Logical positivism, formulated in the 1920s, argued that the truth of a statement is «whatever is consistent with observable facts.»

The concept of a truth principle in modern logic does not imply this – for example, the statement that «all numbers are rational» is not really a statement about what is true, but only about what can be proved.

Logical positivists also do not exclude so-called non-empirical statements.

The statement that «x» or «y» is more likely to be true in the case of «X» as opposed to the case «Y» requires that «X» and «Y» be consistent statements, which they claim to be means that logical positivists must argue that «truths» of this kind are not really «truths» or «truths» of the world.

However, most subsequent systems of epistemology, such as realism, positivism, and analytical philosophy, tend to assume that logical positivists were right in saying that there are non-empirical statements that are also true.

Practical applications such as medicine and legal practice tend to focus on statements that can be falsified or supported, and thus the assertion that true statements are necessarily true is removed from the problem of determining whether a particular statement is true or false…

However, since modern theories of mind and cognition are still often based on the traditional form of empiricism, the problem of non-empirical statements is still relevant.

The statement that «x» is more likely to be true in the case of «X» than in the case of «Y» is often viewed as an example of a reduction axiom with axioms of the form «x» and «y». truth is perceived as an obvious axiom of the existence of a relationship.

However, it has also been argued that such arguments presuppose the idea that there is no cognitive system – and therefore no belief system – that can speak of something other than itself, a view that has not gained widespread acceptance.

A particularly important form of logical positivism that is commonly associated with the scientific method has come to be known as logical empiricism and is closely related to the knowledge argument for the existence of God.

In the nineteenth century, Russell, Frege and most logical positivists defended the strong version of the thesis of the logical positivists: the «logical positivism», i.e. an adequate and correct theory of knowledge itself is a true science. Since then, this thesis has been questioned by some adherents of logical empiricism.

After Wittgenstein’s theory of concepts Wittgenstein influenced the logic, some of whom believe that what is true for proposals (including the logical positivists) is true for any «concepts», and some of them believe that the truth of one kind of truth is usually and necessarily linked with truths of a different kind.

The new thesis arose as a result of the development of Wittgenstein’s philosophy. Most logical positivists denied the possibility of metaphysics; but there were some who thought that metaphysics was wrong on only one occasion, and that was when it gave meaning to things that didn’t really make sense.

Some logical positivists took this position and argued that metaphysics should only be taught in primary schools, if at all, and that metaphysics should have no place in higher education or professions. Others, however, argued that this position is inconsistent.

Russell called the first position «twice negative logic.»

In the second position, «double positive logic» describes the usual human use of language in which there is no opposition between sentences that imply or make sense of each other.