Truthfulness

Proximity to truth , also similarity to truth , is a measure in critical rationalism with which one can compare which of two false theories represents a better approximation of the truth and which of two true theories is more precise. The notion of such a measure is necessarily purely fictional and only applicable as a model, since the actual truth would have to be known in order to apply it to theories in practice. An adequate definition of closeness to the truth would nevertheless make it possible to speak at least meaningfully of the possibility of progress in science.

Popper , the founder of critical rationalism, was initially skeptical about the concept of truth: “In the structure of the cognitive logic outlined by us, we can dispense with the use of the terms 'true' and 'false'.” Only after he got to know Alfred Tarski and with him Having dealt with his semantic concept of truth, he accepted the meaning of the term for science.

definition

Popper's first attempt at a definition was based on the postulate that the similarity of a theory to truth is greater than that of a theory if their truth and falsehood contents can be compared and if one of the following properties is met: ${\displaystyle t_{2}}$ ${\displaystyle t_{1}}$

1. ${\displaystyle t_{2}}$ has a higher truth content, but no higher falsehood than ${\displaystyle t_{1}}$
2. ${\displaystyle t_{1}}$ has a higher falsehood, but no higher truth, than ${\displaystyle t_{2}}$

Truth and falsehood are the set of true or false sentences that can be derived from the theory.

Popper then defines the veracity of a theory as ${\displaystyle a}$

${\displaystyle {\mathit {Vs}}(a)={\mathit {Ct}}_{T}(a)-{\mathit {Ct}}_{F}(a)}$

where and is a measure of the truth or falsity content of the theory. ${\displaystyle {\mathit {Ct}}_{T}(a)}$ ${\displaystyle {\mathit {Ct}}_{F}(a)}$

criticism

Independently of each other, Pavel Tichý and David Miller found that Popper's first definition is inadequate because one can conclude from it that all false theories are equally close to truth. As an alternative, David Miller suggests defining the truthfulness and falsity of a theory not in terms of what can be derived from it, but in terms of classes of models. Miller defines the truth content of a theory as the class of models that do not describe the real world and in which the theory is invalid, and the falsity content as the empty set if the theory is true and the set with the real world model as Element if the theory is wrong. If one defines a theory as being closer to the truth than a theory if and only if the truth content of is a real subset of the truth content of and the falsity content of is a real subset of the falsity content of is, then the validity of the following properties can be shown: ${\displaystyle t_{2}}$ ${\displaystyle t_{1}}$ ${\displaystyle t_{2}}$ ${\displaystyle t_{1}}$ ${\displaystyle t_{1}}$ ${\displaystyle t_{2}}$

1. If is true and can be deduced from it, then is closer to the truth than ${\displaystyle t_{2}}$ ${\displaystyle t_{1}}$ ${\displaystyle t_{2}}$ ${\displaystyle t_{1}}$
2. If is false, then the truth content of is closer to the truth than ${\displaystyle t_{1}}$ ${\displaystyle t_{2}}$ ${\displaystyle t_{1}}$
3. If is wrong and can be deduced from, then is closer to the truth than . At first glance, this is a consequence that is not intuitive and which Miller himself initially disliked. He changed his mind, however, as it harmonizes with the connection of true theories with still very flawed theories about newly explored details. ${\displaystyle t_{1}}$ ${\displaystyle t_{2}}$ ${\displaystyle t_{2}}$ ${\displaystyle t_{1}}$
4. If truer than is and truer than , then is truer than ${\displaystyle t_{2}}$ ${\displaystyle t_{1}'}$ ${\displaystyle t_{1}'}$ ${\displaystyle t_{1}}$ ${\displaystyle t_{2}}$ ${\displaystyle t_{1}}$
5. If none of the above is true , then it is no closer to the truth than ${\displaystyle t_{2}}$ ${\displaystyle t_{1}}$

The attempt to numerically determine the closeness to the truth was not only criticized for the fact that its results were unusable. According to Herbert Keuth, it contains serious conceptual errors in general. It is adversarial and does not define a measure . There is no adequate basis on which elementary propositions can be ascribed values ​​that numerically express how much they claim about reality.

Individual evidence

1. ^ LdF , section 84
2. ^ Alfred Tarski: The concept of truth in the formalized languages. Studia Philosophia 1 (1935), pp. 261-405.
3. ^ Karl Popper: A note on Tarski's definition of truth. Mind 64 (1955).
4. ↑ Pavel Tichý: On Popper's definitions of verisimilitude. The British Journal for the Philosophy of Science. 25 : 2 (June 1974), pp. 155-160.
5. ↑ David Miller: Popper's Qualitative Theory of Verisimilitude. The British Journal for the Philosophy of Science. 25 : 2 (June 1974), pp. 166-177.
6. ↑ See also LdF , * XV
7. ^ Critical Rationalism , Section 10.3.
8. ↑ Herbert Keuth: Reality and Truth. On the critique of critical rationalism. JCB Mohr (Paul Siebeck) Tübingen 1978. ISBN 3-16-840692-9 . P. 120

literature

• Karl Popper: Objective Knowledge
• Karl Popper: About closeness to the truth. Chapter * XV of Logic of Research
• David Miller: Truth, Truthlikeness, Approximate Truth. Chapter 10 of Critical Rationalism .
• Kuipers, TAF (Ed.): What is closer-to-the-truth? A parade of approaches to truthlikeness (Amsterdam: Rodopi, 1987). Volume 10 of Poznan Studies in the Philosophy of the Sciences and the Humanities .

Web links

Entry in Edward N. Zalta (Ed.): Stanford Encyclopedia of Philosophy .