Truth (logic)

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In logic, truth is a term used to stand for "correspondence with facts or reality". This Conservapedia entry focuses on the concept of truth as correspondence with the facts. For "truth" as related to God and society, see truth.

Contents

Difficulties

What is meant by "the facts"? Often the term "fact" is thought to mean "something that is true". If truth is then defined as correspondence to the facts the whole descends into cirularity. This gives rise to the "paradoxes of truth" such as:

Liar's paradox: This sentence is false

If the sentence is false then it correctly describes itself and is, therefore, true. On the other hand if it is true it mis-describes itself and is, therefore, false.

Alfred Tarski, in attempting to formulate a conception of truth that avoided these paradoxes, formulated a way of seperating the concept of truth from "the facts" it was to represent. His Semantic Theory of Truth held that truth was part of a metalanguage, a language that talks about basic languages. The basic languages, known as "object languages" describe, or purport to decribe, the state of the world. The metalanguage then descibes whether or not the basic language has succeeded. Karl Popper recommended thinking of the languages in terms of two different natural languages. [1]. Take, for example, French as the basic language and the statement:

Object language statement: La neige est blanc.

This makes a statement about the world. A good many statements may be made about this statement (meta-statements), one of which would be whether it is true or not. Reverting to English we may say:

Metalanguage statement: "La neige est blanc" is true if, and only if, the snow is white

It can be readily seen that the English statement above is not a statement about the world, but a statement about the French phrase and its relation to the world. It is a meta-statement and is true or false depending on the meaning of the French phrase rather than the actual state of the world. The English phrase would be true even if snow where turquoise.

If the liar's paradox is recast in this way the paradox disappears. "Cet enonce est faux" purports to accurately describe the world, but does it? What conditions can we attach to it, in the metalanguage, to determine when it is true and false? ""Cet enonce est faux" is true if and only if it describes a state of the world which is not the case" or, alterntively, ""Cet enonce est faux" is false if and only if it describes a state of the world which is the case". As the statement "cet enonce est faux" fails to describe a state of the world it can be neither true nor false: it is simply a meaningless string of words. The paradox problem clearly demonstrates that real truth can never be a product of sheer logical pursuits, but rather relies on the inherent meaning of words, as a necessary, but not sufficient premise. This points to the origin of words, or rather, the question about origin itself[2]. Thus, no clear distinction between "logical" and "real" (divine) truth can be made.

See also

External links

References

  1. Popper, K.R. The Open Society and Its Enemies, Vol 2. Routledge. London. 1966. p 369-396
  2. John 1:1, "In the beginning was the Word, and the Word was with God, and the Word was God"
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