasy may run wild and I may imagine to perceive something, maybe an animal or something that is more frightening.

I may repeatedly see similar shadows, but if I haven´t approached them and studied them closely, the perception in each case becomes uncertain and the inductive conclusion will not be significantly credible.

Even when many persons report similar conclusions based on uncertain premises, they still become uncertain.


In order to become credible, an inductive conclusion must be based on several and credible premises.


Credible induction

premise1: I felt pain in my thumb when I accidently hit it when I was nailing.

premise2: I felt pain in my thumb when I again accidently hit it when I was nailing.

premise3: I felt pain in my thumb when I once again accidently hit it when I was nailing.

conclusion: I feel pain in my thumb if I accidently hit it when I am nailing.


The three premises of the reasoning above result in that the conclusion becomes more credible than any one of the individual premises.


Black Swans


The metaphor "black swan" says that something is unexpected.

Do you say no worthy wife is to be found among all these crowds?" Well, let her be handsome, charming, rich and fertile; let her have ancient ancestors ranged about her halls; let her be more chaste than the dishevelled Sabine maidens who stopped the war - a prodigy as rare upon the earth as a black swan.

Juvenal (about 100 CE) - Satire 6, transl. Ramsay GG, Loeb Classical Library 091 Juvenal and Perseus (1928) 161 p.97

If the unexpected something actual happens, this is surprising.


The swans that had been observed in Eurasia at the seventeenth century were white. The strict inductive conclusion reads "every swan observed up to now has been white".

This was interpreted as "all swans are white" and in common life this type of interpretations often function satisfactorily.

But, as discussed below, this interpretation was shown to be erroneous and the example is frequently used by writers who criticize induction and scientific methodology.


It became immense news when early explorers under Willem de Vlamingh around 1697 observed black swans in Australia [Morris]. The image of a black swan is still included in the flag of Western Australia.

How could they report this? Maybe they saw a white, but dirty, swan? Or was it due to that one person dreamt about black swans?

- No, their observations were supported by induction.

Several persons saw multiple birds at various occasions. They maybe even caught two of them [Seal].

The birds were also depicted and 1726 two swans were brought to Jakarta in order to prove their existence [Morris].


Our belief in that black swans actually exist was hence verified through inductive inference, based on repeated, independent and trustworthy premises.

New observations may complete or create new opinions, and the example demonstrates how scientific methodology constantly improves our opinion about the world

The fact that verification of existence of black swans falsified the hypothesis "all swans are white" demonstrate that:

Falsification implies a verification of the negation of a hypothesis

Persson (2013) -


Very credible induction


In case I pick a stone from the ground I believe that it will fall to the ground when I release it.

Every individual on our earth each day perceive the earth's gravity thousands of times, confirming that the stone will fall, and we have never in a credible manner observed that the gravity at the earth's surface does not exist.

We, and other heavy objects, have never spontaneously floated away.

The Swedish comedians Anders and Måns made a joke about that the stone stays at the earth's surface not because gravitation, but due to evolution.

The probability that the stone will fall when I release it is so high that it becomes futile to try and calculate it.

As long as the circumstances resemble them of today, the released stone will fall.

In spite of the high probability, the statement "a released stone falls" is still a probability argument.




Both the credibility of each singular premise and the number of similar premises influence the credibility of the inductive inference.

In spite of the high credibility of that "a released stone falls", arguments that are based on induction correctly are called probability arguments.


That, which may appear misleading, is that the probability for many such arguments is high to the amount that we in common language are not talking about probability but about certainty and truth.

And this is something that we have in common with rationalistic philosophers.

Hume 1777 - Undersökning / Enquiry, ESB 35-36, p.42-43.
Morris 1898 - Austral English, A Dictionary of Australasian Words, Phrases and Usages, p.451
Seal 2015 - The Savage Shore, p.135