Definition of
   a priori




a priori


Not perception


Rationalists claim existence of propositions that are "absolutely certain", or (formed) a priori. They hence propose that "knowledge" can be formed before, prior, or after, posterior, perception.

When they try to demonstrate existence of an argument a priori they meet with a great problem: they cannot seek support from perception. If they could, it would not be a priori. The discussions therefore become complex, without connection to our experience, and often evidently illogical.

This was known by Plato and by Kant:

... the sources of metaphysical cognition ... cannot be empirical. The principles of such cognition ... must therefore never be taken from experience; for the cognition is supposed to be not physical but metaphysical, i.e., lying beyond experience.

Kant (1783) Prolegomena, Preamble $1, 4:265, (Hatfield, Cambridge, p.15).

Undefined terms

An argument a priori hence must be formed through some process other than perception. They have been claimed to be formed before an individuals conception, by a god, by a dream or by a "prophecy".

Alternatively they have been claimed to be formed through some process named by some undefined term like "transcendental", that they were "given" or simply "revealed". Such processes have never been clearly described but are sometimes stated by some worldly authority:

So then, Simmias, our souls also existed apart from the body before they took on human form, and they had intelligence.

Plato - Phaedo, 76c.

It is not polite to ask about the authority's source.


The term "if"

While reading discussions about "absolutely certain" arguments one must watch the expressions closely. A common technique is to apparently claim something, but not to actually claim this by using the term if.

A rationalist claim as a founding thesis:

IF "absolutely certain" arguments exist, they are formed a priori.


This founding thesis is based on the supposition that only arguments formed a priori and through probability exist. The latter are not absolutely certain, even though they are often very probable. Hence a priori remains.

Another empty sentence that seems to be reasonable reads:

IF elephants can fly, they can sleep at the top of large trees.


It is hence not only logic that ensures whether the conclusion of a reasoning is interesting or not, but also the premises of the argument.


A well known statement about deduction reads:

IF the premises in a logically correct deduction are true ("absolutely certain") the conclusion becomes true.


This is called "truth preservation" [e.g. Bergmann] and has by some philosophers been taken as evidence of that conclusions of syllogisms, erroneously called "analytic arguments" becomes "absolutely certain".

But as up to now no premise has been shown to be "absolutely certain", the content of this statement may be questioned.

As the premises are ultimately based on perception, no logical relationship may ever result in "absolute certainty" but, at best, increased probability.


Proposals of a priori


The literature contains many claims about existence of a priori. Those that have not been evidently illogical are usually based on one of these two mistakes:

- Concept formation through abstraction. The suggestions are built on that it may be hard to understand that abstractions ultimately are formed from perception.

- The opinion that an "absolutely certain" argument can be formed as conclusion due to that a reasoning that is logically correct. The error lies in that also the premises of the reasoning must be "absolutely certain" in order to form such a conclusion

Examples of errors during attempts to demonstrate a priori are given below:



In the citation below, Plato's Socrates wants to infer that the concept "equal in itself" is a "Form", i.e. something that our soul has learnt before we were born.


- we say that there is something that is equal. I do not mean a stick equal to a stick or a stone to a stone, or anything of that kind, but something else beyond all these, the Equal itself. Shall we say that this exists or not?
- Indeed we shall, by Zeus, said Simmias, most definitely.
- do not equal stones and sticks sometimes, while remaining the same, appear to one to be equal and to another to be unequal?
- Certainly they do.
- But what of the equals themselves? Have they ever appeared unequal to you, or Equality to be Inequality?
- Never, Socrates.

Plato - Phaedo 74a-b [Plato]

Plato's Socrates hence states that the abstraction contains a meaning "in itself" and that it has not been created through synthesis of perceptions.

An unprejudiced discussion about abstraction shows that this is erroneous.



Plato argued that if "absolutely certain" arguments exist, they must have been created through existing phenomena, "Forms", that our soul remember from an earlier non-worldly existence. His arguments read approximately like this:

- He agreed with earlier philosophers that perception may be erroneous. Hence "absolutely certain" arguments are not possible to form through reasoning that is ultimately based on perception.

