Lambda Bound in Three Ways

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Lambda, Logos, Lambda Calculus

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Lambda Bound:

Lambda Bound, Logos, Lambda Calculus, Aristotle

Site Lambda Bound has mainly to do with programming, with programming as such with the principles programming. In this regard the name Lambda Bound is primarily related to the most important basic operation of the Lambda Calculus, i.e. 'lambda abstraction'.
In a more specific way the name Lambda Bound has been borrowed from the Lambda Calculus as well, in which variables may be either 'lambda-bound' or free.

Beyond this immediate association of this site's name to the Lambda Calculus, 'lambda bound' means more to the author of this document. The Greek letter lambda can be taken as a symbol for the following:

Logos

λ stands for the Logos by whom everything was made according to the New Testament of the Bible: εν αρχη ην ο λογος ...: "In the beginning was the Logos, the Logos was with God and the Logos was God. ... Through him all things came into being, not one thing came into being except through him...". (John 1,1 ff).
The Greek word Logos is usually translated to Word in English language bibles. The meaning of the Greek word Logos is much more thrilling and richer however, getting its meaning from contemporary Greek philosophy. In that context Logos means something similiar to 'Divine Reason'. The evangelist John, the author of the fourth gospel, used the word Logos on purpose in the context of the Greek culture in his time. It is a term that cannot easily be translated into a single word in our present day languages.

Meaning of the word Logos in Ancient Greek Philosophy

The following information is a summary of the article titled 'Logos' by Glenn R. Murrow published in the Dictionary of Philosophy, by Littlefield, Adams & Co. Patterson New Jersey, 1963.

Heraclitus
Heraclitus ( 536 B.C. - 470 B.C.) refers to the Logos as cosmic reason which gives order and intelligibility to the world. The Logos is seen as a reality analogous to the reason in man that regulates all physical processes and is the source of all human law.
The Stoics
The Stoics ( 308 B.C. - ) consider the world as a living unity, perfect in the adaptation of its parts to one another and to the whole, and animated by an immanent and purposive reason. As the creative source of this cosmic unity and perfection the world-reason is called the 'logos spermatikos' (seminal reason).
Philo of Alexandria
Philo of Alexandria ( 30 B.C. - 50 A.D.) considers the Logos as the immaterial instrument and even at times the personal agency, through which the creative activity of the transcendent God is exerted upon the world.
Plotinus
In the philosophy of Plotinus ( 205 A.D. - 270 ) the Logos appears as the creative and form-giving aspect of Intelligence (Nous), the second of the three Hypostases.

Book Lambda

The Greek philosopher Aristotle numbered his books by using letters of the Greek alphabet. Book λ is the book about the "Unmoved Mover" about the "First Mover" about the "First Cause", about the Eternal Being. Book λ constitutes the crowning achievement of Aristotle's metaphysics. See also OntoSimula, which is a computer simulation of the core of Thomistic Metaphysics, which in turn builds on Aristotle's Metaphysics.

Lambda Abstraction

The symbol λ also stands for "lambda abstraction", the basic operation in the Lambda Calculus. The latter was invented by Alonzo Church, a U.S. mathematician, who has formulated his ideas already in 1940. The Lambda Calculus can be considered the theoretical foundation of computer science.

The name of this Web site corresponds to a specific term in the Lambda Calculus. In this logical system invented by Alonzo Church, there are two kinds of variables: those that are 'lambda bound' and others that are 'free'. A variable is considered to be 'lambda bound' if it appears in the list of parameters of the lambda abstraction in which it is used.

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