Nelson's Proof of the Impossibility of the Theory of Knowledge

by Dr. Kay Herrmann

In addressing the possibility of a theory of knowledge, Leonard Nelson noted the contradiction of an epistemological criterion that one would require in order to differentiate between valid and invalid knowledge. Nelson concluded that the inconsistency of such a criterion proves the impossibility of the theory of knowledge.

Had the epistemological criterion had a perception, then it would presume to adjudicate on its own truth (thus epistemological circular argument). However, if one were to assume that the criterion is not knowledge, one would then have to justify how this is a criterion for truth -- yet this would only be possible when it may be considered as an object of knowledge. One would equally have had to predetermine the criterion in order to determine the truth of this knowledge, thereby providing another circular argument. Ostensibly, every criterion of truth fails at its very own test since it cannot guarantee its own truth, just as Munchausen, contrary to his assertion, could not draw himself out of the swamp by tugging on a tuft of his own hair.

Nelson proposed a solution of the epistemological problem (the question of the differentiation between valid and invalid knowledge), that based on Jakob Friedrich Fries' differentiation between proof and deduction. Proof, according to Nelson (in reference to Fries), can be defined as derivation of truth from one statement from another statement. Thus, from the truth in the statement that "all men are mortal", one is then able to say that "Socrates is a man" and thence extrapolate from the truth of the statement that "Socrates is mortal." If knowledge were to be considered somewhat judgmental (in a statement), then an attempt at proof (i.e. recourse to previous judgments) would inevitably lead to an infinite regression in justification, since each judgment would necessitate a further justification from another judgment. Every attempt to prove an epistemological criterion is thus also confronted by this regression in justification.

Nelson's attempt at a solution rests on the assumption of the existence of an immediate knowledge as a justification of the truth (mediate) of knowledge. Nelson considers immediate knowledge to be non-judgmental knowledge. These include intuitions (e. g. seeing-the-red-roof) and also philosophical knowledge that pre-exists in his opinion before a judgmental reflexion (immediate) in our reason (e. g. the principle of causality).

Proof of the truth1 of mediate knowledge can be effected by showing its compliance with attendant immediate knowledge (rational truth = correspondence of mediate knowledge with their immediate knowledge). Nelson considered this as a resolution of the circular epistemological argument. He then writes:

The criterion of truth, such as we may use, no longer provides occasion for the contradiction that we find in the concept of an epistemological criterion. In fact, the criterion of the truth in a judgment may not stand again as a verdict in itself and thus lay beyond judgment, as it resides in immediate cognition which in turn is free of verdicts.2

In regard to philosophical knowledge, Nelson sees these as subject to deduction and not proof. The following example illustrates the goal of deduction:

An approach for deducing the principle of causality:

A) Every change has a cause. (The principle of causality)
A´) A is a reiteration of an immediate knowledge. (Meta-assertion following A)

"A" may not be provable, but A´ may justified, and thus Nelson identified it as a deduction following from A.

Did Nelson essentially chance upon a non-circular criterion of truth?

Nelson's criterion of truth (KN) may be formulated as follows:

KN: x (V(x)yW(x, y))3

x: mediate (judgmental) knowledge; y: immediate (non-judgmental) knowledge; V(x): x is rationally true; W(x, y): x repeats y; KN: Nelson's Criterion of Truth

However, KN is a judgment in itself, and consequently a mediate knowledge. In order to justify KN, one would have to deduce an immediate knowledge yN equivalent to KN. At this point one has to assume the validity of the following identity: V(KN)yW(KN, y)4. Since KN had been applied even before its evaluation as a truth, Nelson's attempt at a solution is thus also demonstrated as circular. One would have to concede that one is dealing with curious knowledge, even if the immediate cognition yN has been found. Because yN, a non-judgmental knowledge in itself, would already contains indicators to the truth of judgments. Moreover, the KN criterion, due to its judgmental character, challenged by Fries' advice to the fallibility of every mediate knowledge:

Thus, all error resides in revisited reflection and not in immediate cognition; though neither in assumptions nor in original rational convictions, but in judgments.5

In principle, one would then have to concede that KN is error-laden. Thus Nelson's attempt at a solution ultimately fails in satisfying the proof of the truth of knowledge, but he has pointed to a general problem of attempts at ultimate justification. Popper's so-called Friesian Trilemma resembles Nelson's Proof of the Theory of the Impossibility of Knowledge. Popper's solution was premised on discarding an absolutely safe foundation of scientific knowledge, as he considered the test-beds of scientific theory to be the so-called basic statements. He concludes that we cannot even afford to become rooted to certain excellent scientific propositions, since each may be audited by another one and a natural conclusion thus never attained. He saw basic statements as "being stipulated through decision and recognised by convention."6


Nelson, L.: Gesammelte Schriften (Collected Works). Hg. von P. Bernays/W. Eichler/A. Gysin/ G. Heckmann/G. Henry-Hermann/F. v. Hippel/S. Körner/W. Kroebel/G. Weisser. 9 Bde., Hamburg 1970-1977


Fries, J. F.: Sämtliche Schriften. Nach den Ausgaben letzter Hand zusammengestellt, eingeleitet und mit einem Fries-Lexikon versehen von G. König/L. Geldsetzer. (Bisher) 26 Bde., Aalen 1967-1997 (The final edition having been compiled, introduced and annotated with a glossary of Fries by G. König/L. Geldsetzer. (to date) 26 Bde., Aalen 1967-1997).



Leonard Nelson (1882-1927)

Jakob Friedrich Fries (1773-1843)

Karl Popper (1902-1994)

History of Philosophy


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1. Nelson speaks of rational truth.

2. "Das Wahrheitskriterium, dessen wir uns dabei bedienen, gibt nicht mehr Anlaß zu dem Widerspruch, den wir in dem Begriff des erkenntnistheoretischen Kriteriums gefunden haben. In der Tat: das Kriterium der Wahrheit der Urteile kann nicht selbst wieder ein Urteil sein, aber es braucht darum nicht außerhalb der Erkenntnis zu liegen; es liegt nämlich in der unmittelbaren Erkenntnis, die ihrerseits nicht wieder in Urteilen besteht." In: Nelson: "Die Unmöglichkeit der Erkenntnistheorie." In: GS 2, p. 473.

3. KN: An oblique cognition x is thus rationally true when there is an immediate cognition y, where y is replicated by KN.

4. KN is held to be rationally true if there is an immediate cognition of, where y is replicated by KN.

5. "Aller Irrthum gehört also der wiederbeobachtenden Reflexion und nicht der unmittelbaren Erkenntniß, er liegt in Urtheilen, aber weder in Anschauungen noch in ursprünglichen Ueberzeugungen der Vernunft." In: Fries: System der Logik, p. 341 (WW 7, p. 509).

6. "durch Beschluß, durch Konvention anerkannt, sie sind Festsetzungen." In: Popper: Logik der Forschung, p. 71.