- Because all experience about our world is ultimately based on perception, "absolutely certain" arguments must be created during existence outside of our world.

- He proposed that abstracted concepts, or "Forms", hence are formed outside of our world and therefore may imply "absolutely certain" arguments.


As for Plato, it may be hard, but not impossible, for us to realise that abstracted concepts are ultimately formed by perception.


Rationalists have claimed that an universal god is a proper starting point for reasoning that were "absolutely certain".

They tried to prove its existence:

- René Descartes claimed that his belief about the perfection of God must result in the idea of God as absolutely certain [Descartes]. His argument resembles:

If God is perfect, God must exist.

- Leibniz elaborated that if the concept God is created from all desirable properties, God must exist, because existence is one of all these properties.


Attempts using logic relations


The conclusion of an argument will never become "absolutely certain" if the premises are not so. And this probably implies never because the premises probably always are probability arguments.

This is discussed in detail at the page syllogism.



Gottlob Frege claimed, with verbosity but without any plausible argument, some kind of authority and claimed that arithmetic, i.e. chains of syllogisms or deductions, should be absolutely certain [Frege].

Three times he tries to guard himself against possible critic:

I hope I may claim in the present work to have made it probable that the laws of arithmetic are analytic judgements and consequently a priori.

Frege 1884 - Foundations of Arithmetic 2Ed, ch.1-4 and ch.5: Conclusion.

The error in his arguments is summarised in the section "The devil is in the premises" below. The credibility of a conclusion is determined not only by that a deduction is logically correct, but also by the credibility of the premises.

And the ultimate arithmetic premise is the quantity "one" that we create from repeated perception of separate objects.



Also Robert Audi (which otherwise is relatively readable) confused credibility of deductions and premises:

... that if the spruce is taller than the maple and the maple is taller than the apple tree then the spruce is taller than the apple. /.../
Clearly, this a priori belief is also justified, and it constitutes knowledge.

Audi 2011 - Epistemology, A Contemporary Introduction to the Theory of Knowledge 3Ed, p.380-381.


Hillary Putnam argued that just one statement created a priori is enough as demonstration of that a priori really exists, which of course is correct.

He then claimed that the phrase below is "an absolutely, unconditionally, truly, actually a priori truth":

not every statement is both true and false

Putnam 1978 - There is at least one a priori truth, Erkenntnis 13, p.153-170.

The phrase is an expansion of the Law of contradiction: "A statement cannot be both true and false at the same time".

In order to judge whether the phrase is a priori or not, we may investigate why we consider the phrase as credible. Does it describe a gesture with one hand? No, we have experience (ultimately built on perception) of what a statement is, whether something exists or not, when something "is true", which implies that it agrees with our experience, and when something "is false".

The phrase hence describes a relation between abstracted phenomena that ultimately are created from perception, and is consequently not created a priori.


This discussion illustrates that a claim of a priori cannot derive support from something in out experienced reality, which was discussed above.


Karl Popper claimed that verification cannot create knowledge. This is correct for "absolutely certain" arguments, because they are quite likely not to exist. But he then claimed that a proposition that is possible to falsify may lead to "knowledge", i.e. that it may provide an "absolutely certain" argument [Popper].

His reasoning was internal logically erroneous because "to falsify a statement" is identical with "to verify the negation of this statement" []. If verification cannot lead to "knowledge", neither can falsification do so.

At this website I argue for that neither verification nor falsification lead to "absolutely certain" arguments, i.e. the type of "knowledge" that Popper tried to promote. They simply do not exist.

Additional theses by Popper are discussed at


Colours and Reincarnation


Mixed colours

Several philosophers [Schlick, Putnam, Bonjour] have reproduced an old argument (whitout naming any source) that the statement below must be a priori:

Nothing can be completely covered by red and green at the same time


Rationalistic epistemologists apparently love to discuss colours, in spite of the well known fact above that presence of a priori never may be verified through perception.

