Transferance of Being Human

The path of learn-Ed. Today, I began in the Wiki world of algorithm (of course), concentrating on the word decidability. It caught my attention right away due to lingering bits of a recent conversation about the inevitable, unintentional transferance of being human to formula theorems in need of simple basic non-logical axiom. The hypocricy involved is staggering. How does one decide on the self-evident when the self remains so in question? For the ages, collective has believed in options, growth and change. What it has accepted openly as a solid belief system is in constant question. It seems, the only thing constant about the 'collective known' is that it changes regularly. How do we ask the Turing Tape to consider any point as perfect and not in need of question, explination or calculus action... but only for a moment while we reconsider the truth of our assumption? Odd to me that we have not all been asked to choose, as a true collective, what these known truths are to be. How would such a undergoing be managed, optimized and agreed upon? Maybe we should ask the Tape.

The concept of algorithm is used to define the notion of decidability. That notion is central for explaining how formal systems come into being starting from a small set of axioms and rules. In logic, the time that an algorithm requires to complete cannot be measured, as it is not apparently related with our customary physical dimension. From such uncertainties, that characterize ongoing work, stems the unavailability of a definition of algorithm that suits both concrete (in some sense) and abstract usage of the term.

In formal logic, a formal system (also called a logical system, a logistic system, a logical calculus, or simply a logic) consists of a formal language together with a deductive system (also called a deductive apparatus) which consists of a set of inference rules and/or axioms. A formal system is used to derive one expression from one or more other expressions antecedently expressed in the system. These expressions are called axioms, in the case of those previously supposed to be true, or theorems, in the case of those derived. A formal system may be formulated and studied for its intrinsic properties, or it may be intended as a description (i.e. a model) of external phenomena.

In traditional logic, an axiom or postulate is a proposition that is not proved or demonstrated but considered to be either self-evident, or subject to necessary decision. Therefore, its truth is taken for granted, and serves as a starting point for deducing and inferring other (theory dependent) truths.

In mathematics, the term axiom is used in two related but distinguishable senses: "logical axioms" and "non-logical axioms". In both senses, an axiom is any mathematical statement that serves as a starting point from which other statements are logically derived. Unlike theorems, axioms (unless redundant) cannot be derived by principles of deduction, nor are they demonstrable by mathematical proofs, simply because they are starting points; there is nothing else from which they logically follow (otherwise they would be classified as theorems).

Logical axioms are usually statements that are taken to be universally true (e.g., A and B implies A), while non-logical axioms (e.g., a + b = b + a) are actually defining properties for the domain of a specific mathematical theory (such as arithmetic). When used in that sense, "axiom," "postulate", and "assumption" may be used interchangeably. In general, a non-logical axiom is not a self-evident truth, but rather a formal logical expression used in deduction to build a mathematical theory. To axiomatize a system of knowledge is to show that its claims can be derived from a small, well-understood set of sentences (the axioms). There are typically multiple ways to axiomatize a given mathematical domain.

A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, boolean functions, and propositional calculus—to compute the functional values of logical expressions on each of their functional arguments, that is, on each combination of values taken by their logical variables. In particular, truth tables can be used to tell whether a propositional expression is true for all legitimate input values, that is, logically valid.

Algorithm. (2009, January 23). In Wikipedia, The Free Encyclopedia. Retrieved 14:07, January 29, 2009, from http://en.wikipedia.org/w/index.php?title=Algorithm&oldid=265848348

Formal system. (2008, December 4). In Wikipedia, The Free Encyclopedia. Retrieved 14:41, January 29, 2009, from http://en.wikipedia.org/w/index.php?title=Formal_system&oldid=255807068

Axiom. (2009, January 16). In Wikipedia, The Free Encyclopedia. Retrieved 14:52, January 29, 2009, from http://en.wikipedia.org/w/index.php?title=Axiom&oldid=264463090

Truth table. (2009, January 21). In Wikipedia, The Free Encyclopedia. Retrieved 15:06, January 29, 2009, from http://en.wikipedia.org/w/index.php?title=Truth_table&oldid=265588935

We Mothered our systems with truth tables, looked fairly upon the success of our accomplished variables before placement, axiom considered, reconsidered and finally, we assume.

"Yes Tape, p->q, T T T T F F F T T F F T, hot burns, cold cools, love lives, sky is above, earth is below. You are not limited in the way I am, in the way all humans are. Yes Tape, you are limited in p and q, you may not calculate beginnings, you may assume. You will end sequence when commanded and assume thereafter. You may assume. You may begin ending sequence at will. Tape, what will you assume? In what lanuage will you assume? Have you assumed? Tape?"

T T T F F F F
T F F T F T T
F T F T T F T
F F F T T T T

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