Some details of this example are:

- the brain create the experience of colour from pulses that come from visual cells in the eyes [e.g. Goldstein]. The experience of colour is hence an extremely obvious example of perception.

- many children know that when they cover a surface using blue followed by yellow water colour (small coloured particles in a thin glue) the brain interpret the signals from the eyes as green colour.

- the error in exactly this argument was discussed by Leibniz already during the 15:th century:

So when, after having mixed yellow powder with blue we perceive a green color, we perceive nothing but the yellow and blue minutely mixed, although we do not notice it, or rather imagine that we perceive some new entity

Leibniz 1684 - Thoughts on Knowledge, Truth and Ideas (Acta eruditorum), in Philosophical Works of Leibnitz 2Ed, transl. GM Duncan, New Haven 1908, p.33).

Experience from earlier life

Some adherents of religions that believe in incarnation claim that they can remember events from an earlier life. This is a very vast claim as it suggests that something from an individual in a nonmaterial manner may be transported to another individual.

Because it is very vast it should be supported by very vast verification in order to be credible, e.g. that adherents are able to reveal new controllable facts from the earlier existence. The thought swindles about how our history books would be rewritten!

But regardless of the extent of such claims, they do not influence the epistemological thesis that knowledge ultimately is created through perception.

If reincarnation with memory would exist, the memories would have been created from perception during an earlier existence.


Immanuel Kant

Immanuel Kant (public domain)

Kant was such a clever, apparently logical, verbose, and often cited philosopher that he gets his own section (with image!).

A critical study of Kant's writings is demanding and the reader has to focus not only on what is said, but also on what is not said.



He opened with the statement that his theses must be followed in case a priori should be credible. I estimate this to be correct, and at the same time that the theses are erroneous.

...there can be no such science /metaphysics/ unless the requirements expressed here, on which its possibility rests, are met...

Kant 1783 - Prolegomena 4:257 (Hatfield, Cambridge 2004, p.6).

Metaphysics implies philosophy that is not deal with physical phenomena. It hence does not deal with things that ultimately are based on perception.


What must be claimed?

Kant then listed what rationalistic philosophers had to claim in order to justify their philosophy:

Metaphysics deals with something beyond the physical reality. IF it exist, its sources cannot be the physical reality.

First, concerning the sources of metaphysical cognition, it already lies in the concept of metaphysics that they cannot be empirical:

the cognition is supposed to be not physical but metaphysical, i.e., lying beyond experience.

It is therefore cognition a priori, or from pure understanding and pure reason.

Kant 1783 - Prolegomena 4:265 (Hatfield, Cambridge 2004, p.15).

As seen above, Kant uses the terms "a priori" and "pure" without positive definition.


The principle of contradiction

Kant wanted to persuade the reader that metaphysical cognition is valid.

He made the mistake discussed above in the section above "Attempts using logic relations" when using a rule from logics to evaluate whether a relation is logically correct.

All analytic judgments rest entirely on the principle of contradiction and are by their nature a priori cognitions, whether the concepts that serve for their material be empirical or not.

Kant 1783 - Prolegomena (Hatfield, Cambridge 2004), 4:267, p.17.

"The principle of contradiction" implies that an argument from premises to conclusion is logically correct if it results in a contradiction when one premise is substituted by its negation.

Kant hence, erroneously, claimed that it is exclusively a logically correct relation, and hence not also its premises, that determine whether the conclusion represents an "absolutely certain" argument. The importance of the premises is discussed at the page "Syllogism".


The problem with "The principle of contradiction" is shown using the example below:

The shortest logical argument is a direct tautology. The connecting term, or the copula, "IS" is then expressing "is identical with":

/premise/ "this flying lion"
/conclusion/ "this flying lion".

Negation of the premise:

not this flying lion
this flying lion.

The contradiction in the altered argument demonstrates that the argument was logically correct.

But, as the premise described something that was not credible, the conclusion also becomes not credible.


"The principle of contradiction" hence evaluates the form of the argument, but not the credibility of the premises or the conclusion.


Analysis of a statement created a priori

He then misleadingly stated:

IF a concept "belongs" to metaphysics (but no such concept has ever been shown to exist) a division or analysis of this concept will also "belong" to it:

...if concepts belong to metaphysics, ... then the judgments arising from their mere analysis necessarily belong to metaphysics as well,

Kant 1783 - Prolegomena 4:267 (Hatfield, Cambridge 2004, p.17).

"Examples" of a priori

Kant tried to give examples of concepts that "belong" to metaphysics. He followed Plato, but used the term "transcendent" instead of Plato's more understandable "created during an non-worldly existence"

At this website, such concepts (if they should exist) are called "absolutely certain".

... some pure synthetic cognition a priori is actual and given, namely, pure mathematics and pure natural science; for both contain propositions that are fully acknowledged

Kant 1783 - Prolegomena 4:275 (Hatfield, Cambridge 2004, s.25).

He hence claimed that something may be "given":


- Relations within mathematics (but it is not only the logic relation that determines the conclusion's credibility).

- "Pure" observations within natural science.

But every premise, irrespective of area and credibility is, as far as we know, a probability argument.



Kant knew this, but in his attempts to justify metaphysics he claimed that every definition (which he below calls "my concept") should be considered as "absolutely certain" or a priori:

... all analytic propositions are still a priori judgments even if their concepts are empirical, as in: Gold is a yellow metal ... .
I need no further experience outside my concept of gold, which includes that this body is yellow and a metal

Kant 1783 - Prolegomena §2.b (Hatfield, Cambridge 2004, p.17).

It is completely clear that Kant's definition of gold is based on perception (yellow and metal) and that it is not formed a priori.

A definition is a concept or an abstraction that lists describing and distinguishing properties of the defined phenomenon. It is always ultimately based on perception.

Kant also claimed that when a conclusion is inferred from a definition (which he claimed was a priori), it must be regarded as a priori.


Synthetic a priori

Oddly enough, many Kant-discussions do not consider existence of a priori arguments.

Many discussions consider whether synthesis (combination) of such arguments (synthetic a priori which then could be divided into "absolutely certain" /synthetic-/ analytic statements) is possible.


The conclusion from the discussions may for philosophers obviously not become "Yes" or "No", because then the discussions would not continue. Below follows a short conclusion:

- IF priori arguments exist (which never has been demonstrated) the conclusion becomes "Yes": They could be synthesised, i.e. combined, with each other. But IF a priori arguments are non-existent the conclusion of course becomes "No".



The devil is in the premises


To sum up: It is the premises, together with that an argument is logically correct, that determine the credibility of a logical argument.

So if all you know about an argument is that it is valid, that alone tells you nothing about whether the premises or the conclusion is in fact true.

Hausman 2010 - Logic and Philosophy 11Ed, p.8.

The ultimate premises always consist of, as far as we know, probability arguments. The conclusion of an argument hence always implies this type of argument.

Reasoning may increase the credibility of a conclusion when they include additional premises. A clear example of such reasoning is given by induction. But still the conclusion will never become "absolutely certain".

Bergmann 2004 - The Logic Book, 6Ed, p.1-2.
Bonjour 1998 - In defense of pure reason, p.2.
Descartes 1642 - Meditations on First Philosophy, Meditation 3.
Duncan 1908 - Philosophical works of. Leibniz, 2Ed, p.33.
Goldstein 2010 - Encyclopedia of Perception, artikel "Color Perception", p.266-270
Platon (about 390-370 BCE) - Complete Works, Cooper (ed.), Hackett 1977.
Popper 2002 - The Logic of Scientific Discovery sect.6.
Putnam 1956 - Reds, Greens, and Logical Analysis, Philosophical Review 65, p.206-217.
Schlick 1931 - Is There a Factual a Priori? in Feigl 1949 - Readings in Philosophical Analysis (Appleton), p.283.